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- Abstract
- Introduction
- Background theory and computational models
- Kubelka–Munk method
- Inverse adding doubling method
- Inverse Monte Carlo method
- Materials and methods
- Data analysis
- Results and discussion
- References

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Lasers Med Sci. Author manuscript; available in PMC 2010 August 18.

Published in final edited form as:

Published online 2009 June 4. doi: 10.1007/s10103-009-0677-0

PMCID: PMC2923491

NIHMSID: NIHMS224938

Dhiraj K. Sardar, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX 78249-0697, USA;

Dhiraj K. Sardar: ude.astu@radrasd

The publisher's final edited version of this article is available at Lasers Med Sci

See other articles in PMC that cite the published article.

Optical properties of bovine ocular tissues were determined at laser wavelengths in the visible region. The inverse adding doubling (IAD), Kubelka–Munk (KM), and inverse Monte Carlo (IMC) methods were applied to the measured values of the total diffuse transmission, total diffuse reflection, and collimated transmission to determine the optical absorption and scattering coefficients of the bovine cornea, lens and retina at 457.9 nm, 488 nm, and 514.5 nm laser lines from an argon ion laser. The optical properties obtained from these three methods were compared, and their validity is discussed.

In recent years there has been considerable interest in the accurate measurement of the optical properties of ocular tissues and, in particular, scattering and absorption coefficients. These are fundamental optical properties of biological tissues and can be used for the diagnosis of various diseases. Since the application of medical lasers in ocular diseases has steadily increased over the past several years, it is critical that we have a clear understanding of the fundamental optical properties of ocular tissues. The optical properties may, indeed, influence the distribution and propagation of light in a tissue medium. Unfortunately, a systematic study of the optical properties of ocular tissues is lacking. Therefore, we present in this article an in-depth characterization of the optical properties of bovine cornea, lens, and retina.

A number of researchers have described the optical properties of ocular tissues [1–5] from various animals such as cattle and pigs. Furthermore, there have been studies contrasting different models to track light distribution in particular tissues [6–8]. However, to the best of our knowledge, there has never been a study of bovine ocular tissues comparing three models: (a) inverse adding doubling (IAD), (b) inverse Monte Carlo (IMC), and (c) Kubelka–Munk (KM). In concurrence with the three models we were able to provide a more accurate estimate of the optical properties, using the MC model. We employed two integrating spheres to measure the diffuse reflectance, diffuse transmittance, and collimated transmittance, for the cornea, lens, and retina of bovine eyes, at 457.9 nm, 488 nm and 514.5 nm lines from an argon ion laser. These values were subsequently applied to these models to determine scattering and absorption coefficients of bovine corneal, lens and retinal tissues at three visible wavelengths of laser light.

The quantitative distribution of light intensity in biological media can be obtained from the radiative transport equation [9].

$$\frac{\mathit{\text{dI}}(r,s)}{\mathit{\text{ds}}}=-({\mu}_{a}+{\mu}_{s})I(r,s)+\frac{{\mu}_{s}}{4\pi}\underset{4\pi}{\int}p(s,{s}^{\prime})I(r,{s}^{\prime})d{\Omega}^{\prime}$$

(1)

where *I*(** r,s**) is the intensity per unit solid angle at the target location

The form of the phase function *p*(**s,s′**) is usually not known for applications, especially for biological media. The Henyey–Greenstein phase function provides a good approximation for turbid media:

$$p(\nu )=\frac{1}{4\pi}\frac{1-{g}^{2}}{{(1+{g}^{2}-2g\nu )}^{3/2}}$$

(2)

where *ν* = cos(θ), and θ is the angle between ** s** and

$$g=\frac{{\int}_{4\pi}p(\nu )\mathit{\text{vd}}{\Omega}^{\prime}}{{\int}_{4\pi}p(\nu )d{\Omega}^{\prime}}$$

(3)

The scattering anisotropy coefficient can also be obtained as the average cosine of the scattering angle [11]. The value of g ranges from −1 for complete backward scattering to +1 for complete forward scattering. The anisotropy value of 0 indicates isotropic scattering. The phase function is normalized so its integral over all space is unity.

