the resolving power of intraocular lens implants M. J. Dunn, M.Sc., M.A.A. Santa Barbara, California The subject of optical quality control for intraocular lens implants (IOLs) has received steady attention over the past two years. 1 - 4 In particular, the resolving power of IOLs (expressed as line-pairs per millimeter of image resolution) has been advanced as a principal figure-of-merit for optical quality. However, the vitrue of this approach has been undercut by the lack of a standard basis of evaluation and comparison. Furthermore, the ophthalmic community has not yet determined the requirements of IOL resolution that are needed for successful aphakic correction. This paper therefore undertakes to review the optics of visual resolution as they apply to IOLs and to human sight, so as to develop a foundation for the evaluation of IOL optical quality.
manufacturers' section
THE MEANING OF RESOLUTION The problem of optical resolution was first investigated by astronomers interested in obtaining high-detail photographs of the heavens. A distant star is a good approximation for a point of light situated at an infinite distance, and telescopes were thus designed to be "emmetropic", or capable of forming images of such points. Unfortunately, they discovered that a star is not imaged by the telescope as a point of light. It is imaged as an "Airy disc", a circular blur surrounded by faint rings. It turns out that this phenomenon is the result of the wave-like nature of light; light waves can only be focused to spots having a diameter of no more than a few wave-lengths. Hence, the astronomers were not looking at the image of the disc of a star - they were looking at the disc of the image of a star, a subtle distinction (the star's image would have been pointlike, otherwise). This meant that problems were experienced whenever the images of two stars were very close to one another, because the discs of the images would overlap. In cases where the overlap was considerable, it was impossible to decide whether there was only one image or whether there were two overlapping images. The separation at which it was considered possible to resolve two points from each other was called the limit of resolution, and it defined the detail with
Address correspondence to: M.]. Dunn, McGhan Medical Corp.l3M Co. P.O. Box 6447, 700 Ward Dr., Santa Barbara, CA 93111 AM INTRA-oCULAR IMPLANT SOC J - VOL. IV, JULY 1978 126
which stars might be photographed or observed. Since those times, the concept of resolution has found wider application. In particular, we are concerned with the ability of the dioptrics of the eye to resolve "points" of light on the retina. This is called visual acuity and is sometimes measured in angular resolution, much like telescopes (20/20 vision corresponds to approximately 1 minute of angular resolutionS ,6). More commonly, we describe the resolving power of an optical system in terms of the maximum number of line-pairs per millimeter (Qp/mm) that can be resolved in the image plane of the system. This generally involves the use of an imaging target, similar to that shown in Figure 1, having alternating bars or stripes of darkness and brightness. The reciprocal of
expressed as the maximum image spatial frequency
(Qp/mm) that can be discerned.
