Eric C. Kintner

A New 'Analytic' Method for Computing the Optical Transfer Function

Using a series expansion in Zernike polynomials to express the pupil function of an optical system, a means for computing the Optical Transfer Function has been found which avoids explicit numerical integration.

Edge-ringing in Partially Coherent Imaging

A simple condition is shown to be necessary and sufficient to suppress edge-ringing in optical imaging. This criterion is valid in the presence of aberrations and apodization, and for all cases of (spatially stationary) partially coherent illumination. The edge-ringing tendencies of an optical system may be assessed through the use of two new performance functions which form a Fourier-transform pair. One of these performance functions is related to the ‘transmission cross-coefficient’ which appears in the theory of partially coherent imaging. In the coherent limit this performance function reduces to the amplitude transfer function (pupil function), and in the incoherent limit it reduces to the Optical Transfer Function (OTF). The use of this performance function for the general assessment of partially coherent imaging systems is suggested.

Some comments on the use of the Zernike polynomials in optics

Abstract The advantages of a modified application of the Zernike polynomials are demonstrated.

Edge-ringing and Fresnel Diffraction

Using the diffraction theory of aberrations, it is shown that edgeringing and Fresnel diffraction may be described as different regimes of the same physical process. Quantitative results are given, and some implications are briefly discussed.

Calculating the Encircled Energy in the Point-spread Function

The light energy in the Point-Spread Function (PSF) enclosed within a circle of specified radius centred on the gaussian image point may be calculated analytically from an orthogonal series representation for the PSF.

An Analytic Recurrence Procedure for Computing the Cross-multiplication Coefficients in an Analytic OTF Method

The cross-multiplication coefficients required in an analytic method for calculating the Optical Transfer Function may be computed analytically through the use of a recurrence relation. The new recurrence procedure is both faster and more accurate than numerical integration, and the results obtained from it suggest that the analytic OTF method will be more accurate and more versatile than suggested earlier.

Two-point Resolution Criteria in Partially Coherent Imaging

The Rayleigh criterion has been investigated as a performance criterion for optical systems imaging in partially coherent light. In numerical tests with moderate amounts of primary spherical aberration—up to 18 u maximum wavefront deviation—the Rayleigh criterion proves to be insensitive to the amount of aberration. This insensitivity appears characteristic of two-point criteria generally.