Optimal parameters for retinal illumination and imaging in fundus cameras

Optimal parameters for retinal illumination and imagingin fundus cameras

E. DeHoog1,* and J. Schwiegerling2,3,1

1Biomedical Engineering Program, University of Arizona, 1657 East Helen Street, Tucson, Arizona 85721, USA2Ophthalmology and Vision Sciences, University of Arizona, 655 North Alvernon Way, Suite 108,

Tucson, Arizona 85711, USA3College of Optical Science, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85721, USA

*Corresponding author: [email protected]

Received 27 June 2008; revised 20 August 2008; accepted 29 October 2008;posted 31 October 2008 (Doc. ID 97963); published 12 December 2008

A fundus camera is a complex optical system for imaging the retina of the eye. Designing a fundus camerarequires the combination of an imaging system and an illumination system to share common optics. Thiscombination of systems results in the need to find an optimal balance between imaging and illuminatingthe retina. We present a series of parameters and methods used to optimize the illumination system of afundus camera while maintaining excellent image quality. © 2008 Optical Society of America

OCIS codes: 120.3899, 120.4570.

1. Background

The modern fundus camera is an adaptation of a re-flex free indirect ophthalmoscope designed in theearly 1900s. The principle of reflex free indirectophthalmoscopy requires that the illumination andimaging pathways pass through different portionsof the optics of the eye to avoid backreflections [1].Further development of this principle has evolvedinto a complex optical system for retinal imagingcalled a fundus camera. This particular device pre-sents a unique set of design challenges consideringthe retina of the eye must be illuminated and imagedsimultaneously. The most common solution to thisdesign challenge is to design two separate systemssharing common optics. One system is used for illu-mination, and the other system is used for imaging. Aschematic of such a device from the patent literatureis provided in Fig. 1 [2]. This particular design waschosen primarily because the basic optical layout issimilar to the system provided by Knoll in 1969 andother patents dated from 2002–2006 [2–5]. Despite

being in existence for at least 40 years, the basic de-sign of the fundus camera has changed little, show-ing the effectiveness of this particular design.

Analysis of a typical fundus camera, shown inFig. 1, gives insight into the design principles in-volved in this device. The imaging system is com-posed of three lenses, labeled 20, 24, and 25, and amirror with a central hole, 21. Lens 20, the objective,forms an intermediate image of the retina, andlenses 24 and 25 relay the intermediate image tothe camera, labeled 27 for snapshot imaging. Trans-lation of lens 24 allows the fundus camera to compen-sate for the defocus present in the patient’s eye. Inthe imaging path the mirror with the central holesimply acts as an aperture placed conjugate to thepupil. The size of the central hole limits the size ofthe pupil that the eye can be imaged through, ima-ging pupil diameter, effectively limiting the entrancepupil diameter of the imaging system. Components30–32 are used for continuous observation of the re-tina by an infrared imaging camera [2,6].

The illumination system is more complex. Asshown in Fig. 1, the illumination and imaging sys-tems share the objective and the eye. When a config-uration like this is used, backreflections from the

0003-6935/08/366769-09$15.00/0© 2008 Optical Society of America

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common optics can be a considerable problem to re-solving the image. Despite using excellent antireflec-tive (AR) coatings, backreflections from the commonoptics can be significantly greater than the light re-flected by the retina [7–9]. In order to overcome back-reflections, creative schemes must be implementedin the design of an illumination system [1].In this particular camera there are two sources, 10

and 13. These sources serve different purposes, aflash source, 13, for snapshot retinal imaging and anincandescent source, 10, for continuous observation.Despite having different purposes, each illuminationpath uses the same principles. The sources are con-jugate to an annular aperture, 16. Lens 17a and 17brelay the image of the annulus to amirror with a holein the center, 21. This central hole in the mirror isconjugate to the plane of the pupil of the eye. Thiscentral hole controls the size of the unilluminatedportion of the pupil of eye. The entire system of opticsrelays the source to the pupil of the eye [2,6,5].As previously mentioned, eliminating backreflec-

