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Use of the waveguide parameter V to determine the difference in the index of refraction between the rat rod outer segment and the interstitial matrix.
The difference in the index of refraction between the receptor outer segment and the interstitial matrix has been determined to be 0.06 by making use of the waveguide properties of rat rod photoreceptors. This was done by determining the cutoff wavelength for the transition between the bilobe or annulus modal patterns and the single-lobe H E 11 modal pattern, and by measuring the diameter of the transmitting cell. These measurements were made on bleached receptors. Enoch, Scandrett, and Tobey had previously shown that bleaching only slightly alters the outer-segment index of refraction and diameter in the frog. Assuming interspecies transfer, and using Sidman's prior estimate of bleached rat rod outer-segment index of refraction, then the index of refraction of the interstitial matrix of the albino rat is estimated to be 1.3476. This estimate was made using two different media in contact with the retinal preparation, a miscible mountant tissue culture medium believed to be compatible with the rat retina, and an encapsulating nonmiscible silicone oil which allows only ocular media from the same eye in contact with the outer segments.
Crystalline lens dispersion.
The spectral dispersions of rabbit, rat, pigeon, and human crystalline lens material have been measured with a Pulfrich refractometer. The refractive indices all increase rapidly at the violet end of the spectrum so tat the chromatic aberrations of the eyes of these species cannot be derived adequately from Cornu's formula, as had previously been assumed.
Optics of the harbor porpoise eye in water.
A two-dimensional ray-tracing model for the harbor porpoise eye is constructed from new measurements, mainly on two enucleated eyes, and from data found in the literature. Model calculations show that the crystalline lens has too much refractive power to focus light on the retina. The cornea has a high refractive index and acts as a diverging lens of considerable refractive power. The cornea corrects the eye to near emmetropia for axial and temporal (caudal) directions of view. The eye is approximately 5-D myopic for nasal (frontal) directions of view. The iris serves a dual role as a stop: the iris determines the shapes of bundles of light that enter the lens and the iris blocks light that leaves the lens anterior to its equator.
Surface refractive index of the eye lens determined with an optic fiber sensor.
The use of a fiber-optic sensor for measurement of the refractive index on the surface of eye lenses is described. The technique makes use of the fact that the amount of light reflected at the interface of two media (Fresnel reflectance) depends on the refractive-index difference between them. The sample is probed with a single-mode fiber, and the refractive index is calculated from the proportion of light reflected at the probe-sample interface.
Graded-index model of a fish double cone exhibits differential polarization sensitivity.
The close apposition of the inner segments of the two cones that combine to form a double cone causes the pair of cone inner segments to guide light as a unitary structure whose transverse sections are roughly elliptical. Electron micrographs of the photoreceptors of a green sunfish (Lepomis cyanellus) retina provide evidence that the refractive index in the ellipsoid region of the inner segments of the double cones is higher in the center than at the perimeter. The hypothesis that the shape and refractive-index gradient could confer differential polarization sensitivity on double cones is examined with a two-dimensional waveguide model of a double-cone inner segment. The model has a dielectric constant that varies parabolically along the narrowest (x) dimension, leading to the index profile: n(x) = nmax[1-(x/x0)2]1/2, where nmax is the peak value of the index and x0 is a parameter specifying the rate at which the index decreases with increasing magnitude of x. A quantity, the polarization contrast, is introduced as a measure of the differential polarization sensitivity of adjacent receptors in the square mosaic of double cones in the sunfish retina. Polarization contrast is proportional to the relative difference in power absorbed by two double cones oriented with their shortest axes orthogonal to each other and stimulated by a field of uniform polarization. Polarization contrast is computed as a function of wavelength for appropriate values of nmax and x0. For normally incident light polarized parallel to one of the two axes of the double cones' cross sections, the polarization contrast is generally between 1% and 5% for wavelengths ranging from 550 to 750 nm. Over most of those wavelengths the polarization contrast of the graded-index-model double cone is approximately five times as large as that of a homogeneous-slab model of the same size and average refractive index. Additional benefits of a graded index, optical isolation of adjacent photoreceptors and antireflection at the photoreceptor entrance, are also discussed.
Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium.
Improved solutions of the diffusion equation for time-resolved and steady-state spatially resolved reflectance are investigated for the determination of the optical coefficients of semi-infinite turbid media such as tissue. These solutions are derived for different boundary conditions at the turbid-medium-air interface and are compared with Monte Carlo simulations. Relative reflectance data are fitted in the time domain, whereas relative and absolute reflectance are investigated in the steady-state domain. It is shown that the error in deriving the optical coefficients is, especially for steady-state spatially resolved reflectance, considerably smaller for the solutions under study than for the commonly used solutions. Analysis of experimental measurements of absolute steady-state spatially resolved reflectance confirms these results.
Radiative transfer implies a modified reciprocity relation.
The usual reciprocity relations of radiative transfer do not hold two points located in regions of different index of refraction. Modified reciprocity relations that involve the relative index are derived. The result has computational as well as theoretical consequences.
Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface.
A novel interferometer based on a conventional phase-shifting design is presented. This interferometer is capable of measuring both the real and the imaginary parts of the complex index of refraction and the surface profile of a test surface, n, k, and h, respectively. Maximum-likelihood-estimation theory is shown to be a viable means of extracting the three parameters of interest from the measured data. A Monte Carlo simulation showed limited success in estimating the complex index parameters. The results exhibited bias or deviation from the true values for the system configuration examined. The estimate on the surface profile showed excellent agreement with the true value, although the error in the estimate was an order of magnitude worse than in the case in which only the surface profile is to be estimated.