In order to solve the transport equation (1), we require the values of *μ _{a}, μ_{s}*, and

The one-dimensional, two-flux, KM model [12] has been widely used to determine both the absorption and scattering coefficients of biological media [13–18], provided the scattering is significantly dominant over the absorption. This model provides rather simple mathematical expressions for determining the optical parameters from the measured values of diffuse reflectance and transmission. In the past, researchers have applied the diffusion approximation to the transport equation to study biological media [15, 16]. Most notably, following the KM model and diffusion approximation, an excellent experimental method has been described by Van Gemert et al. for determining the absorption and scattering coefficients.

Even though an analytical solution to Eq. (1) is not available, an elaborate numerical solution is possible using the Monte Carlo (MC) simulation technique [1, 19, 20]. Furthermore, an important numerical approach known as the IAD [10] method has been employed to solve the radiative transport equation [9]. Both the IAD method and MC simulation technique have provided more accurate estimates of optical properties (*μ _{a}, μ_{s}, g*) for biological tissues than any other models previously used. Since the details are available in the literature, only a synopsis of the IAD method is provided here. Two dimensionless quantities used in the entire process of IAD are the albedo (

$$a={\mu}_{s}/({\mu}_{s}+{\mu}_{a})$$

(4)

and

$$\tau =t({\mu}_{s}+{\mu}_{a})$$

(5)

where *t* is the physical thickness of the sample entered into the program in millimeters. The measured values of the total diffuse reflectance (*R _{d}*), total diffuse transmittance (

The MC method has been used to describe a variety of phenomena that require simulation of random processes. In the case of turbid media, the inhomogeneities and varying refractive indices may be modeled by using this method. When an electromagnetic field is applied to a tissue medium, it responds to the field. As the photons travel through the tissue medium, they may be scattered or absorbed. If a large number of photons is used, these events may be tracked and outcomes tabulated in accordance with probability density distributions. The specific inputs required for the MC method will be described in detail.

The inverse problem is termed the IMC method. In this scheme, the *R _{d}* and

In this article, we describe the scattering and absorption coefficients of the cornea, lens, and retina of bovine ocular tissues at 457.9 nm, 488 nm, and 514.5 nm, and compare the values obtained using different models. Finally, the validity of these methods as applied to our experiment is discussed with the results.

Samples of bovine ocular tissues were provided by the local beef packer plants. A pair of eyes was enucleated freshly and transported in ice (within 1 h) to the research laboratory. Immediately upon their arrival at the research laboratory, the fresh (not frozen) whole eyes were dissected on ice with phosphate-buffered saline (PBS) solution to separate and remove the desired ocular tissues for optical measurement. Each eye was carefully dissected to allow access to the inner structures of the eye (e.g., vitreous humor). The eye was cut and separated into two hemispheres: (1) an anterior segment containing the cornea, and (2) the posterior cup containing the retina and the optic nerve. The cornea, lens and retina were dissected and studied separately. The retina was dissected from the posterior eye cup last. Tissue samples were mounted between glass slides, and spacers were used to ensure the samples were not distorted due to excessive compression. Individual sample thicknesses were measured. A small amount of vacuum grease was applied to the edges of the glass slides to preserve moisture of the tissue samples. The data were collected at room temperature within 2 h of sample preparation.

The total diffuse reflectance (*R _{d}*), total diffuse transmittance (

The schematic of the experimental setup for measuring the total diffuse reflectance and total diffuse transmittance is shown in Fig. 1. The experimental setup was similar to that used by previous authors [21]. The intensity of each laser beam was reduced by neutral density filters to prevent oversaturation of the photomultiplier tube (PMT). The laser beam was directed into the entrance port, A, of integrating sphere 1 (Oriel 70674), whose exit port was coupled with the entrance port of integrating sphere 2. The sample was mounted at the coupling port C. The exit port B of integrating sphere 2 was covered with a cap with a reflective surface identical to that of the integrating spheres. The diameter of each sphere was 6 in., and each port had a diameter of 1.5 in. Light leaving the sample was reflected multiple times from the inner surfaces of the spheres before reaching the PMTs. The inner surfaces of the spheres were coated with a layer of barium sulfate. This coating ensured a highly reflective Lambertian surface.

