BCLA CLEAR – Contact lens optics

      Abstract

      The most fundamental aspect of a contact lens is its optics; the manner in which the refraction of light is managed to optimise vision to the clinical benefit of the lens wearer. This report presents contemporary information on the optical structure of the eye and the optical models employed to understand the correction of refractive error. The design, measurement and clinical assessment of spherical, aspheric, toric, multifocal and myopia control contact lenses are described. The complexity and variety of multifocal lenses is recognised and detailed information is provided for alternating, simultaneous, diffractive, annular, aspheric and extended depth of field lens designs. In terms of clinical assessment, a contemporary review is provided for the measurement of: visual acuity, contrast sensitivity, through focus curves, reading performance, peripheral refraction, toric displacement realignment and patient reported outcomes. Overall, the paper aims to serve as a resource for the prescribing clinician, who can optimise contact lens corrections for patients by building on the optical rationale of these devices; and also highlights future opportunities for research innovation.

      Keywords

      Abbreviations

      ANSI
      American National Standards Institute
      CE
      European Conformity
      CLIQ
      Contact Lens Impact on Quality of Life
      CLUE
      Contact Lens User Experience
      COAS
      Complete Ophthalmic Analysis System
      EDOF
      extended depth of focus
      ETDRS
      Early Treatment Diabetic Retinopathy Study
      FACT
      Functional Acuity Contrast Test
      FDA
      Food and Drug Administration
      HEMA
      hydroxyethyl methacrylate
      HORMS
      higher order root mean square
      ISO
      International Organization for Standardization
      logCS
      logarithm of contrast sensitivity
      logMAR
      logarithm of minimal angle of resolution
      NAVQ
      Near Activity Visual Questionnaire
      NEI-RQL
      National Eye Institute’s Refractive Quality of Life
      NEI-VFQ
      National Eye Institute’s Visual Function Questionnaire
      PREP
      Paediatric Refractive Error Profile
      QOV
      Quality of Vision
      RSVP
      Refractive Status and Vision Profile

      1. Introduction and purpose

      Modern contact lenses are formed from transparent soft or rigid polymers, which, in their simplest representation change the optical path length forming the image of the lens-wearing eye. Historically, these lenses have corrected spherical and regular/irregular astigmatic refractive errors, but more recently, they aim to accomplish even more sophisticated goals, such as allowing a presbyopic wearer to see at multiple viewing distances or controling the growth of a developing eye. As society progresses, contact lens technology will likely continue to aim to accomplish even more than “just” correct vision. As these aims expand, advances in manufacturing, metrology, and prescribing must also occur.

      2. Overview of the optical design of the eye

      2.1 Basic optical structure

      The human adult eye can be approximated as a sphere of 12  mm radius, intersected in front by a second smaller prolate ellipse of roughly 7.8 mm in central radius over a chord of 12 mm, which is transparent and known as the cornea (see CLEAR Anatomy Report [
      • Downie L.E.
      • Bandlitz S.
      • Bergmanson J.P.G.
      • Craig J.P.
      • Dutta D.
      • Maldonado-Codina C.
      • et al.
      CLEAR - anatomy and physiology of the anterior eye.
      ]). Between the two is the iris, which forms the aperture stop of the eye, or pupil. Contraction of the ciliary muscle permits the shape and therefore gradient refractive index and optical power of the crystalline lens to change, and allow near objects to stay in focus. The eye’s ability to increase or decrease power of the crystalline lens is known as accommodation.
      Light from an object entering the eye first encounters the tear film, typically a thin, afocal fluid layer on the anterior corneal epithelium that ensures the first optical surface of the eye is smooth, minimising loss of light energy through scatter. Light is then refracted by the anterior and posterior surfaces of the cornea and crystalline lens, in turn, to form an image on the retina. The entrance pupil of the eye is the image of the iris aperture formed by the cornea, and the exit pupil is the image of the iris aperture imaged by the lens.
      The length, curvature, and refractive indices of the eye’s components create lower order aberrations (myopia, hyperopia, astigmatism). The highly curved and powered refracting surfaces of a non-uniform tear film, the cornea, and crystalline lens also induce higher order aberrations (e.g. spherical aberration, coma, etc.). Spherical aberration is a gradual, radially symmetric power change from centre to the periphery of an optical system. It is present in contact lenses and the structures of the eye. Corneal spherical aberration is partly compensated by its aspheric profile and the gradient refractive index of the crystalline lens [
      • Artal P.
      • Berrio E.
      • Guirao A.
      • Piers P.
      Contribution of the cornea and internal surfaces to the change of ocular aberrations with age.
      ]. The refracting surfaces of the eye may be decentred and/or tilted relative to each other. Additionally, the aperture of the eye, the pupil, is not concentrically aligned to the centre of the cornea, being typically slightly nasal and superior [
      • Yang Y.
      • Thompson K.
      • Burns S.A.
      Pupil location under mesopic, photopic, and pharmacologically dilated conditions.
      ]. Each of these issues create non-rotationally symmetric aberrations (e.g. coma, trefoil, etc.) which can negatively affect retinal image quality [
      • Artal P.
      • Guirao A.
      Contributions of the cornea and the lens to the aberrations of the human eye.
      ]. In addition to these monochromatic aberrations, the eye also suffers from approximately 2 dioptres (D) of longitudinal chromatic aberration [
      • Thibos L.N.
      • Bradley A.
      • Zhang X.
      Effect of ocular chromatic aberration on monocular visual performance.
      ]. Contact lenses can correct and induce lower and higher order aberrations of the eye and lens system either by chance or by design. This will be discussed in several of the sections to follow.

      2.1.1 Optical axes of the eye

      When describing the optics of the eye, a contact lens on an eye, or how the eye aligns with any imaging system, it is convenient to describe alignment relative to some reference axes (Fig. 1). However, since the corneal surfaces, lenticular surfaces, and the retina are not rotationally symmetrical and may be decentred and/or tilted relative to each other, the eye cannot be described like most optical systems where the optical and geometrical centres of their optical elements coincide along a common optical axis. The most commonly-used theoretical optical axes of the human eye, are the pupillary axis — the line perpendicular to the cornea that intersects the centre of the entrance pupil, and the primary line of sight — the line that connects the fixation point in the object space with the centre of the entrance pupil and the centre of the exit pupil with the fovea [
      • El Hage S.G.
      • Le Grand Y.
      ]. Angle kappa is the angle between the line of sight and the pupillary axis (in the object space) and is typically larger in hyperopes than myopes due to the difference in axial length between these eyes, everything else being equal [
      • Tabernero J.
      • Benito A.
      • Alcón E.
      • Artal P.
      Mechanism of compensation of aberrations in the human eye.
      ].
      Fig. 1
      Fig. 1Optical axes of the eye (adapted from [
      • Bennett Rabbetts R.
      Rabbett’s clinical visual optics.
      ] redrawn by Paul Gifford PhD, MCOptom).

      2.1.2 Optical models of the eye

      When representing the optics of the eye, simplified optical models are often used. The simplest optical models of the eye are paraxial in nature and assume alignment of the optical surfaces and homogeneity of the optical elements. The simplest contain only one refracting surface [
      • Emsley H.
      Visual optics.
      ]. Adding three or four refracting surfaces allows the surface radii and refractive indices to approach those of the human eye for more realistic outcomes [
      • El Hage S.G.
      • Le Grand Y.
      ,
      • Emsley H.
      Visual optics.
      ,
      • Gullstrand A.
      Appendices II and IV.
      ]. Though useful for performing relatively simple calculations of refractive power or relative retinal image size, these simplified models do not allow calculations of the impact of aberrated and decentred surfaces found in the human eye [
      • Norrby S.
      • Piers P.
      • Campbell C.
      • van der Mooren M.
      Model eyes for evaluation of intraocular lenses.
      ,
      • Atchison D.A.
      • Thibos L.N.
      Optical models of the human eye.
      ].
      ‘Wide angle’ model eyes introduce aspheric and/or non-rotationally symmetric surfaces and gradients of refractive index as found in the crystalline lens to predict the impact of ocular aberrations, corrective lens decentration/tilt and object rays coming from a peripheral field location, on the retinal image quality [
      • Lotmar W.
      Theoretical eye model with aspherics.
      ,
      • Navarro R.
      • Santamaría J.
      • Bescós J.
      Accommodation-dependent model of the human eye with aspherics.
      ,
      • Liou H.-L.
      • Brennan N.A.
      Anatomically accurate, finite model eye for optical modeling.
      ]. Most wide-angle models are typically based on ocular parameters that represent the population average; however, more individualised eye models are becoming available [
      • Einighammer J.
      • Oltrup T.
      • Feudner E.
      • Bende T.
      • Jean B.
      Customized aspheric intraocular lenses calculated with real ray tracing.
      ].
      ‘Multiple optical’ models represent individual eyes from a representative patient population to predict the retinal image quality across the population as might be found clinically [
      • Canovas C.
      • Artal P.
      Customized eye models for determining optimized intraocular lenses power.
      ,
      • Rosales P.
      • Marcos S.
      Customized computer models of eyes with intraocular lenses.
      ,
      • Navarro R.
      • González L.
      • Hernández-Matamoros J.L.
      On the prediction of optical aberrations by personalized eye models.
      ,
      • Kingston A.
      • Cox I.
      Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality.
      ]. While these models do not directly replace actual clinical testing, they provide a powerful tool for the designers of ophthalmic corrections to greatly reduce the timeline and cost of lens design in refining concepts prior to human testing.

      2.2 Changes of the eye with age

      The optics of the human eye are not static across the lifespan. In particular, the human eye changes rapidly within the first year of birth, with increases in corneal diameter and radius, and reduction of corneal astigmatism [
      • Read S.A.
      • Collins M.J.
      • Carney L.G.
      A review of astigmatism and its possible genesis.
      ], increases in lenticular diameter and decreases in lens thickness, and a relatively large increase in axial length. Continued changes in the corneal and crystalline lens dimensions, along with axial length increases occur during the next 10–15 years of life as part of the emmetropisation process, with the rate of change decreasing with time during this period [
      • Chakraborty R.
      • Read S.A.
      • Vincent S.J.
      Understanding myopia: pathogenesis and mechanisms. Updat. Myopia.
      ].
      During young and middle adult life, the crystalline lens optics largely compensate for the astigmatism and monochromatic higher order aberrations of the cornea; optimizing the optics of the total eye until the fourth decade of life [
      • Brunette I.
      • Bueno J.M.
      • Parent M.
      • Hamam H.
      • Simonet P.
      Monochromatic aberrations as a function of age, from childhood to advanced age.
      ]. Thereafter, ongoing increases in lens diameter and thickness cause an increased curvature of both surfaces, that is compensated by changes to lenticular gradation in refractive index to allow the lens power to remain relatively constant rather than increase as it otherwise would [
      • Richdale K.
      • Bullimore M.A.
      • Sinnott L.T.
      • Zadnik K.
      The effect of age, accommodation, and refractive error on the adult human eye.
      ]. These balanced changes do, however, result in a gradual increase in the total higher order aberrations of the eye with increasing age [
      • Artal P.
      • Berrio E.
      • Guirao A.
      • Piers P.
      Contribution of the cornea and internal surfaces to the change of ocular aberrations with age.
      ]. In particular, spherical aberration becomes more positive with increasing age, increasing approximately 0.05 μm (over a 6 mm pupil) with every decade of life [
      • Kingston A.
      • Cox I.
      Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality.
      ]. Other higher order aberrations increase in the sixth and later decades of life, particularly with the refractile changes in the lens that accompany cataract formation [
      • Wu C.-Z.
      • Jin H.
      • Shen Z.-N.
      • Li Y.-J.
      • Cui X.
      Wavefront aberrations and retinal image quality in different lenticular opacity types and densities.
      ,
      • Rocha K.M.
      • Nosé W.
      • Bottós K.
      • Bottós J.
      • Morimoto L.
      • Soriano E.
      Higher-order aberrations of age-related cataract.
      ].
      With age, the accommodative power of the lens decreases due to a gradual stiffening of the lens fibrils [
      • Glasser A.
      • Campbell M.
      Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia.
      ], until around the fourth or fifth decade of life when the typical reading near point is closer than the residual accommodation necessary to provide comfortable viewing for extended periods without a supplemental reading addition. As presbyopia increases, so do the higher order aberrations of the eye, as the natural compensatory relationship of aberrations between the cornea and lens is lost [
      • López-Gil N.
      • Fernández-Sánchez V.
      • Legras R.
      • Montés-Micó R.
      • Lara F.
      • Nguyen-Khoa J.L.
      Accommodation-related changes in monochromatic aberrations of the human eye as a function of age.
      ,
      • Berrio E.
      • Tabernero J.
      • Artal P.
      Optical aberrations and alignment of the eye with age.
      ].
      The cornea shows relatively little change from childhood through to the fourth decade of adult life. In later years, however, the prevalence of with-the-rule astigmatism decreases while against-the-rule astigmatism increases [
      • Namba H.
      • Sugano A.
      • Nishi K.
      • Murakami T.
      • Nishitsuka K.
      • Konta T.
      • et al.
      Age-related variations in corneal geometry and their association with astigmatism.
      ]. Monochromatic aberrations of the anterior corneal surface increase only slightly with age. In younger patients, the total ocular aberrations are lower than corneal aberrations, while in the older patients the opposite is true [
      • Artal P.
      • Berrio E.
      • Guirao A.
      • Piers P.
      Contribution of the cornea and internal surfaces to the change of ocular aberrations with age.
      ,
      • Lyall D.A.M.
      • Srinivasan S.
      • Gray L.S.
      Changes in ocular monochromatic higher-order aberrations in the aging eye.
      ].