For any optical system, a theoretical limit of resolution can be calculated, given that the optical system is free of physical flaws and the image is degraded only by diffraction effects arising from the wave-like nature of light. This theoretical limit is symbolized by Po, and is given as:
T
. u, Po = ( 2n) SIn
Equation 1
where Po is in Qp/mm, n is the refractive index of the medium in which the image is situated, A is the vacuum wavelength of the illuminating light, and u is the semi-vertex angle of the light converging to form the image. 7 If we apply this to an isolated intraocular lens, the geometry illustrated in Figure 2 gives us tan u
= d/2f,
Equation 2
where d is the aperture diameter of the system, and f is the effective focal length. (This is assuming that we are imaging an infinitely-distant object.) We know that the focal length of an intraocular lens in air is given by the formula 8 :
---r-----___1_____ _ d
]:JlsrA)./cc Figure 1. (Dunn, MJ) The Alternating-Bar Target and its Brightness Distribution
the distance spanning one dark and one bright bar is the equivalent spatial frequency in Qp/mm. When such a target is imaged by a camera or a telescope (or a pseudophakic eye), the appearance of the resultant image is made indistinct by reason of the light-wave diffraction effects. The sharp boundary lines are blurred, just as points are similarly blurred into Airy discs. As the target spatial frequency is increased (the lines becoming finer and finer), a point is reached at which the image is all blurred together. It is then impossible to distinguish one bright line from another, because everywhere the image has become uniformly grey. This is the limit of resolution and is
--U: --- - ... __.- . . . t
,- ------ -(--....,·1
Figure 2. (Dunn, MJ) Relation of Aperture, Focal Length and Semi-Vertex Convergence Angle
where fl is the focal length of IOL (in air), nl is the refractive index of air (nl = 1.0003), n2 is the refractive index of polymethylmethacrylate (n2 = 1.493 @ 555 nm), n3 is the refractive index of aqueous and vitreous humor (n3 = 1.336), and D is the implanted dioptric power of IOL. From Equations 1, 2, and 3 we can therefore calculate the variation of the limit of resolution as a function of IOL dioptric power. Typical values are
AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 127
shown in Table I for an aperture of 3 mm diameter and for light of 555 nm wavelength (corresponding to photopic peak sensitivity). We find, for example, that a 19.5 D lens will have a theoretical resolution of 329.4 Qp/mm. But this will only be true for an IOL surrounded by air. If we calculate the limit of resolution for a lens immersed in the ocular medium, we must use an "immersed" focal length (f3) given by: Equation 4 and we must use the ocular medium refractive index in Equation 1 instead of that for air. These results are also shown in Table I, and we find that under these conditions, a 19.5 D lens has a limit of only 105.4 Qp/mm. It is therefore necessary to specify the details of the test conditions before one can speak meaningfully about the resolution limit of an optical system. Table 1. Limit of Resolution (All calculations assume an IOL refractive index of 1.493, an aperture diameter of 3 mm, and an illumination wavelength of 555 nm.) Dioptric Power of IOL
14 14.5 15 15.5 16 16.5
Theoretical Resolution Limit In Air In Ocular Medium
'237.0 Qp/mm
75.7 Qp/mm
17.5 18 18.5 19
245.4 253.8 262.2 270.6 279.1 287.5 295.9 304.3 312.6 321.0
19.5
329.4
105.4
20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25
337.8 346.1 354.5 362.9 371.2 379.6 387.9 396.2 404.5 412.9 421 .2
108.1 110.8 113.5 116.2 118.9 121.6 124.3 127.0 129.7 132.4 135.1
17
All calculations performed for: an IOL refractive index of an aperture diameter of an illumination wavelength of
78.4 81.1 83.8 86.5 89.2 91.9 94.6 97.3 100.0 102.7
1.493
3.0mm 555 nm
MEASUREMENT OF RESOLUTION It is one thing to calculate a theoretical limit; it is quite another to live up to it. While it is never
possible for any lens to exceed the diffraction-limited theoretical resolution, a substantial percentage of this limit can be achieved by proper design and production methods. A method for measuring the actual resolution limit (call it VL) is shown in Figure 3. r-41l6~1'
I'ATT£RiJ
rtl'-'01')
./"'.
