Wavefront optics toolbox

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During this project, we have worked with the WavefrontOpticsToolbox, located in a SVN repository at https://platypus.psych.upenn.edu/repos/toolboxes/WavefrontOpticsToolbox/trunk. This toolbox models the optics of the human eye using scalar diffraction theory from Fourier Optics. In particular, the aberrations of the human cornea, pupil, and lens, as well as the Stiles-Crawford effect from the retinal cone cells, are modeled by the amplitude and phase of the eye's pupil function. This pupil function is then Fourier transformed to compute the eye's point spread function (PSF).

The project is split into two phases: 1) code clean-up and commenting and 2) the creation of a MATLAB tutorial to demonstrate some of the features of the toolbox.

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Background

Ray optics, or geometric optics, is concerned with modeling how light rays travel through optical systems like that of our eyes. However, to fully consider the effects of small pupil size, as well as variations in the geometry and chromatic aberrations of the eye's lenses, wave optics and diffraction must be accounted for. Fourier optics, or scalar diffraction theory, cleanly handles effects such as wavefront aberrations, finite pupil size, and apodizing filtering, so we will first briefly give a background of Fourier optics. Next, we will discuss how wavefront aberrations are modeled, namely by the basis set of Zernike polynomials. Finally, we will describe the Stiles-Crawford effect, the physical cause of this effect, and how it is modeled.

Fourier optics

Fourier optics is built upon the idea that the wave nature of light is modeled by the Huygens-Fresnel principle -- that every point on a wavefront of light is the source of new spherical waves. The summed interaction of these spherical waves at some observation plane determines what is observed at that plane. Here, it is assumed that the polarization of the electromagnetic field can be neglected, and instead, light can simply be modeled by a wavefunction that obeys the standard wave equation and represents electric or magnetic field. Hence, this is called scalar diffraction theory.

A direct result of this theory is that the diffraction effects of any imaging system can be modeled very cleanly by Fourier transforms. In fact the point spread function of an imaging system is given by

$h(u,v)=A/\lambda z_i\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\iint }}P(x,y)exp\{-j2\pi /\lambda z_i(ux+vy)\}\mathrm{d}x\mathrm{d}y$

Wavefront aberrations and Zernike polynomials

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Stiles-Crawford effect

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Toolbox code clean-up

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$OI{F}_k=\frac{\sum _{n=1}^3\Vert {𝐱}_n-{\overline{𝐱}}_n)\Vert }{|{𝐱}_1^T{𝐱}_2|+|{𝐱}_1^T{𝐱}_3|+|{𝐱}_2^T{𝐱}_3|}$

Tutorial

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Zernike polynomials

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Stiles-Crawford effect

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Human eye aberrations and correction using eyeglasses

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Conclusions and future directions

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References

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Appendix I - Code and Data

Code

File:T Zernike.m

Data

Wavefront measurements of human eyes are part of the SVN repository. Wavefront optics toolbox

Appendix II - Work partition

Matthew Lew - Heavily edited wvfComputePupilFunction.m to remove unnecessary nested loops; removed sizeOfFieldPixels field of the wvf struct so that all parameters are defined in terms of physical dimensions, not pixels; constructed sections of tutorial dealing with SCE and vision correction with eyeglasses

Kevin Phuong - Constructed core of t_Zernike.m to demonstrate Zernike polynomials and their effect on PSFs; updated various functions of the toolbox to use wvfGet() and wvfSet().