Fourier transform deflection mapping

Arie Dahan; Gabi Ben-Dor; Ezra Bar-Ziv

doi:10.1117/12.134052

1 May 1993 Fourier transform deflection mapping

Arie Dahan, Gabi Ben-Dor, Ezra Bar-Ziv

Author Affiliations +

Optical Engineering, Vol. 32, Issue 5, (May 1993). https://doi.org/10.1117/12.134052

Abstract

In a previous paper in 1992, we presented a flow visualization technique based on deflection mapping. We now present a new method for the interpretation of deflection mapping of small angles obtained by Ronchi gratings. In this method, a Fourier transform is operated on the transmission pattern of the Ronchi grating and the individual sine terms are then obtained by applying an inverse Fourier transform of each harmonic separately. The extraction of the deflection angle profile from the sine term is straightforward. The theory of Fourier transform deflection mapping is presented and the methodology for determining the deflection angle profile is discussed. The method was validated by measurements of transmission patterns of long-focal-length (4-m) lenses. A parallel light beam was passed through a lens, then traversed a Ronchi grating, and the transmission pattern was measured at a distance from the grating. The transmission patterns were measured by two methods (1) scanning with a photomultiplier tube over the grating and (2) using a linear 4096-photodiode array. A fast Fourier transform (FFT) code was used to isolate the various harmonics and the deflection angle profile was determined from the first harmonic. The focal lengths were determined by the present method with precision better than 99.999%, whereas the focal length was within 1% of the value provided by the manufacturer. Special emphasis was given to evaluating the errors associated with the technique and detectibility limits were given.

Citation Download Citation

Arie Dahan, Gabi Ben-Dor, and Ezra Bar-Ziv "Fourier transform deflection mapping," Optical Engineering 32(5), (1 May 1993). https://doi.org/10.1117/12.134052

Published: 1 May 1993

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