Conventional Shark-Hartmann wavefront sensors (SHWS) only get the slope information of the wavefront in each subaperture. In this paper, Fourier demodulation technology and finite difference method are used to process the Light spot column plot of the SHWS, and the slope and curvature information of the wavefront in each subaperture can be obtained. With the slope and curvature information of the wavefront obtained by the algorithm as input, the distorted wavefront of the input is reconstructed by using the slope and curvature hybrid wavefront reconstruction technology. Simulation results show that the relative reconstruction error of wavefront is between 1%-5% under ideal conditions. In the noisy condition, the relative reconstruction errors of the wavefront are also between 1%-5%, and the wavefront can be recovered well. Compared with the traditional spatial centroid detection algorithm, this algorithm is simple and convenient to process information in the frequency domain, and has strong anti-noise ability.
The four-hole amplitude-modulated wavefront sensor (FHAM-WS) can detect the slope and curvature of local wavefront in each subaperture using a four-hole mask modulated microlens array. In this paper, an efficient method is proposed to improve the precision and noise immunity of slope and curvature extraction algorithm in FHAM-WS. Firstly, preprocessing of the spot diagram for all subapertures acquired by FHAM-WS is conducted using a hybrid filter in both frequency and spatial domains. Then the spot image in each of the subapertures is labeled and divided into two parts: the central lobe and the side lobes. Slope of each local wavefront is detected using centroid estimation based on the central lobe. A hexagonal detection window is used to identify the central lobe and then the high moment algorithm is applied to estimate the centroids with the central lobe. Curvatures of each local wavefront are detected using intensity response expressions calculated from the side lobes. Simulations of the slope and curvature detection with ideal spot image under different noise conditions are conducted to verify the proposed method. The results demonstrate that the precision and noise immunity of the centroid estimation and intensity response for the proposed method are superior to those of the previous methods.
Error calibration is one of the most important factors to realize the quadri-wave lateral shearing interferometer (QWLSI)
with high accuracy. The misalignment errors of QWLSI, such as the tilt of grating and the tilt of charge coupled device
(CCD), will affect the measurement accuracy. The astigmatism errors induced by the tilt of grating and CCD during the
alignment process of QWLSI, which are neglected in previous studies, are analyzed and presented in analytical
expressions in this paper. Firstly, the additional phase difference in X and Y directions induced by the tilt of grating and
CCD are analyzed using the optical wave interference theory. Representing the phase difference in the two directions and
the test wavefront with the combinations of Zernike polynomials respectively, we further obtain the analytical expressions
between the Zernike coefficients of the phase difference and the Zernike coefficients of the test wavefront, according to
the wavefront reconstruction theory. Then the analytical expressions for the measurement errors induced by the tilt of
grating and CCD, which are mainly astigmatism, can be obtained. The analytical results show that the misalignment
induced astigmatism errors are inversely proportional to the shearing ratio and proportional to the tilt angle of grating and
CCD. The alignment experiment of a home-made QWLSI under null test condition is conducted to verify the correctness
of the theoretical analysis. With different shearing ratios for the QWLSI, the astigmatism errors, which are induced by the
tilt of grating in experimental results, are consistent with the theoretical analysis results. This paper can provide technical
support for the alignment of QWLSI with small shearing ratio and high precision.
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