Human Optics as a Function of Eccentricity

Introduction

Anatomically close schematic eye models that can reproduce optical properties are extremely beneficial as these models can simulate the performance of a human eye. These models can be used for research and development purposes such as for ophthalmic lens design, refractive surgery, and studying the features of optical component systems[1]. Optical properties such as spherical and chromatic aberrations along with polychromatic point spread functions (PSF) and modulation transfer function (MTF) have been studied on axis.

While a real eye is not rotationally symmetric, the schematic models are taken to be axially symmetric. Several wide angle models have been designed which provide good predictions for on- and off-axis aberrations but do not fit exactly each aberration at every retinal location due to rotational symmetry. Off-axis performance of the human eye is comparatively less understood. Resultantly, verification of eye models are required. In this project, we quantify the off-axis performance of the Navarro model by calculating optical images of a slanted bar at different angles away from the center of the retina, and quantifying the MTF at each of these locations. We can compare the performance with known values in the literature.

Background

Several schematic eye models have been compared in literature to the data from real eyes to assess their relative utility with metrics such as their wavefront aberrations, image quality metrics and peripheral refraction profiles. The Navarro eye model is of particular interest in this project. The following figures are from the Williams[4] paper, and are the known results for the Navarro eye model from literature which will be compared to our results.

Figure 1: MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye in the horizontal meridian of the temporal retina.

Figure 2: MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye at the tangential and sagittal focii of the temporal retina.

The slant edge target is used as the test scene. It is the optical equivalent of an electrical step function. The illuminance plot of the test scene across the boundary is the edge spread function, and its Fourier transform is the Modulation Transfer Function. Effective resolution of the lens is greater due to slant since spacing of “samples” of ESF is calculated as pixel pitch times the angle of rotation of the target[3].

Methods

We developed an automation algorithm to measure a high resolution MTF within the user’s selected region of interest on the retina from the Navarro eye model. The methods followed to create the algorithm will be detailed in the Methods section, however our extensively commented code in Appendix I will serve as a great resource for a user to understand the algorithm line-by-line.

One goal of the eccentricity automation algorithm is to not require a high resolution rendering of a large field of view image. Rendering such an image is often times prohibitively computationally expensive. Resultantly, the eccentricity automation algorithm provides the same benefits of having rendered a full, high resolution image in fractions of the computational cost (exact reduction depends on the region of interest and is parameter dependent). Second, the modulation transfer function data from the selected region of interest at different eccentricities is calculated and plotted for the user to interpret utilizing the built-in ISO12233 function in ISET.

The user selected input to the function is the retinal region of interest in units of degrees relative to the fovea (in both the x and y direction) and the crop-window resolution. The hard-coded parameters of the algorithm are FOV4MTF which determines the number of degrees each crop-window spans, and LOW_RES which is the low resolution of the entire FOV image to locate the crop windows off of. It was determined that a crop-window of 2 degrees contained enough information and the entire blurred edge even at eccentricities of 30 degrees as seen in Figure 3.

Figure 3: A crop-window at an eccentricity of 0 and 30 degrees.

Appendix

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