Fengzhao Dai

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer-Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.

Use of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms

A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry

A new zonal wavefront reconstruction method for lateral shearing interferometry was presented. The proposed algorithm allows shear amounts equal to arbitrary integral multiple of the sample intervals. High spatial resolution reconstruction is achieved with only two difference wavefronts measured in orthogonal shear directions. The presented algorithm was generalized to be applicable for general aperture shape by using zero padding and Gerchberg-type iterative methods. The capability of the presented algorithm was demonstrated by some numerical examples. Also, the reconstruction error was analyzed theoretically and numerically.

Depth-dependent dispersion compensation for full-depth OCT image

A depth-dependent dispersion compensation algorithm for enhancing the image quality of the Fourier-domain optical coherence tomography (OCT) is presented. The dispersion related with depth in the sample is considered. Using the iterative method, an analytical formula for compensating the depth-dependent dispersion in the sample is obtained. We apply depth-dependent dispersion compensation algorithm to process the phantom images and in vivo images. Using sharpness metric based on variation coefficient to compare the results processed with different dispersion compensation algorithms, we find that the depth-dependent dispersion compensation algorithm can improve image quality at full depth.

High spatial resolution zonal wavefront reconstruction with improved initial value determination scheme for lateral shearing interferometry

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

Wavefront reconstruction for lateral shearing interferometry based on difference polynomial fitting

The wavefront reconstruction method for shearing interferometry using difference Zernike polynomial fitting has been the easiest algorithm to implement up to now. The method is extended to using general basis functions in this paper. Simulations and experiments verify that highly accurate reconstructions can be achieved based on difference polynomial fitting regardless, of the pupil shape and the orthogonality of the basis functions. The reconstruction accuracy mainly depends on whether the used terms of the polynomials are enough to represent the wavefront. When the used terms cannot perfectly represent the wavefront, the reconstruction accuracy of Taylor monomials is a little higher than that of Zernike polynomials. It is also presented and proved that the reconstruction accuracy can be estimated using the deviation between the reconstructed difference fronts and the measured difference fronts.

Monocular Vision-Based Underwater Object Detection

In this paper, we propose an underwater object detection method using monocular vision sensors. In addition to commonly used visual features such as color and intensity, we investigate the potential of underwater object detection using light transmission information. The global contrast of various features is used to initially identify the region of interest (ROI), which is then filtered by the image segmentation method, producing the final underwater object detection results. We test the performance of our method with diverse underwater datasets. Samples of the datasets are acquired by a monocular camera with different qualities (such as resolution and focal length) and setups (viewing distance, viewing angle, and optical environment). It is demonstrated that our ROI detection method is necessary and can largely remove the background noise and significantly increase the accuracy of our underwater object detection method.

Zernike polynomials as a basis for modal fitting in lateral shearing interferometry: a discrete domain matrix transformation method

A Zernike-polynomials-based wavefront reconstruction method for lateral shearing interferometry is proposed. Shear matrices are calculated using matrix transformation instead of mathematical derivation. Simulation results show that the shear matrices calculated using the proposed method are the same as those obtained from mathematical derivation. The advantage of the proposed method is that high order shear matrices can be obtained easily; thus, wavefront reconstruction can be extended to higher order Zernike terms, and reconstruction accuracy can be improved.

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry

The Zernike-polynomials-based modal reconstruction method is an important wavefront reconstruction method for lateral shearing interferometry. There are four typical Zernike-polynomial-based modal reconstruction methods: the Rimmer-Wyant method, the elliptical orthogonal transformation method, the numerical orthogonal transformation method (NOT), and the difference Zernike polynomial fitting method (DZF). In a previous paper [Appl. Opt. 51, 5028 (2012)], the overall performances of these four methods were comprehensively compared with each other. The conclusions showed that NOT and DZF have the highest reconstruction accuracies among these four methods. In addition, it was shown that the performance of NOT is identical to that of DZF; however, the reason behind this was not known until now, to our knowledge. In the present paper, we present a strictly mathematical proof for this highly significant result

Analysis of lateral shearing interferometry without self-imaging limitations.

In lateral shearing interferometry, interferograms with a good contrast can be obtained at any distance without self-imaging limitations based on a modified Hartmann mask (MHM) and a randomly encoded hybrid grating (REHG). The present study analyzes and compares the diffraction orders, the contrast of carrier fringes, the available spectral bandwidth, and the wavefront measurement accuracy of the lateral shearing interferometer using MHM and REHG. Numerical simulations show that the performance of the REHG is superior to that of the MHM with respect to fringe contrast, available spectral bandwidth, and wavefront measurement accuracy. For the REGH, if the phase step of the phase chessboard is within the range of (2n+1±0.2)π, the contrast of the carrier fringes is almost invariant along the propagation axis, and the wavefront reconstruction error generated from higher diffraction orders is small enough to be neglected. Optimal quantization of the REHG is also studied. When M is equal to 2 and N is not less than 5, the quantization result can meet the requirement of the measurement accuracy.