Zernike vs. Bessel circular functions in visual optics

Treviño, Jorge; Gómez-Correa, J. E.; Iskander, D. Robert; Chávez-Cerda, Sabino

doi:10.1111/opo.12065

Cited by 31 publications

(16 citation statements)

References 31 publications

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“…The calculation of higher-order Zernike or Q-type polynomials is relatively tedious. Trevino et al 85 selected the first-class Bessel circular functions for characterizing a complex corneal surface. Svechnikov et al 86 discussed the lateral resolving capacity of circular Zernike polynomials and the accuracy of representing complex freeform surfaces, such as Gaussian and Gaussian-like surfaces.…”

Section: Representation Methods For Freeform Surfaces With Strong Slomentioning

confidence: 99%

Review of optical freeform surface representation technique and its application

Chen

et al. 2017

Opt. Eng

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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.

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Section: Representation Methods For Freeform Surfaces With Strong Slomentioning

confidence: 99%

Review of optical freeform surface representation technique and its application

Chen

et al. 2017

Opt. Eng

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“…In high-energy lasers production, opticians strongly prefer the Zernike polynomial set to reconstruct wavefronts and to decompose imperfections into well-known aberration components [ 11 ]. However, other sets have been proposed to be used for reconstructing surfaces (see, for instance, [ 12 ]). On the bright side, the Zernike-based reconstruction has been shown to outperform the iterative Fourier when reconstructing wavefront aberrations from slope data.…”

Section: Introductionmentioning

confidence: 99%

Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients

Solano-Altamirano

Vázquez-Otero²,

Khikhlukha

et al. 2017

Sensors

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In this paper, we propose a new algorithm to reconstruct optics surfaces (aka wavefronts) from gradients, defined on a circular domain, by means of the Spherical Harmonics. The experimental results indicate that this algorithm renders the same accuracy, compared to the reconstruction based on classical Zernike polynomials, using a smaller number of polynomial terms, which potentially speeds up the wavefront reconstruction. Additionally, we provide an open-source C++ library, released under the terms of the GNU General Public License version 2 (GPLv2), wherein several polynomial sets are coded. Therefore, this library constitutes a robust software alternative for wavefront reconstruction in a high energy laser field, optical surface reconstruction, and, more generally, in surface reconstruction from gradients. The library is a candidate for being integrated in control systems for optical devices, or similarly to be used in ad hoc simulations. Moreover, it has been developed with flexibility in mind, and, as such, the implementation includes the following features: (i) a mock-up generator of various incident wavefronts, intended to simulate the wavefronts commonly encountered in the field of high-energy lasers production; (ii) runtime selection of the library in charge of performing the algebraic computations; (iii) a profiling mechanism to measure and compare the performance of different steps of the algorithms and/or third-party linear algebra libraries. Finally, the library can be easily extended to include additional dependencies, such as porting the algebraic operations to specific architectures, in order to exploit hardware acceleration features.

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“…For this reason modal representations such as Zernike, Fourier or Taylor analysis were introduced, which seem especially well suited for reconstructing elevation topography from Scheimpflug images . Other localised functions such as Bessel functions, adaptive arrays of Gaussians, or algorithms combining local and modal fitting were also proposed. But given the oversensitivity of most of these methods to irregular corneal shapes, the relatively stable and reproducible Zernike polynomials became the most popular methods for global representation despite their potential limitations …”

Section: Introductionmentioning

confidence: 99%

Eigencorneas: application of principal component analysis to corneal topography

Rodríguez

Navarro

Rozema

2014

Ophthalmic Physiologic Optic

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The combination of Zernike fit and Principal Component Analysis yields a strong reduction of dimensionality of elevation topography data, to only 19 independent parameters (18 DoF plus population average), which indicates a high degree of correlation existing between anterior and posterior surfaces, and between eyes. The resulting eigencorneas are especially well suited for practical applications, as they are uncorrelated and orthonormal linear combinations of Zernike polynomials.

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Zernike vs. Bessel circular functions in visual optics

Cited by 31 publications

References 31 publications

Review of optical freeform surface representation technique and its application

Review of optical freeform surface representation technique and its application

Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients

Eigencorneas: application of principal component analysis to corneal topography

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