Theoretical analysis for moiré deflectometry from diffraction theory

Abstract

Theories of moiré deflectometry are presented based on scalar diffraction theory. It is shown that the moiré effect is not a pure geometric phenomenon but actually the result of multishearing interference. By performing zeroth-order or first-order filtering, the field in the plane of observation is seen to be the result of double- or triple-shearing interference, respectively. With first-order filtering, the intensity distribution is proved to be a strict cosinusoidal intensity distribution, and the diffraction effect, which depends on the distance between two gratings, affects just the phase shift of the moiré fringes. Compared with previous research, a more precise relation between the unwrapped phase and the deflection angles is obtained. The results will be very useful for image processing of moiré patterns with Fourier transform profilometry and phase-shift methods.

Phase-shifting lateral shearing interferometry using wedge-plate and interferometric grating

“…The fringe signal detected at the image plane beyond grating G1 can be written as [16] Ix; y; t I 0 x; yf1 cosΔϕx; y δtg; (1) where I 0 x; y is the intensity bias, Δϕ is the phase difference as measured through the shearing interferometer, and δt is the time-varying phase shift.…”

“…A spatial-filtering mechanism has been incorporated to segregate the first order. It has been demonstrated by Song et al [16] that first-order spatial filtering facilitates a strict cosinusoidal intensity distribution and a more precise relation between the unwrapped phase and the deflection angles. Hence, it is easier to incorporate the Fourier transform or phase-shifting methods into the moire-based setups.…”

Real 3-D flow fields reconstruction by interferometric volume computerized tomography (IVCT)

“…Temperature distribution is an essential parameter to diagnose the flow field [18,19]. Meanwhile, it is also very important to evaluate the reconstruction quality.…”

Four-step spatial phase-shifting lateral shearing interferometry by a crossed grating and a linear grating

“…In spatial phase-shift method, at least three or four interferograms are needed to exact phase distribution. In order to obtain four shearing interferograms, an optical configuration which consists of three Ronchi gratings is presented [12]. In this paper, only a cross grating and a linear grating are used to produce four different spatial phase-shift lateral shearing interferograms.…”