-, 'f
CD''''''ATI)/II,
------- --------------rr~
l'1A6£
"'... TrD\t.J
.........-~ 0----------__ h ~ ---._-------- -------------- -------~
(y., '''-I' )
Figure 3. (Dunn, MJ) Schematic of Standard Resolution Test
A target pattern having a spatial frequency Vtarget is projected by a collimating lens of focal length F, making it appear to be at an infinite distance. The IOL under test, of focal length f, forms an image of the target having a spatial frequency Vim age' These quantities are related as follows 7 : Equation 5 The image formed by the IOL is examined with a high-power (200x) microscope. By observing targets of successively higher spatial frequencies (Vtarget), eventually a target frequency is reached that is just barely resolved by the intraocular lens. Once this is found, Vim age is calculated from Equation 5 and taken as the actual resolution limit VL (in Qp/mm). Considerable discretion is needed for such a measurement because the steps between consecutive target pattern frequencies of the most commonly used target (the USAF 1951 test target)9 increase by 12% from one element to the next. This means that measurements made by this method are not likely to be much more accurate than ±12%. (For a 19.5 D lens in air, thIS would mean as much as ±40 Qp/mm.) Because the theoretical resolution limit varies so widely with lens power and aperture, it is very misleading to attempt to evaluate IOL resolution on the basis of VL alone (in Qp/mm). A more consistent method of evaluation is to compare resolution efficiencies, computed as a percentage of the theoretical resolution that is actually obtained by the lens under test. The resolution efficiency is figured as: resolution efficiency (%) == 100 X
(~/Vo)
Equation 6
A very good lens may have a resolution efficiency between 70-90%. (Even using this method of evaluation, it is still necessary to standardize or specify such variables as aperture diameter and illuminating wavelength.)
AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 128
IOt.
VISUAL CORRECTION At this juncture, it is important to consider the resolving properties of the human eye. We have already been exposed to the statement that 20/20 acuity corresponds to an angular resolution of about 1 minute of arc. What does this mean in terms of line-pairs per millimeter? If one were to behold a target object situated at the point of closest focus (about 100 mm from the eye), 1 minute of angular resolution would correspond to a target pattern frequency of nearly 17 Qplmm. (This compares with the figure of 12 Qplmm cited by Blaker. 2) As anyone can discover for himself, this is a difficult thing to achieve. On the other hand, if we consider the structure of an image formed at the retina, 1 minute of angular resolution corresponds to about 220 Qplmm.lO This poses an interesting question: if an IOL immersed in the ocular medium can give only half this value (Table I), how can a surgeon hope to correct a patient to 20/20 acuity? Yet we know this has been done. The paradox is explained by recalling that the pseudophakos must function as an adjunct to the cornea. The cornea contributes on the order of 50 diopters of refractive power, to which the IOL contributes a little less than 20 diopters. Hence, the cornea is responsible for about 2/3 of the total power of the emmetropic eye. What are some reasonable boundaries on the resolution capability of the normal eye? Research indicates that the maximum retinal sensitivity is equivalent to the diffraction-limited performance of the eye,11,12 which corresponds to an angular resolution of 0.80-0.75 minute of arc (or 260-300 Qplmm). This compares well with the theoretical resolution that we can calculate for the normal eye (pupil aperture = 3 mm; posterior chamber depth = 21 mm) to be about 340 Qplmm. The cornea is known to be aspheric 6 and consequently introduces various optical aberrations into the dioptrics of the eye. 13 These aberrations bring the resolution efficiency of the normal eye to something between 85-65%. The implications for IOL optical quality are not easy to determine. It is not known, for instance, whether and to what extent the human crystalline:; lens compensates for corneal aberrations. An intraocular lens may function slightly differently from the crystalline lens in this respect, simply because there are structural differences between the pseudophakos and the natural lens. Furthermore, the resolution measurement of an IOL in an atmospheric environment is more likely to be degraded by spherical aberration than is the f hI' measurement 0 t e same ens III an aqueous environment (due to the different refractive indices of the surrounding media). Thus, an IOL that might be
