Fourier fringe analysis with improved spatial resolution

Abstract

The spatial resolution of the phase image derived from the interferogram by Fourier fringe analysis is limited by the necessity to isolate a first order in the Fourier plane. By use of the two complementary outputs of the interferometer, it is possible to eliminate the zero order and thus to improve the spatial resolution by a factor of approximately 2. The theory of this improvement is presented and confirmed experimentally.

Phase retrieval errors in standard Fourier fringe analysis of digitally sampled model interferograms

“…Then Eq. (9) is transformed to (12) where B stands for the expression in braces in Eq. (11) and the occ(FCM) contains the remainder of the former central maximum (FCM) intensity.…”

“…Equation (12) shows that, in spite of the expectation of extracting information contained in the first positive maximum only [second term in Eq. (12)], there is an inevitable, although much smaller, contribution from the former first negative maximum [first term in Eq. (12)].…”

“…(12)], there is an inevitable, although much smaller, contribution from the former first negative maximum [first term in Eq. (12)]. At this step we differ significantly from the analysis presented by Kostianovski et al 2 in which the term that belongs to the first negative maximum [the first term in Eq.…”

“…Further enhancement of the reliability of the phase retrieval depends, up to certain limits, on the extent to which one is ready to sacrifice the ͑x, y͒ spatial resolution. 12…”

Quantitative measurement of domain inversion in RuO2:LiNbO3 crystal by digital holographic interferometry

“…The numerical method named as angular spectrum backward propagation method that we are using for the hologram reconstruction is based on Fourier-transform method, [26][27][28][29] which can be easily performed by computer. Making the discrete digital hologram a fast Fourier transformation,…”