In Vitro Multispectral Diffuse Reflectance Measurements of the Porcine Fundus

Abstract

purpose. To quantify the reflectance of the swine fundus as a function of illumination angle and wavelength using a novel technique of intravitreal illumination.

methods. Enucleated swine eyes were illuminated with a scanning monochromator coupled to a fiber-optic probe placed in the vitreous at several locations. Intravitreal illumination was used to reduce the effects of extraneous reflections and scatter from the anterior structures of the eye, including glints from the internal limiting membrane and blood vessels. Intravitreal illumination provided different light paths and additional information to apply to retinal reflectance modeling. A 25-mm² region of the illuminated fundus was imaged while the angle of illumination was varied over a maximum range of 22°. Multispectral images from areas free of large blood vessels were acquired. The diffusely reflected intensity was integrated over the pupil with a solid angle of 0.028 steradians. The spectral reflectance function was calculated for multiple illumination angles.

results. Multispectral fundus image sets were obtained for two enucleated swine eyes by using intravitreal illumination. The fundus spectral reflectance function showed decreasing reflectance with increasing illumination angle, rapid changes in the 430- to 480-nm range, and a fairly consistent reflectance decrease for 480 to 700 nm.

conclusions. Variations in fundus spectral reflectance with change in the illumination angle were found to deviate from Lambertian behavior, varying from Lambertian by 5% across the spectrum in one sample and 20% in a second sample. Intravitreal illumination resulted in markedly decreased extraneous reflections.

Optical methods for diagnosing and treating ocular disease rely on a fundamental understanding of the interaction between light and ocular tissue. Data obtained from noninvasive optical techniques such as fundus photography, optical coherence tomography, and laser polarimetry may benefit from improved characterization of the reflectance and scattering properties of the fundus. 

Several studies of the optical properties of the fundus have been performed. ^{1 2 3 4 5 6 7 8 9} Van Norren and Tiemeijer ² measured reflectance in the foveal and peripheral fundus and mathematically modeled the fundus. Their reflectance model used two reflective and four absorbing layers to describe the fundus. Delori and Pflibsen ³ performed in vivo spectral reflectance measurements in human subjects with a wide range of fundus pigmentation and applied the model of van Norren and Tiemeijer ² to the resultant data. Delori and Pflibsen ³ also applied the model of Kubelak and Munk ¹⁰ to their data and achieved a better fit to measured spectra. Kubelak and Munk introduced a two-constant theory for the description of the reflectance properties of a material: the absorption and the scattering coefficients. The adaptation of this model by Delori and Pflibsen ³ treats the choroid as a diffuse absorbing scatterer backed by a reflecting sclera. Hammer and Schweitzer ⁴ performed high-spectral-resolution studies with imaging spectroscopy at high spatial resolutions along a bar-shaped field in the retina. 

The earlier works in fundus reflectometry used transcorneal illumination. The illuminating light entered the eye through the cornea, passing through the anterior chamber, lens, and vitreous to illuminate the fundus. ^{1 2 3 4 5 6 7 8 9} Transcorneal fundus reflectance measurements are impeded by extraneous reflections, or glints, from the cornea, retinal vessels, and the fundus, as well as backscattering from the anterior chamber, lens, and vitreous. The illumination and the measurement directions are nearly the same for transcorneal illumination. In the previous studies, the fundus was generally assumed to be a perfectly diffuse or Lambertian structure. A primary objective of this research was to assess the validity of this assumption. 

We introduce the novel technique of intravitreal illumination for the measurement of fundus reflectance in enucleated swine eyes. The use of intravitreal illumination allows for variation of illumination angle, eliminates the corneal and retinal vessel glints, and reduces the errors in quantitative spectroradiometry arising from multiple passes through the anterior ocular structures. Our technique results in light reflected from the fundus undergoing a single pass through the anterior chamber. The illumination direction is varied and measurements of fundus reflectance are made from a fixed viewing angle. Reflectance measurements for various illumination angles are compared with each other and with the predictions of the Lambertian model. 

Methods

All experiments adhered to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research, as well as to local government regulations for the experimental use of animals. 