      3. Contemporary contact lens designs

      3.1 Spherical

      Historically, spherical anterior and posterior optical surfaces were utilised by contact lens manufacturers because they were easier to fabricate using traditional non-computer numeric control (CNC) lathing manufacturing methods than aspheric surfaces (one alternative manufacturing method, spin casting, could generate posterior aspheric surfaces but was protected by patents until the late 1980’s) [
      • Lamb J.
      • Bolton T.
      History of contact lenses.
      ]. These lathing methods could be used either directly by generating a lens from a plastic button or the fabrication of metal optical tooling to use in a cast-moulding manufacturing process. In this approach, the posterior surface curvature is dictated by the radius or sag necessary to provide an acceptable clinical fitting (movement with blinking and centration on the cornea) of the contact lens, while the anterior surface curvature is selected based on the refractive index of the material and the lens back vertex power necessary for correcting hyperopia or myopia.
      While spherically surfaced single vision lenses are primarily prescribed for correcting eyes dominated by hyperopic or myopic defocus, spherical rigid corneal lenses can also correct some amounts (e.g. up to around 2 D before lens fit becomes unstable) of corneal astigmatism by vaulting the central corneal surface and allowing the tear film to fill the intervening space. Because the refractive index of the tears (∼1.336) is close to that of the cornea (∼1.376), this tear layer creates optical power. Patients with primarily corneal astigmatism can then be corrected with just the defocus correction of the spherical optics of the rigid corneal lens. If the fit is unstable or residual astigmatism is present, peripheral toricity can be added for rotational stability and front surface toricity can be added to the optical zone. With corneal toricities greater than 2.00 D, a back surface toric in the central optical zone may be needed to stabilise the lens fits. The toric base curve will orient with the astigmatic cornea thus stabilizing lens rotation. In this situation the front surface must also be toric as the toric base curve will not mask astigmatism as in the case of a spherical base curve [
      • Bier N.
      • Lowther G.E.
      Contact lens correction.
      ,
      • Mandell R.
      Contact Lens practice.
      ].
      Even though soft contact lenses largely conform to the corneal surface, early clinical reports suggested that patients with up to 1 D of refractive astigmatism could have their regular corneal astigmatism “masked” with soft contact lenses [
      • Cho P.
      • Woo G.C.
      Vision of low astigmats through thick and thin lathe-cut soft contact lenses.
      ]. However, this is not the case with studies utilizing relatively thick hydroxyethyl methacrylate (HEMA) soft lenses, which conform to the central anterior corneal surface [
      • Harris M.G.
      • Goldberg T.
      • McBride D.
      • Thromburg L.
      Residual astigmatism and visual acuity with hydrogel contact lenses: a comparative study.
      ,
      • Snyder C.
      • Talley D.K.
      Masking of astigmatism with selected spherical soft contact lenses.
      ,
      • Bernstein P.R.
      • Gundel R.E.
      • Rosen J.S.
      Masking corneal toricity with hydrogels: does it work?.
      ,
      • Edmonson L.
      • Edmonson W.
      • Price R.
      Masking astigmatism: ciba focus night and day vs focus monthly.
      ]. Alternatively, the spherical equivalent power is often prescribed in spherical lenses for patients with low amounts of astigmatism in the range of up to 0.50 D. It has been shown that visual acuity can be improved relative to spherical correction with soft toric lenses utilizing as low as 0.75 D of cylinder [
      • Richdale K.
      • Berntsen D.A.
      • Mack C.J.
      • Merchea M.M.
      • Barr J.T.
      Visual acuity with spherical and toric soft contact lenses in low- to moderate-astigmatic eyes.
      ,
      • Dabkowski J.A.
      • Roach M.P.
      • Begley C.G.
      Soft toric versus spherical contact lenses in myopes with low astigmatism.
      ,
      • A-KM Logan
      • Datta A.
      • Skidmore K.
      • Tomiyama E.S.
      • Hu C.
      • Chandler M.A.
      • et al.
      Randomized clinical trial of near visual performance with digital devices using spherical and toric contact lenses.
      ].
      The highly curved contact lens surfaces that are required to align with the corneal curvature inherently produce primary spherical aberration in spherically surfaced lenses. Specifically, they contain levels of spherical aberration that vary approximately linearly as a function of lens power with minus lenses containing negative spherical aberration and plus lenses positive spherical aberration [
      • Dietze H.H.
      • Cox M.J.
      On- and off-eye spherical aberration of soft contact lenses and consequent changes of effective lens power.
      ,
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ]. (The highest levels of spherical aberration exist in the highest power lenses. However, the human eye itself has, on average, 0.18 μm positive spherical aberration over a 6 mm pupil for the 18–45 year old population [
      • Kingston A.
      • Cox I.
      Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality.
      ]. This increases with age and pupil size [
      • Porter J.
      • Guirao A.
      • Cox I.G.
      • Williams D.R.
      Monochromatic aberrations of the human eye in a large population.
      ]. Therefore, what is important for vision is the sum of the eye optics and lens (plus tear film) optics. For example, for soft lenses which conform to the eye, it has been shown that the average eye’s positive spherical aberration is approximately cancelled by the spherical aberration of lens powers around -7.00 D, but that substantial amounts of spherical aberration can be induced by other lens powers including the most commonly prescribed -1.00 to -6.00 D range [
      • Dietze H.H.
      • Cox M.J.
      On- and off-eye spherical aberration of soft contact lenses and consequent changes of effective lens power.
      ]. These levels of spherical aberration can have a negative impact on vision for the wearer.
      Additionally, any decentration of a lens relative to the cornea, and perhaps more importantly, relative to the primary line of sight, induces other aberrations that are directly proportional to the amount of decentration [
      • Guirao A.
      • Williams D.R.
      • Cox I.G.
      Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations.
      ,
      • Atchison D.A.
      Aberrations associated with rigid contact lenses.
      ]. Therefore, any decentration of spherically surfaced lenses with spherical aberration from the eye’s primary line of sight will induce coma. This too can have a significant visual impact in some patients. With large decentration, the edge of the optic zone could also encroach on the pupil boundary resulting in glare and flare under low luminance conditions (e.g. night driving). However, well fitted lenses do not typically decentre to this magnitude to cause such problem [
      • Tomlinson A.
      • Ridder W.H.
      Effect of lens movement on vision with RGP contact lenses.
      ,
      • Pointer J.S.
      The influence of eye movement on soft contactlens visual performance.
      ].

      3.2 Aspheric

      To improve alignment with the cornea [
      • Kok J.H.
      A European fitting philosophy for aspheric, high-Dk RGP contact lenses.
      ] and to counteract some of the aberration issues common to spherical lenses described above, contact lenses with aspheric surfaces have also been created. Computer Numerical Controlled lathing brought the ability to design and manufacture a wide variety of aspheric surfaces. Historically this term has been used to describe any lens with a radially symmetric surface that is not spherical.
      Several early aspheric designed soft lenses had surfaces which were not optimally controlled by today’s terms and exhibited large aberration changes as a function of lens power [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ]. However, more recently several soft contact lens companies, including Bausch + Lomb [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ,
      • McAlinden C.
      • Pesudovs K.
      • Moore J.E.
      The development of an instrument to measure quality of vision: the Quality of Vision (QoV) questionnaire.
      ], CooperVision [
      • Kollbaum P.
      • Bradley A.
      Aspheric contact lenses: fact or fiction?.
      ,
      • Kollbaum P.S.
      Optical aberrations of contact lenses and eyes corrected with contact lenses.
      ], Alcon [

      Ye M, McKenney CD, McNally J. Series of aspherical contact lenses 2009.

      ], and Menicon (personal communication with Steve Newman) have aimed to control the level of spherical aberration as a function of lens power through the creation of aspheric lens profiles. Although some lenses have been manufactured aiming to introduce no spherical aberration, more are made to introduce an amount of spherical aberration equal in magnitude but opposite in sign to the average eye (during relaxed accommodation), with or without the incorporation of additional aberration of the lens power [
      • Kollbaum P.S.
      Optical aberrations of contact lenses and eyes corrected with contact lenses.
      ] to reduce the total overall aberration when on the eye. Additionally, the level of spherical aberration can be mitigated as a function of average pupil size to compensate for myopic shifts in mesopic lighting. Correction of the measured population’s average spherical aberration with contact lenses provides potential to improve visual performance for distance vision in a large number of lens wearers, especially under low-light, large-pupil conditions [
      • Wang Y.
      • Zhao K.
      • Jin Y.
      • Niu Y.
      • Zuo T.
      Changes of higher order aberration with various pupil sizes in the myopic eye.
      ]. However, spherical aberration varies with accommodation and across the population, and is only one of several significant high-order aberrations that coexist in the eye [
      • Porter J.
      • Guirao A.
      • Cox I.G.
      • Williams D.R.
      Monochromatic aberrations of the human eye in a large population.
      ]. For example, non-rotationally symmetrical aberrations, such as coma or trefoil, cannot be corrected with an on axis aspherical surfaced lens. In particular, decentration of any lens with spherical aberration relative to the centre of the pupil will induce significant levels of other aberrations (e.g. coma), which may temper the visual benefits generated by the reduction of the spherical aberration of the eye and or contact lens [
      • Atchison D.A.
      Aberrations associated with rigid contact lenses.
      ,
      • López-Gil N.
      • Castejón-Mochón J.F.
      • Benito A.
      • Marín J.M.
      • Lo-a-Foe G.
      • Marin G.
      • et al.
      Aberration generation by contact lenses with aspheric and asymmetric surfaces.
      ]. Given this issue and that most contact lenses decentre temporally from the pupil centre when on eye, it has not yet been fully established if aiming for correcting the average population spherical aberration is the optimal approach [
      • Werner J.S.
      • Elliott S.L.
      • Choi S.S.
      • Doble N.
      Spherical aberration yielding optimum visual performance: evaluation of intraocular lenses using adaptive optics simulation.
      ,
      • Piers P.A.
      • Manzanera S.
      • Prieto P.M.
      • Gorceix N.
      • Artal P.
      Use of adaptive optics to determine the optimal ocular spherical aberration.
      ,
      • Parker K.E.
      • Marsack J.D.
      • Elswick J.D.
      • Brunstetter T.J.
      • Applegate R.A.
      Controlled induction of spherical aberration with custom soft contact lenses.
      ] or if some other approach, such as aberration free surfaces, is more optimal for a larger number of patients.

      3.3 Toric

      To correct astigmatism, a toroidal surface is generated, whereby two different perpendicularly arranged curves of differing radii are generated on either the front or between the front and back surfaces of the contact lens. When fitting rigid corneal lenses to an astigmatic cornea, such curvature differences can improve corneal alignment and subsequent in vivo stability [
      • Bier N.
      • Lowther G.E.
      Contact lens correction.
      ,
      • Mandell R.
      Contact Lens practice.
      ]. For current soft lenses, placing the toricity on the back surface of the lens does not lead to improved stabilization [
      • Harris M.G.
      • Laconic M.
      • Ward J.
      Stability of back-toric prism-ballast hydrogel contact lenses.
      ]. In practice, low modulus soft lens materials conform to the cornea and the toricity is transferred to the front surface of the lens (print through effect). For simplicity in manufacturing, most modern day moulded toric contact lenses contain the spherical power on the front surface and the cylinder power on the back surface; the lens axis being determined by the rotational arrangement between the two [
      • Newman S.
      • Noack D.
      Soft contact Lens for the correction of astigmatism.
      ].
      Soft and front surface rigid corneal toric lens designs must be rotationally stabilised to ensure the cylinder axis is in the appropriate alignment on the eye. Methods of stabilization are based on varying the thickness profile of the lens and can be described in three general categories: prism ballast, peri-ballast or modified prism ballast, and dual thin zone (Table 1) [
      • Sulley A.
      • Hawke R.
      • Lorenz K.O.
      • Toubouti Y.
      • Olivares G.
      Resultant vertical prism in toric soft contact lenses.
      ].
      Table 1Comparative stabilization methods used in current soft toric designs.
      TypeProfileAverage prismEffect on optics
      Prism ballastBase down prism applied to whole lens to increase inferior lens thickness0.81–1.12Induces vertical prism within the optic zone
      Peri ballastBase down prism applied to select areas of the lens to increase inferior lens thickness0.52–0.96Prism effect within the optic zone can be lessened depending on design
      Dual thin zone, slab-off, or dynamic stabilizationInferior and superior thinned to create thicker 3 and 9 o'clock zones<0.03Minimal or no optical prism allowing lens to be thinner compared to other designs
      The stabilization mechanisms of lenses may also inherently induce asymmetric aberrations, causing a reduction in image quality. For instance, Fig. 2 shows the higher order aberration maps of a prism stabilised soft toric lens with three different lens powers measured on a Shack-Hartmann aberrometer with an 8 mm analysis diameter. Rather than a uniform colour aberration map, vertical coma is present.
      Fig. 2
      Fig. 2Wavefront error (μm, 8 mm pupil) of prism ballasted toric lens showing induced vertical coma for a -8.00 (a), -3.00 (b), and +4.00 (c) D lens (all -1.25 cylinders).

      3.4 Multifocal

      Multifocal designs were developed to ameliorate the visual consequences of presbyopia and can be manufactured in rotationally symmetrical or non-rotationally symmetrical forms. Non-rotationally symmetric designs were originally utilised to correct astigmatism but are also being explored in some new technologies described below. Rotational stability of these designs is achieved in the same way as a single vision toric lens. Rotationally symmetric designs, however, remain most common. More recently, multifocal designs have also been utilised to modify peripheral refraction to slow myopia progression in children [
      • Kang P.
      Optical and pharmacological strategies of myopia control.
      ,
      • Wildsoet C.F.
      • Chia A.
      • Cho P.
      • Guggenheim J.A.
      • Polling J.R.
      • Read S.
      • et al.
      IMI – interventions for controlling myopia onset and progression report.
      ].

