Image distortion, pupil coma, and relative illumination

Abstract

Relative illumination is affected by image distortion, pupil coma, and pupil magnification. Image and pupil aberrations have a known relationship that also can be written in terms of pupil magnification. Pupil coma is the stretching or compression of the pupil along the field axis, which directly affects relative illumination. Front-stopped designs have pupil aberrations on the exit pupil while rear-stopped systems have pupil aberrations on the entrance pupil. Of the primary pupil aberrations, pupil coma can have the largest effect on the relative illumination in optical designs with significant image distortion (ex: fisheye lens). The Lagrange invariant holds for systems with image distortion using a paraxial approximation of pupil coma. Relative illumination can be written in terms of % distortion, pupil magnification, and object–space field angle.

4‐2: Design of MLA‐based Integrated Projection System Using Radial Basis Function Mapping Method

“…The ray tracing, RBF-based interpolation, and image pre-distortion methods are described in detail in Section 3. The optical information associated with the projection imaging process reflects the brightness of an image point on the projection plane as a function of illumination (9,10). The illumination distribution of the integrated projection image can be represented as following:…”

Image irradiance in the absence of aplanatism and isoplanatism

“…By way of reversibility, if all of the rays from these SSFs were to travel towards the lens, they would fill the exit pupil, so the image irradiance for those rays would be determined by integrating over the exit pupil. This integration is precisely what is done to obtain relative illumination in computer-aided lens design programs [12][13][14][15][16]. However, calculations for relative illumination in lens design programs generally either assume that the object is sufficiently extended, or otherwise, if ray aberrations are present, then these aberrations would first be corrected prior to determining the relative illumination [12].…”

“…where x and y are coordinates at the image plane, E is the image irradiance given by radiometry, V is the volume of the PSF, P(x − x , y − y ) is the PSF, and G(x , y ) is the image distribution (with unit irradiance) predicted by geometrical optics. Note that E in equation ( 3) is of course generally regarded as a function of x and y (such as that given by the relative illumination of a lens system, which would be computed through any of the methods discussed in references [12][13][14][15][16]), but the explicit writing of E(x, y) in equation ( 3) has been omitted in order to minimize clutter in the expression. Equation ( 3) is not just an expression of the relative distribution of the image given by convolution that is discussed in the subject of Fourier optics.…”

Optical Design of Imaging Spectrometer Based on Linear Variable Filter for Nighttime Light Remote Sensing

“…Pupil spherical aberration makes the location of the entrance pupil at the edge of the field of view deviate from the ideal position, thus it mainly affects the calibration of the chief ray and has less influence on the relative illumination. Pupil coma can make the beam width of the off-axis field at the entrance pupil larger than that of the center field when both of them completely fill the stop aperture [ 41 ]. Such vignetting effect of pupil aberration can ensure that the off-axis object has a larger aperture than the on-axis object, so it is very beneficial to improve the relative illumination.…”