The point spread function in paraxial optics

Russell A. Chipman; Wai Sze Tiffany Lam

doi:10.1117/12.2188916

3 September 2015 The point spread function in paraxial optics

Proceedings Volume 9578, Current Developments in Lens Design and Optical Engineering XVI; 957803 (2015) https://doi.org/10.1117/12.2188916
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

Abstract

Paraxial optics is generally regarded as yielding ideal spherical wavefronts. The ideal point spread function for a circular aperture with an ideal spherical wavefront is an Airy disk. In paraxial optics a small rotation of the exiting polarization state occurs off-axis in the direction perpendicular to the meridional plane. This is a linear form of skew aberration. The resulting apodization of the co and crossed-polarized components in the exit pupil modify the point spread function (PSF) of paraxial optics. In the cross-polarized term, the pupil amplitude varies linearly through a value of zero along the meridional plane, like the function f(x,y) = k x. The Fourier transform of this pupil function is the Fourier transform of the derivative of the Airy disk, which results in a cross-polarized PSF component much larger than the Airy disk. The cause of this polarization rotation, known as skew aberration, is related to the parallel transport of the polarization state through the optical system along skew rays, and to the Berry phase. These cross-polarized PSF components, which although very small in paraxial optics, are nevertheless not zero. Since they occur within paraxial optics they are thus intrinsically interesting. These polarization effects are not related to the Fresnel equations or to any coating–induced polarization but occur in a nonpolarizing or polarizing optical systems.

Citation Download Citation

Russell A. Chipman and Wai Sze Tiffany Lam "The point spread function in paraxial optics", Proc. SPIE 9578, Current Developments in Lens Design and Optical Engineering XVI, 957803 (3 September 2015); https://doi.org/10.1117/12.2188916

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KEYWORDS

Polarization

Point spread functions

Spherical lenses

Optical spheres

Fourier transforms

Ray tracing

Refraction

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