      3.4.1 Alternating versus simultaneous designs

      The simplest type of non-rotationally symmetric lens design to correct presbyopia is the “alternating” or “translating” design. The alternating design principle employs corrective rigid corneal lenses that aim to translate when the gaze is directed from distance to near, or vice versa. They provide one primary optic in front of the pupil at a time, analogous to spectacle bifocals. Translation of the lens on eye is needed to provide adequate distance and near vision. Centration and orientation, which are essential, are optimised by incorporating base-down prism ballast and/or lens truncation. Although alternating lenses can be successful in rigid corneal lens designs [
      • Wolffsohn J.S.
      • Davies L.N.
      Presbyopia: effectiveness of correction strategies.
      ], and some early bi- or multifocal soft contact lenses employed this alternating vision principle [
      • Borish I.M.
      • Soni S.
      Bifocal contact lenses.
      ,
      • Toshida H.
      Bifocal contact lenses: history, types, characteristics, and actual state and problems.
      ], these designs often suffer from issues of discomfort, insufficient translation, or rotational instability [
      • Borish I.M.
      • Soni S.
      Bifocal contact lenses.
      ].
      In simultaneous-image designs, light rays pass simultaneously through multiple zones with all rays contributing to the characteristics of the image that is formed. These contact lenses can be designed to contain: (i) zones of two different optical powers (e.g. powered to focus light when viewing at distance or near (bifocal, two-foci) or (ii) a smooth transition between the powers necessary to focus light when viewing at distance and near (multifocal, multiple foci). Of note, abrupt transitions in optical powers are often difficult to manufacture and, as such, often create a smoothing of optical power providing some multifocality. In either the simultaneous image bifocal or multifocal case the retina receives both in-focus and out-of-focus images simultaneously [
      • Benjamin W.J.
      Simultaneous vision contact lenses: why the dirty window argument doesn’t wash.
      ,
      • Charman W.N.
      • Walsh G.
      Retinal images with centred aspheric varifocal contact lenses.
      ]. The spread of light from the out-of-focus images, or “ghosting,” may impair the contrast of the desired image, but often does not reduce the peak attainable visual acuity [
      • Charman W.N.
      • Walsh G.
      Retinal images with centred aspheric varifocal contact lenses.
      ,
      • Charman W.N.
      • Saunders B.
      Theoretical and practical factors influencingthe optical performance of contact lenses for the presbyope.
      ].
      Simultaneous-image correction can be achieved in a variety of ways: diffractive, zonal, concentric or annular, aspheric, or extended depth of focus designs and may be made as centre-near or centre-distance [
      • Bennett E.S.
      Contact lens correction of presbyopia.
      ,
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ,
      • Pérez-Prados R.
      • Piñero D.P.
      • Pérez-Cambrodí R.J.
      • Madrid-Costa D.
      Soft multifocal simultaneous image contact lenses: a review.
      ,
      • Benjamin W.J.
      • Borish I.M.
      Presbyopic correction with contact lenses.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      • Papas E.
      Inherent ocular spherical aberration and multifocal contact lens optical performance.
      ,
      • Llorente-Guillemot A.
      • García-Lazaro S.
      • Ferrer-Blasco T.
      • Perez-Cambrodi R.J.
      • Cerviño A.
      Visual performance with simultaneous vision multifocal contact lenses.
      ]. These designs are summarised schematically in Fig. 3.
      Fig. 3
      Fig. 3Simultaneous-image optical designs of contact lenses. Red, green and yellow colours represent the areas for distance, near and intermediate vision, respectively. The annular / zonal and aspheric designs illustrated here have a central distance correction: designs with centre near correction are also available. EDOF: extended depth of focus (see 3.4.5).

      3.4.2 Diffractive

      Diffractive lenses are designed to specifically introduce half wavelength (or other fraction of a wavelength) optical (path length) changes between zones [
      • Davison J.A.
      • Simpson M.J.
      History and development of the apodized diffractive intraocular lens.
      ,
      • Klein S.A.
      Understanding the diffractive bifocal contact lens.
      ]. These optical path length changes create constructive interference (and resulting images) at focal distances specified by the given ring geometry [
      • Buralli D.A.
      • Morris G.M.
      Design of a wide field diffractive landscape lens.
      ]. Half wavelength (pi) shifts in phase between zones produces a bifocal [
      • Davison J.A.
      • Simpson M.J.
      History and development of the apodized diffractive intraocular lens.
      ,
      • Ravikumar S.
      • Bradley A.
      • Thibos L.N.
      Chromatic aberration and polychromatic image quality with diffractive multifocal intraocular lenses.
      ] and other phase step combinations can create other designs (e.g. trifocal) [
      • Lee S.
      • Choi M.
      • Xu Z.
      • Zhao Z.
      • Alexander E.
      • Liu Y.
      Optical bench performance of a novel trifocal intraocular lens compared with a multifocal intraocular lens.
      ,
      • Alió J.L.
      • Plaza-Puche A.B.
      • Alió del Barrio J.L.
      • Amat-Peral P.
      • Ortuño V.
      • Yébana P.
      • et al.
      Clinical outcomes with a diffractive trifocal intraocular lens.
      ,
      • Cochener B.
      • Boutillier G.
      • Lamard M.
      • Auberger-Zagnoli C.
      A comparative evaluation of a new generation of diffractive trifocal and extended depth of focus intraocular lenses.
      ]. The basic diffractive design consists of a saw-tooth pattern of concentric, annular, Fresnel-type diffractive echelettes (Fig. 4A). Unlike in the annular or concentric designs, in diffractive lenses every location across the lens contributes to each optical power [
      • Schwiegerling J.
      • Choi J.
      Application of the polychromatic defocus transfer function to multifocal lenses.
      ,
      • Schwiegerling J.
      Analysis of the optical performance of presbyopia treatments with the defocus transfer function.
      ,
      • Zheleznyak L.
      • Kim M.J.
      • MacRae S.
      • Yoon G.
      Impact of corneal aberrations on through-focus image quality of presbyopia-correcting intraocular lenses using an adaptive optics bench system.
      ].
      Fig. 4
      Fig. 4Surface diffractive profiles in radius-squared (r2) space: the profile zone width (w) and the phase shift specify the add power and the intensity distribution of light (wavelength λ) focused on each of the image planes: (a) a standard diffractive bifocal with a saw-tooth profile; (b) a diffractive bifocal with refractive periphery; and (c) a diffractive bifocal with a variable (apodised) step profile (adapted from Cohen, 1993 [
      • Cohen A.L.
      Diffractive bifocal lens designs.
      ]).
      In a normal diffractive bifocal, the step heights at the edge of each diffractive zone are the same for all zones, so that the split of light between the near and distant foci is independent of pupil diameter. In a typical diffractive bifocal, about 80 % of the light passing through the pupil is diffracted into each of the distance (zero order) and near (first order) images in an equal proportion (i.e., 40 % and 40 %, respectively). As a result, the distance and near powers are each effective over the full pupil. The remaining light is either diffracted into unwanted orders (16 %) or scattered (4 %), with both of these effects leading to a significant decrease of low contrast visual acuity and a degree of light scatter in dim light conditions [
      • Charman W.N.
      • Saunders B.
      Theoretical and practical factors influencingthe optical performance of contact lenses for the presbyope.
      ].
      The basic diffractive bifocal design may be modified to include both a diffractive profile and a refractive surface within the optic zone (Fig. 4B). The diffractive bifocal design has the major theoretical advantage that the retinal image quality is not influenced by variations in pupil size, since all parts of the optic zone contribute to both the distance and near images.
      By minor modifications in manufacturing technology, it is possible to adjust the relative proportions of diffracted light contributing to the near and far images on the retina, according to the visual demands [
      • Freeman M.H.
      • Charman W.N.
      An exploration of modified monovision with diffractive bifocal contact lenses.
      ]. In “apodised” or pupil-size dependent designs (Fig. 4C), the step heights are reduced with increasing diameter zones in the lens. Specifically, for a small pupil the lens behaves like a “standard” bifocal, whereas with increasing pupil diameter light passes through the outer zones where the step heights become progressively smaller. Hence increasing amounts of light go into just one of the foci (the distant one), favouring distance vision.

      3.4.3 Annular

      Annular, concentric or zonal designs incorporate a central circular zone, intended either for distance or near viewing, surrounded by one or more rings of near/intermediate or distance correction, respectively. The diameter of the central annulus can be chosen to enhance either distance or near vision.
      Fig. 5 depicts power profiles of step and linear zonal (annular) designs. The central distance area of these lenses shows a constant power over the central circular region of radius 1.5 mm; although the measured power is slightly positive. The intermediate annular zone, which extends to a pupil radius of 2.1 mm, shows a roughly linear increase in the positive power with the gradient increasing with the nominal add power. The outer zones of the lenses show a slow, linear, positive increase in power with a gradient which is almost independent of the nominal add power.
      Fig. 5
      Fig. 5Power profiles for two characteristic centre-distance zonal designs, displaying step (left) and smooth (right) changes in power across lens radius. Two add powers of medium (Med) and high (High) are plotted for each profile. The power in the step zonal design alternates between the nominal distance (in these cases plano) and near powers, while a gradual overall change in power in the negative direction as the zonal radius increases is also observed. The linear design shows three zones: a central distance zone, an intermediate annular zone of gradually increasing power for intermediate vision and an outer “near” zone. Replotted data from [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ].
      The performance of these designs is highly dependent on the relationship between pupil size of the wearer and zone geometry (number of zones, zone width, etc.) [
      • Bradley A.
      • Nam J.
      • Xu R.
      • Harman L.
      • Thibos L.
      Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality.
      ]. Lenses can be fitted with matched designs in each eye or following a “modified monovision” approach whereby one eye is biased more to either distance or near correction either by incorporating a larger central zone diameter compared to the fellow eye, or fitting a centre distance design to one eye and a centre near design to the fellow eye.

      3.4.4 Aspheric

      Aspheric multifocal designs involve a progressive, rotationally symmetric, gradation of power from the centre to the edge of the optical zone. This is achieved by the use of at least one aspheric lens surface. This asphericity introduces spherical aberration and produces progressively greater power either in the lens centre (centre-near, introducing negative spherical aberration) or the periphery (centre-distance, introducing positive spherical aberration). One way of specifying the rate of power change is by the eccentricity (e) value, which describes the rate of change of surface curvature with distance from lens axis [
      • Charman W.N.
      • Walsh G.
      Retinal images with centred aspheric varifocal contact lenses.
      ,
      • Charman W.N.
      • Saunders B.
      Theoretical and practical factors influencingthe optical performance of contact lenses for the presbyope.
      ]. Another method, spherical aberration, represents the dioptric difference in lens power at the periphery from the lens centre. The spherical aberration or rate of change may also be described in microns wavefront error.
      Fig. 6 presents sagittal power profile data, obtained by averaging the power around each zone of the lenses, for a single-aspheric and two bi-aspheric multifocal lenses. It is evident that the power for the “low add” lens has a smooth, continuous, parabolic profile and can be fitted [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ] by the following equation:
      Py = P0 + by2,
      (1)