Schematic for the diffuse reflection and transmission measurements of bovine ocular tissues. DM=Digital multimeter, PS=Power source, PMT=Photomultiplier tube, ND=Neutral density filter, Arrows indicate laser beam path

Reflecting baffles within the spheres shielded the PMTs from the direct light from the sample. Port A was equipped with a variable aperture so that the beam diameter could be properly controlled. The reflected and transmitted light intensities were detected by two identical PMTs (Newport model 77348). These detectors were attached to the two measuring ports of integrating spheres 1 and 2. The PMTs were powered by a common high voltage power supply (Spectra Physics model 70705). The high voltage was kept at 400 V for all measurements. The signals from the PMTs were measured by two identical Fluke digital multimeters (model 77 series II). The measured light intensities were then utilized to determine the total diffuse reflectance (*R _{d}*) and total diffuse transmittance (

$${R}_{d}=\frac{{X}_{r}-Y}{{Z}_{r}-Y}$$

(6)

and

$${T}_{d}=\frac{{X}_{t}-Y}{{Z}_{t}-Y}$$

(7)

where *X _{r}* is the reflected intensity detected by PMT-1 with the sample at C,

The unscattered collimated transmittance (*T _{c}*) was measured to determine the total attenuation coefficient. We measured the collimated laser beam intensities by placing an integrating sphere approximately 2 m behind the sample so that the photons scattered off the sample would not be able to enter the aperture of approximately 3 mm in diameter at the entrance port of the sphere. The sample was aligned at a right angle to the incident beam. The

$${T}_{c}=\frac{{X}_{c}}{{Z}_{c}}$$

(8)

where *X _{c}* is the collimated light intensity detected by a PMT (Newport model 77348) attached to the measuring port C of the integrating sphere and

Additional details on the experimental design can be found in Sardar et al. [22].

The KM coefficients, *K* and *S*, can be expressed in terms of *μ _{a}* and

$$K=2{\mu}_{a}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}S=\frac{3}{4}(1-g){\mu}_{s}-\frac{1}{40}{\mu}_{a},$$

(9)

where *g* is the scattering anisotropy coefficient. These coefficients can be expressed in terms of sample thickness (*t*), diffuse reflectance (*R _{d}*), and diffuse transmittance (

$$K=S(a-1)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}S=\frac{1}{bt}\text{ln}\phantom{\rule{0.2em}{0ex}}\left[\frac{1-{R}_{d}(a-b)}{{T}_{d}}\right]$$

(10)

where

$$a=\left(\frac{1+{R}_{d}^{2}-{T}_{d}^{2}}{2{R}_{d}}\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=\sqrt{{a}^{2}-1}.$$

(11)

The collimated transmittance (*T _{c}*) can be written in terms of the absorption and scattering coefficients following Beer's law:

$$-\text{ln}\phantom{\rule{0.2em}{0ex}}[{T}_{c}]=({\mu}_{a}+{\mu}_{s})t,$$

(12)

where *t* is the sample thickness, measured in centimeters. By combining equations (9) through (11), we can solve for the values of *μ _{a}, μ_{s}*, and

In order to obtain the values of *μ _{a}* and

$$\mathit{\text{error}}=\left|\frac{{R}_{d}^{\mathit{\text{measured}}}-{R}_{d}^{\mathit{\text{calculated}}}}{{R}_{d}^{\mathit{\text{measured}}}+{10}^{-6}}\right|+\left|\frac{{T}_{d}^{\mathit{\text{measured}}}-{T}_{d}^{\mathit{\text{calculated}}}}{{T}_{d}^{\mathit{\text{measured}}}+{10}^{-6}}\right|$$

(13)

The default tolerance was set at 0.0001.