acceptable for use in the ocular environment may demonstrate poorer performance when tested in the air. (For various practical and sterile considerations, optical testing of IOLs in an aqueous solution is not feasible for production purposes.) Given these considerations, we arrive at the following reasoning: whatever the performance of an IOL may be, the more closely it conforms to diffraction-limited performance when measured in air, the more closely it may be expected to conform to theoretical performance when in another medium. Therefore, if we implant an IOL that achieves near-theoretical performance, we can expect that it will not compromise the dioptrics of the eye - and that corneal aberrations will remain the limiting consideration for visual acuity. In practical terms, this implies the desirability of IOLs achieving upwards of 75% resolution efficiency. (There is no basis, however, for splitting hairs over differences of 10-15% between one lens and the next.) Currently, most intraocular lens manufacturers offer lenses that generally exceed 50% resolution efficiency, and there is good reason to think that this level of resolving ability is adequate for ophthalmic purposes; many patients have achieved 20/20 correction with such lenses. A resolving efficiency lower than 50% becomes problematical and should be cautiously regarded. REFERENCES
1. Galin MA: Optical and mechanical considerations of intraocular lenses. Am Intra·Ocular Implant Soc ] 2:22-23,1976 2. Blaker JW: Quality control of intraocular lens optics. Am Intra-Ocular Implant Soc] 3:128-129, 1977 3. Richard DA: An outline for the testing and subsequent analysis of the resolving power of intraocular lenses. Am Intra-Ocular Implant Soc] 3 :229-231,1977 4. McReynolds WU, Snider NL: The quick, simple measurement of intraocular lens power and lens resolution at surgery. Am Intra-Ocular Implant Soc] 4:15-17,1978 5. Visual optics and Refraction, DD Michaels, C.V. Mosby Co., St. Louis (1975), pp. 165-185. 6. Adler's Physiology of the Eye, 6th ed., RA Moses (ed.), C.V. Mosby Co., St. Louis (1975), pp. 500-528,38. 7. Modern Optical Engineering, WJ Smith, McGraw-Hill Book Co., New York (1966), pp. 319,433 & 320-321. 8. Dunn MJ: Factors influencing the specification of intraocular lens dioptric power. Am Intra-Ocular Implant Soc] 3:130-133,1977 9. Military Standard ISO-A, paragraph 5.1.1.7. 10. Modern Ophthalmology, Vol. 1 (Basic Aspects), 2nd ed., A Sorsby (ed.), J .B. Lippincott Co., Philadelphia (1972), pp.310-313. 11. Snyder AW, Miller WH: Photoreceptor diameter and spacing for highest resolving power. ] Opt Soc Am 67:696-698,1977 12. Frisen L, Glansholm A: Optical and neural resolution in peripheral vision. Invest OphthaI14:528-536, 1975 13. Giles MK: Aberration tolerances for visual optical systerns.] Opt Soc Am 67-634-643, 1977 AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 129
manufacturers' section
THE MEANING OF RESOLUTION The problem of optical resolution was first investigated by astronomers interested in obtaining high-detail photographs of the heavens. A distant star is a good approximation for a point of light situated at an infinite distance, and telescopes were thus designed to be "emmetropic", or capable of forming images of such points. Unfortunately, they discovered that a star is not imaged by the telescope as a point of light. It is imaged as an "Airy disc", a circular blur surrounded by faint rings. It turns out that this phenomenon is the result of the wave-like nature of light; light waves can only be focused to spots having a diameter of no more than a few wave-lengths. Hence, the astronomers were not looking at the image of the disc of a star - they were looking at the disc of the image of a star, a subtle distinction (the star's image would have been pointlike, otherwise). This meant that problems were experienced whenever the images of two stars were very close to one another, because the discs of the images would overlap. In cases where the overlap was considerable, it was impossible to decide whether there was only one image or whether there were two overlapping images. The separation at which it was considered possible to resolve two points from each other was called the limit of resolution, and it defined the detail with
Address correspondence to: M.]. Dunn, McGhan Medical Corp.l3M Co. P.O. Box 6447, 700 Ward Dr., Santa Barbara, CA 93111 AM INTRA-oCULAR IMPLANT SOC J - VOL. IV, JULY 1978 126
which stars might be photographed or observed. Since those times, the concept of resolution has found wider application. In particular, we are concerned with the ability of the dioptrics of the eye to resolve "points" of light on the retina. This is called visual acuity and is sometimes measured in angular resolution, much like telescopes (20/20 vision corresponds to approximately 1 minute of angular resolutionS ,6). More commonly, we describe the resolving power of an optical system in terms of the maximum number of line-pairs per millimeter (Qp/mm) that can be resolved in the image plane of the system. This generally involves the use of an imaging target, similar to that shown in Figure 1, having alternating bars or stripes of darkness and brightness. The reciprocal of
expressed as the maximum image spatial frequency
(Qp/mm) that can be discerned.