      where y is the radial distance from the centre of the lens (in mm), P0 is the paraxial power (at y = 0), Py is the power at radius y and b (in D/mm2) is a constant which characterises the power changes as a function of y, corresponding to negative primary spherical aberration, which for the low addition lens is about 0.18 D/mm2.
      Fig. 6
      Fig. 6Power profiles for aspheric multifocal lenses, displaying a single aspheric (for low add corrections, i.e. PureVision multifocal low add) and two bi-aspheric (for high add corrections, i.e. Air Optix Aqua multifocal high add (red line) and PureVision multifocal high add (blue line)) optical designs. Lines represent second-order fitted functions. Replotted data from Plainis, Atchison and Charman, 2013 [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ].
      The changes in the power as a function of lens zonal radius for the “high” addition lenses cannot be fitted by a single second-order function. Since these lenses have bi-aspheric designs, the data for the central and peripheral zones can be well fitted by separate parabolic functions, each valid for the appropriate range of zonal radii. The b values for the “high” addition lenses are very similar in lens periphery (∼-0.18 D/mm2) but significantly higher in lens centre (-0.50 and -0.70 D/mm2, respectively).
      Several groups have provided representations of multifocal lens power maps and/or power profiles using various technologies [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ,
      • Kim E.
      • Bakaraju R.C.
      • Ehrmann K.
      Reliability of power profiles measured on NIMO TR1504 (Lambda-X) and effects of lens decentration for single vision, bifocal and multifocal contact lenses.
      ,
      • Madrid-Costa D.
      • Ruiz-Alcocer J.
      • García-Lázaro S.
      • Ferrer-Blasco T.
      • Montés-Micó R.
      Optical power distribution of refractive and aspheric multifocal contact lenses: Effect of pupil size.
      ,
      • Tilia D.
      • Bakaraju R.C.
      • Chung J.
      • Sha J.
      • Delaney S.
      • Munro A.
      • et al.
      Short-term visual performance of novel extended depth-of-focus contact lenses.
      ,
      • Wagner S.
      • Conrad F.
      • Bakaraju R.C.
      • Fedtke C.
      • Ehrmann K.
      • Holden B.A.
      Power profiles of single vision and multifocal soft contact lenses.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      Extended depth of focus contact lenses vs. two commercial multifocals: part 1. Optical performance evaluation via computed through-focus retinal image quality metrics.
      ,
      • Kollbaum P.S.
      • Bradley A.
      Correction of presbyopia: old problems with old (and new) solutions.
      ]. Fig. 7 (Adapted from Kim et al. [
      • Kim E.
      • Bakaraju R.C.
      • Ehrmann K.
      Reliability of power profiles measured on NIMO TR1504 (Lambda-X) and effects of lens decentration for single vision, bifocal and multifocal contact lenses.
      ]) shows comparative power profiles of several commercially available presbyopic designs. In large part, centre near aspheric lens designs (upper left subplot) appear quite similar optically but are distinctly different from the higher add (upper right subplot) and zonal designs (lower row of subplots). These optical power profiles also provide further insight into specific lens geometry (e.g. zone width). Different on-eye performance would be expected by lenses with different optical profiles.
      Fig. 7
      Fig. 7Power profiles of commercial multifocal lenses, all nominally labelled -3.00 D distance power, were replotted using published data [
      • Kim E.
      • Bakaraju R.C.
      • Ehrmann K.
      Reliability of power profiles measured on NIMO TR1504 (Lambda-X) and effects of lens decentration for single vision, bifocal and multifocal contact lenses.
      ]. A Matlab data extraction tool (https://au.mathworks.com/matlabcentral/fileexchange/7173-grabit) was used to reproduce the plots from the described published image source by Ravi Bakaraju, BOptom, PhD.
      When a lens is placed on the eye, the multifocality achieved for the wearer is the sum of that provided by the eye and the lens [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      • Papas E.
      Inherent ocular spherical aberration and multifocal contact lens optical performance.
      ,
      • Bradley A.
      • Nam J.
      • Xu R.
      • Harman L.
      • Thibos L.
      Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality.
      ]. Therefore, the significant positive spherical aberration exhibited by older eyes, may augment the spherical aberration of any lens with positive spherical aberration (centre-distance aspheric designs). However, in lens designs which contain negative spherical aberration (centre-near aspheric designs), there is high potential for the lens design to actually subtract from the multifocality provided by the eye [
      • Kollbaum P.S.
      Optical aberrations of contact lenses and eyes corrected with contact lenses.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      • Papas E.
      Inherent ocular spherical aberration and multifocal contact lens optical performance.
      ,
      • Bradley A.
      • Nam J.
      • Xu R.
      • Harman L.
      • Thibos L.
      Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality.
      ]. Therefore, ocular spherical aberration may be either an aid or hindrance to the on-eye success of aspheric multifocal designs, and likely contributes to the variable patient responses often experienced with these multifocal designs [
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      • Papas E.
      Inherent ocular spherical aberration and multifocal contact lens optical performance.
      ].
      Thus, although the “best” image on the retina is degraded by greatly increased spherical aberration, this trade-off is required in simultaneous image lenses to increase the depth-of-focus of the wearer. Higher “add” value lenses require higher levels of spherical aberration than lower add designs. To achieve more effective near additions, bi-aspheric surfaces have been designed, in which the power profile is discontinuous, with the near portion (∼2.5 mm in diameter) in centre-near designs showing higher e-values (higher amounts of negative spherical aberration) compared to the outer portion of the lens [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ]. Lenses with higher levels of spherical aberration will induce higher levels of comatic aberration with decentration.

      3.4.5 Extended depth of focus (EDOF)

      The newest hybrid classification of multifocal lens options has taken on the broad terminology of “extended depth of focus” contact lenses. This term is somewhat ambiguous because, as described above, all multifocal lenses aim to do this. However, this category of lenses broadly encompasses lenses that may contain non-monotonic, non-aspheric, and/or aperiodic profiles. In some instances, these designs are broadly similar to aspheric lenses, utilizing alterations of spherical aberration to generate their multifocality, but more purposefully including other multiple higher order spherical aberration terms (e.g. EDOF [
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      Extended depth of focus contact lenses vs. two commercial multifocals: part 1. Optical performance evaluation via computed through-focus retinal image quality metrics.
      ] and conical surfaces that create axial focus called ‘axicons’ [
      • Ares J.
      • Flores R.
      • Bará S.
      • Jaroszewicz Z.
      Presbyopia compensation with a quartic axicon.
      ]). Other designs being explored have unique angular optical elements [
      • de Gracia P.
      • Dorronsoro C.
      • Marcos S.
      Multiple zone multifocal phase designs.
      ]. One such lens is called the “light sword lens” [
      • Kakarenko K.
      • Ducin I.
      • Grabowiecki K.
      • Jaroszewicz Z.
      • Kolodziejczyk A.
      • Mira-Agudelo A.
      • et al.
      Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale.
      ,
      • Kołodziejczyk A.
      • Bará S.
      • Jaroszewicz Z.
      • Sypek M.
      The light sword optical element—a new diffraction structure with extended depth of focus.
      ,
      • Torres-Sepúlveda W.
      • Mira-Agudelo A.
      • Barrera-Ramírez J.F.
      • Petelczyc K.
      • Kolodziejczyk A.
      Optimization of the light sword lens for presbyopia correction.
      ,
      • Mira-Agudelo A.
      • Torres-Sepúlveda W.
      • Barrera J.F.
      • Henao R.
      • Blocki N.
      • Petelczyc K.
      • et al.
      Compensation of presbyopia with the light sword Lens.
      ], which is an asymmetric optical element divided into infinitesimal angular sectors, each with different additions of optical power [
      • Kakarenko K.
      • Ducin I.
      • Grabowiecki K.
      • Jaroszewicz Z.
      • Kolodziejczyk A.
      • Mira-Agudelo A.
      • et al.
      Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale.
      ]. Another unique design theorised is called the “peacock optical element”, which is a particular type of diffractive element capable of focusing light onto segments of arbitrary length, inclination, orientation, and longitudinal intensity distribution [
      • Romero L.A.
      • Millán M.S.
      • Jaroszewicz Z.
      • Kolodziejczyk A.
      Double peacock eye optical element for extended focal depth imaging with ophthalmic applications.
      ,
      • Torres W.
      • Barrera J.F.
      • Henao R.
      • Jaroszewicz Z.
      • Kakarenko K.
      • Mira-Agudelo A.
      • et al.
      Imaging with extended depth of field by means of the peacock eye optical element.
      ]. These designs contrast with the power profiles of centre-distance or centre-near aspheric multifocals, which are monotonic in nature, where the power distribution either gradually changes from distance to near or vice versa. Several other designs also contrast with annular and concentric-ring designs, which are non-monotonic but periodic in nature (i.e. alternating distinct zones for distance and near correction separated over the optic zone diameter) [
      • Tilia D.
      • Bakaraju R.C.
      • Chung J.
      • Sha J.
      • Delaney S.
      • Munro A.
      • et al.
      Short-term visual performance of novel extended depth-of-focus contact lenses.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      Extended depth of focus contact lenses vs. two commercial multifocals: part 1. Optical performance evaluation via computed through-focus retinal image quality metrics.
      ,
      • Sha J.
      • Tilia D.
      • Diec J.
      • Fedtke C.
      • Yeotikar N.
      • Jong M.
      • et al.
      Visual performance of myopia control soft contact lenses in non-presbyopic myopes.
      ,
      • Bakaraju R.C.
      • Tilia D.
      • Sha J.
      • Diec J.
      • Chung J.
      • Kho D.
      • et al.
      Extended depth of focus contact lenses vs. two commercial multifocals: part 2. Visual performance after 1 week of lens wear.
      ].

      3.4.6 Myopia control

      Optical interventions for myopia control may utilise optical approaches somewhat similar to designs for presbyopia. In particular, both contain muliple optical powers, but unlike in presbyopic designs which aim to reduce presbyopic near defocus, myopic designs aim to induce myopic defocus in order to reduce myopia progression [
      • Smith E.L.
      • Ramamirtham R.
      • Qiao-Grider Y.
      • Hung L.-F.
      • Huang J.
      • Kee C.
      • et al.
      Effects of foveal ablation on emmetropization and form-deprivation myopia.
      ]. Contact lens myopia control interventions have been described as including annular, aspheric, multisegment, and EDOF designs [
      • Kang P.
      Optical and pharmacological strategies of myopia control.
      ,
      • Wildsoet C.F.
      • Chia A.
      • Cho P.
      • Guggenheim J.A.
      • Polling J.R.
      • Read S.
      • et al.
      IMI – interventions for controlling myopia onset and progression report.
      ], but, to date, only one dual focus contact lens design, the MiSight® 1 day lens (CooperVision Inc., Pleasanton, CA, USA) has achieved both FDA and European Conformity (CE) approval for slowing myopia progression [
      • Chamberlain P.
      • Peixoto-de-Matos S.C.
      • Logan N.S.
      • Ngo C.
      • Jones D.
      • Young G.
      A 3-year randomized clinical trial of MiSight lenses for myopia control.
      ] and two orthokeratology lenses, the Bloom Night (Menicon Co. Ltd., Nagoya, Japan) and Paragon Corneal Reshaping Therapy (Gilbert, Arizona, USA) received CE approval for myopia control [
      • Bullimore M.A.
      • Richdale K.
      Myopia Control 2020: where are we and where are we heading?.
      ].

      3.5 Decentred lens optics

      As mentioned above, contact lens decentration will induce higher order aberrations that reduce visual quality. This issue is increasingly important with lenses with inherent higher levels of aberration (e.g. higher add aspheric multifocal lenses). To counteract on-eye positioning differences relative to the primary line of sight, some rotationally stabilised lenses with decentred optical zones have been explored [
      • Fujikado T.
      • Ninomiya S.
      • Kobayashi T.
      • Suzaki A.
      • Nakada M.
      • Nishida K.
      Effect of low-addition soft contact lenses with decentered optical design on myopia progression in children: a pilot study.
      ,
      • Morgan C.F.
      • Lindacher J.M.
      Contact lens having an optimized optical zone.
      ]. Decentred optic designs have shown good success at improving vision, especially in aberrated eyes [
      • Suzaki A.
      • Koh S.
      • Maeda N.
      • Asonuma S.
      • Oie Y.
      • Soma T.
      • et al.
      Efficacy of the standardized asymmetric soft contact lens with a decentered optic zone design for correcting visual performance in patients with keratoconus.
      ]. Despite their benefits, decentred optical zone lenses are only available from a few companies including SpecialEyes [
      • SpecialEyes
      SpecialEyes 54 multifocal now available with OptiSync technology.
      ] and Menicon [
      • Menicon
      Miru 1month menicon multifocal.
      ]. The pupil centre position moves nasally with accommodation [
      • Mathur A.
      • Gehrmann J.
      • Atchison D.A.
      Influences of luminance and accommodation stimuli on pupil size and pupil center location.
      ] and these stabilised lenses decentre the optic zone to align over the average pupil centre or the patient’s line of sight during near viewing. In particular, the Menicon design employs a symmetric structure so that the same lens is either put in right-side up for the right eye or up-side down for the left eye, in order to align the lens centre to the average pupil centre location with just one lens design. The direction is marked with an arrow for guiding the wearer in the correct insertion orientation for each eye. This design, therefore, has the advantage of just needing one lens, but does require the user to note proper orientation.