Eye Preparation

Two enucleated American Yorkshire swine eyes were obtained from the University of Arizona Meat Sciences Laboratory. The eye preparation was identical for both specimens. Experiments were performed 6 to 12 hours after the death of the animals. A 4-mm infusion cannula was placed through the pars plana and sutured in place. The infusion cannula was attached to a physiologic saline solution (BSS; Alcon, Fort Worth, TX) gravity-feeding system to maintain intraocular pressure at levels comparable to in vivo conditions. A contact vitrectomy lens (F36202.08; Bausch & Lomb, Rochester, NY) was placed onto the cornea with an index matching (index of refraction: n _d = 1.337) viscoelastic coupling agent (Goniosol; Bausch & Lomb). The plane formed by the anterior surface of the contact lens was made parallel to the iris plane by suturing the contact lens ring concentrically with the iris. Different illumination angles were accomplished by accessing multiple sclerotomies created along an arc line. Figure 1shows the mounted eye. 

Imaging System

Light from a scanning monochromator (Spectral Luminator; Oriel, Irvine, CA) was coupled into a fiber-optic intraocular illuminator (Alcon Laboratories) which was inserted into the vitreous to illuminate the retina. The monochromator was operated at a spectral resolution of 10 nm, with an approximately Gaussian power distribution within the spectral band. The output power was approximately 150 μW per wavelength band. The measurement area of the fundus was imaged with a 3.3× macro zoom lens (model 56-524; Edmund Scientific, Barrington, NJ) onto the charge-coupled device (CCD) camera, a 12-bit high-speed digital monochrome camera (Ca-D1; Dalsa Corp., Waterloo, Ontario, Canada). Figure 2illustrates the illumination system. 

Data Collection

The fiber-optic intraocular illuminator was placed in the first sclerotomy, the closest one to the pupil. This sclerotomy provided the smallest angle of illumination (θ) between the fiber-optic intraocular illuminator and the optic axis for the target area. The illuminated fundus was focused on the camera. A suitable vessel-free target area was identified by using the retinal vessels as landmarks. The depth of the fiber-optic intraocular illuminator was adjusted to maximize the dynamic range of the camera (i.e., the brightest pixel in the image is nearly saturated). An image was acquired at each of the 36 wavelengths listed in Table 1 . The wavelengths were referenced with respect to the peak of the in-band spectral power distribution. The reflected light was collected over a solid angle of 0.028 steradians, the solid angle subtended by the eye’s pupil, which was the aperture stop of this system. 

To determine the angle of the fiber-optic illuminator, an image of the experimental apparatus was taken with a digital camera (Cool Pix 4300; Nikon Corp., Tokyo, Japan) aligned orthogonally to the plane defined by the sclerotomies. Orthogonality was insured by using an optical table equipped with a railed carrier system. The digital image was analyzed to determine the angle of the fiber-optic illuminator in the eye. We estimated the systematic error in angular measurement at ±2°. This systematic error is indicative of the error in the absolute value of the measured angles, but the relative differences between measured angles are affected only slightly. 

The fiber-optic illuminator was successively inserted into each sclerotomy and illuminated the target area of the fundus at increasing angles. The multispectral image-acquisition process was repeated for each sclerotomy. The appropriate depths of the fiber-optic illuminator for the remaining sclerotomies were determined based on illumination geometry, so that the end of the illuminator was kept at a constant distance from the fundus. The depth of the fiber-optic illuminator was verified by measuring the length of the fiber-optic illuminator exterior to the sclera. The only variable between spectral image sets was the angle of illumination in the plane of the sclerotomies. For all sclerotomies, the brightest portion of the illuminating light beam was placed on the target area of the fundus by using retinal blood vessels as landmarks. Four angles of illumination were used for the first enucleated swine eye and three for the second eye. Table 2lists the angles of illumination used for the two eyes. 

A calibration image set was acquired on completion of data collection. A lined integrating sphere (Spectralon; Labsphere, North Sutton, NH) was illuminated by the fiber-optic intraocular illuminator, and the exit pupil of the sphere was imaged by the camera system. This calibration set was used to correct for the spectral intensity variation in the illuminating source and the spectral response of the CCD. 

