Artificial pupils and Maxwellian view · 2017. 7. 31. · effects of the pupil diameter (0.5-5 mm...

Artificial pupils and Maxwellian view

Robert J. Jacobs, Ian L. Bailey, and Mark A. Bullimore

When control of the pupil size is required, the simplest method is to use a physical artificial pupil oraperture that is placed in the spectacle plane. In some clinical applications (e.g., the potential acuitymeter) an optical artificial pupil is imaged in the plane of the natural pupil by a Maxwellian view opticalsystem. We compared visual performance with physical and Maxwellian artificial pupils by measuring theeffects of the pupil diameter (0.5-5 mm in range) and defocus (5-D myopia to 4-D hyperopia) on minimumangles of resolution (MAR's) and on angular blur disk diameters. For pupil diameters down to 2.0 mmthere were no meaningful differences between the visual resolution that is obtained with the physical andthe Maxwellian pupils. At the smallest diameter (0.5 mm) the physical artificial pupils caused the MAR toincrease because of the diffraction limitation on resolution, and defocus no longer affected MAR. With thesmall Maxwellian pupils vision did not become diffraction-limited so that maximum resolution could stillbe obtained. MAR was still affected by defocus. The angular blur disk diameters measured with thesmaller Maxwellian pupils were slightly but significantly larger than those found with physical artificialpupils. For physical artificial pupils, field-of-view restrictions may result from vignetting with the eyepupil. Thus small physical artificial pupils can act as pinholes causing resolution to become impaired butinsensitive to defocus. Also vignetting by the eye pupil can restrict the field of view. Small optical artificialpupils from Maxwellian viewing do not impair resolution, and the resolution may remain sensitive todefocus. The eye pupil does not cause any field restriction, although, if small, it may filter higher spatialfrequencies out of the retinal image.

Key words: Pupils, Maxwellian view, resolution, visual acuity, defocus, minimum angle of resolution,angular blur disk diameter.

Introduction

The simplest method for controlling the pupil size invision research and in clinical applications is to centeran aperture of the required size in front of the eye.Such an aperture is usually placed in the spectacleplane.' If optical instruments are used in manipulat-ing the visual image, optical methods of controllingthe pupil size can be used.

One optical method is to use the exit pupil of aKeplerian telescope (or microscope) system as theartificial pupil. The size and shape of the artificialpupil are determined by the aperture stop of theoptical system, and its image becomes the exit pupil ofthe system. This image is an optical artificial pupil,and it is usually made to be coincident with the pupilof the eye. In such systems all the light entering theaperture stop is imaged through the optical pupil.

R. J. Jacobs is with the Department of Optometry, The Univer-sity of Auckland, Private Bag, 92109 Auckland, New Zealand; I. L.Bailey and M. A. Bullimore are with the School of Optometry,University of California, Berkeley, Berkeley, California 94720.

Received 9 August 1991.0003-6935/92/193668-10$05.00/0.c 1992 Optical Society of America.

Examples of such systems are the ocular-focus stimu-lator of Crane and Cornsweet2 and the telemicro-scopic system used by van Meeteren and Dunnewold3

to image a remote grating target through an 0.8-mmoptical pupil.

Another optical method of presenting visual stim-uli has become known as the Maxwellian view. In theMaxwellian view the exit pupil of the optical system isan image of the effective light source. Schor et al.4

used a Maxwellian system to induce a small exit pupil(- 0.75 mm) (Ref. 5) to increase the depth of focus ofthe eye sufficiently to open the accommodative loop.

Maxwellian View

In the original Maxwellian view optical system, thesource and the exit pupil were slits, but small circularsources are more common today.6 Such optical sys-tems are used widely in vision research where uni-formly illuminated fields of light need to be generatedfrom sources of relatively low power.7 Experimentsthat utilize monochromatic or narrow chromatic band-pass light often use the Maxwellian view to achieveluminances in a photopic range without requiringhigh-intensity lamps (such as the xenon arc), which

3668 APPLIED OPTICS / Vol. 31, No. 19 / 1 July 1992

would be needed if the stimulus were to be projectedonto a screen and viewed directly. Maxwellian viewoptical systems are also used where a point of entryinto the eye is to be controlled, such as in the studiesof the Stiles-Crawford effects.8 9 They are also used insome interferometers for measuring visual acuity(see Ref. 10).