tions is of key importance in the design of a funduscamera. Backreflections from the cornea are elimi-nated with careful placement of the annular aper-ture, the holed mirror and iris, 22 in the system.The holed mirror is critical in the coupling of the ima-ging and illumination paths and managing systembackreflections. This component allows the outeredges of the pupil to be illuminated, hence illuminat-ing the retina, and leaving the center of pupil unillu-minated for the purpose of imaging the retina whileminimizing corneal backreflections. The annularaperture blocks stray light from the illumination sys-tem that could pass through the hole in the center ofthe mirror and cause difficulty in resolving the im-age. The iris blocks any remaining cornea backreflec-tions located at the edges of the image. Eliminatingbackreflections from the objective is accomplished byuse of a black dot, 19. The black dot is placed conju-

gate to the front surface of the objective. Light thatwould be backreflected from the front surface of theobjective is absorbed by the black dot [2,6,5].

The design objectives of the illumination system ofthe fundus camera are to eliminate backreflectionsfrom the cornea and maximize the irradiance on theretina and the detector or camera while maintainingcomplete illumination across the portion of the retinabeing imaged. Completing a successful design re-quires understanding the trade-offs that come withthe three criteria listed. The goal of our paper is toexplore trade-offs involved in design of the illumina-tion system of a fundus camera. These trade-offs in-clude: resolution, detector irradiance, efficiency, anduniformity. Existing literature only gives schematicsthat do not include enough information to recreate aworking system. This leaves the engineer to deter-mine which parameters are optimal for the task ofretinal imaging and illumination and how changingthese parameters affects the performance of the sys-tem. Our study is presented to better understand afew of the parameter involved in fundus cameradesign.

2. Methods

A model of a simplified fundus camera was con-structed using the sequential and nonsequential cap-abilities of ZEMAX. The simplified system, Table 1,consists of the optics common to the illumination andimaging system, the eye, E, an objective, 21, and aholed mirror, 21; see Fig. 2. In this configurationthe holed mirror is conjugate to the physical pupilof the eye model. Considering the source is conjugateto the holed mirror, the mirror, 21, itself was modeledas an annulus of point emitters. In the center of theannulus a detector was placed to measure the lightreflected by the retina and/or cornea. To minimizeaberrations, an aspheric objective, 21, is used. Forthe purpose of this study, backreflections from the ob-jective were not considered. Our previous models ofan entire fundus camera have shown that the blackdot and annular aperture in the preceding illumina-tion optics eliminate backreflections from the objec-tive [10]. These results are consistent with the claimsmade by patent literature [2,5]. The sequential andnonsequential eye models are based on the Escuderoand Navarro eye model [11]. Depending on the pur-pose of the simulation being preformed, the retina ofthe eye was modeled either as an absorbing media ora scattering media with Lambertian properties con-sistent with the literature [7,8]. The pupil was set toa maximum diameter of 7:5mm to simulate the eyebeing dilated [9]. Using this configuration, a series

Fig. 1. Design schematic of a fundus camera from a patent filed in2003 [2]. The imaging path is shown with solid rays. The illumina-tion path is shown with dashed rays. The annular illuminationpattern is created at the iris of the eye by the center of the illumi-nation path using an annulus, 16, and a mirror with a central hole,21, located at the conjugate planes of the iris. A plate with a blackdot, 19, is placed conjugate to the objective, 20, to remove backre-flections from the objective.

Table 1. Simplified Camera Prescription

Radius(mm) Conic

Thickness(mm) Glass

Working distance 0 0 25Objective 29.1 −2:2 10 n-sk16Source distance −29:1 −2:2 124.5

6770 APPLIED OPTICS / Vol. 47, No. 36 / 20 December 2008

of simulations were conducted to determine theoptimal configuration for retinal illumination andimaging.A series of parameters must be defined to under-

stand the optimization process. The first parameteris the illumination ratio, IR, defined as

IR ¼ RL

Ri; ð1Þ

where RL is the inner radius of the illumination an-nulus and Ri is the radius of the imaging pupil; seeFig. 3. This parameter is useful for quantifying thedifference between RL and Ri necessary to eliminatecorneal backreflections. Note that Ri is fixed by thesize of the hole in the mirror and/or the iris behindthe mirror. The second parameter is the normalizeddetector irradiance, NDI, defined as