For any optical system, a theoretical limit of resolution can be calculated, given that the optical system is free of physical flaws and the image is degraded only by diffraction effects arising from the wave-like nature of light. This theoretical limit is symbolized by Po, and is given as:
T
. u, Po = ( 2n) SIn
Equation 1
where Po is in Qp/mm, n is the refractive index of the medium in which the image is situated, A is the vacuum wavelength of the illuminating light, and u is the semi-vertex angle of the light converging to form the image. 7 If we apply this to an isolated intraocular lens, the geometry illustrated in Figure 2 gives us tan u
= d/2f,
Equation 2
where d is the aperture diameter of the system, and f is the effective focal length. (This is assuming that we are imaging an infinitely-distant object.) We know that the focal length of an intraocular lens in air is given by the formula 8 :
---r-----___1_____ _ d
]:JlsrA)./cc Figure 1. (Dunn, MJ) The Alternating-Bar Target and its Brightness Distribution
the distance spanning one dark and one bright bar is the equivalent spatial frequency in Qp/mm. When such a target is imaged by a camera or a telescope (or a pseudophakic eye), the appearance of the resultant image is made indistinct by reason of the light-wave diffraction effects. The sharp boundary lines are blurred, just as points are similarly blurred into Airy discs. As the target spatial frequency is increased (the lines becoming finer and finer), a point is reached at which the image is all blurred together. It is then impossible to distinguish one bright line from another, because everywhere the image has become uniformly grey. This is the limit of resolution and is
--U: --- - ... __.- . . . t
,- ------ -(--....,·1
Figure 2. (Dunn, MJ) Relation of Aperture, Focal Length and Semi-Vertex Convergence Angle
where fl is the focal length of IOL (in air), nl is the refractive index of air (nl = 1.0003), n2 is the refractive index of polymethylmethacrylate (n2 = 1.493 @ 555 nm), n3 is the refractive index of aqueous and vitreous humor (n3 = 1.336), and D is the implanted dioptric power of IOL. From Equations 1, 2, and 3 we can therefore calculate the variation of the limit of resolution as a function of IOL dioptric power. Typical values are
AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 127
shown in Table I for an aperture of 3 mm diameter and for light of 555 nm wavelength (corresponding to photopic peak sensitivity). We find, for example, that a 19.5 D lens will have a theoretical resolution of 329.4 Qp/mm. But this will only be true for an IOL surrounded by air. If we calculate the limit of resolution for a lens immersed in the ocular medium, we must use an "immersed" focal length (f3) given by: Equation 4 and we must use the ocular medium refractive index in Equation 1 instead of that for air. These results are also shown in Table I, and we find that under these conditions, a 19.5 D lens has a limit of only 105.4 Qp/mm. It is therefore necessary to specify the details of the test conditions before one can speak meaningfully about the resolution limit of an optical system. Table 1. Limit of Resolution (All calculations assume an IOL refractive index of 1.493, an aperture diameter of 3 mm, and an illumination wavelength of 555 nm.) Dioptric Power of IOL
14 14.5 15 15.5 16 16.5
Theoretical Resolution Limit In Air In Ocular Medium
'237.0 Qp/mm
75.7 Qp/mm
17.5 18 18.5 19
245.4 253.8 262.2 270.6 279.1 287.5 295.9 304.3 312.6 321.0
19.5
329.4
105.4
20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25
337.8 346.1 354.5 362.9 371.2 379.6 387.9 396.2 404.5 412.9 421 .2
108.1 110.8 113.5 116.2 118.9 121.6 124.3 127.0 129.7 132.4 135.1
17
All calculations performed for: an IOL refractive index of an aperture diameter of an illumination wavelength of
78.4 81.1 83.8 86.5 89.2 91.9 94.6 97.3 100.0 102.7
1.493
3.0mm 555 nm
MEASUREMENT OF RESOLUTION It is one thing to calculate a theoretical limit; it is quite another to live up to it. While it is never
possible for any lens to exceed the diffraction-limited theoretical resolution, a substantial percentage of this limit can be achieved by proper design and production methods. A method for measuring the actual resolution limit (call it VL) is shown in Figure 3. r-41l6~1'
I'ATT£RiJ
rtl'-'01')
./"'.