In the Maxwellian view system light is usuallycaptured by a collimating lens that is positioned closeto the light source. This light can then be manipu-lated optically without losses resulting from theinverse square law before being channeled into theeye passing through an image of the light source thatis formed in the plane of the observer's eye pupil. Thisimage of the light source is the exit pupil of theMaxwellian view system.

If the Maxwellian exit pupil lies entirely within theobserver's eye pupil, by geometrical optics theory theobserver's eye pupil would be effectively replaced withan optical pupil having the size and shape of theMaxwellian exit pupil located in the plane of theobserver's eye pupil. For a Maxwellian viewing sys-tem geometrical optics theory can be inadequatebecause it ignores physical optics properties that canbe quite important to image quality.

Westheimer's 7 analyses for Maxwellian viewingsystems show that when the source of illumination issmall and monochromatic, the image quality is inde-pendent of the exit pupil size and dependent only onthe size of the eye-pupil aperture. In such conditionsthe illumination is essentially coherent. Since thesource of illumination is made large and if it is notmonochromatic, the illumination becomes only par-tially coherent or incoherent. Westheimer calculatesthat incoherent imagery occurs for Maxwellian exitpupils when diameters are greater than 2.2 mmand that a diameter of less than 0.06 mm isrequired for coherent imaging properties.

The coherence of light affects imaging properties inMaxwellian viewing systems when the eye pupil orthe ocular media act as spatial filters to limit therange of the spatial frequencies within the Fourierspectrum of the image. When unstructured fields areused as targets, such effects would be seen only aschanges in the clarity or the nature of the edge of thefield. However, when spatially structured targets,such as acuity targets or other stimuli with finedetail, are presented in a Maxwellian viewing system,the use of coherent light affects the retinal images ofthe targets themselves.

With coherent light in a Maxwellian system, aFourier transform of the target amplitude function(i.e., the Fraunhofer diffraction pattern that is pro-duced by light passing through the target) is formedin the plane of the entrance pupil of the eye. Thehigher-spatial-frequency information is representedin the more peripheral regions of this diffractionimage. It is possible for the eye pupil to act as alow-pass filter by blocking the more peripheral partsof the diffraction image. Bradley et al. 1 calculate thatthe width of the diffraction image should be at least

1.2 mm to create a 30-cycle/deg retinal image for lightof 700-nm wavelength. An eye-pupil size of 2.5 mmwould be required to ensure the passing of all poten-tially visible spatial frequencies.

Physical Artificial Pupils

Physical artificial pupils are apertures that, by virtueof their placement in front of the eye, take over thelight-limiting functions of the eye pupil. Small physi-cal artificial pupils have a low-pass filtering effectbecause of diffraction restricting the range of spatialfrequencies in the image so that the image quality canbe significantly reduced. Small optical artificial pupilsfrom Maxwellian viewing systems do not lead to theconstraint of the diffraction image that formed in thepupil plane, and thus they do not have the samelow-pass filtering effect.

The purpose of this study was to measure differ-ences in visual performance with Maxwellian andphysical artificial pupils as a function of pupil size.Smith12 argues that the angular blur disk diameter isbetter than the object vergence for quantifying defo-cus because the effects of defocus are so stronglydependent on pupil size,' and the angular blur diskdiameter reflects both the defocus and the pupil size.Both visual acuity and depth of focus should berelated to the angular blur disk diameter, and, sinceblur disk diameters are so closely related to pupil size,we measured both the minimum angles of resolution(MAR) and the angular blur disk diameters (ABDD's)for the various pupil sizes and for both types ofartificial pupil in both clear and defocused conditions.