NDI ¼ Φd

ΦsAd; ð2Þ

where Φd is the power on the detector, Ad is the areaof the detector, and Φs is the power emitted by thesource. The irradiance ratio gives a measure of howeffectively light from the source is being transferred

to the retina and back to the individual pixels of theimaging detector. Next, efficiency is defined as

η ¼ Φd

Φs� 100%: ð3Þ

Efficiency, η, measures how efficiently light emittedby the source is transferred to the detector. Finally,uniformity, U, is used to measure the how power dis-tribution on the retina deviated from a uniform dis-tribution. Uniformity is defined as 1 minus thepercent difference between the power at 85% of theradius of the illuminated area, Φ85%, to the power atthe center of the illuminated area, Φcenter. Mathema-tically, U can be expressed:

U ¼ 1 −

jΦcenter −Φ85%jΦmax

: ð4Þ

Before characterizing the illumination parameters,it is necessary to determine the effect of imaging pu-pil size on retinal image quality. This is determinedby measuring the rms wavefront error as a functionof pupil size. From the data a Strehl ratio can be com-puted as a metric for image quality [12].

To determine the optimal configuration for retinalimaging and illumination a series of simulations areconducted. First, it is important to measure the illu-mination ratio for a given configuration. This is a cri-tical step, considering it is necessary to find theproper illumination ratio that removes cornea back-reflections from the detector. Any corneal backreflec-tions, which can be as much as 2% of the incidentpower, are significantly greater than the power re-flected from the retina (based on Fresnel reflection,calculation between refractive indices cornea and air[7,8]). To isolate backreflections from the cornea, theretina is set as a perfect absorbing material. Thenthe illumination ratio is determined by setting thesize of the detector (size of the hole in the mirror, 21,in a full system), corresponding to the conjugate ima-ging pupil diameter, Ri, and varying size of the innerradius of the source annulus (size of the inner radiusof the annular illumination pattern on the mirror),corresponding to the conjugate inner radius of the il-lumination annulus, RL, until the power on the de-tector is zero. The effects of the working f -number,WF#, of the objective lens and divergence angle of thesource on the illumination are then characterized.

An important aspect to illuminating the retina forimaging is to provide a relatively uniform distribu-tion. If this is not accomplished, retinal images arelikely to have dark regions where information cannotbe gathered. When designing the illumination opticsthat relay the source to the holed mirror, it is impor-tant to consider the numerical aperture, NA, of thebeam incident to the holed mirror. In our case the in-cident NA is modeled as the source angle at eachpoint.

After determining the illumination ratio necessaryto null corneal backreflections, the retina surface

Fig. 2. Simplified retinal illumination system consisting of amodel eye, an objective, and a holed mirror. The holed mirror,21, reflects the image of source object.

Fig. 3. Illumination annulus and imaging pupil located at the pu-pil of the eye. Ri designates the radius of the imaging pupil. RL

designates the inside radius of the annular illumination patternat the pupil. The white annulus betweenRL andRi is space neededbetween parameters to prevent corneal backreflections.


property is changed to a scattering material withcharacteristics from the literature [7,8]. A series ofsimulations are conducted to determine the amountof power transferred from the source to the detector.In these simulations, the WF# of the system and cor-responding illumination ratio are varied and thesource angle remains constant. From these datathe efficiency and normalized detector irradiance aredetermined.To determine the effects of the working distance on

retina illumination, the pupil of the eye is movedfrom the focus of the objective by varying the workingdistance between the eye and the objective, shown inFig. 4. WF#, source angle, and source distance re-mains fixed. The illumination ratio, efficiency, unifor-mity, and normalized detector irradiance are thendetermined for each defocused position.As a final experiment, the eye model is changed to

decentered eye model proposed by Liou and Brennan[13]. The decentered eye model is tilted to align thevisual axis along the optical axis of the system. Pre-viously performed experiments are repeated andcompared to data from the decentered eye model.