      4. Contact lens metrology

      4.1 In-vitro (off-eye) measurement

      4.1.1 Measurement devices

      On-eye accuracy is predicated on the valid manufacturing of lenses. Off-eye measurements to verify accurately manufactured lenses can be accomplished in several ways. Similar to spectacle or other rigid corneal lens measures which are done off-eye, some traditional optical techniques were first applied to contact lens measures. These include optical focimeters [
      • Zhang J.
      • Wang L.
      • Ma Z.
      Research and analysis on new test lenses for calibration of focimeters used for measuring contact lenses.
      ,
      • Pearson R.M.
      • Evans B.J.W.
      A comparison of in-air and in-saline focimeter measurement of the back vertex power of spherical soft contact lenses.
      ] or the knife-edge technique [
      • Ho A.
      • Ehrmann K.
      A knife-Edge system for evaluating contact lenses.
      ]. The focimeter can measure sphere and toric lenses and can be used to measure multifocal lenses if it is used in conjunction with a Scheiner disc apparatus that has been designed to detect deviation from the apical power at specified chord widths across the optic zone. The focimeter method is fast and simple but requires competent technique and measurement speed (< 10 s) to be effective. Although these remain common techniques, they only describe limited aspects of the lower order optics and suffer relatively poor sensitivity [
      • Belda-Salmerón L.
      • Madrid-Costa D.
      • Ferrer-Blasco T.
      • García-Lázaro S.
      • Montés-Micó R.
      In vitro power profiles of daily disposable contact lenses.
      ].
      Soft lenses add extra measurement complexity due to their thin, flexible materials. Additionally, given their high water content, they begin to dehydrate immediately when exposed to air leading to inaccurate measures [
      • Bauer G.T.
      • Lechner H.B.
      Measurement of the longitudinal spherical aberration of soft contact lenses.
      ]. To overcome this issue, soft lenses can be measured in a wet cell (typically filled with saline) and their optical effect scaled to an in-air on-eye equivalence [
      • Benjamin W.J.
      Optical phenomena of contact lenses.
      ]. This scaling in itself is not problematic, except it requires detailed knowledge of the lens and medium [
      • Kollbaum P.
      • Jansen M.
      • Thibos L.
      • Bradley A.
      Validation of an off-eye contact lens shack-Hartmann wavefront aberrometer.
      ], and because the immersion of contact lenses in saline solution produces a decrease in its power refraction [
      • Heideman K.C.
      Surface metrology of contact lenses in saline soultion.
      ].
      Several interferometric techniques are quite sensitive to measurements in other areas of optics [
      • Malacara-Hernández D.
      • Malacara-Doblado D.
      Optical testing and interferometry.
      ]. Therefore, several techniques have been applied to contact lens metrology in laboratory settings. These include a Mach-Zender interferometer [
      • Williby G.A.
      • Smith D.G.
      • Brumfield R.B.
      • Greivenkamp J.E.
      Interferometric testing of soft contact lenses.
      ,
      • Seong K.
      • Greivenkamp J.E.
      Surface reconstruction based on transmission interferometric testing.
      ], Twyman-Green interferometer [
      • Rottenkolber M.
      • Podbielska H.
      High precision Twyman-Green interferometer for the measurement of ophthalmic surfaces.
      ], and Moiré interferometer [
      • de Angelis M.
      • De Nicola S.
      • Ferraro P.
      • Finizio A.
      • Pierattini G.
      Analysis of moiré fringes for measuring the focal length of lenses.
      ]. Commercially, another interferometric technique, deflectometry, has been implemented in the Nimo TR1504 (Lambda-X SA, Belgium), and has been widely used to measure lenses off of the eye [
      • Kim E.
      • Bakaraju R.C.
      • Ehrmann K.
      Reliability of power profiles measured on NIMO TR1504 (Lambda-X) and effects of lens decentration for single vision, bifocal and multifocal contact lenses.
      ,
      • Joannes L.
      • Hough T.
      • Hutsebaut X.
      • Dubois X.
      • Ligot R.
      • Saoul B.
      • et al.
      Reproducibility of contact lens power measurements using the phase shifting schlieren method.
      ,
      • Domínguez-Vicent A.
      • Marín-Franch I.
      • Esteve-Taboada J.J.
      • Madrid-Costa D.
      • Montés-Micó R.
      Repeatability of in vitro power profile measurements for multifocal contact lenses.
      ,
      • Rodríguez-Vallejo M.
      • Montagud D.
      • Monsoriu J.A.
      • Furlan W.D.
      On the power profiles of contact lenses measured with NIMO TR1504.
      ,
      • Monsálvez-Romín D.
      • Domínguez-Vicent A.
      • García-Lázaro S.
      • Esteve-Taboada J.J.
      • Cerviño A.
      Power profiles in multifocal contact lenses with variable multifocal zone.
      ].
      A novel ptychographic imaging technique [
      • Maiden A.M.
      • Rodenburg J.M.
      • Humphry M.J.
      Optical ptychography: a practical implementation with useful resolution.
      ,
      • Maiden A.M.
      • Humphry M.J.
      • Zhang F.
      • Rodenburg J.M.
      Superresolution imaging via ptychography.
      ] has also been employed to quantify lens power [
      • Plainis S.
      • Atchison D.A.
      • Charman W.N.
      Power profiles of multifocal contact lenses and their interpretation.
      ]. A series of diffraction patterns are recorded from adjacent neighbouring points that are then used to reconstruct the lens thickness profile, from which power can be determined [
      • Elder Smith A.
      Oxygen: are your corneae getting enough?.
      ]. This technique has advantages of having very high resolution [
      • Maiden A.M.
      • Rodenburg J.M.
      • Humphry M.J.
      Optical ptychography: a practical implementation with useful resolution.
      ,
      • Maiden A.M.
      • Humphry M.J.
      • Zhang F.
      • Rodenburg J.M.
      Superresolution imaging via ptychography.
      ], and can successfully measure abrupt power changes, even those found in multi-ring concentric designs. This technique has been employed in a device called the PhaseFocus Lens Profiler (Phase Focus, Sheffield, UK).
      Photoacoustic microscopy [
      • Tserevelakis G.J.
      • Tsagkaraki M.
      • Tsilimbaris M.K.
      • Plainis S.
      • Zacharakis G.
      Photoacoustic imaging methodology for the optical characterization of contact lenses.
      ] and optical coherence tomography [
      • Karnowski K.
      • Grulkowski I.
      • Mohan N.
      • Cox I.
      • Wojtkowski M.
      Quantitative optical inspection of contact lenses immersed in wet cell using swept source OCT.
      ] are other techniques being explored in laboratory settings. The optical coherence tomography technique is not unlike the on-eye techniques but utilising slightly different wavelength light. Photoacoustic microscopy, however, capitalises on optical absorption spectra. Lenses are first tinted on both sides with two thin ink layers, each with distinctly different absorption properties. Acoustic waves are generated following the absorption of intensity-modulated optical radiation by the material. Both of these techniques first allow elevation data to be measured, from which contact lens thickness, curvature, and power can be derived.
      Shack-Hartmann aberrometry has also been employed in several commercially available devices. A perforated screen or honeycomb of small lenslets is used to sub-sample a wavefront deviation captured on Charge Coupled Device sensor. The accuracy and repeatability of the ClearWave Contact Lens Precision Aberrometer (Lumetrics, Rochester, NY) has been assessed as having errors of <1 % [
      • Kollbaum P.
      • Jansen M.
      • Thibos L.
      • Bradley A.
      Validation of an off-eye contact lens shack-Hartmann wavefront aberrometer.
      ]. Good repeatability has been reported for the commercially available Optocraft system (SHSOphthalmic, Erlangen, Germany) [
      • Wagner S.
      • Conrad F.
      • Bakaraju R.C.
      • Fedtke C.
      • Ehrmann K.
      • Holden B.A.
      Power profiles of single vision and multifocal soft contact lenses.
      ]. The Omnispect system is another high-resolution Shack-Hartmann system with a semi-open cell to allow other aspects of lens inspection.

      4.1.2 Measurement standards

      Lens manufacturers need to conform to International Organization for Standardization (ISO) [
      • ISO
      ISO 18369-2.
      ], American National Standards Institute (ANSI), or other relevant standards for the products they make to be approved for sale in particular territories. These standards provide for the minimum necessary accuracy to which the manufacturer can guarantee the lens power and parameters and allow practitioners to receive lenses from different manufacturers with reasonable consistency.
      The ISO standard (18369-3:2017, Annex B, B2) allows one of three measurement methods: focimetery, Moiré deflectometry, or the Shack-Hartmann technique. To verify consistency, manufacturers utilise one of these optical metrology techniques along with one of the accepted inspection strategies: inspection of 100 % of lenses, acceptance sampling (a system of single sampling for inspection lot-by-lot), or statistical estimation of performance (a representative sample is used to determine and estimate larger group performance). Some types of lenses (e.g., custom) lend themselves more easily to 100 % inspection. As the majority of commercially available lenses are mass produced soft lenses, the most commonly adopted method is the acceptance sampling method, or acceptance quality limit. Different manufacturers may choose differing sample plans. Specific methodology employed by manufacturers is often not published, nor is it the same between manufacturers.
      It should be noted, however, that the methods for measuring contact lenses with these techniques specified in the ISO standards, do not represent real world use of the lens but rather set a standard base from which the lenses can be judged. Such in vitro standards are attempting to arrive at a balance between viable manufacturing efficiencies and clinical performance. For example, clinically relevant tolerances in commonly available soft contact lenses include power ≤10.00D ± 0.25D (ISO 18369-2:2017,4.3), diameter ±0.20 mm (ISO 18369-2:2017,4.2), and back surface radius ±0.20 mm (ISO 18369-2:2017,4.4). ISO standards do not currently cover more complex optical designs such as multifocals as stand-alone devices but rather expect the manufacturer to determine the best way to assign the most appropriate power(s) to such lens types (ISO 18369-3:2017, 4.3.7).

      4.2 In-vivo (on-eye) methodology

      Both manufacturers and practitioners want to know the detailed optical effects of lenses on-eye to know if the desired user optical goals are actually being realised. Current ISO standards are insufficient in their scope or relevance to truly match in vitro parameters to in vivo performance expectations. Off-eye measurements simply do not replicate the real-world situation in several ways, so on-eye measures become increasingly important. For example, ISO standards stipulate that the lens should be measured in saline at 20−25 °C (ISO 18369-3:2017,Annex B, B4.2.1); however the lens is worn on the eye at a temperature of approximately 34 °C [
      • Efron N.
      • Young G.
      • Brennan N.A.
      Ocular surface temperature.
      ]. This can lead to changes in dimensional parameters due to water loss [
      • Purslow C.
      • Wolffsohn J.S.
      Ocular surface temperature.
      ]. Such effects can change the sagittal depth, modulus and refractive index of the lens and impact both the apical power and the aberrations of the lens [
      • Plainis S.
      • Charman W.N.
      On-eye power characteristics of soft contact lenses.
      ]. Additionally, the soft lens may not completely conform to the cornea, depending on its modulus, lens thickness, and optical power [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ,
      • Kollbaum P.S.
      Optical aberrations of contact lenses and eyes corrected with contact lenses.
      ,
      • Cox I.G.
      • Holden B.A.
      Soft contact lens-induced longitudinal spherical aberration and its effect on contrast sensitivity.
      ].
      Several of the methods employed for off-eye analysis do not transfer well to on-eye metrology methods. For instance, due to the very low reflectivity of the contact lenses (especially in wet cells), many off-eye metrology techniques are single pass systems where light passes through the lens once and is quantised on the other side (such as a Charge Coupled Device sensor). However, on-eye systems require light to not only pass through the system once, but then reflect back out of the eye to be quantised. To accomplish this double-pass methodology many of these off-eye techniques would require significantly higher light, than meet the safety standards established by ANSI [
      • Delori F.C.
      • Webb R.H.
      • Sliney D.H.
      Maximum permissible exposures for ocular safety (ANSI 2000), with emphasis on ophthalmic devices.
      ].
      One technique that has been successfully applied in vivo is the Shack-Hartmann technique [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ,
      • Cheng X.
      • Himebaugh N.L.
      • Kollbaum P.S.
      • Thibos L.N.
      • Bradley A.
      Test–retest reliability of clinical shack-hartmann measurements.
      ]. The first attempt to use the Shack-Hartmann sensor to evaluate the human eye aberrations was by Liang et al. [
      • Liang J.
      • Williams D.R.
      • Miller D.T.
      Supernormal vision and high-resolution retinal imaging through adaptive optics.
      ], and since then this technique has become commonly utilised throughout optometry and ophthalmology. The first commercial system was the Complete Ophthalmic Analysis System (COAS) Shack-Hartmann aberrometer (AMO Wavefront Sciences, Albuquerque, NM). It was found to have good accuracy, repeatability, and dynamic range [
      • Cheng X.
      • Himebaugh N.L.
      • Kollbaum P.S.
      • Thibos L.N.
      • Bradley A.
      Test–retest reliability of clinical shack-hartmann measurements.
      ], and has been successfully applied to many contact lens measures both on-axis [
      • Kollbaum P.S.
      • Bradley A.
      • Thibos L.N.
      Comparing the optical properties of soft contact lenses on and off the eye.
      ] and off-axis [
      • Shen J.
      • Spors F.
      • Tsang D.
      • McNaughton L.E.
      • Egan D.J.
      In-vivo evaluation of peripheral refraction changes with single vision and multifocal Soft contact lenses.
      ].
      An alternative on-eye system currently available is based on the pyramidal sensor. In this technique a pyramid-shaped prism creates four images that are combined into a single image [
      • Ragazzoni R.
      Pupil plane wavefront sensing with an oscillating prism.
      ]. This system has been reported to have excellent accuracy and repeatability with the Osiris aberrometer (Costruzione Strumenti Oftalmici, Firenze, Italy) [
      • Singh N.K.
      • Jaskulski M.
      • Ramasubramanian V.
      • Meyer D.
      • Reed O.
      • Rickert M.E.
      • et al.
      Validation of a clinical aberrometer using pyramidal wavefront sensing.
      ]. This particular instrument has other advantages of measuring 45,000 sampling points, which may make it useful for measuring complex optical designs and/or off-axis optical measures [
      • Singh N.K.
      • Jaskulski M.
      • Ramasubramanian V.
      • Meyer D.
      • Reed O.
      • Rickert M.E.
      • et al.
      Validation of a clinical aberrometer using pyramidal wavefront sensing.
      ].
      A third alternative for on-eye lens measures is based on ray tracing, or the principle of isolating ray bundles to measure optical deviation. This instrument is commercially available (Tracey Technologies, Houston, TX) and the principle has also been built into wide-angle instruments to measure off-axis [
      • Mazzaferri J.
      • Navarro R.
      Wide two-dimensional field laser ray-tracing aberrometer.
      ]. These types of measures have also been found to be accurate, but of lower within-eye repeatability [
      • Xu Z.
      • Hua Y.
      • Qiu W.
      • Li G.
      • Wu Q.
      Precision and agreement of higher order aberrations measured with ray tracing and Hartmann-Shack aberrometers.
      ].
      As lens designs and the methods to manufacture them become more sophisticated, the technology also requires advancement. Specifically, off-eye techniques and standards need to continuous development, and must aim to closely align in vitro results with in vivo outcomes. Ideally, manufacturers can work to provide clinicians not only information on the power of their lenses, but the assumptions used to verify such power so as to allow the clinician the opportunity to enhance their clinical decision with regard to the optical designs.