Methods

The apparatus is shown schematically in Fig. 1. A pairof + 10-D achromatic lenses (Melles Griot 01LAL017)mounted on an optical bench were separated by 60cm. For the Maxwellian viewing system an incandes-cent lamp illuminated a translucent diffusing screenthat was immediately behind and in contact withaperture AM, which was positioned in the primaryfocal plane of the first lens (L1). An image AM' wasformed in the secondary focal plane of the second lens(L2) and was equal in size to aperture AM. Theobserver's eye was positioned so that the eye pupilwas in the same plane and centered on the image AM'.This creates a telecentric Badal optometer,13 since thesecondary focal point is at the entrance pupil of theeye. The position of the targets for the visual resolu-tion and the blur disk diameter measurements wasvaried over a range of - 5-15 cm from the secondlens. Such a system allows the vergence of light fromthe target incident on the eye to be varied over arange of approximately +5 to -5 D while angularmagnification remains constant.

The conversion from Maxwellian viewing to normalviewing through the physical artificial pupil wasachieved by placing a large white externally illumi-nated screen, which was 50 cm in front of lens L2, andinserting the physical artificial pupils (Ar) 15 mmbefore the focal plane of lens (L2). A filter holder (with

1 July 1992 / Vol. 31, No. 19 / APPLIED OPTICS 3669

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an aperture of 45 mm x 39 mm) that was situated 40cm from lens L2 limited the effective area of thebackground screen. For all conditions the retinalilluminance was set at 30 Td (as for a test targetluminance of 160 cd/M2 as seen through a 0.5-mmpupil) by using appropriate neutral density filtercombinations. Thus for both Maxwellian viewing andviewing through the physical artificial pupil the sub-jects saw a 22-deg circular field containing the targetand its background, which was uniformly illuminatedand kept free of discernible texture and unaffected bytarget position.

Targets for the measurement of the minimumangle of resolution were either a transparent Roches-ter Institute of Technology alphanumeric test object(RP-1-71) or reduced-size transparent Bailey-Loviecharts.'4 Both charts gave comparable visual acuityscores. Resolution threshold sizes of 50% were foundby using probit analysis with appropriate correctionfor guessing that is associated with the five (Roches-ter Institute of Technology) or ten (Bailey-Lovie)alternatives in the forced choice procedures.

The target for the measurement of the perceivedblur disk diameters (ABDD's) produced by defocuswas a pair of retroilluminated apertures (diameters of

150 ,um) of variable separation. This target wasplaced in the same planes as the acuity targets, andthe separation of the sources was adjusted by thesubject until the two blur disks that were perceived bythe subject appeared to just touch. At least fivemeasurements were made for each viewing condition.This technique is similar to that introduced by Smith' 2

and used by Chan et al. 15All measurements were made with the subject's eye

pupil dilated, and accommodation was paralyzed for

the emmetropic and hyperopic defocus conditions.The subject's head and eye position were maintainedby using a bite bar, and a secondary optical systemwas used to detect transverse displacement of the eyepupil. In this secondary system a quadruple prismwas used to create four exit pupils symmetricallydisposed around the primary Maxwellian exit pupil.The longitudinal movement of prisms caused radialdisplacement of these secondary exit pupils, whichwere focused on the observer's iris close to the marginof the dilated pupil. The light source for this systemwas green, and any movement from alignment by theobserver's eye caused a green border to become visibleat the edge of the field. This indicated the presenceand direction of misalignment. For these experimentsthe exit pupil of the stimulus system was coincidentwith the center of the observer's eye pupil. For bothsubjects it was determined that the primary achro-matic (or visual axis) passed within 0.25 mm of thecenter of the eye pupil.

In the first experimental sessions myopic defocuslevels (target vergence at the eye pupil > 0.0 D) wereused, and emmetropic (target vergence = 0.0 D) andhyperopic defocus (target vergence < 0.0 D) werepresented in subsequent sessions. Within sessionsdefocus levels were presented randomly, and, withindefocus levels, pupil size changes were in randomsequence. The defocus levels covered a range of 5-Dmyopia to 4-D hyperopia in 1-D steps, and these werereferenced to the subject's refractive error deter-mined by finding the most remote target position thatallowed maximum resolution when a viewing througha physical artificial pupil of 3-mm diameter. At eachpupil size MAR was measured before ABDD measure-ments were taken. For each condition the order of theartificial pupil type (physical or Maxwellian) waschosen randomly. For the myopic defocus levels 1%tropicamide was used for mydriasis. The observer'sfar point was measured before and after each pupilsize change, and the position of targets with respectto the second 10-D lens L2 was adjusted if the changesin the refractive error were > 0.1 D. For the emme-tropic and hyperopic conditions 1% cyclopentolatewas used for mydriasis and cycloplegia.