Data Analysis

The software package (Mathematica; Wolfram Research, Inc., Champaign, IL) was used to perform image calibration, subtraction, averaging, and plotting. Reflected spectra were constructed for each angle of illumination for each eye. The reflectance spectra were averaged over 25 pixels in the target area and were normalized to the value obtained in the brightest image for each eye. The brightest image corresponded to the smallest illumination angle for each eye. 

Results

Figure 3shows the 520-nm images taken at different illumination angles in the first (Fig. 3A)and second (Fig. 3B)eye, respectively. The top row contains 520-nm images that were obtained at illumination angles of 26°, 33°, 37°, and 48°, and the bottom row contains 520-nm images taken at illumination angles of 34°, 37°, and 48°. Note the absence of glints along the retinal vessels. The black squares indicate the 5 × 5-pixel area over which pixel intensities were averaged for the determination of the reflectance spectra. 

Figures 4 and 5show the normalized fundus reflectance spectra as a function of illumination angle in the two eyes. The curves in Figure 4were normalized to the largest intensity value in eye 1 taken at 26°. The curves in Figure 5(eye 2) were similarly normalized. The reflectance monotonically decreased with increasing illumination angle. 

Figures 6 and 7show the normalized reflectance as a function of illumination angle and wavelength, with a subset of wavelengths shown. Each vertical collection of symbols represents the spectra for a particular illumination angle. The decrease in reflectance with increasing illumination angle is apparent. 

Several trends are evident in Figures 4 5 6 and 7 . Fundus reflectance decreased with increasing illumination angle. Fundus reflectance was lowest in the blue (430 nm) and increased sharply between 430 and 480 nm. A local minimum occurred at approximately 555 nm. Reflectance generally increased at wavelengths longer than 555 nm, with a reflectance maximum at 660 nm. The smallest variation of reflected intensity with illumination angle occurred in the blue. At wavelengths longer than 450 nm, the variation of reflectance with illumination angle increased. 

Discussion

The results indicate that the spectral reflectance of the swine fundus deviates from the Lambertian model that is customarily used to model fundus reflectance. A Lambertian reflector has three defining reflectance properties: (1) the angular distribution of reflected flux is independent of illumination angle; (2) for a given illumination angle, reflected intensity is independent of viewing angle; and (3) the total reflected intensity decreases according to Lambert’s law (also called the cosine law), ¹¹  

\[I_{\mathrm{diffuse}}{=}I_{0}\ {\cdot}\ \mathrm{cos}({\theta})\]

where I _diffuse is the total reflected intensity, I ₀ is the incident intensity, and θ is the angle between the surface normal and the incident light, as illustrated in Figure 8 . 

Optical density is a parameter for describing absorbance, which is defined as OD = log(1/T) where T is the transmittance associated with a medium. 

This experiment tested only the third Lambertian property. The reflectance decrease predicted by Lambert’s law was compared with the measured reflectance decrease. The measured reflectance from the smallest illumination angle (26°) was used to generate the three Lambertian reflectance curves for the remaining illumination angles. The third property of the Lambertian model specifically states that the total reflected intensity varies with the cosine of the respective illumination angles, so the measurements in eye 1 should vary as the ratio cos(27°):cos(33°):cos(37°):cos(48°). The percent difference between this prediction and the measurement is plotted in Figure 9A . For a Lambertian reflector these percent errors would be zero. Figure 9Bis the corresponding plot for eye 2. 

The results of this research indicate that the fundus is not a perfectly diffuse reflector, because the measured intensity at larger illumination angles is less than that predicted by Lambert’s law. In addition, the variation from Lambertian is spectrally dependent. The characteristic spectra of fundus pigments and retinal blood may have a significant dependence on illumination angle. These preliminary findings imply that an accurate model of fundus reflectance requires consideration of illumination angle. Further studies are necessary to determine the analytical form of this term. 

Conclusions

Fundus spectral reflectance data obtained using intraocular illumination is presented. Intravitreal illumination allows for variation in illumination angle and avoids problems with extraneous reflections (i.e., glints) from the anterior region of the eye and from the retinal vasculature. The invasive nature of this method excludes it from use in clinical settings. The usefulness of this technique as a research tool in enucleated eyes and animal models, however, is clear because of the new capabilities it provides for quantifying fundus reflectance. 

