Abstract

A laser beam is deflected and focused by a holographic optical element (HOE). The hologram can be described by a phase function Φ(x, y). While displacing the HOE, the incident beam moves along a line x(s) in the hologram plane, and the image point describes another line y(t) in space. We present a method to calculate the phase function Φ, which is necessary to generate a particular line y(t) in space. It can be shown analytically, using second-order (paraxial) approximation, that a circular motion x(s) cannot generate a straight line y(t) in space without astigmatism of the focal spot.

© 1987 Optical Society of America

Holographic optical scanning elements with minimum aberrations

Hans Peter Herzig and Rene Dandliker
Appl. Opt. 27(22) 4739-4746 (1988)

Analytic design of optimum holographic optical elements

J. N. Cederquist and J. R. Fienup
J. Opt. Soc. Am. A 4(4) 699-705 (1987)

Holographic optical elements with optimized phase-transfer functions

Yuzo Ono and Nobuo Nishida
J. Opt. Soc. Am. A 3(1) 139-142 (1986)

Analytical design of holographic optical elements for Fourier transform

Katsuya Goto and Akihiko Terasawa
J. Opt. Soc. Am. A 7(11) 2109-2118 (1990)

Analytic optimization for holographic optical elements

E. Hasman and A. A. Friesem
J. Opt. Soc. Am. A 6(1) 62-72 (1989)