Phase retrieval from the phase-shift moiré fringe patterns in simultaneous dual-wavelength interferometry

Abstract

Simultaneous dual-wavelength interferometry (SDWI) could extend the measured range of each single-wavelength interferometry. The moiré fringe generated in SDWI indirectly represents the information of the measured long synthetic-wavelength phase, thus the phase demodulation is rather arduous. To address this issue, we present a method to convert the moiré fringe pattern into a synthetic-wavelength interferogram (moiré to synthetic-wavelength, MTS). After the square of the moiré fringe pattern in the MTS method, the additive moiré pattern is turned into a multiplicative one. And the synthetic-wavelength interferogram could be obtained by a low-pass filtering in spectrum of the multiplicative moiré fringe pattern. Therefore, when the dual-wavelength interferometer is implemented with the π/2 phase shift at a sequence of synthetic-wavelength phase-shift interferograms with π/2 phase shift could be obtained after the MTS method processing on the captured moiré fringe patterns. And then the synthetic-wavelength phase could be retrieved by the conventional phase-shift algorithm. Compared with other methods in SDWI, the proposed MTS approach could reduce the restriction of the phase shift and frame numbers for the adoption of the conventional phase-shift algorithm. Following, numerical simulations are executed to evaluate the performance of the MTS method in processing time, frames of interferograms and the phase shift error compensation. And the necessary linear carrier for MTS method is less than 0.11 times of the traditional dual-wavelength spatial-domain Fourier transform method. Finally, the deviations for MTS method in experiment are 0.97% for a step with the height of 7.8 μm and 1.11% for a Fresnel lens with the step height of 6.2328 μm.

Hierarchical phase unwrapping for dual-wavelength digital holographic microscopy

“…This implies a potential of reducing the integer part estimation error. Assuming the errors of optical phases are e 1 and e 2 , respectively, we analyze the estimation error with equation (5).…”

“…For the reflection-mode DHM, the measurement range is half the optical wavelength. When measuring microstructures, such as steps and grooves, of which the depths are larger than half the optical wavelength, dual-wavelength DHM is used to unwrap the phase [3][4][5]. In dual-wavelength DHM, the difference of two optical phases, j 1 and j 2 , is calculated as j D =j 1 −j 2 , which corresponds to a longer synthetic wavelength, Λ D =λ 1 λ 2 /(λ 2 −λ 1 ).…”

Investigation into the Co-Phase Detection Methodology for Segmented Plane Mirrors Utilizing Grazing Incidence Interferometry

“…While the tilt error detection technique has achieved a certain degree of maturity, the predicament surrounding piston error detection remains unresolved, primarily attributable to issues such as 2π blurring and related challenges [5]. Various methodologies are available for the detection of segmented plane mirrors, including broad-and narrow-band Shack-Hartmann detection [6], dispersion fringe method [7], pentaprism scanning detection [8], dual-wavelength co-phase detection [9], and interference detection method [10]. Refer to Table 1 for an elucidation of their respective merits and demerits.…”