Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances

Abstract

Common-path interferometers have been used to perform phase visualization for over 40 years. A number of techniques have been proposed, including dark central ground, phase contrast (π/2 and π), and field-absorption interferometers. The merits of the interferometers have been judged ad hoc by either tests with a small number of phase objects or by computer simulation. Three standardized criteria, which consolidate the work of others, are proposed to evaluate common-path interferometers: fringe visibility, fringe irradiance, and fringe accuracy. The interferometers can be described as one generic class of Fourier-plane filters and can be analyzed for all input conditions. Closed-form expressions are obtained for visibility and irradiance under the forced condition that little inaccuracy is tolerated. This analysis finds that the π-phase-contrast interferometer is a good choice if the optical phase disturbance is at least 2π; for smaller disturbances, the Π/2 filter selected by Zernike is near optimum. It is shown mathematically that the resulting fringe visibility is highly object dependent, and good results are not ensured. By allowing the optical beam to be 50% larger than the phase object, the interferometer performs well under all conditions. With this approach and a combination π-phase/field-absorption filter, interference fringe visibility is greater than 0.8 for all phase objects.

<title>Review of the nonlinear common path interferometer</title>

“…quadratic phase objects, the technique only requires that the illuminating light beam area be larger than the phase object area in order to obtain highly contrasted interference fringes. Fulfilling this requirement allows the formation of the Zernike-like filter and the optimization ofthe interferometric fringes contrast [7].…”

“…At this point a nonlinear medium (1DM) is placed in such way that it acts as a self-aligned photoinduced Zemike-like filter due to the larger intensity concentrated in the zero frequency. The complete formalism has been treated by other authors [7] in which is proven that the filter acts as a source for a common path interferometer where a coherent summations of the reference beam and the object beam under test takes place. …”

Off-axis interferometer with adjustable fringe contrast based on polarization encoding

“…A major parameter that controls the OPD accuracy is the interference fringe contrast. Poor fringe contrast results in insufficient phase modulation depth, decreasing the signal-to-noise ratio, and essentially deteriorating the quality of the OPD maps [20,21].…”

Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics

“…Common-path interferometry can be implemented using WFDI on-axis geometry, 5 requiring the acquisition of several phase-shifted interferograms for each instance of the sample, or using off-axis geometry, 4,6 requiring the acquisition of only one interferogram per sample instance. The latter approach, however, requires the use of a diffraction grating and often other elements in the beam paths, which necessitates a dedicated optical system design and an additional alignment.…”