By Virendra N. Mahajan
Wavefront Analysis is a component III of a sequence of books on Optical Imaging and Aberrations. It has advanced out of the author's paintings and lectures through the years on wavefront research as utilized to optical layout and checking out. Its concentration is at the use of orthonormal polynomials that signify balanced classical aberrations in optical imaging platforms with scholars of varied shapes. After a quick advent to optical imaging, aberrations, and orthonormalization of a suite of polynomials over a undeniable area to acquire polynomials which are orthonormal over one other area, this publication describes intimately the polynomials applicable for varied shapes of the approach student. beginning with the method that's most typical in imaging, specifically, the single with a round scholar, platforms with annular, hexagonal, elliptical, oblong, sq., and slit scholars are thought of. integrated during this checklist also are structures with round and annular scholars with Gaussian illumination, anamorphic structures with sq. and round students, and people with round and annular zone scholars. those chapters begin with a short dialogue of aberration-free imaging that comes with either the PSF and the OTF of a process. A separate bankruptcy is dedicated to a dialogue of the pitfalls of utilizing the Zernike circle polynomials for platforms with noncircular students via employing them to structures with annular and hexagonal students. equally, a bankruptcy is dedicated to the calculation of orthonormal aberration coefficients from the wavefront or the wavefront slope info. every one bankruptcy ends with a short precis that describes the essence of its content material.
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Additional resources for Optical Imaging and Aberrations, Part III: Wavefront Analysis
The outer radius of an annular pupil is unity, as in Figure 3-1a. The corners of the hexagon in Figure 3-1b lie at a distance of unity. Figure 3-1c illustrates an ellipse with an aspect ratio of b, and its semimajor axis has a length of unity. For each of these pupils, the coefficient of a classical aberration represents its peak value. Figure 3-1d shows a rectangle with a half width a and its corners at a distance of unity from its center. Similarly, Figure 3-1e shows a square of half width 1 2 so that its corners are also at a distance of unity from its center.
When an image is formed in free space, as is often the case in practice, then n = 1. The angle G ~ P0cP0s R between the ideal ray QP0c and the actual ray QP0s is called the angular ray aberration. The distribution of rays in an image plane is called the ray spot diagram. We will refer to the aberration W x, y as the wave aberration at a projected point Q x, y in the plane of the exit pupil. If r, T are the polar coordinates of this point, as illustrated in Figure 2-5, they are related to its rectangular coordinates x, y according to x, y r cos T, sin T .
3-1) will not be satisfied exactly. This error decreases as the number of data points increases. 4 ORTHONORMALIZATION OF ZERNIKE CIRCLE POLYNOMIALS OVER NONCIRCULAR PUPILS The Zernike circle polynomials (discussed in Chapter 4) are orthogonal over a circular pupil. They uniquely represent balanced classical aberrations and include wavefront tilt and defocus aberrations. The corresponding polynomials F j ( x , y ) that are orthogonal over a noncircular pupil can be obtained by orthogonalizing the circle polynomials Z j ( x , y ) using the Gram–Schmidt orthonormalization process .