The scattering, absorption, and scattering anisotropy coefficients were obtained from a Monte Carlo (MC) simulation. The simulation involved the tracking of a large number of photons through a turbid medium, and it kept a tally of the absorption and scattering events, using a probability distribution. This was an iterative process. The values of *R _{d}*, and

$$\delta ={\left(\frac{{({R}_{d})}_{\mathit{\text{cal}}}-{R}_{d}}{{R}_{d}}\right)}^{2}+{\left(\frac{{({T}_{d})}_{\mathit{\text{cal}}}-{T}_{d}}{{T}_{d}}\right)}^{2}$$

(14)

If the difference was smaller than the error threshold as determined by the program, δ < 0.0004, the values of μ_{a}, μ_{s}, and *g* were validated.

The accuracy of values of the absorption coefficient (*μ _{a}*) and scattering coefficient (

Measurements of *R _{d}, T_{d}*, and

Wavelength-dependent absorption coefficient (*μ*_{a}) and scattering coefficient (*μ*_{s}) as determined by the Kubelka–Munk formula, IAD, and IMC, using the measured diffuse reflectance (*R*_{d}), diffuse transmittance (*T*_{d}), and collimated transmittance **...**

Wavelength-dependent absorption coefficient (μ_{a}) and scattering coefficient (*μ*_{s}) as determined by the Kubelka—Munk formula, IAD, and IMC, using the measured diffuse reflectance (*R*_{d}), diffuse transmittance (*T*_{d}), and collimated transmittance **...**

Wavelength-dependent absorption coefficient (*μ*_{a}) and scattering coefficient (*μ*_{s}) as determined by the Kubelka–Munk formula, IAD, and IMC, using the measured diffuse reflectance (*R*_{d}), diffuse transmittance (*T*_{d}), and collimated transmittance **...**

Wavelength-dependent average diffuse reflectance (*R*_{d}) and diffuse transmittance (*T*_{d}) determined by experimental and computational techniques

The measured values of *R _{d}* and

The computed scattering coefficients for all tissues and wavelengths agreed very well, within 9% difference between the computational methods, as can be seen in Tables 1–3. There was a wider degree of variation among the absorption coefficients, particularly in the IMC-computed values of *μ _{a}*, which were significantly lower than those calculated by the other methods. This was likely because the IMC algorithm only converged to a solution for smaller computational photon packets (hundreds or thousands of photons). Despite this difficulty in achieving the optical coefficients using IMC, we found that the results for

The scattering and absorption coefficients of the cornea showed some variation across the wavelength studied. When the blood supply is removed from corneal tissues, the cornea tends to absorb the aqueous humor and the transparent cornea becomes opaque. This may alter any unique variations of the coefficients at any wavelengths, but, since our data were obtained 2–3 h after the animal had been killed, the errors in the coefficients were kept at a minimum.

However, the coefficients of the lens at all wavelengths investigated were significantly lower than those of the retina. This was because the primary function of the lens is to focus the light onto the retina and any loss of light would affect the resultant image, as in cataracts and presbyopia. The retina is also more opaque than the clear biconvex lens, which also explains why the absorption and scattering coefficients were the lowest of all the tissues examined.

The scattering in the retinal tissue was found to be significantly higher than the absorption, which concurred with previous studies that reported high transmittance values for retinal tissues in the visible region of the spectrum. The low absorption coefficients could be caused by the unreplenished visual pigments within the retina that absorb the photons in the process that turns light into electrical signals. Once the visual pigments have been exhausted, there is an oversaturation of light in which the laser light cannot be absorbed and just passes through the thin tissue, causing a high scattering value. If the visual pigments were constantly replenished, then we should see a much higher absorption value, but the only way this could be possible is if a sample were to be used in vivo. The values of the attenuation coefficients of retina can also be attributed to some inadvertent cross-contamination of the retina with melanin granules from the retinal pigment epithelium (RPE) during sample preparation. The transmittance values in the visible region have been reported in previous studies on retinal tissues [3, 25]. Geerates and Berry reported that in the visible region transmittance was greater than 80% in human, rabbit, and monkey retinal tissues [25]. However, van den Berg and Spekreijse argued that the data presented by Boettner and Wolter [26] could be explained only on the basis of pure water content in the ocular tissues [3].

