The Ronchi fractional test

In practical applications, spherically aberrated lenses always exist in optical systems; therefore it is necessary to study the behavior of light beams propagation through these systems. In this paper a new optical technique based on the fractional Fourier transform is applied to described the Ronchi test; it techniques feasibility is demonstrated. A beam of coherent light is brought to focus by an optical system that is undergoing tests to determine its aberrations. A diffraction grating, also referred as a Ronchi ruling, may be as simple as a low-frequency wire-grid, or as sophisticated as a modern short-pitched, phase/amplitude grating. The position of the grating should be adjustable in the vicinity of focus, so that it may be shifted back and forth along the optical axis. This grating is placed perpendicular to the optical axis and breaks up the incident beam into several diffraction orders. The diffracted orders propagate independently of each other, and are collected by a pupil relay lens, which forms an image of the exit pupil of the object under test at the observation plane. Using the Collins formula and the fractional Fourier transform (FRFT)an analytical formula is derived, scaled variables and scaled field amplitudes are defined by complying with mathematical consistency. This relation provide a convenient way for analyzing optical systems with aberrated lenses.