-, 'f
CD''''''ATI)/II,
------- --------------rr~
l'1A6£
"'... TrD\t.J
.........-~ 0----------__ h ~ ---._-------- -------------- -------~
(y., '''-I' )
Figure 3. (Dunn, MJ) Schematic of Standard Resolution Test
A target pattern having a spatial frequency Vtarget is projected by a collimating lens of focal length F, making it appear to be at an infinite distance. The IOL under test, of focal length f, forms an image of the target having a spatial frequency Vim age' These quantities are related as follows 7 : Equation 5 The image formed by the IOL is examined with a high-power (200x) microscope. By observing targets of successively higher spatial frequencies (Vtarget), eventually a target frequency is reached that is just barely resolved by the intraocular lens. Once this is found, Vim age is calculated from Equation 5 and taken as the actual resolution limit VL (in Qp/mm). Considerable discretion is needed for such a measurement because the steps between consecutive target pattern frequencies of the most commonly used target (the USAF 1951 test target)9 increase by 12% from one element to the next. This means that measurements made by this method are not likely to be much more accurate than ±12%. (For a 19.5 D lens in air, thIS would mean as much as ±40 Qp/mm.) Because the theoretical resolution limit varies so widely with lens power and aperture, it is very misleading to attempt to evaluate IOL resolution on the basis of VL alone (in Qp/mm). A more consistent method of evaluation is to compare resolution efficiencies, computed as a percentage of the theoretical resolution that is actually obtained by the lens under test. The resolution efficiency is figured as: resolution efficiency (%) == 100 X
(~/Vo)
Equation 6
A very good lens may have a resolution efficiency between 70-90%. (Even using this method of evaluation, it is still necessary to standardize or specify such variables as aperture diameter and illuminating wavelength.)
AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 128
IOt.
VISUAL CORRECTION At this juncture, it is important to consider the resolving properties of the human eye. We have already been exposed to the statement that 20/20 acuity corresponds to an angular resolution of about 1 minute of arc. What does this mean in terms of line-pairs per millimeter? If one were to behold a target object situated at the point of closest focus (about 100 mm from the eye), 1 minute of angular resolution would correspond to a target pattern frequency of nearly 17 Qplmm. (This compares with the figure of 12 Qplmm cited by Blaker. 2) As anyone can discover for himself, this is a difficult thing to achieve. On the other hand, if we consider the structure of an image formed at the retina, 1 minute of angular resolution corresponds to about 220 Qplmm.lO This poses an interesting question: if an IOL immersed in the ocular medium can give only half this value (Table I), how can a surgeon hope to correct a patient to 20/20 acuity? Yet we know this has been done. The paradox is explained by recalling that the pseudophakos must function as an adjunct to the cornea. The cornea contributes on the order of 50 diopters of refractive power, to which the IOL contributes a little less than 20 diopters. Hence, the cornea is responsible for about 2/3 of the total power of the emmetropic eye. What are some reasonable boundaries on the resolution capability of the normal eye? Research indicates that the maximum retinal sensitivity is equivalent to the diffraction-limited performance of the eye,11,12 which corresponds to an angular resolution of 0.80-0.75 minute of arc (or 260-300 Qplmm). This compares well with the theoretical resolution that we can calculate for the normal eye (pupil aperture = 3 mm; posterior chamber depth = 21 mm) to be about 340 