The scattering coefficients for each tissue in this study at all wavelengths were consistently higher than the absorption coefficients, showing that, at these wavelengths, light passes through each layer effectively. Additional studies on the spectral properties of ocular media, ranging from ultra violet (UV) through near-infrared, have been reported by other authors, which have been taken into consideration in this report [4, 5, 11, 23, 27–29]. The high transmittance and very low reflectance in the visible region reported by those authors did, in fact, correspond with our values, although there may have been some slight differences due to sample variation and preparation. For example, Hammer et al. [1] reported on the absorption and scattering coefficients of the bovine retina obtained through a similar double integrating sphere setup; our values were in general agreement with the trends and relative scale of values reported in that study. However, there was some difference between our values and those of Hammer et al. Specifically, those coefficients obtained through KM and IAD were closest to those of Hammer and colleagues, differing by less than a factor of two. Again, IMC values differed the most, which was due to the same reasons discussed previously. That study had a different approach towards the preparation of the whole retina sample, placing the excised tissue flat in a cuvette and filling the remaining volume with saline solution, as opposed to our slide technique. Also, that study assumed accepted values for tissue layer thicknesses, while we did physically measure this parameter. Because of differences in sample preparation such as this, some amount of disagreement between the optical properties reported herein and those previously reported, such as in Hammer et al., is to be expected.

The actual values of the absorption and scattering coefficients for the retinal tissues reported in this study have importance for practical applications requiring the prediction of light transport through pigmented tissue, e.g., in the design of treatment models for laser-induced thermotherapy or photodynamic therapy in the eye, where the degree of pigmentation at the target sites may vary. Variable pigmentation obviously complicates the laser dosimetry for such treatment modes, because the amount of light delivered will have to be adjusted, based on the amount of tissue pigmentation, in order to achieve some standard clinical effect [22].

The suitability of the KM theory for use in biological tissues is currently the subject of a lively discussion in the light–tissue interaction community. Although the linearity of the relationship between K and S and the true physical optical parameters was questioned by Yang and Kruse [30], their proposed revisions to the theory were evaluated theoretically and experimentally by Edström [31] and shown to yield significant errors. The available literature is inconclusive on the validity of the revised theory. As this was the case at the time this paper was written, the original KM theory, a cornerstone in radiative transport studies, was utilized for obtaining *μ _{a}* and

All of the methods used to determine the absorption and scattering coefficients in this work operate under the assumption of diffuse light transport. This is a valid and very useful approximation, which is widely used when biological materials are being studied. However, it does begin to break down as the sample thickness decreases. In the case of the retina, which is indeed quite thin, some skepticism towards the calculated optical properties is warranted when one is working under the diffuse light assumption, because the total sample thickness may only allow for one or two scattering events along the propagation axis. Despite this shortcoming of the theory, the diffuse light techniques are still some of the best and most straightforward methods available to determine properties, such as absorption and scattering coefficients, of turbid media. Indeed, comparisons of work done under this approximation with those utilizing ballistic transport models would only add to the understanding of light transport in turbid media and illuminate how the different treatments of data differ. This is an area which requires more study, however, and is beyond the scope of this paper.