Results

Blur Disk Size

The relationships between the ABDD's and defocusfor the two pupil types and the various pupil diame-ters are shown for subject RJJ in Fig. 2. The resultsfor the second subject showed closely similar pat-terns. On each graph of Fig. 2 a dashed curve showsthe relationship between the blur disk size and thedefocus that is predicted by applying simple geomet-ric optics theory to the Gullstrand 1 Exact ModelEye16 for both types of artificial pupil for each of theeight diameters. When the defocus simulates myopiathe predicted blur disk diameters for Maxwellian viewpupils are slightly larger than for those with physicalartificial pupils, and the converse is true for simu-lated hyperopic defocus. The dashed curves on these


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For pupil diameters of 2 mm or more there was aconsistent tendency for the measured ABDD's to belarger than predicted for myopic defocus and smallerfor simulated hyperopia. This could be explained bythe positive spherical aberration, which enlarges blurdisks in myopia and reduces them in hyperopia. Forall pupil diameters the minimum ABDD was - 4 or 5arcmin.

The technique for measuring ABDD's is a psycho-physical measure that reflects the angular diameterof the point-spread function of the eye. For conditionsthat provide the best quality retinal image, the ABDDwas 4.5 arcmin, which was slightly smaller than the5.2 arcmin that was found by Chan et al. 15 Campbelland Gubisch17 measured the luminance profile of theprojection of a retinal image of a point source. Theirresults suggest that the minimal ABDD's were be-tween 2 and 5 arcmin, depending on how much of thetail of the luminance profile is included in the blurdisk. It may be that psychophysical measures ofABDD, such as those that are used in this study,overestimate the point spread function since theimages take on a starlike appearance that makes theedge of the disk more difficult to locate.

For the smallest pupil size (0.5 mm) the ABDD'sfor physical pupils were virtually unaffected by defo-cus, while the ABDD's in Maxwellian viewing werestill substantially affected by the higher magnitudesof defocus. At the four smallest pupil sizes theABDD's tended to be larger for the Maxwellian pupilthan for physical pupils, especially at higher defocuslevels.

A four-factor analysis of variance (pupil type, pupilsize, defocus, and subject) confirmed that the pupilsize and defocus have statistically significant effectson the ABDD's. There were no significant differencesbetween the two subjects, but there were significantinteractions between pupil type and pupil size, pupiltype and defocus, and pupil size and defocus.

Visual Resolution

The effects of defocus on the threshold minimumangles of resolution (MAR's) for the two types ofviewing system and the eight pupil sizes are shown onlogarithmic scales in Fig. 3. This figure presents theresults for one subject (RJJ), and the results for thesecond subject showed quite similar patterns. Oneach graph of Fig. 3 is a dashed curve that indicatesthe expected relationship between logMAR and defo-cus, which would be obtained if there were a constantratio between ABDD's and the MAR's that are mea-

sured in the same viewing conditions. The shape ofthese expected curves is determined by the predic-tions of ABDD for the Gullstrand 1 Exact Eye. Thevertical placement of the curves depends on thechosen ratio of ABDD to MAR. The ABDD/MAR ratiorepresented here is 4.6:1, and this value was found byaveraging the ABDD/MAR ratios across all defocuslevels for both pupil types and all pupil sizes.

For pupil sizes of 2 mm and larger there was littledifference between the visual acuities that are ob-tained with the two types of artificial pupil, althoughboth tended to provide better acuities than thoserepresented by the expected curves, especially at themoderate levels of defocus.