      5. Clinical assessment of optical design efficiency

      5.1 Visual acuity

      The most repeatable and standardised method of measuring visual acuity is using logarithm of the minimal angle of resolution (logMAR) charts. The two most common types being the Bailey-Lovie [
      • Bailey I.L.
      • Bullimore M.A.
      • Raasch T.W.
      • Taylor H.R.
      Clinical grading and the effects of scaling.
      ] and the ETDRS (Early Treatment Diabetic Retinopathy Study) [
      • Ferris F.L.
      • Kassoff A.
      • Bresnick G.H.
      • Bailey I.
      New visual acuity charts for clinical research.
      ] charts. Each line on the logMAR charts contains five letters of equal size, separated by equal distance. The spacing between lines is the same as the height of the preceding line and there is a uniform line size reduction of 0.1 logMAR. Each individual letter is assigned a value of 0.02 logMAR, allowing for visual acuity to be measured and specified on a by-letter basis. This improves the repeatability of the measurement and allows more precise specification of visual acuity [
      • Raasch T.W.
      • Bailey I.L.
      • Bullimore M.A.
      Repeatability of visual acuity measurement.
      ]. Visual acuity testing can be made more rigorous by forcing the patient to guess letters even if they say they cannot read them and employing a fixed criterion for ending the test, usually when three or more letters on a line are incorrectly read [
      • Carkeet A.
      Modeling logMAR visual acuity scores: effects of termination rules and alternative forced-choice options.
      ].
      Near and intermediate visual acuity are often tested in contact lenses worn by presbyopic patients. Of course, these measures should not differ significantly from distance visual acuity in pre-presbyopes [
      • Subbaram M.V.
      • Bullimore M.A.
      Visual acuity and the accuracy of the accommodative response.
      ]. Charts based on logMAR principles are preferred, be the reduced-size Bailey-Lovie and ETDRS charts or charts containing lower case words that follow a logarithmic progression such as Bailey-Lovie word reading charts [
      • Bailey I.L.
      • Lovie J.E.
      New design principles for visual acuity letter charts.
      ] or the Minnesota Low-Vision Reading Test (MNRead) [
      • Legge G.E.
      • Ross J.A.
      • Luebker A.
      • LaMay J.M.
      Psychophysics of reading. VIII. The Minnesota low-vision reading test.
      ] (see Section 5.4). Testing of intermediate visual acuity may be conducted at 100, 80 or 66 cm and near visual acuity at 40 or 33 cm, depending on the regulatory standards and practice for a given country [
      • Zhang J.
      • Liu J.
      • Jasti S.
      • Suryakumar R.
      • Bullimore M.A.
      Visual demand and acuity reserve of Chinese versus English newspapers.
      ]. These correspond to vergence ranges from -1.00 D to -3.00 D.

      5.2 Contrast sensitivity

      Contrast sensitivity may offer a more comprehensive assessment of visual performance than visual acuity [
      • Pelli D.G.
      • Bex P.
      Measuring contrast sensitivity.
      ]. It is traditionally measured with sine wave gratings wherein the luminance varies sinusoidally. The target is defined by its contrast and spatial frequency—the former usually defined as Michelson contrast:
      (luminancemaximum – luminanceminimum)/(luminancemaximum + luminanceminimum)


      and the latter in cycles/degree (cycles/deg). The contrast sensitivity function is a plot of contrast sensitivity (1/threshold contrast) as a function of spatial frequency. The human contrast sensitivity function shows a typical band-pass filter shape peaking at around 4 cycles per degree with sensitivity dropping off either side [
      • Pelli D.G.
      • Bex P.
      Measuring contrast sensitivity.
      ].
      Letters contain multiple spatial frequencies. For small letters, the stroke width is related to the spatial frequency needed to identify the letter, but the relationship is more complex for larger letters [
      • Alexander K.R.
      • Xie W.
      • Derlacki D.J.
      Spatial-frequency characteristics of letter identification.
      ,
      • Chung S.T.L.
      • Legge G.E.
      • Tjan B.S.
      Spatial-frequency characteristics of letter identification in central and peripheral vision.
      ,
      • Majaj N.J.
      • Pelli D.G.
      • Kurshan P.
      • Palomares M.
      The role of spatial frequency channels in letter identification.
      ]. Nonetheless, the contrast sensitivity function can be assessed by using letters of fixed size and varying the contrast [
      • Arditi A.
      Improving the design of the letter contrast sensitivity test.
      ,
      • Pelli D.G.
      • Robson J.G.
      • Wilkins A.J.
      The design of a new letter chart for measuring contrast sensitivity.
      ,
      • Rabin J.
      Small letter contrast sensitivity: an alternative measure of visual resolution for aviation candidates.
      ], or vice versa [
      • Regan D.
      • Neima D.
      Low-contrast letter charts as a test of visual function.
      ]. For letters, the Weber definition of contrast is used (Δluminance/background luminance).
      The reduction in sensitivity at low spatial frequencies cannot be characterised with conventional letters and spatially filtered, or band-passed, letters are needed in order to fully characterise the contrast sensitivity function. Of course, low spatial frequencies are of little interest in the assessment of contact lenses and other optical devices.
      Measuring contrast sensitivity at multiple spatial frequencies can be time consuming, so clinical researchers proposed that the function may be adequately characterised by two features: the high frequency cut-off and the peak. The former corresponds to conventional visual acuity measure and the latter could be assessed with any broad band target, be it an edge [
      • Haymes S.A.
      • Chen J.
      Reliability and validity of the melbourne edge test and High/Low contrast visual acuity chart.
      ] or large letters [
      • Pelli D.G.
      • Robson J.G.
      • Wilkins A.J.
      The design of a new letter chart for measuring contrast sensitivity.
      ]. It was recently concluded that any contrast sensitivity function can be approximated by a normal function shifted horizontally and vertically to account for the impaired acuity and contrast sensitivity [
      • Chung S.T.L.
      • Legge G.E.
      Comparing the shape of contrast sensitivity functions for normal and low vision.
      ].
      Low contrast visual acuity charts are identical in design to high contrast logMAR charts but have lower contrast or varying degrees of “grey” letters. The Weber contrast is typically between 5 and 20 %. In normally sighted patients, low contrast visual acuity is typically 0.2 to 0.4 logMAR worse than high contrast visual acuity and thus reflects contrast sensitivity at spatial frequencies around 8 cycles/deg and higher. This makes the test ideal for assessing aberrations and multifocal corrections.
      The Vistech Contrast Sensitivity Charts require identification of the orientation of sine-wave gratings as vertical, diagonally left, or diagonally right [
      • Ginsburg A.P.
      A new contrast sensitivity vision test chart.
      ]. The chart assesses five spatial frequencies — 1.5, 3, 6, 12, and 18 cycles/deg — that have nine levels of contrast at each. The decrease in contrast levels is not uniform, but the average step size is about 0.23 log unit or a 70 % decrease between levels. The Functional Acuity Contrast Test (FACT) is a modification of the original Vistech chart but with a smaller decrease between each contrast level (0.15 logarithm of contrast sensitivity (logCS)) [
      • Montés-Micó R.
      • Charman W.N.
      Choice of spatial frequency for contrast sensitivity evaluation after corneal refractive surgery.
      ,
      • Pesudovs K.
      • Hazel C.A.
      • Doran R.M.L.
      • Elliott D.B.
      The usefulness of Vistech and FACT contrast sensitivity charts for cataract and refractive surgery outcomes research.
      ]. The manufacturers recommend a strict 3-alternative forced choice measurement paradigm with subjects forced to guess. The FACT chart is incorporated into Optec 6500 Vision Tester (Stereo Optical Company, Inc., Chicago, Illinois, USA) where its illumination can be controlled. The CSV-1000 (VectorVision, Greenville, Ohio, USA) is a grating chart with internal retroillumination [
      • Pomerance G.N.
      • Evans D.W.
      Test-retest reliability of the CSV-1000 contrast test and its relationship to glaucoma therapy.
      ]. The retroillumination may decrease the uneven lighting that often occurs with printed charts. Four spatial frequencies are tested — the same as the Vistech and FACT charts without 1.5 cycles/deg. The contrast levels decrease successively by about 0.16 logCS.
      The repeatability for contrast testing is poorer for grating-based tests than for letter-based tests [
      • Elliott D.B.
      • Bullimore M.A.
      Assessing the reliability, discriminative ability, and validity of disability glare tests.
      ,
      • Kelly S.A.
      • Pang Y.
      • Klemencic S.
      Reliability of the CSV-1000 in adults and children.
      ,
      • Kollbaum P.S.
      • Jansen M.E.
      • Kollbaum E.J.
      • Bullimore M.A.
      Validation of an iPad test of letter contrast sensitivity.
      ,
      • Thurman S.M.
      • Davey P.G.
      • McCray K.L.
      • Paronian V.
      • Seitz A.R.
      Predicting individual contrast sensitivity functions from acuity and letter contrast sensitivity measurements.
      ]. This is predictable given the larger changes in contrast and the high probability of guessing for grating charts with two or three choices [
      • Raasch T.W.
      • Bailey I.L.
      • Bullimore M.A.
      Repeatability of visual acuity measurement.
      ,
      • Pelli D.G.
      • Robson J.G.
      • Wilkins A.J.
      The design of a new letter chart for measuring contrast sensitivity.
      ]. The Pelli-Robson Contrast Sensitivity Chart (Precision Vision, Woodstock, Illinois, USA) was the first letter contrast sensitivity test and uses Sloan letters arranged in 16 groups of 3 letters [
      • Pelli D.G.
      • Robson J.G.
      • Wilkins A.J.
      The design of a new letter chart for measuring contrast sensitivity.
      ]. All letters are 5 cm high, corresponding to 6/190 and 1.0 cycles/deg at the specified 1 m test distance. Contrast decreases by 0.15 logCS each triplet and the option of 10 Sloan letters makes correct guessing unlikely. Better repeatability is achieved by giving 0.05 logCS credit for each letter correct [
      • Elliott D.B.
      • Bullimore M.A.
      • Bailey I.L.
      Improving the reliability of the Pelli-Robson contrast sensitivity test.
      ] and counting C and O when miscalled as correct [
      • Elliott D.B.
      • Whitaker D.
      • Bonette L.
      Differences in the legibility of letters at contrast threshold using the Pelli-Robson chart.
      ]. The Mars Test (Mars Perceptrix Cooperation, Chappaqua, New York, USA) is a smaller derivative of the Pelli-Robson chart [
      • Arditi A.
      Improving the design of the letter contrast sensitivity test.
      ,
      • Dougherty B.E.
      • Flom R.E.
      • Bullimore M.A.
      An evaluation of the mars letter contrast sensitivity test.
      ], designed for near testing (0.5 m). The contrast decreases by 0.04 logCS for adjacent letters. The test ends when the patient identifies two consecutive letters incorrectly. Finally, there is the Small Letter Contrast Sensitivity Test [
      • Rabin J.
      Optical defocus: differential effects on size and contrast letter recognition thresholds.
      ,
      • Rabin J.
      • Wicks J.
      Measuring resolution in the contrast domain: the small letter contrast test.
      ]. The commercial version has 5 letters per 0.25 logCS increment (0.05 logCS per letter) and is equivalent to 6/12.
      The emergence of tablets and slim LCD displays has led to new tests being available. For example, there is a validated iPad-based letter contrast sensitivity test (Ridgevue Vision, Boulder, Colorado, USA) designed for testing at 1 m [
      • Kollbaum P.S.
      • Jansen M.E.
      • Kollbaum E.J.
      • Bullimore M.A.
      Validation of an iPad test of letter contrast sensitivity.
      ]. Contrast decreases by 0.1 logCS per screen, with two letters at each contrast level, so like the Pelli-Robson Chart, each letter is worth 0.05 logCS. The M&S Technologies (Niles, Illinois, USA) Clinical Trial Suite is a computer-driven LCD system that includes a number of contrast sensitivity tests including letter contrast sensitivity, traditional gratings and rotationally symmetric gratings (bull’s eye patterns). Some of the tests have poorer repeatability [
      • Thurman S.M.
      • Davey P.G.
      • McCray K.L.
      • Paronian V.
      • Seitz A.R.
      Predicting individual contrast sensitivity functions from acuity and letter contrast sensitivity measurements.
      ] although the letter contrast sensitivity test shows good agreement with the Pelli-Robson test [
      • Chandrakumar M.
      • Colpa L.
      • Reginald Y.A.
      • Goltz H.C.
      • Wong A.M.F.
      Measuring contrast sensitivity using the M&S smart system II versus the pelli-robson chart.
      ]. Finally, the quick Contrast Sensitivity Function method uses a Bayesian adaptive procedure and an information maximisation criterion to select only informative stimuli; testing times to precisely estimate the whole contrast sensitivity function are reduced to 2−5 min (Adaptive Sensory Technology, San Diego, California, USA). By avoiding presenting stimuli that do not provide informative data, the method originally estimated the whole contrast sensitivity function in 50–100 trials using sinewave gratings of two possible orientations [
      • Lesmes L.A.
      Bayesian adaptive estimation of the contrast sensitivity function: the quick CSF method.
      ]. Several researchers subsequently implemented the use of ten Sloan letters, bandpass-filtered with a raised cosine window with peak frequency of 4 cycles per letter [
      • Hou F.
      • Lesmes L.A.
      • Kim W.
      • Gu H.
      • Pitt M.A.
      • Myung J.I.
      • et al.
      Evaluating the performance of the quick CSF method in detecting contrast sensitivity function changes.
      ,
      • Hou F.
      • Lesmes L.
      • Bex P.
      • Dorr M.
      • Lu Z.-L.
      Using 10AFC to further improve the efficiency of the quick CSF method.
      ,
      • Zheng H.
      • Wang C.
      • Cui R.
      • He X.
      • Shen M.
      • Lesmes L.A.
      • et al.
      Measuring the contrast sensitivity function using the qCSF method with 10 digits.
      ,
      • Zheng H.
      • Shen M.
      • He X.
      • Cui R.
      • Lesmes L.A.
      • Lu Z.-L.
      • et al.
      Comparing spatial contrast sensitivity functions measured with digit and grating stimuli.
      ]. As a result, the number of trials can be further reduced to 25 for rapid testing times, or 50 for “very high precision.”