This work was supported by the National Science Foundation (NSF)-sponsored Center for Biophotonics Science and Technology at the University of California (UC) Davis under cooperative agreement no. PHY 0120999. The authors would like to thank Scott Prahl (Oregon Medical Laser Center) for the use of the IAD source code, Steven L. Jacques (Oregon Medical Laser Center), and Lihong Wang (Washington University, St. Louis, MO) for the use of the source code for the Monte Carlo model. The source codes for both of these programs are available at http://omlc.ogi.edu/software/. Additionally, we acknowledge Xin-Hua Hu (East Carolina University) for the use of the Inverse Monte Carlo (IMC) code. This is available at http://bmlaser.physics.ecu.edu/. We also thank C.D. Clark for his assistance with the code for the inverse Monte Carlo model.

Dhiraj K. Sardar, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX 78249-0697, USA.

Brian G. Yust, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX 78249-0697, USA.

Frederick J. Barrera, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX 78249-0697, USA.

Lawrence C. Mimun, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX 78249-0697, USA.

Andrew T. C. Tsin, Department of Biology, University of Texas at San Antonio, San Antonio, TX, USA.

1. Hammer M, Roggan A, Schweitzer D, Muller G. Optical properties of ocular tissues—an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation. Phys Med Biol. 1995;40:963–978. doi: 10.1088/0031-9155/40/6/001. [PubMed] [Cross Ref]

2. Sardar DK, Swanland GY, Yow RY, Thomas RJ, Tsin ATC. Optical properties of ocular tissues in the near infrared region. Lasers Med Sci. 2007;22:46–52. doi: 10.1007/s10103-006-0421-y. [PubMed] [Cross Ref]

3. van den Berg TJ, Spekreijse H. Near infrared light absorption in the human eye media. Vision Res. 1997;37:249–253. doi: 10.1016/S0042-6989(96)00120-4. [PubMed] [Cross Ref]

4. Vos JJ, Munnik AA, Boogaard J. Absolute spectral reflectance of the fundus oculi. J Opt Soc Am. 1965;55:573–574. doi: 10.1364/JOSA.55.000573. [Cross Ref]

5. Maher EF. Transmission and absorption coefficients for ocular media of the rhesus monkey. USAF School of Aerospace Med; Brooks AF Base, TX: 1978. Report SAM-TR-78-32.

6. Bashkatov AN, Genina EA, Kochubey VI, Gavrilova AA, Kapralov SV, Grishaev VA, Tuchin VV. Optical properties of human stomach mucosa in the spectral range from 400 to 2000 nm: prognosis for gastroenterology. Med Laser Appl. 2007;22:95–104. doi: 10.1016/j.mla.2007.07.003. [Cross Ref]

7. Gebhart SC, Lin WC, Mahadevan-Jansen A. In vitro determination of normal and neoplastic human brain tissue optical properties using inverse adding-doubling. Phys Med Biol. 2006;51:2011–2027. doi: 10.1088/0031-9155/51/8/004. [PubMed] [Cross Ref]

8. Yaroslavsky AN, Schulze PC, Yaroslavsky IV, Schober R, Ulrich F, Schwarzmaier HJ. Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range. Phys Med Biol. 2002;47:2059–2073. doi: 10.1088/0031-9155/47/12/305. [PubMed] [Cross Ref]

9. Chandrasekhar S. Radiative transfer. Dover; New York: 1960.

10. Prahl SA, Van Gemert MJC, Welch AJ. Determining the optical properties of turbid media by using the adding-doubling method. Appl Opt. 1993;32:559–568. doi: 10.1364/AO.32.000559. [PubMed] [Cross Ref]

11. Sardar DK, Yow RM, Tsin ATC, Sardar R. Optical scattering, absorption, and polarization of healthy and neovascularized human retinal tissues. J Biomed Opt. 2005;10:515011–515018. doi: 10.1117/1.2065867. [PubMed] [Cross Ref]

12. Kubelka P. New contributions for the optics of intensely light-scattering materials. J Opt Soc Am. 1948;38:448–457. doi: 10.1364/JOSA.38.000448. [PubMed] [Cross Ref]

