Line of Sight of an Aberrated Optical System
Abstract
The line of a sight (LOS) of an aberrated optical system is defined in terms of the centroid of its point spread function (PSF) and also in terms of its optical transfer function as well as its pupil function. Although the PSFs obtained according to wave diffraction optics and ray geometrical optics are quite different, they have the same centroid. For an aberration-free pupil, different amplitude distributions across it give the same centroid location; for an aberrated pupil, not only the phase but also the amplitude distribution affects the centroid location. It the amplitude across a pupil is uniform, the centroid may be obtained from the aberration along its perimeter only, without regard for the aberration across its interior regardless of shape. Next, an optical system with aberrated but uniformly illuminated annular pupil is considered. The aberration function is expanded in terms of Zernike annular polynomials. It is shown that only those aberrations that vary with angle as cos theta or sin theta contribute to the LOS. A simple expression is obtained for the LOS in terms of the Zernike aberration coefficients. Similar results are obtained for annular pupils with radially symmetric illumination. Specific results are discussed for annular pupils aberrated by classical primary and secondary coma. As an example of a radially symmetric illumination, we obtain numerical results for Gaussian illumination of aberrated annular pupils. It is emphasized that the centroid and the peak of the PSFs aberrated by coma are not coincident, and, as the amount of the aberration increases, separation of the centroid and peak locations also increases.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 14, 1985
- Accession Number
- ADA157683
Entities
People
- V. N. Mahajan
Organizations
- The Aerospace Corporation