With the smallest physical artificial pupil (0.5 mm)the visual resolution was essentially unaffected bydefocus even though the acuity that was obtained wassignificantly less than the best acuities that could beobtained at zero defocus with the larger pupil sizes.For Maxwellian viewing with 0.5-mm pupils excellentvisual acuity could be obtained at zero defocus butacuity declined substantially with increasing defocus.This result is not predicted by geometrical opticstheory relating to blur disk diameters. For pupil sizesof 2 mm or less there was a consistent tendency forMaxwellian viewing to give slightly poorer visualresolution than that obtained by viewing throughphysical artificial pupils of the same size and atequivalent levels of defocus.

When pupil sizes were 2 mm and larger, there waslittle difference between results for the physical andMaxwellian artificial pupils. Increasing defocus pro-duced an increase in MAR, and this effect becamemore pronounced with increasing pupil size.

Relationships Between Resolution and Blur Disk DiameterGeometrical optics theory predicts direct proportion-ality between the resolution limit and the size of theblur patch on the retina. Assuming that there isdirect proportionality between the resolution limitand our psychophysical measure of MAR and betweenthe extent of the retinal image and our measure ofABDD, there should be a direct proportionality be-tween the measures of MAR and ABDD. A previousstudy' 8 found a direct proportionality between MARfor Landolt rings and ABDD as measured with thedual-fiber optic apparatus of Chan et al.15 Theiraverage ABDD/MAR ratio was 3.8:1, but the range ofindividual proportionality constants was 3.3-4.3.

Figure 4 shows the relationship between MAR andABDD for Maxwellian and physical artificial pupils atfour of the different pupil sizes for subject RJJ. Thesecond subject showed a similar pattern of results. Oneach graph is a reference line, MAR = ABDD/4.6,since 4.6 was the average ABDD/MAR ratio for allconditions for this subject. On these reference lines ismarked the ABDD's that are predicted for the variousdefocus levels for the Gullstrand 1 Exact Model Eye.For the second subject the average ABDD/MAR ratiowas 3.


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From Fig. 4 it can be seen that for the smallestphysical artificial pupil (0.5 mm), the points aretightly clustered since both MAR and ABDD werevirtually unaffected by defocus. MAR values were allin the range of 1.0-1.5 arcmin, and the ABDD valuesranged between 5 and 7 arcmin. For Maxwellianviewing with the 0.5-mm optical pupil, better acuity(MAR of 0.5 arc min) could be obtained, but therewas a much wider range of MAR and ABDD values.The resolution in defocused conditions was found tobe poorer than might be expected from the associatedABDD.

For the 1-mm physical artificial pupil the blur diskdiameters were smaller than predicted by geometricaloptics, and the MAR values were commensuratelysmaller except for the two highest levels of myopicdefocus when the resolution was poorer than ex-pected from the measured ABDD values. For the 1.0-and 2.0-mm Maxwellian view pupils and for viewingwith the 2-mm physical artificial pupil, the measuredblur disk sizes were close to the geometrical predic-tions. The consistent ABDD:MAR ratio was 4.6 formost points, but there was a tendency for this ratio tobe higher for the high levels of myopic defocus.

At the larger pupil diameters (the data for the4-mm pupils are shown in Fig. 4) there were virtuallyno differences between the results for the Maxwellianand the physical artificial pupils. For both pupil typesat the larger diameters there was a consistent patternof ABDD's being larger for myopic defocus than forequivalent magnitudes of hyperopic defocus. SubjectRJJ showed a clear trend for the visual acuity to bebetter than predicted from the measured ABDDvalues and the ABDD/MAR ratio of 4.6.

Discussion

The results of these experiments show that physicaland Maxwellian pupils are essentially equivalent forpresenting resolution targets only if the pupil size is 2mm or larger. For smaller pupil diameters there aresignificant differences between the two types of artifi-cial pupil. At a diameter of 0.5 mm the physicalartificial pupil causes vision to become diffraction-limited so that visual acuity becomes reduced. Theresolution remains independent of defocus at leastover the range of 5-D myopia to 4-D hyperopia.