13. Wan S, Anderson RR, Parish JA. Analytical modeling for the optical properties of the skin with in vitro and in vivo applications. Photochem Photobiol. 1981;34:493–499. [PubMed]

14. Ertefai S, Profio AE. Spectral transmittance and contrast in breast diaphanography. Med Phys. 1985;12:393–400. doi: 10.1118/1.595701. [PubMed] [Cross Ref]

15. Reynolds L, Johnson CC, Ishimaru A. Diffuse reflectance from a finite blood medium: application to the modeling of fiberoptic catheters. Appl Opt. 1978;15:2059–2067. doi: 10.1364/AO.15.002059. [PubMed] [Cross Ref]

16. Groenhuis RJA, Ferwerda HA, Ten Bosch JJ. Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory. Appl Opt. 1983;22:2456–2462. [PubMed]

17. Van Gemert MJC, Welch AJ, Star WM, Motamedi M. Tissue optics for a slab geometry in diffusion approximation. Lasers Med Sci. 1987;2:295–302. doi: 10.1007/BF02594174. [Cross Ref]

18. Kottler F. Turbid media with plane-parallel surfaces. J Opt Soc Am. 1960;50:483–490. doi: 10.1364/JOSA.50.000483. [Cross Ref]

19. Hourdakis J, Perris A. A Monte Carlo estimation of tissue optical properties for use in laser dosimetry. Phys Med Biol. 1995;40:351–364. doi: 10.1088/0031-9155/40/3/002. [PubMed] [Cross Ref]

20. Jacques SL, Wang L. Monte Carlo modeling of light transport in tissues. In: Welch AJ, van Gemert MJC, editors. Optical-thermal response of laser-irradiated tissue. Plenum; New York: 1995.

21. Beek JF, Staveren HJ, Posthumus P, Sternborg HJCM, van Gemert MJC. In vitro double-integrating-sphere optical properties of tissue between 630 and 1064 nm. Phys Med Biol. 1997;42:2255–2261. doi: 10.1088/0031-9155/42/11/017. [PubMed] [Cross Ref]

22. Sardar DK, Mayo ML, Glickman RD. Optical characterization of melanin. J Biomed Opt. 2001;6:404–411. doi: 10.1117/1.1411978. [PubMed] [Cross Ref]

23. Fowler RW, McLeod DS, Pitts SM. The effect of blood on ocular fundus reflectance and determination of some optical properties of retinal blood vessels. Invest Ophthalmol Vis Sci. 1978;17:562–565. [PubMed]

24. Prahl SA, Keijzer M, Jacques SL, Welch AJ. A Monte Carlo model of light propagation in tissue. SPIE Inst Adv Opt Technol Ser. 1989;5:102–111.

25. Geerates WJ, Berry ER. Ocular spectral characteristics as related to hazards from lasers and other light sources. Am J Ophthalmol. 1968;66:15–20. [PubMed]

26. Boettner EA, Wolter JR. Transmission of the ocular media. Invest Ophthalmol. 1962;1:776–783.

27. Delori FC, Pflibsen KP. Spectral reflectance of the human ocular fundus. Appl Opt. 1989;28:1061–1077. doi: 10.1364/AO.28.001061. [PubMed] [Cross Ref]

28. Knighton RW, Jacobson SG, Kemp CM. The spectral reflectance of the nerve fiber layer of the macaque retina. Invest Ophthalmol Vis Sci. 1989;30:2393–2402. [PubMed]

29. Sardar DK, Salinas FS, Perez JC, Tsin ATC. Optical characterization of bovine retinal tissues. J Biomed Opt. 2004;9:624–631. doi: 10.1117/1.1688813. [PubMed] [Cross Ref]

30. Yang L, Kruse B. Revised Kubelka-Munk theory. I. Theory and application. J Opt Soc Am. 2004;21:1933–1941. [PubMed]

31. Edström P. Examination of the revised Kubelka-Munk theory: considerations of modeling strategies. J Opt Soc Am. 2007;24:548–556. [PubMed]

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