Window function influence on phase error in phase-shifting algorithms

Abstract

We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

Noise in phase shifting interferometry

“…In the past several attempts have been made to analyze the effect of noisy interferograms over the estimated phase in PSI [1][2][3][4][5]. Despite of these efforts to our view, no general enough study has been given; in one way or another these authors [1-5] assume particular PSI algorithms to estimate their signal to noise ratios and no mention is made on the influence of the interferograms' preprocessing.…”

Windowed equivalence principle for open surfaces

“…This paper proposes to apply well-known window functions, such as "generalized cosine windows" (which are commonly used in signal processing applications [3] and in other branches of science [4]…”

Complex-wave retrieval from a single off-axis hologram

“…The general method has been improved in many ways, for example to compensate for nonideal acquisition devices and conditions. [29][30][31][32][33][34][35] A number of spatial demodulation algorithms have been proposed that are able to demodulate interferograms with closed fringes. [36][37][38][39][40] Thus, they might also form the basis of a two-step procedure to reconstruct digital offaxis holograms acquired in the presence of a microscope lens, since such general setups possibly yield closed fringes.…”

“…Once the change of variables is performed, the remaining mathematics is essentially the same as for phase-shifting algorithms: For specific choices of the reference wave (for example, a plane wave whose wave vector is horizontal) and a suitable one-dimensional weighting function, the linear part of our formulation is equivalent to previously proposed spatial phase-shifting algorithms. 17,24,25,27,31,32 One notable difference, however, is that we consider a two-dimensional spatial weighting function that allows for a much less restrictive choice of the reference wave's form (plane, parabolic, etc.) and orientation.…”