Three-dimensional coherent transfer function for reflection confocal microscopy in the presence of refractive-index mismatch.
The three-dimensional (3-D) coherent transfer function for reflection confocal microscopy of high-numerical-aperture objectives is derived and calculated in the presence of refractive-index mismatch when a laser beam is focused into a medium of refractive index different from its immersion medium. This aberrated coherent transfer function is then used to estimate the readout efficiency of 3-D data bits recorded in a thick medium. It is shown that the readout efficiency of confocal microscopy for 3-D bit data storage is decreased with the focal depth of an objective in a recording medium. However, a high readout efficiency can be maintained if the tube length of a reading objective is linearly altered to compensate for the spherical aberration caused by the refractive-index mismatch.
Effect of the polarization on ocular wave aberration measurements.
Measurement of the eye's wave aberrations has become fairly standard in recent years. However, most studies have not taken into account the possible influence of the polarization state of light on the wave aberration measurements. The birefringence properties of the eye's optical components, in particular corneal birefringence, can be expected to have an effect on the wave aberration estimates obtained under different states of polarization for the measurement light. In the work described, we used a psychophysical aberrometer (the spatially resolved refractometer) to measure the effect of changes in the polarization state of the illumination light on the eye's wave aberration estimates obtained in a single pass. We find, contrary to our initial expectation, that the polarization state of the measurement light has little influence on the measured wave aberration. For each subject, the differences in wave aberrations across polarization states were of the same order as the variability in aberrations across consecutive estimates of the wave front for the same polarization conditions.
Retinal images seen through a cataractous lens modeled as a phase-aberrating screen.
Light propagation through a cataractous lens was modeled on the basis of a phase-aberrating medium. The optical frequency characteristics of the modeled optical system were estimated, and examples of foveal images with different values of aberration characteristics were calculated. The phase-aberration effects caused by relatively smooth fluctuations of the refractive index were found to cause a significant deterioration of the foveal image. This theoretical result gives an indication of the main factor that produces image degradation as shown in previous experiments and that is likely to occur in the cataractous eye.
Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas.
We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.
Validity conditions for the radiative transfer equation.
We compare the radiative transfer equation for media with constant refractive index with the radiative transfer equation for media with spatially varying refractive indices [J. Opt. A Pure App. Opt. 1, L1 (1999)] and obtain approximate conditions under which the former equation is accurate for modeling light propagation in scattering media with spatially varying refractive indices. These conditions impose restrictions on the variations of the refractive index, the gradient of the refractive index, the divergence of the rays, the frequency of modulation, and the widths of light pulses, which are related to the mean refractive index, the absorption coefficient, and the reduced scattering coefficient of the medium. Each condition is geometrically interpreted. Some implications of the results are discussed.
Light scattering by multiple red blood cells.
The interaction of light with multiple red blood cells was systematically investigated by the finite-difference time-domain method (FDTD). The simulations showed that the lateral multiple scattering between red blood cells is very weak and that the polarization has an almost insignificant influence on the distribution of the scattered light. The numerical results of the FDTD method were compared with the results from the Rytov approximation and the discrete dipole approximation (DDA). The agreement with the DDA was excellent.
Chromatic dispersions of the ocular media of human eyes.
Of the commonly used chromatic dispersion equations, only the Sellmeier and the Cauchy equations seem to be theoretically based. Cauchy's equation is derived from the Sellmeier equation, is simpler to implement, and was found to give an excellent fit to published refractive-index data of the human eye. We used Cauchy's equation to model the chromatic difference in refraction of the Gullstrand number 1 schematic eye with a gradient-index lens. To estimate the dispersion at different refractive-index levels within the lens, a single dispersion equation at one nominal refractive index was linearly scaled. This scaling was justified after exploring the effect of mean refractive index on dispersion by using Sellmeier's equation and finding that a dispersion equation for one wavelength is just a linearly scaled version of the dispersion equation at any other wavlength. Because Cauchy's equation is theoretically based and gives excellent fit to data in the visible spectrum, it can be used to extrapolate results into the near infrared with confidence.
Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens.
We present an iterative tomographic algorithm to reconstruct refractive-index profiles for meridional planes of the lens of the spherical fish eye from measurements of deflection angles of refracted rays. Numerical simulations show that the algorithm allows accuracy up to the fourth decimal place, provided that the refractive index can be regarded as an analytical function of the radial coordinate and the experimental errors are neglected. An experimental demonstration is given by applying the algorithm to retrieve the refractive-index profile of a spherical fish lens. The method is conceptually simple and does not require matching of the index of the surrounding medium to that of the surface of the lens, and the related iterative algorithm rapidly converges.
High-sensitivity determination of birefringence in turbid media with enhanced polarization-sensitive optical coherence tomography.
Polarization-sensitive optical coherence tomography provides high-resolution cross-sectional characterization of birefringence in turbid media. Weakly birefringent biological tissues such as the retinal nerve fiber layer (RNFL) require advanced speckle noise reduction for high-sensitivity measurement of form birefringence. We present a novel method for high-sensitivity birefringence quantification by using enhanced polarization-sensitive optical coherence tomography (EPS-OCT) and introduce the polarimetric signal-to-noise ratio, a mathematical tool for analyzing speckle noise in polarimetry. Multiple incident polarization states and non-linear fitting of normalized Stokes vectors allow determination of retardation with +/-1 degrees uncertainty with invariance to unknown unitary polarization transformations. Results from a weakly birefringent turbid film and in vivo primate RNFL are presented. In addition, we discuss the potential of EPS-OCT for noninvasive quantification of intracellular filamentous nanostructures, such as neurotubules in the RNFL that are lost during the progression of glaucoma.