Adaptive optics for high-resolution imaging

Hampson, Karen M.; Turcotte, Raphaël; Miller, Donald T.; Kurokawa, Kazuhiro; Males, Jared R.; Ji, Na; Booth, Martin J.

doi:10.1038/s43586-021-00066-7

Cited by 115 publications

(92 citation statements)

References 202 publications

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“…They are orthogonal polynomials on the unit disk and have two independent variables: a radius and an azimuthal angle, e.g., [2], [6, §4], [16]. They are used to measure and describe optical wavefront aberrations such as defocus, astigmatism, and coma, and have applications in optometry, telescope mirror alignment such as in the James Webb Space Telescope [13], and adaptive optics [12]. Adaptive optics is used, for example, in large terrestrial telescopes such as at the Keck Observatory [21] to reduce wavefront aberrations caused by atmospheric turbulence, and de-twinkle stars.…”

Section: Bernstein and Zernike Radial Polynomialsmentioning

confidence: 99%

Change of Basis from Bernstein to Zernike

Wolfram¹

2022

Preprint

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We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones.The minimum degrees of polynomials in an ascending basis can increase such as with bases of Bernstein and Zernike Radial polynomials. They have applications in computer-aided design and optics.We give coefficient functions for mappings from the monomials to descending bases of Bernstein polynomials, and ascending ones of Zernike Radial polynomials and prove their correctness.Allowing for parity, we define eight general change of basis matrices and the related equations for composing their coefficient functions.A main example is the change of basis from shifted Legendre polynomials to Bernstein polynomials considered by R. Farouki [7]. The analysis enables us to find a more general hypergeometric function for the coefficient function, and recurrences for finding coefficient functions by matrix row and column. We show the column coefficient functions are equivalent to the Lagrange interpolation polynomials of their elements. We also provide a solution to an open problem [7] by showing there is no general closed form expression for the coefficient function from Gosper's Algorithm.Truncation, alternation and superposition increase the scope further. Alternation enables, for example, a change of basis between Bernstein and Zernike Radial polynomials. A summary shows that the groupoid of change of basis matrices is a small category, and triangular and alternating change of basis matrices are morphisms in full subcategories of it. Truncation is a covariant functor.

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Section: Bernstein and Zernike Radial Polynomialsmentioning

confidence: 99%

Change of Basis from Bernstein to Zernike

Wolfram¹

2022

Preprint

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“…This had made it the sensor of choice in state-of-the-art, high-performance telescopes. In microscopy, the same properties are also convenient both for aberration correction in high-resolution microscopy [7,8] and quantitative phase microscopy [9].…”

Section: Introductionmentioning

confidence: 99%

Use of a Rotating Square Spatial-Frequency Filter to Map the Optical Path Length Variation in Microscopic Biological Samples

Iglesias

2022

Sensors

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Gradient images can be obtained using a rotating square mask to filter the angular spectra of the wavefront generated by a complex transmittance object. This method can be applied to measure the three-dimensional structure of microscopic biological samples through the relationship of the phase with the optical path length. This work describes the implementation of a system using an inverted optical microscope and shows the experimental results of phase maps generated by boar sperm cells.

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“…The commonly used geometrical optics (ray tracing) method is a crude approximation of wave optics, yet it provides powerful tools to design thick elements and complex stacks of lenses. However, geometrical optics is not suitable for applications such as phase retrieval [1][2][3][4], adaptive optics [5,6], PSF engineering [7][8][9][10], or more generally, any application that requires either correctly modelling the diffraction-limited PSF or employing optical elements that manipulate the phase, amplitude, or polarization of light. Such applications require Fourier optics [11], which can account for diffraction effects, but is usually limited to thin-element and paraxial approximations.…”

Section: Introductionmentioning

confidence: 99%

Diffractive optical system design by cascaded propagation

Ferdman,

Saguy,

Alalouf

et al. 2022

Preprint

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Modern design of complex optical systems relies heavily on computational tools. These typically utilize geometrical optics as well as Fourier optics, which enables the use of diffractive elements to manipulate light with features on the scale of a wavelength. Fourier optics is typically used for designing thin elements, placed in the system's aperture, generating a shiftinvariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffraction optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.

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Adaptive optics for high-resolution imaging

Cited by 115 publications

References 202 publications

Change of Basis from Bernstein to Zernike

Change of Basis from Bernstein to Zernike

Use of a Rotating Square Spatial-Frequency Filter to Map the Optical Path Length Variation in Microscopic Biological Samples

Diffractive optical system design by cascaded propagation

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