The extreme value of interference (EVI) algorithm is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames in which the phase shift between interferograms can be determined by searching the maximum and the minimum of the normalized interference patterns, then the measured phase is obtained by an arctangent function. Compared with other two-frame demodulation algorithms, the EVI algorithm has great advantages. Firstly, the EVI algorithm is simple and the calculation speed is fast. Secondly and more importantly, it works very well even if the number of fringes of the interferogram is less than one. However, to make this method work, the fringe should be normalized in advance, which is sometimes not a satisfactory requirement. The effects of uneven background terms, modulation amplitude variations, and random noise in the fringe pattern will make the normalization of the fringes extremely complex. Therefore, by employing the HilbertHuang transform (HHT) based prefiltering in this paper, the background intensities and modulation amplitudes of the two interferograms are suppressed and normalized respectively. Then, phase demodulation is implemented using the EVI method. Because of the HHT process, the demodulation result is greatly improved in plenty of situations. Both simulation and experimental studies have shown that the proposed improved method makes it easier to determine the phase distribution with high precision even under complex conditions.
Transport of Intensity Equation (TIE) is a simple and efficient method for phase retrieval by solving the equation between the intensity axial derivative and phase. In this method, the estimation of the axial derivative of intensity is very crucial. Simply, we use two defocused intensity images to estimate the axial derivative by finite difference method. However, the result is still unsatisfactory even though the optimal defocused distance is adopted. The reason lies in that the intensity’s axial change is not linear in the propagation of light. Simply using the finite difference between the two defocused images will ignore higher order axial derivatives. In other words, the estimation of the axial derivative of intensity will contain nonlinear errors. To solve this problem, we propose an extrapolation-based method to estimate the axial derivative of intensity using multiple intensity images. With Taylor expansion and a series of combination and eliminations on these images, high order terms of axial derivative errors are removed. As a result, the nonlinear errors in estimation of the axial derivative will be reduced. The performance of our proposed method for different types of phases under different illumination conditions is investigated. Compared with normal TIE, our method can obtain a much more accurate phase profile.
Annular sub-aperture stitching interferometry (ASSI) has provided an alternative solution to measure rotationally symmetric aspheric surfaces with low cost and high flexibility. It is an effective way to test the aspheric surface with a larger aperture and larger relative aperture without null compensation. In this paper, two kinds of annular sub-aperture stitching algorithms, pairwise sequential stitching (PSS) and global synchronously stitching (GSS), were studied. The detailed mathematical expressions are shown in the form of matrix. Besides, the influence of the noise and number of sub-apertures to the two algorithms was also studied by simulation. At last, experimental results of a convex hyperboloid surface by using the two stitching algorithms are presented.