Robert P. Herloski

Gaussian beam ray-equivalent modeling and optical design.

It is shown that the propagation and transformation of a simply astigmatic Gaussian beam by an optical system with a characteristic ABCD matrix can be modeled by relatively simple equations whose terms consist solely of the heights and slopes of two paraxial rays. These equations are derived from the ABCD law of Gaussian beam transformation. They can be used in conjunction with a conventional automatic optical design program to design and optimize Gaussian beam optical systems. Several design examples are given using the CODE-V optical design package.

Strehl ratio for untruncated aberrated Gaussian beams

Analytic formulas for the variance of an aberration of arbitrary order over a specified exit pupil with either uniform or untruncated Gaussian weighting are derived, and closed-form solutions are presented for the actual Strehl ratio of an untruncated Gaussian-beam system suffering from a primary aberration, except in the case of coma, for which an integral solution is given. These formulas are valid for an arbitrary magitude of the given primary aberration. It is shown that the aberration variance and Strehl ratio solutions for untruncated Gaussian-beam illumination depend on a reference-radius to beam-radius ratio, and judicious choice of this ratio allows one to apply the results of Strehl ratio calculations for uniformly illuminated systems to untruncated Gaussian-beam systems.

Analytical computation of integrating cavity effect

In document imaging systems, integrating cavity effect (ICE) is defined as the increase in perceived reflectance of the imaged portion of a document done due to the reflectance of the surrounding portion of that document. The illuminator kernel function, or one trip spread function (OTSF), characterizes the ICE present during an imaging operation. Insight into the functional form of the OTSF of a complex system can be gained from an analysis of the OTSF of simpler, related systems. Closed form expressions for the OTSF of a simple strip illumination system are derived. These expressions are shown to be a good approximation to the exact OTSF of this system by comparison to Monte Carlo- based illumination ray tracing results. Using the closed form expressions one can easily calculate the approximate magnitude of ICE present in similar systems.