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Chapter 10:
Line of Sight of an Aberrated Optical System
Author(s): Virendra N. Mahajan
Published: 1991
DOI: 10.1117/3.43000.ch10
10.1 Introduction In this chapter we consider the line of sight (LOS) of an aberrated optical system. The LOS is assumed here to coincide with the centroid of its diffraction point-spread function (PSF). For an aberration-free system, it coincides with the center of the PSF. For an aberrated system, it depends on the various orders of its coma aberrations. Thus, a coma aberration not only reduces the central value of the PSF like any other aberration, but it also shifts its centroid. We consider here PSFs aberrated by primary coma and give numerical results on the location of their peaks and centroids. 10.2 Theory The LOS of an aberration-free optical system coincides with the center of its diffraction PSF. For an aberrated system, let us define its LOS as the centroid of its aberrated PSF. Thus, if I(x,y) represents the irradiance distribution of the aberrated image of a point object, its centroid representing the LOS error of the system is given by <x<=1 P ∫xI(x,y)dxdy and <y<=1 P ∫xI(x,y)dxdy, where P is the total power in the image. It can be shown that the centroid thus obtained is identical to that obtained from the geometrical PSF. For a system with a circular exit pupil, let its aberration function in terms of Zernike circle polynomials (see Section 8.3.7) be given by W(ρ,θ)=∑ n=0 ∞ ∑ m=0 n ϵ m 2(n+1) − − − − − − − √ R m n (ρ)(c nm cosmθ+s nm sinmθ), where c nm and s nm are the Zernike aberration coefficients representing the standard deviations of the corresponding aberration terms across the pupil (with the exception of the piston term n=0=m , which has a standard deviation of zero).
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Point spread functions

Monochromatic aberrations


Aberration theory

Error analysis



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