Even at the smallest pupil size Maxwellian viewingdoes not cause a comparable diffraction limitation onresolution. Maximum resolution can still be obtained,and also MAR and ABDD remain dependent on themagnitude of defocus. Thus Maxwellian view systemsdo not create the same pinhole effect that is shown bythe physical artificial pupils. This can have clinicalrelevance in clinical instruments such as the poten-tial acuity meter, which uses the Maxwellian view.This instrument presents an acuity chart to thepatient's eye through a 0.15-mm Maxwellian pupil.This instrument requires a focus adjustment to cor-rect ametropia to maintain clarity of the target, andthe need for this feature is predictable from the

results of our experiment. Bradley et al. 11 have shownthat defocus affects the acuities that are measuredwith the potential acuity meter.

For smaller pupil diameters. (<2 mm) the Max-wellian pupils produce slightly larger ABDD's thanthe corresponding physical artificial pupils do, and,for the smallest Maxwellian pupils the ABDD's re-main dependent on defocus. Westheimer19 presents amathematical treatment of blur disk formation incoherently illuminated Maxwellian view systems andshows that retinal image blur disks are affected by thetarget defocus. Subjects in our experiment observedthat, for smaller pupil diameters at larger magni-tudes of target defocus, Maxwellian viewing createdblur disks that had indistinct margins, and someringing was evident. For the physical artificial pupilsof the same size, the blur disks appeared to havesharp borders. The reduction in visual acuity withincreasing defocus for the smallest Maxwellian view-ing pupils was disproportionately larger than theincreased ABDD's. We attribute this to defocus,which produces phase distortions that degrade thespatial fidelity of the retinal image and so reduceresolution but that have less effect on the appearanceof the blur disk.

The progression of the differences between Max-wellian and physical artificial pupils that occur whendiameters are <2 mm is expected because of thecoherence properties of light becoming more impor-tant to image quality when pupil diameters becomesmaller. When detailed targets are viewed with aMaxwellian pupil size of 0.5 mm, light may be consid-ered to be essentially coherent, and the plane of theMaxwellian pupil contains the spatial transform ofthe target being viewed. This diffraction image of aMaxwellian view system occupies an area that issignificantly larger than its exit pupil, and providedthis diffraction image is not blocked by the eye pupilor media opacities, high-spatial-frequency informa-tion may be conveyed to the retinal image. In contrastsmall physical artificial pupils act to limit resolutionby filtering some higher-spatial-frequency contentfrom the image.

Blur disk diameters and resolution performanceare essentially identical and for viewing with physicaland optical artificial pupils when pupil sizes are 2.0mm or greater. There are, however, significant devia-tions from the geometrically based predictions ofABDD and MAR. First, blur disk sizes were found tobe larger than predicted for myopic defocus andsmaller for simulated hyperopia. These effects couldbe attributed to positive spherical aberration of theeye. Second, when pupil sizes are larger the visualacuity in defocused conditions was better than thatpredicted from the blur disk size. This may be a resultof the Stiles-Crawford effect, which Westheimer19suggests is probably equivalent to an apodizing filterwith a radially symmetric gradient of density beingplaced over the eye pupil. The Stiles-Crawford effectshould cause the blur disks to have effectively a more


gradually tapered profile, which was neither observednor accounted for in our measurements of ABDD butwhich could be responsible for acuity improvementsthat are disproportionate to the perceived blur diskdiameter.

Retinal illuminance differences could possibly con-tribute to the perceived ABDD. It is conceivable thatsystematic errors in the control of retinal illuminancemay have contributed to the trend for ABDD's to belarger for Maxwellian viewing when pupil diameterswere 2 mm or less. We therefore conducted anexperiment measuring relationships between ABDDand defocus over a 4-log unit range of retinal illumi-nances for a full range of pupil sizes, and for thisexperiment we used a third subject. Over this range(0.003-30 trolands) retinal illuminance had littleeffect on measured ABDD's, and no systematicchanges were observed. During the main experimentsthere were no noticeable variations in target lumi-nance observed by our subjects, and we conclude thatif there were errors in controlling retinal illuminancethey were small and did not contribute to any system-atic trends in our results.