3. Results

A. Imaging Pupil Diameter

Ideally, a fundus camera should provide maximumirradiance on the retina and excellent image quality.From a purely radiometric standpoint, as the size ofthe imaging pupil increases, the amount of light thatcan be collected by the objective increases, and theamount of light entering the eye decreases. Basedsolely on these considerations, the geometry of thesituation states the power reflected from the retinais maximized when the area of the illuminating an-nulus and the area of the imaging pupil are the same.For a 7:5-mm pupil this results in an approximately5:2-mm imaging diameter, while the outer annulus isused for illumination [14]. This simple analysis,however, does not take into account the effects of pu-pil size on imaging quality. The Strehl ratio for var-ious pupil diameters is calculated at 633nm usingthe definition

s ¼ expð−σ2Þ; ð5Þ

where is σ rms wavefront error [12]. According to theeye models, a Strehl ratio of greater than 80% ismaintained for an imaging pupil diameter smallerthan 2mm (Escudero and Navarro) and 3:5mm (Liouand Brennan), Fig. 5; the Strehl ratio deteriorates ra-pidly for larger pupil sizes [12]. Similar results havebeen shown in previous experiments in which theMTF of the eye is measured for different pupil sizes[15,16]. It should be noted the Liou and Brennanmodel has notably different levels of spherical aber-ration than most other eye models and underesti-mates the dispersion of the ocular media, and thesedifferences potentially affect the outcomes of thisanalysis [17–19]. Consequently, the optimal pupilsize may be different than what is suggested by thismodel. A more recent decentered anatomically accu-rate eye model shows that a Strehl ratio of 80% orgreater is maintained for pupil sizes smaller than1:5mm and drops more rapidly for larger pupil sizesthan other eye models used [20]. This exercise de-monstrates that it is ideal to image the retina at asmaller imaging pupil diameter to reduce the effectsof ocular aberrations on the image quality of thesystem.

B. Source Angle

When beginning the design of the illumination sys-tem of a fundus camera, the characteristics of thesource and optics relaying the source to the holedmirror must be considered. The relay optics, respon-sible for imaging the source onto the mirror, must bedesigned to meet a minimum image space numericalaperture (NA). By meeting this minimum NA, thelight incident the mirror will be distributed over theentire retinal field of view, FOV, of the imaging sys-tem. Failure to meet the minimum NA will result inan annular illumination pattern on the retina that isunacceptable; see Fig. 6(b). A calculation based onthe illumination ratio can be used to determine theminimum angle, α, for complete illumination of theretina; see Fig. 7. If a cross section of the eye is con-sidered, then the objective lens focuses light from thesource to a point on the pupil. The angular subtense

Fig. 4. Simplified fundus camera with the pupil of the eye dis-placed from the objective focal point. Fig. 5. Strehl ratio of the eye as a function of pupil diameter.


of the convergent beam is β. Through refraction atthe various surfaces of the eye, the angular subtenseof the beam is compressed to α. To achieve uniformillumination on the retina, αmust cover from the cen-ter of the retina to the edge of the FOV. A smallerangle α will fail to illuminate the central retina.Based on the knowledge of the eye model, the re-quired β can be calculated from α and, consequently,the parameters of the objective lens defined. Know-ing the angular flux distribution of the source, α canbe adjusted accordingly to ensure an acceptable de-gree of complete illumination.In our simulations using the centered eye model,

lens diameter (WF#) and source angle (image spaceNA) are varied to determine their effects on the uni-formity of the retinal illumination pattern. To simpli-fy our simulations, we used Gaussian and uniformangular source distributions. Leaving the source an-gle (divergence angle of the source) constant andvarying the WF#, we found little effect on the unifor-mity retinal illumination pattern. However, leaving

the WF# constant and varying the source anglehas a significant effect on the uniformity. Both sourcedistributions show decreasing the source angle yieldsa decrease in uniformity and an annular illuminationdistribution. These effects are shown in Figs. 6(a)and 6(b). Percent of aperture filled is calculated by

P ¼0@d × tan

�θ2

�

DL2

1A

2

; ð6Þ

where P is the percentage of the lens aperture filled,d is the source distance, θ is the source angle, and DLis the diameter of the objective; see Fig. 4.

