The Ronchi fractional test

C. O. Torres, L. Mattos, G. Baldwin, Y. Torres

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationRIAO/OPTILAS 2007 - 6th Ibero-American Conference on Optics (RIAO) and the 9th Latin-American Meeting on Optics, Lasers and Applications (OPTILAS)
PublisherAmerican Institute of Physics Inc.
Number of pages5
ISBN (Print)9780735405110
StatePublished - 2008
Event6th Ibero-American Conference onOptics and 9th Latin-American Meeting on Optics, Lasers and Applications, RIAO/OPTILAS 2007 - Campinas, Sao Paulo, Brazil
Duration: 21 Oct 200726 Oct 2007

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference6th Ibero-American Conference onOptics and 9th Latin-American Meeting on Optics, Lasers and Applications, RIAO/OPTILAS 2007
CityCampinas, Sao Paulo


  • Fractional fourier transformation
  • Ronchi test
  • Spherically aberrated lenses


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