Fields of View

When physical artificial pupils are located just infront of the eye, the artificial pupil and the eye pupilmay create vignetting effects that restrict the field ofview. For example, calculations show that a 1-mmartificial pupil located 12 mm before a 5-mm eye pupilwill cause vignetting to begin at 19 deg, and for an eyepupil of 8 mm vignetting commences when the fieldsize is 32.5 deg (see Table I). To ensure wide fields ofview when using physical artificial pupils, the artifi-cial pupil aperture should be close to the eye, and theeye pupil should be dilated.

Maxwellian viewing is free from such vignettingproblems, and the field of view is limited by theMaxwellian lens with only a small influence from thesize of the Maxwellian pupil. The proximity of theMaxwellian exit pupil to the eye pupil can affect theresolution.20 When the illumination from a Max-wellian view system can be considered coherent, the

eye pupil may act as a spatial filter removing poten-tially visible spatial frequencies if the eye-pupil diam-eter is <2.4 mm or if the Maxwellian exit pupil isdecentered so that it comes too close to the edge of theeye pupil. For Maxwellian view systems in which highspatial frequencies should be passed, the size andposition of the eye pupil should be controlled so that itdoes not occlude part of the diffraction image that isformed in the plane of the eye pupil.

Conclusions

We set out to determine the extent to which physicaland Maxwellian artificial pupils could be consideredto be equivalent. Provided that the pupil diametersare 2 mm or greater, both physical and Maxwellianartificial pupils provide essentially equivalent visualresolution and angular blur disk diameters over awide range of defocus values. When physical artificialpupils of 2 mm or larger are used, the eye pupil shouldbe dilated to avoid undue limitations of the field ofview. At large pupil diameters spherical aberration ofthe eye may have different effects for myopic andhyperopic defocus, and the Stiles-Crawford effectmay serve to enhance visual acuity.

For small pupil sizes physical artificial pupils canact as pinholes. A 0.5-mm physical artificial pupilcauses vision to become diffraction-limited so thatvisual acuity is reduced even for in-focus imagery,and with such pupils the resolution remains unaf-fected by defocus. When the smaller optical artificialpupils are used in appropriately arranged Maxwellianviewing conditions, the visual resolution is alwaysexcellent for in-focus vision, but the resolution is stillaffected by defocus.

This work was supported by a grant from theUniversity of Auckland and the National Institutes ofHealth grant EY06365.

We thank Pare Keiha for acting as a subject andRay Applegate, Arthur Bradley, Stanley Klein, LarryThibos, and Xiaoxiao Zhang for helpful discussions.

Applegate et al. independently conceived andplanned a similar experiment investigating relation-

Table . Fields of View with Physical Artificial Pupilsa

Field Stop Eye, Pupil (mm)3.0 5.0 8.0

Aperture Stop, Artificial Pupil (mm)

Angular Fields of Viewb 1 2 1 2 1 2

Field-full illumination (Vignetting begins) 9.5 4.8 18.9 14.3 32.5 28.1Field-half illumination (Half-vignetting) 14.3 14.3 23.5 23.5 36.9 36.9Absolute field (Vignetting complete) 18.9 23.5 28.1 32.5 41.1 45.2

Widths of Fields of Viewc

Field-full illumination (Vignetting begins) 1.6 0.6 3.2 2.3 5.7 4.8Field-half illumination (Half-vignetting) 2.5 2.5 4.2 4.2 6.7 6.7Absolute field (Vignetting complete) 3.4 4.4 5.1 6.0 7.6 8.5

aField sizes in degrees.bWidths in centimeters at 10 cm from eye pupil.


ships between visual acuity and the diameter ofphysical and Maxwellian pupils. They reported theirresults in R. A. Applegate, A. Bradley, and L. N.Thibos, "Visual acuity and pupil size in Maxwellianand free view systems with and without refractiveerror," in Noninvasive Assessment of the VisualSystem, Vol. 1 of OSA 1992 Technical Digest Series(Optical Society of America, Washington D.C., 1992),pp. 170-174.

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Artificial pupils and Maxwellian view · 2017. 7. 31. · effects of the pupil diameter (0.5-5 mm...

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