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Li M.,University of Sichuan | Li D.,University of Sichuan | Wang Q.,University of Sichuan | Wang Q.,State Key Laboratory of Fundamental Science on Synthetic Vision | And 3 more authors.
Zhongguo Jiguang/Chinese Journal of Lasers | Year: 2012

An orthonormal square Zernike basis set is generated from circular Zernike polynomial apodized square mask by use of the linearly independent set Gram-Schmidt orthogonalization technique. Based on the concepts of inner product, Euclidean space and norm in the linear algebra, a standard Zernike polynomial set is made orthogonal and a new orthonormal basis of polynomials named Z-square polynomial is established. Wavefront data in square aperture can be fitted with our new orthonormal set. It can not only fit the wavefront data with Z-square basis set itself, but also can be linearly composed of standard Zernike basis set by linear reverse transform and endows the decomposed wavefront modes with a correspondent aberration meaning. The experimental results show that the Z-square polynomial set can fit the wavefront aberration data in lens design efficiently and can also fit the practical wavefront phase data of Hartmann-Shack wavefront sensor testing, it provides a method of wavefront data analysis.


Li D.-H.,University of Sichuan | Qi X.-P.,University of Sichuan | Wang Q.-H.,University of Sichuan | Wang Q.-H.,State Key Laboratory of Fundamental Science on Synthetic Vision | And 3 more authors.
Optics Letters | Year: 2010

We propose a mathematic formula that can be applied to work out the amplitude distribution of a tested laser beam from its radial-shearing interferogram accurately, even if the amplitude distribution is extremely uneven. Provided that the background irradiance distribution of a tested beam is extracted from its cyclic radial-shearing (CRS) interferogram first, then using the radial-shearing ratio of the CRS interferometer, the amount of lateral shear along the orthogonal directions and the irradiance ratio, the amplitude distribution of a tested beam can be reconstructed accurately by the proposed formula. The simulation computation and experimental results show that the formula allows any amount of lateral shear to happen, as long as the contracted beam maintains its location inside its corresponding expanded version. © 2010 Optical Society of America.


Zhang C.,University of Sichuan | Liu C.,University of Sichuan | Li D.,University of Sichuan | Li M.,University of Sichuan | And 2 more authors.
Guangxue Xuebao/Acta Optica Sinica | Year: 2013

Radial shearing interferometry has been widely used to test distorted wavefront. However, the result of wavefront measurement by using this technique includes two parts, one is the real phase information of wavefront under test and the other is the system errors in radial shearing interferometer. A calibration method of a radial shearing interferometer is presented. First of all, several fringe patterns of the phase difference distribution are obtained by a tested component with different positions. Then, the maximum likelihood method is used to combine the phase difference data and create a maximum likelihood function. After that, the wavefront under test and system errors can be separated. The simulation results show that the maximum likelihood method can deal with the issue of the calibration of a radial shearing interferometer. Furthermore, the method is used to reduce the effect of the system errors on extracting and reconstructing the wavefront under test.


Li M.,University of Sichuan | Li D.,University of Sichuan | Zhang C.,University of Sichuan | E K.,University of Sichuan | And 3 more authors.
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2015

We present a modal wavefront reconstruction from slope measurements for rectangular optical components of high-power laser systems. Wavefront reconstruction with slope data is an important approach used for wavefront control or correction in high-power systems. In this work, we derive a complete set of orthonormal wavefront slope polynomials for rectangular apertures and describe the modal method for obtaining wavefront representation with the aberration balancing property. Error propagation properties for the modal method are evaluated and compared with the Southwell method. The cross-coupling error is also discussed. Numerical experiments are conducted to illustrate that the modal method can achieve a higher accuracy than the Southwell method. In addition, we also investigate the influence of noise on the modal method compared with that of the Southwell method. © 2015 Optical Society of America.


Guo D.,Chinese Research Institute of Highway | Wang Q.,State Key Laboratory of Fundamental Science on Synthetic Vision
Zhongguo Jiguang/Chinese Journal of Lasers | Year: 2014

When investigating the scattering intensity distribution produced by a glass bead which is illuminated by a collimated beam with single length, Debye theory can be used to simulate and discuss the scattering properties. It is found that the intensity distribution of the k-order rainbow recorded by a detector which is on the left of a spherical particle is the superposition of the diffracted rays, the external reflected rays and the k time internal reflected rays primarily. The intensity distribution of the k-order rainbow on the right of the spherical particle is the superposition of the diffracted rays, the transmitting rays and the k time internal reflected rays mostly. When the wavelength of incident light is constant, the refractive index of the glass beads will change the degrees of the minimum deviation angle in the scattered light intensity distribution on the detector, and their diameters have no effect on the position of minimum deviation angle. Experimentally, the scattered intensity distribution of the first and the second rainbows of the glass beads with different refractive indices and radius are analyzed, and are compared with the geometrical method, which agrees with the result of simulation in Debye theory. This result shows that the proposed assumptions are reasonable, which can be used to measure the refractive index of the glass beads through testing the minimum deviation angle formed by the light scattering.

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