      5.3 Through-focus curves

      Through-focus or depth-of-focus curves provide a more comprehensive description of the multifocal properties of a presbyopic correction than measuring visual acuity at two or three distances. In these methods, corrected visual acuity is measured at distance (e.g. using logMAR charts) and target vergence is then varied by the addition of minus lenses to simulate near viewing distances, and visual acuity re-measured [
      • Gupta N.
      • Wolffsohn J.S.W.
      • Naroo S.A.
      Optimizing measurement of subjective amplitude of accommodation with defocus curves.
      ]. Testing may be monocular or binocular, although the latter may cause vergence challenges in individuals with residual accommodation. The protocol is arduous for the patient as visual acuity is measured at multiple times, but can provide valuable information on the effectivity of the lens through a range of viewing distances. Computerised or multiple different versions of letter charts are ideal to minimise memorisation.
      The technique has been used extensively in vision science [
      • Tucker J.
      • Charman W.N.
      The depth-of-focus of the human eye for snellen letters.
      ]. In the early 1990s it was found to be particularly useful in describing the effectivity of multifocal lenses [
      • Bradley A.
      • Rahman H.A.
      • Soni P.S.
      • Zhang X.
      Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses.
      ,
      • Bullimore M.A.
      • Jacobs R.J.
      Subjective and objective assessment of Soft bifocal contact Lens performance.
      ]. Since then, multiple other studies have compared monofocal [
      • Plainis S.
      • Ntzilepis G.
      • Atchison D.A.
      • Charman W.N.
      Through-focus performance with multifocal contact lenses: effect of binocularity, pupil diameter and inherent ocular aberrations.
      ] or multifocal designs using this approach [
      • Gupta N.
      • Naroo S.A.
      • Wolffsohn J.S.
      Visual comparison of multifocal contact lens to monovision.
      ,
      • García-Lázaro S.
      • Albarrán-Diego C.
      • Ferrer-Blasco T.
      • Radhakrishnan H.
      • Montés-Micó R.
      Visual performance comparison between contact lens-based pinhole and simultaneous vision contact lenses.
      ,
      • Madrid-Costa D.
      • García-Lázaro S.
      • Albarrán-Diego C.
      • Ferrer-Blasco T.
      • Montés-Micó R.
      Visual performance of two simultaneous vision multifocal contact lenses.
      ,
      • Sivardeen A.
      • Laughton D.
      • Wolffsohn J.S.
      Randomized crossover trial of silicone hydrogel presbyopic contact lenses.
      ].
      An alternative method for generating through-focus data is by optical modelling. This can be done in several ways. First, theoretical lens design data could be generated, such as by using an adaptive optics system and measuring acuity of individuals viewing through these theoretical lens designs (e.g. [
      • Li Y.
      • Bradley A.
      • Xu R.
      • Kollbaum P.S.
      Liquid crystal spatial light modulators for simulating zonal multifocal lenses.
      ,
      • Benard Y.
      • Lopez-Gil N.
      • Legras R.
      Subjective depth of field in presence of 4th-order and 6th-order Zernike spherical aberration using adaptive optics technology.
      ,
      • Zheleznyak L.
      • Sabesan R.
      • Oh J.-S.-S.
      • MacRae S.
      • Yoon G.
      Modified monovision with spherical aberration to improve presbyopic through-focus visual performance.
      ]). Zhelezsnyak et al. demonstrated with this modelling approach that centre-distance (positive spherical aberration) designs may provide slightly enhanced near acuity, whereas centre-near (negative spherical aberration) designs may provide slightly enhanced intermediate vision [
      • Zheleznyak L.
      • Sabesan R.
      • Oh J.-S.-S.
      • MacRae S.
      • Yoon G.
      Modified monovision with spherical aberration to improve presbyopic through-focus visual performance.
      ]. Alternate modelling approaches have utilised model of theoretical eyes [
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      • Papas E.
      Inherent ocular spherical aberration and multifocal contact lens optical performance.
      ]. Although less realistic than on-eye clinical measures, without the variability caused by human factors, these approaches allow very specific input and direct comparisons of known lens designs (e.g. add design, zone geometry) or ocular parameters (e.g. pupil size, ocular aberration). These methods show some success [
      • Kollbaum P.S.
      Optical aberrations of contact lenses and eyes corrected with contact lenses.
      ,
      • Bakaraju R.C.
      • Ehrmann K.
      • Ho A.
      Extended depth of focus contact lenses vs. two commercial multifocals: part 1. Optical performance evaluation via computed through-focus retinal image quality metrics.
      ] in exploring and optimising design features, but further work is needed to understand the transference of these modelling techniques to clinical outcomes.

      5.4 Reading performance

      Since many activities of daily living rely on reading, it is not surprising that reading difficulty has been found to form a strong predictor of vision-related quality of life [
      • Mangione C.M.
      Psychometric properties of the national eye institute visual function questionnaire (NEI-VFQ).
      ]. The key parameters utilised to evaluate visual performance include reading acuity, mean, maximal or optimal reading speed and critical print size [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Radner W.
      Reading charts in ophthalmology.
      ]. Reading acuity is the smallest letter size that can be read [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Radner W.
      Reading charts in ophthalmology.
      ]. Reading speed (or rate) is defined as the number of words read per minute and can be calculated at either a supra-threshold or threshold acuity level or over varying sizes of text [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Radner W.
      Reading charts in ophthalmology.
      ]. Critical print size is often defined as the smallest print size that can be read at the maximum reading speed [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Radner W.
      Reading charts in ophthalmology.
      ]. It is important to note that these metrics are not simply measures of resolution acuity, but also measure cognitive and non-visual processes [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Gupta N.
      • Wolffsohn J.S.W.
      • Naroo S.A.
      Comparison of near visual acuity and reading metrics in presbyopia correction.
      ]. These metrics yield unique measures of visual performance and can provide important information on relative (within-subject) function with different corrections [
      • Gupta N.
      • Wolffsohn J.S.W.
      • Naroo S.A.
      Comparison of near visual acuity and reading metrics in presbyopia correction.
      ].
      There are various methods to test and calculate reading acuity, reading speed and critical print size. One widely used method is the Minnesota Reading Test (MNREAD) acuity chart (Precision Vision, Woodstock, Illinois, USA), which consists of standardised sentences displayed in a wide range of letter sizes, and decrease logarithmically down the chart [
      • Mansfield J.S.
      • Atilgan N.
      • Lewis A.M.
      • Legge G.E.
      Extending the MNREAD sentence corpus: computer-generated sentences for measuring visual performance in reading.
      ]. The words are at a 8 to 9-year-old reading level to allow testing on a wide variety of subject populations [
      • Mansfield J.S.
      • Atilgan N.
      • Lewis A.M.
      • Legge G.E.
      Extending the MNREAD sentence corpus: computer-generated sentences for measuring visual performance in reading.
      ]. Recently, computer algorithms were developed to create electronic MNREAD charts with over 9 million random sentence options [
      • Mansfield J.S.
      • Atilgan N.
      • Lewis A.M.
      • Legge G.E.
      Extending the MNREAD sentence corpus: computer-generated sentences for measuring visual performance in reading.
      ]. The RADNER reading chart (Precision Vision, Woodstock, Illinois, USA) is another method commonly used to assess visual function [
      • Radner W.
      Reading charts in ophthalmology.
      ]. This test was also recently converted to a digital application and shown to have good to better repeatability than the standard paper chart [
      • Kingsnorth A.
      • Wolffsohn J.S.
      Mobile app reading speed test.
      ]. Other reading tests include some with mixed contrast or longer passages and are intended for use in subjects with reduced vision, and some others with visual or cognitive impairment [
      • Rubin G.S.
      Measuring reading performance.
      ,
      • Radner W.
      Reading charts in ophthalmology.
      ].
      In addition to reducing issues of memorisation, computer/tablet/smart-phone based digital reading tests can aid in the assessment of more real-world outcomes since over half of waking hours are spent on digital devices [
      The Nielsen total audience report: Q3 2018.
      ]. Some applications also incorporate voice recording to check for reading errors, and can track variations in working distance, screen luminance and contrast, and can provide automated data analysis to improve usability [
      • Kingsnorth A.
      • Wolffsohn J.S.
      Mobile app reading speed test.
      ]. The digital RADNER app has been used to examine presbyopes fitted with various corrections, including multifocal and monovision contact lenses, and suggested that not only near visual acuity but also critical print size and reading speed are important visual metrics to assess visual corrections in presbyopia [
      • Gupta N.
      • Wolffsohn J.S.W.
      • Naroo S.A.
      Comparison of near visual acuity and reading metrics in presbyopia correction.
      ]. The same app has been used to demonstrate improvements in critical print size measured for subjects fitted with toric compared to spherical equivalent contact lenses (Logan et al. [
      • A-KM Logan
      • Datta A.
      • Skidmore K.
      • Tomiyama E.S.
      • Hu C.
      • Chandler M.A.
      • et al.
      Randomized clinical trial of near visual performance with digital devices using spherical and toric contact lenses.
      ]). By using a combination of modern methods to measure visual performance, clinicians and researchers can more fully evaluate visual function with various corrections.

      5.5 Peripheral refraction

      Over the last 200+ years (likely dating back to Thomas Young in 1801 [
      • Young T.
      On the mechanism of the eye.
      ]), researchers have attempted to find ways to examine the highly aberrated, difficult to measure, peripheral optics of the eye. Early attempts relied on clinical techniques, such as subjective refraction. However, due to the considerable patient judgement with reduced visual function, these measures are not ideal [
      • Wang Y.Z.
      • Thibos L.N.
      • Lopez N.
      • Salmon T.
      • Bradley A.
      Subjective refraction of the peripheral field using contrast detection acuity.
      ,
      • Lundström L.
      • Gustafsson J.
      • Svensson I.
      • Unsbo P.
      Assessment of objective and subjective eccentric refraction.
      ,
      • Mathur A.
      • Gehrmann J.
      • Atchison D.A.
      Pupil shape as viewed along the horizontal visual field.
      ]. Retinoscopy has also been attempted, but is not very repeatable and requires considerable examiner skill, especially due to the irregular off-axis pupil shape [
      • Zadnik K.
      • Mutti D.O.
      • Adams A.J.
      The repeatability of measurement of the ocular components.
      ].
      Over the last 15+ years, more advanced techniques have emerged. Several current methods of peripheral refraction are summarized below, including those that measure refractive state and those that measure the entire optical aberration profile from which refractive state can be derived, if desired. Recent reviews discuss details surrounding implementation of these techniques in clinical trials [
      • Fedtke C.
      • Ehrmann K.
      • Holden B.A.
      A review of peripheral refraction techniques.
      ,
      • Wolffsohn J.S.
      • Kollbaum P.S.
      • Berntsen D.A.
      • Atchison D.A.
      • Benavente A.
      • Bradley A.
      • et al.
      IMI – clinical myopia control trials and instrumentation report.
      ], and thus are not discussed here.
      Measurement of the peripheral optics of the eye with ‘off-the-shelf’ clinical instruments is ideal in many ways for their potential ease of use and clinical availability. In some ways, their use is necessary (e.g. clinical practice and multi-site clinical trials). However, users are often trying to make instruments capture measures and/or describe data in a way they were not designed to do. This then necessitates substantial alteration to the instrument and/or the measurement technique. The Grand-Seiko (WAM-5500) or the equivalent Shin-Nippon (NK-5001) open-view autorefractor is a well-accepted method for clinical refractive assessment, and employed in many clinical trials [
      • Fedtke C.
      • Ehrmann K.
      • Holden B.A.
      A review of peripheral refraction techniques.
      ,
      • Wolffsohn J.S.
      • Kollbaum P.S.
      • Berntsen D.A.
      • Atchison D.A.
      • Benavente A.
      • Bradley A.
      • et al.
      IMI – clinical myopia control trials and instrumentation report.
      ]. As an open-view instrument it is possible to capture off-axis measures of refractive state with relatively few alterations; namely, additional targets for the subject to peripherally fixate [
      • Atchison D.A.
      • Rosén R.
      The possible role of peripheral refraction in development of myopia.
      ,
      • Fedtke C.
      • Ehrmann K.
      • Thomas V.
      • Bakaraju R.C.
      Peripheral refraction and aberration profiles with multifocal lenses.
      ,
      • Mutti D.O.
      • Sinnott L.T.
      • Reuter K.S.
      • Walker M.K.
      • Berntsen D.A.
      • Jones-Jordan L.A.
      • et al.
      Peripheral refraction and eye lengths in Myopic Children in the bifocal lenses in nearsighted kids (BLINK) study.
      ]. These measures have largely been along the horizontal midline, up to 40 degrees peripherally, but some vertical measures have also been performed [
      • Mutti D.O.
      • Sinnott L.T.
      • Reuter K.S.
      • Walker M.K.
      • Berntsen D.A.
      • Jones-Jordan L.A.
      • et al.
      Peripheral refraction and eye lengths in Myopic Children in the bifocal lenses in nearsighted kids (BLINK) study.
      ]. Some have indicated that these instruments may report erroneous measures in lenses with rapid power changes or power discontinuities, so have advocated not measuring through a multifocal but rather measure the alternate eye not wearing a contact lens [
      • Tarrant J.
      • Severson H.
      • Wildsoet C.F.
      Accommodation in emmetropic and myopic young adults wearing bifocal soft contact lenses.
      ]. However, recent work has shown that this instrument can accurately measure through these diverse designs, including those with concentric rings, as long as care is taken to consistently measure at the same point within the pupil [
      • Altoaimi B.H.
      • Almutairi M.S.
      • Kollbaum P.S.
      • Bradley A.
      Accommodative behavior of young eyes wearing multifocal contact lenses.
      ,
      • Romashchenko D.
      • Rosén R.
      • Lundström L.
      Peripheral refraction and higher order aberrations.
      ].
      Clinical aberrometers have also been employed to measure the entire optical profile of the eye while viewing off axis [
      • Shen J.
      • Clark C.A.
      • Soni P.S.
      • Thibos L.N.
      Peripheral refraction with and without contact lens correction.
      ,
      • Philip K.
      • Sankaridurg P.R.
      • Ale J.B.
      • Naduvilath T.J.
      • Mitchell P.
      Profile of off-axis higher order aberrations and its variation with time among various refractive error groups.
      ,
      • Berntsen D.A.
      • Mutti D.O.
      • Zadnik K.
      Validation of aberrometry-based relative peripheral refraction measurements.
      ]. Custom modifications to commercial aberrometers have typically included monocular or binocular (e.g. periscope) mirror systems. Although possible, these modifications are not always ideal for typical clinical environments (e.g. size, ease of use) and can make it difficult to maintain alignment. Whereas autorefractors measure just the lower order refractive state, aberrometers also provide information about the higher order aberrations of the off-axis eye. However, care must be taken to correctly interpret the data obtained. In particular due to the off-axis elliptical pupil [
      • Mathur A.
      • Atchison D.A.
      Peripheral refraction patterns out to large field angles.
      ] and/or through zonal lenses [
      • Wolffsohn J.S.
      • Kollbaum P.S.
      • Berntsen D.A.
      • Atchison D.A.
      • Benavente A.
      • Bradley A.
      • et al.
      IMI – clinical myopia control trials and instrumentation report.
      ], where typical Zernike fitting approaches are problematic.
      Taking repeated measures, which may be necessary in order to best represent the true optics, can become time consuming, cause fatigue of the subject, and lead to erroneous measurements. Measurement off the horizontal axis can be especially challenging for patients to maintain fixation. Therefore, there is a growing desire for instruments that can facilitate swift off-axis measurements requiring no change in fixation, and/or instrument realignments. Such efforts have included the development of prototype equipment such as eccentric scanning photo-retinoscopes [
      • Tabernero J.
      • Schaeffel F.
      A new fast scanning infrared photoretinoscope to measure peripheral refraction as a function of accommodation.
      ] or scanning Shack-Hartmann aberrometers [
      • Wei X.
      • Thibos L.
      Design and validation of a scanning Shack Hartmann aberrometer for measurements of the eye over a wide field of view.
      ].

