Phase Of Synthetic Wavelength Research Articles

Fast phase extraction of a synthetic wavelength from a dual-wavelength interferogram through Hilbert transformation.

Phase imaging is an important measurement method in optical metrology, and phase extraction is one of its essential components. A method using one-frame dual-wavelength interferometry (DWI) for fast phase extraction is proposed. Using this method, the Hilbert transform (HT) is applied twice to a wavelength-multiplexed interferogram to obtain two images. The HT is then applied twice to the sum of the squares of these two images. The synthetic wavelength phase can then be obtained. Compared with other common multiple-frame DWI methods, the proposed approach requires only one multiplexed interferogram and does not have to consider parameter changes in interferograms of different frames. Furthermore, the proposed method was determined to require the least calculation time, and the simulation and experimental results confirmed its high accuracy and efficiency. It suggests that the proposed method is suitable for real-time measurements.

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

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.

Dual-wavelength interferometry based on the spatial carrier-frequency phase-shifting method.

From a single-frame dual-wavelength spatial carrier-frequency interferogram (SCFI), we propose a novel phase retrieval method of dual-wavelength interferometry (DWI). First, by continuously moving the intercepted area pixel-by-pixel in a single-frame SCFI along the horizontal and vertical directions, we construct a sequence of phase-shifting sub-interferograms. Second, the wrapped phases of each single wavelength can be retrieved from those phase-shifting sub-interferograms via the least-squares iteration algorithm. Third, the phase of synthetic wavelength can be obtained by subtraction between the wrapped phases of single wavelengths. Both the numerical simulation and the experimental result demonstrate that the proposed method reveals greater accuracy and convenience. Furthermore, because only single-frame SCFI can perform the phase retrieval of DWI, the proposed method offers better ability in resisting external vibration and disturbance, which will greatly facilitate the application of DWI in the dynamic phase measurement.

Single-wavelength phase retrieval method from simultaneous multi-wavelength in-line phase-shifting interferograms.

From a sequence of simultaneous multi-wavelength phase-shifting interferograms (SMWPSIs), a novel single-wavelength phase retrieval method based on the least-squares iterative algorithm is proposed and utilized in dual-wavelength interferometry. Firstly, only one time phase-shifting procedure implements the phase shifts of all illumination wavelengths simultaneously, and then the accurate wrapped phases of each single-wavelength can be respectively retrieved from SMWPSIs by the least-squares iterative operation, so the phase of synthetic wavelength can be obtained by the subtraction easily. Using the proposed method, both the simulation and the experimental results demonstrate that the optical setup is simpler; the requirements for the displacement of the phase-shifting device and the number of the captured interferograms are smaller compared to the traditional phase-shifting multi-wavelength interferometry or off-axis multi-wavelength interferometry. Even in the case that the phase-shifts are unknown, the wrapped phases and the phase-shifts of each single-wavelength can be obtained by the proposed method.