Qplmm. The cornea is known to be aspheric 6 and consequently introduces various optical aberrations into the dioptrics of the eye. 13 These aberrations bring the resolution efficiency of the normal eye to something between 85-65%. The implications for IOL optical quality are not easy to determine. It is not known, for instance, whether and to what extent the human crystalline:; lens compensates for corneal aberrations. An intraocular lens may function slightly differently from the crystalline lens in this respect, simply because there are structural differences between the pseudophakos and the natural lens. Furthermore, the resolution measurement of an IOL in an atmospheric environment is more likely to be degraded by spherical aberration than is the f hI' measurement 0 t e same ens III an aqueous environment (due to the different refractive indices of the surrounding media). Thus, an IOL that might be
acceptable for use in the ocular environment may demonstrate poorer performance when tested in the air. (For various practical and sterile considerations, optical testing of IOLs in an aqueous solution is not feasible for production purposes.) Given these considerations, we arrive at the following reasoning: whatever the performance of an IOL may be, the more closely it conforms to diffraction-limited performance when measured in air, the more closely it may be expected to conform to theoretical performance when in another medium. Therefore, if we implant an IOL that achieves near-theoretical performance, we can expect that it will not compromise the dioptrics of the eye - and that corneal aberrations will remain the limiting consideration for visual acuity. In practical terms, this implies the desirability of IOLs achieving upwards of 75% resolution efficiency. (There is no basis, however, for splitting hairs over differences of 10-15% between one lens and the next.) Currently, most intraocular lens manufacturers offer lenses that generally exceed 50% resolution efficiency, and there is good reason to think that this level of resolving ability is adequate for ophthalmic purposes; many patients have achieved 20/20 correction with such lenses. A resolving efficiency lower than 50% becomes problematical and should be cautiously regarded. REFERENCES
1. Galin MA: Optical and mechanical considerations of intraocular lenses. Am Intra·Ocular Implant Soc ] 2:22-23,1976 2. Blaker JW: Quality control of intraocular lens optics. Am Intra-Ocular Implant Soc] 3:128-129, 1977 3. Richard DA: An outline for the testing and subsequent analysis of the resolving power of intraocular lenses. Am Intra-Ocular Implant Soc] 3 :229-231,1977 4. McReynolds WU, Snider NL: The quick, simple measurement of intraocular lens power and lens resolution at surgery. Am Intra-Ocular Implant Soc] 4:15-17,1978 5. Visual optics and Refraction, DD Michaels, C.V. Mosby Co., St. Louis (1975), pp. 165-185. 6. Adler's Physiology of the Eye, 6th ed., RA Moses (ed.), C.V. Mosby Co., St. Louis (1975), pp. 500-528,38. 7. Modern Optical Engineering, WJ Smith, McGraw-Hill Book Co., New York (1966), pp. 319,433 & 320-321. 8. Dunn MJ: Factors influencing the specification of intraocular lens dioptric power. Am Intra-Ocular Implant Soc] 3:130-133,1977 9. Military Standard ISO-A, paragraph 5.1.1.7. 10. Modern Ophthalmology, Vol. 1 (Basic Aspects), 2nd ed., A Sorsby (ed.), J .B. Lippincott Co., Philadelphia (1972), pp.310-313. 11. Snyder AW, Miller WH: Photoreceptor diameter and spacing for highest resolving power. ] Opt Soc Am 67:696-698,1977 12. Frisen L, Glansholm A: Optical and neural resolution in peripheral vision. Invest OphthaI14:528-536, 1975 13. Giles MK: Aberration tolerances for visual optical systerns.] Opt Soc Am 67-634-643, 1977 AM INTRA-OCULAR IMPLANT SOC J - VOL. IV, JULY 1978 129
