Generalized Phase-shifting Interferometry Research Articles

Three-frame generalized phase-shifting interferometry by a Euclidean matrix norm algorithm

Generalized phase-shifting interferometry (GPSI) is one of the most effective techniques in imaging of a phase object, in which phase retrieval is an essential and important procedure. In this paper, a simple and rapid algorithm for retrieval of the unknown phase shifts in three-frame GPSI is proposed. Using this algorithm, the value of phase shift can be calculated by a determinate formula consisting of three different Euclidean matrix norms of the intensity difference between two phase shifted interferograms, and then the phase can be retrieved easily. The algorithm has the advantages of freeing from the background elimination and less computation, since it only needs three phase-shifted interferograms without no extra measurements, the iterative procedure or the integral transformation. The reliability and accuracy of this algorithm were demonstrated by simulation and experimental results.

特殊点的两步广义相移干涉相移值提取算法

特殊点的两步广义相移干涉相移值提取算法

An evaluation method for phase shift extraction algorithms in generalized phase-shifting interferometry

A method to evaluate quantitatively the performance of the phase shift extraction algorithms in generalized phase-shifting interferometry (GPSI) is proposed. A parameter named as reconstruction signal-to-noise ratio (R-SNR) is used as the evaluation measure. The R-SNR is defined with the reconstructed object image as the signal and the residual of the DC term and conjugate image as noise. The more accurate the extracted phase shift is, the less residual of the DC term and conjugate image there is, and then the higher R-SNR is obtained. To avoid the overlap of the DC term and conjugate image and the object image, the off-axis digital holography configuration is adopted. The correctness and effectiveness of the proposed method have been verified by both computer simulation and optical experiments. The major advantage of the proposed method is that it utilizes the experimental detectable data and not only the computer simulation results.

Phase-Shift Extraction and Wavefront Reconstruction in Generalized Phase-Shifting Interferometry with a Standard Phase Object

A method to extract phase shifts and reconstruct the object wave in generalized phase-shifting interferometry (GPSI) is proposed. The phase distribution of a standard phase object and the least-square method are used to extract phase shifts over a wide range from 0 to π. Consequently, the tested object wave can be further reconstructed with the extracted phase shifts. It is accurate and applicable for GPSI of any frame number N (N ≥ 2). Computer simulation has verified its feasibility and validity.

广义相移干涉术相移提取算法的分类与评估方法

广义相移干涉术相移提取算法的分类与评估方法

Advanced Aperture Synthesis by Wave-Front Combination in Generalized Phase-Shifting Interferometry

An approach to improve the image quality by aperture synthesis in generalized phase-shifting interferometry is proposed. The aperture of the holographic system is enlarged by increasing the recording area to receive a more diffusive spectrum by moving a singular CCD. The sub-object wave fronts are combined with the index of their intensities. This method can avoid the negative effect of environmental disturbance and improve the synthesis efficiency by hundreds of times. The optical experiments have shown that it is simple and robust to stitch the complex object wave front accurately and to improve the imaging quality greatly, especially for the recording of large scale objects.

Accurate Phase Shift Extraction for Generalized Phase-Shifting Interferometry

An accurate phase shift extraction method for generalized phase-shifting interferometry is suggested. Based on the nearly random phase distribution of the diffraction field of the object, a singular formula is derived to calculate the unknown phase shift without the requirements of an iteration process or the selection of the correct value from two or more possible phase shift solutions as needed before. This method can be used in the cases of two or more frames with both smooth and diffusing object surfaces. Computer simulations and optical experiments have satisfactorily verified the efficiency and accuracy of this method.

Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry

A direct phase shift extraction and wavefront reconstruction method in two-step generalized phase-shifting interferometry (GPSI) with arbitrary unknown phase shift is proposed. In this method the unknown phase shift α can be extracted by a determinate formula directly without iteration or additional judgment of its correct value from two or more phase shift solutions as necessary before. By an appropriate formula of GPSI the complex object field in the recording plane can be calculated and then the object wavefront in the original object plane obtained. This method is applicable for GPSI of any frame number K≥2 and for both the amplitude and phase objects. Computer simulations have shown that the phase shift extraction errors are below 0.01 rad in a wide range of 0.4 rad<α<2.6 rad and the computation time is greatly reduced by a factor of about 20 compared with the previous method. The effectiveness and accuracy of this method are also verified by optical experiments.

Optical experimental verification of two-step generalized phase-shifting interferometry

A wavefront reconstruction technique by two-step generalized phase-shifting interferometry （GPSI） is proposed and verified by optical experiments. According to the statistical characters of the diffractive field, a blind extraction algorithm is developed, by which the unknown phase shift value in interferometry can be successfully extracted. The proposed method can retrieve the real amplitude of object wave field by using two interferograms, the recorded object and reference wave intensities, and an extracted phase shift, without the assistance of additional Fourier spectrum analysis or digital filtering. In optical experiments, the feasibility of this method for both the indirect object （digital images cast on a spatial light modulator, SLM） and the direct three-dimensional diffused object inputs has been discussed and investigated in detail, and the experimental results have convincingly verified the usefulness and effectiveness of this scheme in practice.

Wavefront reconstruction by two-step generalized phase-shifting interferometry

A wavefront reconstruction method by two-step generalized phase-shifting interferometry (GPSI) with blind phase shift extraction algorithm is verified by both the computer simulations and optical experiments. This method can retrieve complex object wave field by using two interferograms, the recorded object and reference wave intensities, and an unknown phase shift without additional processing. The simulations with irregular wavefronts have shown the effectiveness and high accuracy of this method for blind phase-shift extraction and wavefront reconstruction over a wide range of phase-shifts, while the optical experiments for both the direct and indirect objects have yielded satisfactory results with a higher resolution of reconstructed image than those reported recently.

Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry

We have investigated the effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry (GPSI) systematically. A general formula of the mean square wave reconstruction error for different phase shift selection and different phase shift errors is derived, and its specific expressions for the equal, linear, and random phase shift errors are deduced. The results reveal that there is a wide range for phase shift selection in GPSI, and the equal phase step algorithm is superior to the one of unequal step where the three kinds of phase shift errors are concerned. Specifically, the phase step leads to the minimum wave reconstruction error in the cases of equal and linear phase shift errors, while the phase step 1.91 rad yields the smallest wave reconstruction error for random phase shift errors. These results have been verified by a large number of computer simulations with over 100,000 samples.

Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments

An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number >or=2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.