The presented results are from two enucleated swine eyes, and only one location on each fundus was measured. Spectral data indicate that fundus reflectance deviates from that of a perfectly Lambertian scatter: This difference was measured at 5% in one sample and 20% in the second sample. Some variation in fundus reflectance is expected due to the directional reflectance of the retinal never fiber layer (RNFL). ¹² In future work, we intend to employ our technique of intravitreal illumination to study the directional reflectance behavior of the RNLF. A further source of error is found in the systematic error we encountered in the measurement of the angle of illumination. This error lowers the accuracy of the absolute value of the measured illumination angle, but affects the relative differences between each measured angle only slightly. Improvement on the technique for measuring the angle of illumination would improve the accuracy of these measurements. Differences from animal to animal and differences from swine to human are to be expected. These in vitro results are likely to differ from in vivo measurements. Similar studies in live animal experiments are planned to elucidate these differences. 

Swine eyes were selected for their anatomic similarities to the human eye. ¹³ Reflectance of the human fundus varies significantly from the fovea to the periphery. Thus, reflectance measurements performed on a human fundus require knowledge of the proximity of the measurement location to the fovea for proper interpretation. Swine have no fovea, and so sensitivity to target position is reduced. To our knowledge, no studies have been published in which the reflectance properties of the human fundus were compared with those of the peripheral swine fundus. The applicability of the results of these swine eye studies to human fovea studies is unknown. 

 Submitted for publication August 24, 2004; revised November 17, 2004 and January 7 and 27 and February 16, 2005; accepted February 18, 2005.

 Disclosure: D.A. Salyer, None; K. Twietmeyer, None; N. Beaudry, None; S. Basavanthappa, None; R.I. Park, None; R. Chipman, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

An enucleated swine eye is sutured to a custom eye mount. The infusion cannula is inserted into the eye through the pars plana and the sutured contact lens is placed on the cornea. Posterior to the limbus are two columns of scleral plugs marking the location of the sclerotomies.

Figure 2.

 

Diagram of imaging system and illumination configuration. An example of two illumination angles is provided. The fiber-optic illuminator was kept a constant distance from the target area.

Table 1.

 

Illumination Wavelengths for Multispectral Image Sets

Wavelength Range (nm)	Spectral Step Size (nm)
430–460	10
460–540	20
543–600	3
605–615	5
620–700	10

Table 2.

 

Illumination Angles Used to Illuminate the Fundus for the Enucleated Eye Samples

Sample	Illumination Angles (deg)
Eye 1	26	33	37	48
Eye 2	34	37	48	—

Figure 3.

 

Shown are 520-nm images of (A) eye 1 and (B) eye 2 taken at a set of illumination angles. The values within the black square were averaged for the spectral reflectance calculation.

Figure 4.

 

Normalized reflectance versus wavelength in eye 1 at illumination angles 26°, 33°, 37°, and 48°. There was a large change from 430 to 480 nm (20% and 30% decreases, respectively) over the 22° illumination angle variation. From 480 to 700 nm, the change in reflectance decreased by an average of 31.20% ± 0.3%.

Figure 5.

 

Normalized reflectance versus wavelength in eye 2 for illumination angles 34°, 37°, and 48°. There was again a large change from 430 to 480 nm (from a 39% decrease at 430 nm to a 30% decrease at 480 nm) over the 14° degree illumination angle range for eye 2. From 480 to 700 nm, the reflectance decreased by a average of 31.20% ± 1.8%.

Figure 6.

 

Normalized reflected intensity versus illumination angle in eye 1.

Figure 7.

 

Normalized reflected intensity versus illumination angle in eye 2.

Figure 8.

 

In the model of perfectly diffuse reflectors called Lambertian surfaces, the diffusely reflected light flux decreased along with the cosine of the illumination angle, indicated by decreasing arrow length from left to right. The diffusely reflected light flux is independent of the viewing angle.

Figure 9.

 

(A) The ratio of the measured decrease in fundus reflectance to the decrease predicted by Lambert’s law in eye 1. The diffuse reflectance of the fundus decreased faster than Lambert’s law predicts as the angle of illumination increased. (B) Percentage difference between the measured decrease in fundus reflectance and that predicted by Lambert’s law for a perfectly diffuse reflector in eye 2.