      5.6 Toric displacement realignment

      Toric lens rotation is defined as the angle between a vertical axis and the lens marking, while stability incorporates variation in the degree of lens rotation. Fluctuating vision with toric lenses is primarily due to unstable rotation. Rotation and stability can be affected by patient factors such as blinking and eye movements, head position, magnitude of spherical and cylindrical refractive error, corneal shape or size, palpebral aperture size or variations in eyelid position or tonicity [
      • Zikos G.A.
      • Kang S.S.
      • Ciuffreda K.J.
      • Selenow A.
      • Ali S.
      • Spencer L.W.
      • et al.
      Rotational stability of toric soft contact lenses during natural viewing conditions.
      ,
      • McIlraith R.
      • Young G.
      • Hunt C.
      Toric lens orientation and visual acuity in non-standard conditions.
      ,
      • Momeni-Moghaddam H.
      • Naroo S.A.
      • Askarizadeh F.
      • Tahmasebi F.
      Comparison of fitting stability of the different soft toric contact lenses.
      ,
      • Chamberlain P.
      • Morgan P.B.
      • Moody K.J.
      • Maldonado-Codina C.
      Fluctuation in visual acuity during Soft toric contact lens wear.
      ]. Rotation and stability are also known to vary by lens material and stabilisation design [
      • Zikos G.A.
      • Kang S.S.
      • Ciuffreda K.J.
      • Selenow A.
      • Ali S.
      • Spencer L.W.
      • et al.
      Rotational stability of toric soft contact lenses during natural viewing conditions.
      ,
      • McIlraith R.
      • Young G.
      • Hunt C.
      Toric lens orientation and visual acuity in non-standard conditions.
      ,
      • Momeni-Moghaddam H.
      • Naroo S.A.
      • Askarizadeh F.
      • Tahmasebi F.
      Comparison of fitting stability of the different soft toric contact lenses.
      ,
      • Chamberlain P.
      • Morgan P.B.
      • Moody K.J.
      • Maldonado-Codina C.
      Fluctuation in visual acuity during Soft toric contact lens wear.
      ,
      • Tan J.
      • Papas E.
      • Carnt N.
      • Jalbert I.
      • Skotnitsky C.
      • Shiobara M.
      • et al.
      Performance standards for toric Soft contact lenses.
      ].
      Subjective estimation of on-eye contact lens rotation can vary by examiner, especially with larger amounts of rotation [
      • Snyder C.
      • Daum K.M.
      Rotational position of toric soft contact lenses on the eye - clinical judgements.
      ]. Thus, lens rotation is ideally assessed using a slit-lamp beam and integrated protractor gauge. Rotation is often simply estimated as the number of degrees of misalignment. However, some groups have also manually rotated the lens and recorded the time required to return to its starting position with normal blinking [
      • Momeni-Moghaddam H.
      • Naroo S.A.
      • Askarizadeh F.
      • Tahmasebi F.
      Comparison of fitting stability of the different soft toric contact lenses.
      ], or the number of degrees recovered after a specified number of blinks [
      • Tan J.
      • Papas E.
      • Carnt N.
      • Jalbert I.
      • Skotnitsky C.
      • Shiobara M.
      • et al.
      Performance standards for toric Soft contact lenses.
      ]. A combination of an expanded near logMAR chart with peripheral letter targets in the eight cardinal positions of gaze to test the effects of eye movements of 25–40 degrees has been used [
      • Chamberlain P.
      • Morgan P.B.
      • Moody K.J.
      • Maldonado-Codina C.
      Fluctuation in visual acuity during Soft toric contact lens wear.
      ]. Even though lens rotation was still assessed with standard slit-lamp techniques, the technique demonstrated significant reductions in acuity following diagonal eye movements [
      • Chamberlain P.
      • Morgan P.B.
      • Moody K.J.
      • Maldonado-Codina C.
      Fluctuation in visual acuity during Soft toric contact lens wear.
      ]. Other groups have photographed lenses or developed video systems to monitor lens stability real-time during reading tasks or with changes in head or eye positions [
      • Zikos G.A.
      • Kang S.S.
      • Ciuffreda K.J.
      • Selenow A.
      • Ali S.
      • Spencer L.W.
      • et al.
      Rotational stability of toric soft contact lenses during natural viewing conditions.
      ,
      • McIlraith R.
      • Young G.
      • Hunt C.
      Toric lens orientation and visual acuity in non-standard conditions.
      ].
      The astigmatism induced by a rotating toric lens can be calculated using a number of vector-based methods, the most intuitive being that of Thibos et al. [
      • Thibos L.N.
      • Wheeler W.
      • Horner D.
      Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error.
      ]. These are incorporated into online calculators or applications, some of which are freely available from manufacturers. The axis of the induced astigmatism will be ±45 degrees from the midpoint of the prescription axis and the axis of the rotated lens. The magnitude of the induced astigmatism is roughly 10 % of the prescription cylinder (and that of the lens) for each 3 degrees of rotation. For 30 degrees of rotation the over-refraction will have the same cylinder power as that of the lens, but a new axis.
      The following performance standards have been proposed in evaluating soft toric contact lenses: a lens with excellent performance should have comfort ≥ 90 (1–100 scale where 100 is excellent), lens rotation of ≤ 6°, and a rotational recovery when lenses are physically misaligned by 30° of > 10° per 10 blinks [
      • Tan J.
      • Papas E.
      • Carnt N.
      • Jalbert I.
      • Skotnitsky C.
      • Shiobara M.
      • et al.
      Performance standards for toric Soft contact lenses.
      ]. Sulley et al. proposed alternate standards to assess fit:
      • i
        Orientation: Stable orientation after settling (i.e. orientation stability ≤ 20°)
      • ii
        Fit: Complete corneal coverage, acceptable lens movement, no substantial decentration or edge lift
      • iii
        Visual acuity (VA): Binocular Snellen VA within one line of spectacle VA
      • iv
        Subjective vision: ‘Good’, ‘very good’ or ‘excellent’ overall quality of vision
      • v
        Comfort: ‘Good’, ‘very good’ or ‘excellent’ overall comfort [
        • Sulley A.
        • Young G.
        • Lorenz K.O.
        • Hunt C.
        Clinical evaluation of fitting toric soft contact lenses to current non-users.
        ].
      Of note, the sphere to cylinder ratio also plays an important role in tolerance to axis mislocation.

      5.7 Patient reported outcomes for quality of vision

      Patient reported outcomes allow direct measures of user’s preferences and feelings about various treatments, including contact lenses. The selection of the appropriate patient reported outcomes tool is critical to understanding wearers perception of various contact lens designs. While patient reported outcome tools have been developed to address a number of areas related to refractive correction (e.g. symptoms, activity limitations), the focus of this review will be quality of vision with contact lenses. Quality of vision is an especially important attribute as there are several instances of where objective measures are not predictive of patient satisfaction (e.g. multifocal contact lenses which create multiple images). Although simple numeric or analogue rating scales have been found to detect some subtle changes in optical design [
      • Kollbaum P.S.
      • Jansen M.E.
      • Rickert M.E.
      Comparison of patient-reported visual outcome methods to quantify the perceptual effects of defocus.
      ], several multi-item patient reported outcome tools have been created. These tools include: National Eye Institute’s Refractive Quality of Life (NEI-RQL) [
      • Berry S.
      • Mangione C.M.
      • Lindblad A.S.
      • McDonnell P.J.
      Development of the National Eye Institute refractive error correction quality of life questionnaire.
      ,
      • Hays R.D.
      • Mangione C.M.
      • Ellwein L.
      • Lindblad A.S.
      • Spritzer K.L.
      • McDonnell P.J.
      Psychometric properties of the national eye institute–refractive error quality of life instrument.
      ] and Visual Function Questionnaire (NEI-VFQ) [
      • Mangione C.M.
      Development of the 25-list-item national eye institute visual function questionnaire.
      ], Refractive Status and Vision Profile (RSVP) [
      • Vitale S.
      The refractive status and vision profile A questionnaire to measure vision-related quality of life in persons with refractive error.
      ], Quality of Vision (QOV) [
      • McAlinden C.
      • Pesudovs K.
      • Moore J.E.
      The development of an instrument to measure quality of vision: the Quality of Vision (QoV) questionnaire.
      ], Contact Lens Impact on Quality of Life (CLIQ) [
      • Pesudovs K.
      • Garamendi E.
      • Elliott D.B.
      The contact lens impact on quality of life (CLIQ) questionnaire: development and validation.
      ], Pediatric Refractive Error Profile (PREP) [
      • Walline J.J.
      • Jones L.A.
      • Chitkara M.
      • Coffey B.
      • Jackson J.M.
      • Manny R.E.
      • et al.
      The adolescent and child health initiative to encourage vision empowerment (ACHIEVE) study design and baseline data.
      ], Near Activity Visual Questionnaire (NAVQ) [
      • Buckhurst P.J.
      • Wolffsohn J.S.
      • Gupta N.
      • Naroo S.A.
      • Davies L.N.
      • Shah S.
      Development of a questionnaire to assess the relative subjective benefits of presbyopia correction.
      ] and the Contact Lens User Experience (CLUE) [
      • Wirth R.J.
      • Edwards M.C.
      • Henderson M.
      • Henderson T.
      • Olivares G.
      • Houts C.R.
      Development of the contact lens user experience.
      ]. A systematic review suggested that, of these, the tools with the best psychometric properties that could be used in studies with contact lens wearers are the CLIQ, QOV and NAVQ survey tools [
      • Kandel H.
      • Khadka J.
      • Goggin M.
      • Pesudovs K.
      Patient-reported outcomes for assessment of quality of life in refractive error.
      ].
      The CLIQ tool has 20 questions, only four of which are vision-related and query issues with glare, dim lighting, fluctuating vision and focusing [
      • Pesudovs K.
      • Garamendi E.
      • Elliott D.B.
      The contact lens impact on quality of life (CLIQ) questionnaire: development and validation.
      ]. It is intended for use in pre-presbyopic adults. The QOV assesses 10 vision-related concerns and was written at a 12-year-old comprehension level, but has only been tested in adults [
      • McAlinden C.
      • Pesudovs K.
      • Moore J.E.
      The development of an instrument to measure quality of vision: the Quality of Vision (QoV) questionnaire.
      ]. Not only does the Rasch-tested QOV questionnaire show good validity and repeatability, the scores were well correlated with objective assessments of vision (acuity, aberrations, contrast sensitivity) when tested in adults [
      • McAlinden C.
      • Pesudovs K.
      • Moore J.E.
      The development of an instrument to measure quality of vision: the Quality of Vision (QoV) questionnaire.
      ]. The NAVQ was also developed using Rasch analysis and has 10 items assessing near vision for presbyopic patients [
      • Buckhurst P.J.
      • Wolffsohn J.S.
      • Gupta N.
      • Naroo S.A.
      • Davies L.N.
      • Shah S.
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      ]. NAVQ scores were moderately correlated with near acuity and critical print size [
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      ]. While the psychometric properties of the PREP survey have not been fully tested, it remains the only survey designed for use in children as young as 8 years of age and includes questions related to near, far and overall vision quality [
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      ,