Imagery of One-Dimensional Patterns

TLDR: In this article, the light distribution in the image of a sinusoidal and of a bar (crenelate or square-wave) pattern produced by diffraction at a "slit" aperture (straight-sided and infinitely long) and at a circular aperture was derived.

Abstract: Expressions are derived for the light distribution in the image of a sinusoidal and of a bar (crenelate or “square-wave”) pattern produced by diffraction at a “slit” aperture (straight-sided and infinitely long) and at a circular aperture. In every case, when the pattern has an infinite number of repetitions, the distribution is uniform for the spatial frequency that represents Rayleigh’s limit for two-line sources and a slit aperture; this is thus the absolute objective limit of resolution. In practice, radiation detectors have different thresholds, and, since the rate at which the contrast in the image diminishes as the frequency approaches the limit varies with the type of object pattern and the shape of the diffracting aperture, the measured value of resolving power also varies. A table of the line spread-function for a circular aperture is given.