Differences between source distributions becomemore pronounced at larger angles due to vignettingeffects. A uniform source distribution shows a moresignificant drop in illumination around the edges ofthe illumination pattern as the source angle in-creases when compared to a Gaussian source distri-bution. The only notable difference as a result ofusing a decentered eye model is the presence of vig-netting at the edge of the positive x axis. Due the pu-pil of the eye being decentered along the x axis withrespect to the illumination annulus, some of thealong the light is clipped by misalignment. This iseffect is further demonstrated in Fig. 8. The generaltrend of uniformity changing with source angle isstill apparent. However, there is roughly a 20% dropin power distribution at the edge of the x axis of theillumination profile due to the decentering of the pu-pil from the visual axis by roughly 0:5mm [13]. Morerecent eye models incorporate a smaller decentrationvalue (∼0:3mm) resulting in a smaller drop in powerat the edge of the illumination profile [20]. Thoughthe difference in the profile may seem significant,the percentage of total power lost is minimal, leavinglittle affect on the other illumination parameters. Asituation in which the illumination annulus is vig-netted due to the decentration of the pupil of theeye is unlikely considering the clinician who is takingthe retinal image is likely to align the illuminationannulus concentric to the pupil of the eye. If this isthe case, the vignetting effects due the decentration

Fig. 6. Effects of the source angle on retinal illumination for aWF#1 system: (a) uniformity versus percent of aperture filledand (b) illumination patterns on the retina for different sourcesangles. For (b) the top left plot corresponds to 100% of the aperturefilled, while the bottom right plot corresponds to 8% of the aperturefilled. Intermediate plots range between 8% to 100% of the objec-tive’s aperture filled.

Fig. 7. Diagram showing the minimum angle, α, of illuminatingoptics necessary for full illumination of the retina. RL is the innerradius of the illumination annulus, and β is the angle subtended bythe illumination path focused on the pupil of the eye.


of the pupil of the eye disappear, leaving the illumi-nation profile undisturbed.

C. Illumination Ratio

Determining the proper illumination ratio is one ofthe first steps in the design process. In an unaber-

rated optical system the IR equals 1 because the spotsize on the pupil of the eye is small. This will allowthe illumination annulus to equal the imaging pupilradius without the need for a buffer to eliminatebackreflections. In an aberrated system the spot sizeincreases, and RL must increase to eliminate backre-flections because Ri is fixed by the diameter of thehole in the mirror or iris behind the mirror. For afixed WF# and source angle it is clear that an in-creased illumination ratio results in decreased effi-ciency. From our results using the centered eyemodel, shown in Fig. 7, we see that due to the opticalaberrations induced by the objective, the spot size onthe pupil enlarges, resulting in an increased illumi-nation ratio. Figure 9 shows the presence of cornealbackreflections on the detector as a function of illu-mination ratio for a WF#1 system. Figure 10 demon-strates the effects of WF# and imaging pupildiameter on the illumination ratio. Increasing WF#results in a decreased illumination ratio. These re-sults are expected considering the spot size at the pu-pil plane of the eye is a function of the F# of theobjective [12]. Results also show that increasingthe imaging pupil diameter decreases the illumina-tion ratio. The illumination ratio is unaffected bythe difference in eye models considering the radiusand conic value for the front surface of the corneavary little between eye models.

D. Efficiency and Normalized Detector Irradiance

Efficiency and normalized detector irradiance areimportant metrics in determining the performanceof an illumination system. Ideally we want a systemthat is highly efficient with maximum detector irra-diance. Figures 11(a) and 11(b) show the relation-ships between WF#, pupil diameter, normalizeddetector irradiance, and efficiency for a fixed sourceangle filling the aperture. As expected, themaximumefficiency for each configuration is around a 5:2-mmpupil diameter, consistent with our previous findings[14]. In contrast, we see that detector irradiance de-creases as a function of increased pupil diameter anddecreased WF#. An 80% Strehl ratio and WF#consideration showed minimal changes for pupildiameters up to 2mm. Taking these results into ac-count, we conclude there is minimal benefit to in-creasing the imaging pupil diameter beyond 2mm.

Fig. 8. (a) Illumination annulus at the decentered pupil. (b),(c) Profiles of illumination distribution on the retina for varioussource angles using a Gaussian angular source. Power and x axisare normalized for comparison of eye models. Percentages refer tothe percentage of the objective aperture filled. (b) Escudero andNavarro eye model. (c) Decentered eye model.

Fig. 9. Illumination pattern on the detector as a result of cornealbackreflections for a WF#1 with a 2-mm imaging pupil at the fol-lowing illumination ratios: (a) 1.0, (b) 1.2, and (c) 1.4. Higher IR toeliminate backreflections results in lower efficiency.


