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Wei Wang

Bio: Wei Wang is an academic researcher from Nanjing University of Science and Technology. The author has contributed to research in topics: Zernike polynomials & Orthogonal polynomials. The author has an hindex of 4, co-authored 7 publications receiving 60 citations.

Papers
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Journal ArticleDOI
TL;DR: Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.
Abstract: Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

34 citations

Journal ArticleDOI
TL;DR: The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified, indicating that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.
Abstract: Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.

24 citations

Journal ArticleDOI
TL;DR: In this paper, the use of numerical orthogonal polynomials for reconstructing a wavefront with a general shaped aperture over the discrete data points is presented, and the results demonstrate the adaptability, validity, and accuracy of numerical Orthogonal Polynomial for estimating the wavefront over a general shape aperture from a regular boundary to an irregular boundary.
Abstract: In practical optical measurements, the wavefront data are recorded by pixelated imaging sensors. The closed-form analytical base polynomial will lose its orthogonality in the discrete wavefront database. For a wavefront with an irregularly shaped aperture, the corresponding analytical base polynomials are laboriously derived. The use of numerical orthogonal polynomials for reconstructing a wavefront with a general shaped aperture over the discrete data points is presented. Numerical polynomials are orthogonal over the discrete data points regardless of the boundary shape of the aperture. The performance of numerical orthogonal polynomials is confirmed by theoretical analysis and experiments. The results demonstrate the adaptability, validity, and accuracy of numerical orthogonal polynomials for estimating the wavefront over a general shaped aperture from regular boundary to an irregular boundary.

8 citations

Patent
09 Nov 2016
TL;DR: In this paper, an optical heterogeneity measurement device and method based on a dual wavelength fizeau interferometer is presented. But the measurement steps are simple, and the defects that the traditional absolute measurement method has tedious steps and is vulnerable to air disturbance are tackled
Abstract: The invention discloses an optical heterogeneity measurement device and method based on a dual wavelength fizeau interferometer With the dual wavelength fizeau interferometer, interferograms of a reference light wave and a light wave reflected by the front surface of a to-be-tested flat mirror are sequentially collected, and wavefront aberration data [delta]W11(x,y) and [delta]W21(x,y) corresponding to wavelengths [Lambda]1 and [Lambda]2 are obtained by first phase shift measurement; interferograms of the reference light wave and a light wave passing through the to-be-tested flat mirror and reflected by the rear surface of the to-be-tested flat mirror are collected, and wavefront aberration data [delta]W12(x,y) and [delta]W22(x,y) corresponding to the wavelengths [Lambda]1 and [Lambda]2 are obtained by phase shift measurement; and a difference value is calculated by the wavefront aberration data corresponding to the wavelengths obtained by two-stepped measurement, and the optical heterogeneity of the to-be-tested flat mirror is obtained The invention does not require a standard reflector, and completely eliminates influences of the surface shape of the standard reflector on measurement results The measurement steps are simple, and the defects that the traditional absolute measurement method has tedious steps and is vulnerable to air disturbance are tackled

4 citations

Patent
24 Jun 2015
TL;DR: In this article, a bifocal wave zone plate interference microscopic-inspection apparatus for detecting flat mask defect is presented, where light passes through the aperture diaphragm to form a spot light source, and then passes through a positive lens to form parallel light, parallel light passes along the semi-reflecting and semi-transmitting spectroscope and realizes incidence on the Bifocal Wave Zone plate, 0-grade diffracted light satisfies a refraction principle.
Abstract: The invention discloses a bifocal wave zone plate interference microscopic-inspection apparatus for detecting flat mask defect. According to the apparatus, a light source, an aperture diaphragm, a positive lens, a semi-reflecting and semi-transmitting spectroscope, a bifocal wave zone plate, a flat mask to be detected, light passes through the aperture diaphragm to form a spot light source, and then passes through a positive lens to form parallel light, parallel light passes through the semi-reflecting and semi-transmitting spectroscope and realizes incidence on the bifocal wave zone plate, 0-grade diffracted light satisfies a refraction principle, +1 grade diffracted light realizes converge under regulation and control of a bifocal wave zone plate phase function, and light having the phase information of the surface of the flat mask to be detected is reflected to form a return light path. By employing a bifocal wave zone plate interference system of reference light and test light common path, bifocal wave zone plate realizes diffraction condition of coexistence focal length and no focal length, Compared with a several sheets lens transmission group system, quantity of the lens transmission groups can be reduced, The bifocal wave zone plate interference microscopic system realizes synchronous detection function of amplitude-type defect and phase-type defect.

2 citations


Cited by
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Journal ArticleDOI
TL;DR: A detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences is presented.
Abstract: Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques.

63 citations

Proceedings ArticleDOI
TL;DR: This work derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror, and extends this work to elliptical, rectangular, and square pupils.
Abstract: This paper derives closed-form orthonormal polynomials over noncircular apertures using the Gram-Schmidt orthogonalization process. Isometric plots, interferograms, and point-spread functions are illustrated. Their use in wavefront analysis is discussed.

29 citations

Journal ArticleDOI
TL;DR: The mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, is used to describe shape of a mirror surface.
Abstract: In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

27 citations

Journal ArticleDOI
TL;DR: The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified, indicating that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.
Abstract: Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.

24 citations

Journal ArticleDOI
TL;DR: In this article, the mathematical apparatus of orthogonal polynomials defined over a square aperture was used to describe shape of a mirror surface, which was developed before for the tasks of wavefront reconstruction.
Abstract: In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/#=2.5 and FoV=7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

23 citations