The results from the decentered eye models showedslightly lower values due to the vignetting of the il-lumination annulus but followed the same trendsin Fig. 11.

E. Pupil Defocus

For the previous simulations the focus of the objec-tive is fixed at the pupil of the eye. In this seriesof simulations the pupil of the eye is moved awayfrom the focus of the objective to determine the ef-fects of relocating the focus of the illumination annu-lus. The source distance, source angle, and WF# ofthe system are fixed for this series of experiments.In our simulations, moving the focus inside the eyeis regarded as a negative, and moving the focus out-side the eye is regarded as positive. For each defo-cused position, efficiency, NDI, illumination ratio,and uniformity are measured. Figures 12(a) and12(b) show the illumination ratio and NDI as a func-tion of pupil position. The illumination ratio appearsto increase quadratically with pupil distance fromthe focus. This outcome is expected because spot sizeincreases quadratically with displacement from fo-cus [12]. NDI increases as the focus is brought insidethe eye. Interestingly, the optimal position appearsto be between the principal planes and nodal pointsof the eye [9]. An efficiency versus pupil position plot,not shown, shows the same results as the NDI plot.Results using the decentered model did not deviatesignificantly from the centered eye model.Results from the efficiency and NDI versus

pupil position mean that moving the illumination an-nulus into the eye will improve performance. How-ever, when the uniformity versus pupil position isexamined, we find this not necessarily true. Fig-ures 13(a) and 13(b) show the uniformity of the illu-mination pattern decreases as the focus is movedinside the eye. To find the optimal position, it is ne-cessary to determine the acceptable level of unifor-mity. Based on our results, we conclude an optimalfocal position is between the pupil and 1mm insidethe pupil. For practical purposes it should also be

noted that this particular parameter is adjusted inthe clinic and most likely varies between patientssince it is highly dependent on shapes of the variousparts of the eye.

4. Conclusion

Analysis of our results can be used to derive generalprinciples useful for implementing the design of thefundus camera. Examination of the Strehl ratio andnormalized detector irradiance versus imaging pupildiameter demonstrate the need to limit the imagingpupil diameter to 2mm or less. This is due to the de-crease in both image quality and detector irradiance.The illumination ratio should be determined in orderto null corneal backreflections that overpower thesignal from the retina on the detector. The illumina-tion ratio of the system is controlled by reducing theaberrations induced by the objective. For this reason,it is important to consider the image quality of theobjective in image and object space. Ideally when

Fig. 10. Illumination ratio versus pupil diameter for differentWF# systems.

Fig. 11. (a) Efficiency versus pupil diameter for varying WF#s.(b) Normalized detector irradiance versus pupil diameter for vary-ing WF#s.


designing a fundus camera it is ideal to keep the il-lumination ratio as small as possible. This will in-crease efficiency and NDI. Uniform illumination ofthe retina is determined by the properties of thesource used to illuminate the retina and the relay op-tics used to image the source onto the mirror with thecentral hole. This information must be used to findthe NA of the relay optics necessary for the desireddegree of uniformity. To ensure a full coverage overthe entire FOVof the imaged retina it is important touse a source with a large angular divergence to pre-vent an annular illumination pattern shown in Fig. 6(b). Finally, it is important to consider the location ofthe focus of the objective relative to the pupil. Basedon our simulation we suggest placing the focus of theobjective at or slightly inside the pupil of the eye tothe optimize illumination parameters.

The authors would like to thank Research to Pre-vent Blindness for the support of this research and R.John Koshel for many helpful discussions regardingthis project.

References and Notes

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Fig. 12. (a) Illumination versus pupil position for aWF#1 system.(b) Normalized detector irradiance pupil position for a WF#1.

Fig. 13. Effects of moving the pupil from the objective focus onretinal illumination uniformity. (a) Plot of uniformity versus pupilposition. (b) Illumination patterns at the retina top left correspondto the objective focus 5mm behind the pupil; bottom right corre-sponds to the objective focus at the pupil. Intermediate images aretaken at 1mm intervals between 5 and 0mm behind the pupil.


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Optimal parameters for retinal illumination and imaging in fundus cameras