Aberration Theory Made Simple

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Aberration Theory Made Simple

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Aberration Theory Made Simple

01 Jul 1991-

TL;DR: In this paper, the authors provide a clear, concise, and consistent exposition of what aberrations are, how they arise in optical imaging systems, and how they affect the quality of images formed by them.

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Abstract: This book provides a clear, concise, and consistent exposition of what aberrations are, how they arise in optical imaging systems, and how they affect the quality of images formed by them. The emphasis of the book is on physical insight, problem solving, and numerical results, and the text is intended for engineers and scientists who have a need and a desire for a deeper and better understanding of aberrations and Their role in optical imaging and wave propagation.

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Citations

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Journal Article•DOI•

Accuracy and precision of objective refraction from wavefront aberrations

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Larry N. Thibos¹, Xin Hong¹, Arthur Bradley¹, Raymond A. Applegate²•Institutions (2)

Indiana University¹, University of Houston²

23 Apr 2004-Journal of Vision

TL;DR: It is concluded that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise and wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.

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Abstract: We determined the accuracy and precision of 33 objective methods for predicting the results of conventional, sphero-cylindrical refraction from wavefront aberrations in a large population of 200 eyes. Accuracy for predicting defocus (as specified by the population mean error of prediction) varied from -0.50 D to +0.25 D across methods. Precision of these estimates (as specified by 95% limits of agreement) ranged from 0.5 to 1.0 D. All methods except one accurately predicted astigmatism to within +/-1/8D. Precision of astigmatism predictions was typically better than precision for predicting defocus and many methods were better than 0.5D. Paraxial curvature matching of the wavefront aberration map was the most accurate method for determining the spherical equivalent error whereas least-squares fitting of the wavefront was one of the least accurate methods. We argue that this result was obtained because curvature matching is a biased method that successfully predicts the biased endpoint stipulated by conventional refractions. Five methods emerged as reasonably accurate and among the most precise. Three of these were based on pupil plane metrics and two were based on image plane metrics. We argue that the accuracy of all methods might be improved by correcting for the systematic bias reported in this study. However, caution is advised because some tasks, including conventional refraction of defocus, require a biased metric whereas other tasks, such as refraction of astigmatism, are unbiased. We conclude that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise. If objective refractions are more precise than subjective refractions, then wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.

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560 citations

Cites background from "Aberration Theory Made Simple"

...Eliminating second-order Zernike aberrations is equivalent to minimizing the root mean squared (RMS) wavefront error, but this minimization does not necessarily optimize the quality of the retinal image (King, 1968; Mahajan, 1991)....
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Journal Article•DOI•

Foldscope: Origami-Based Paper Microscope

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James S. Cybulski¹, James Clements¹, Manu Prakash¹•Institutions (1)

Stanford University¹

18 Jun 2014-PLOS ONE

TL;DR: An ultra-low-cost origami-based approach for large-scale manufacturing of microscopes, specifically demonstrating brightfield, darkfield, and fluorescence microscopes that can survive harsh field conditions while providing a diversity of imaging capabilities.

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Abstract: Here we describe an ultra-low-cost origami-based approach for large-scale manufacturing of microscopes, specifically demonstrating brightfield, darkfield, and fluorescence microscopes. Merging principles of optical design with origami enables high-volume fabrication of microscopes from 2D media. Flexure mechanisms created via folding enable a flat compact design. Structural loops in folded paper provide kinematic constraints as a means for passive self-alignment. This light, rugged instrument can survive harsh field conditions while providing a diversity of imaging capabilities, thus serving wide-ranging applications for cost-effective, portable microscopes in science and education.

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297 citations

Cites background from "Aberration Theory Made Simple"

...or focal ratio, which is defined in terms of the focal length (f) and the aperture radius (a) as, 23 a f F 2 (Eq. 4) RMS Spot Size can be approximated by RMS blur radius (r RMS ), which is given by (2,3), 4 3 8 1 8 / 2 / RSS # r RMS F S (Eq. 5) where F = focal ratio, S = peak aberration coefficient, and Λ = normalized longitudinal aberration. At best focus, Λ=1 and the approximate expression fo...
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...egral part of “frugal science and engineering” (2). For example, manufacturing via folding has emerged as a powerful and general-purpose design strategy with applications from nanoscale self-assembly (3) to large-aperture space telescopes (4). More recently, possibilities of folding completely functional robots have been explored (5-7), with actuators, sensors and flexures integrated in a seamless fa...
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...le empirical expression given by Mahajan (4), 2SZ O2 SR e s (Eq. 12) where ω s = RMS wavefront error at the best focus. The RMS wavefront error due to spherical aberration at best focus is given by (2,3), 180 S Z s (Eq. 13) where S = peak aberration coefficient as given by (Eq. 7). Substituting (Eq. 7) and (Eq. 13) into (Eq. 12), the Strehl ratio can be written as, 8 SR e C 1 a , 2 1 3 5 ¸ · ¨ © ...
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Journal Article•DOI•

Corneal wave aberration from videokeratography: accuracy and limitations of the procedure.

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Antonio Guirao¹, Pablo Artal¹•Institutions (1)

University of Murcia¹

01 Jun 2000-Journal of The Optical Society of America A-optics Image Science and Vision

TL;DR: The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05-0.2 microm, rendering the method adequate for many applications.

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Abstract: A procedure to calculate the wave aberration of the human cornea from its surface shape measured by videokeratography is presented. The wave aberration was calculated as the difference in optical path between the marginal rays and the chief ray refracted at the surface, for both on- and off-axis objects. The corneal shape elevation map was obtained from videokeratography and fitted to a Zernike polynomial expansion through a Gram–Schmidt orthogonalization. The wave aberration was obtained also as a Zernike polynomial representation. The accuracy of the procedure was analyzed. For calibrated reference surface elevations, a root-mean-square error (RMSE) of 1 to 2 μm for an aperture 4–6 mm in diameter was obtained, and the RMSE associated with the experimental errors and with the fitting method was 0.2 μm. The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05–0.2 μm for a pupil 4–6 mm in diameter, rendering the method adequate for many applications.

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222 citations

Cites methods from "Aberration Theory Made Simple"

...(17), the RMSE was calculated as RMSE 5 H 1 N (i51 N...
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...z~ri! 5 R 2 ~R2 2 K(2)ri 2!1/2 K2 , (17)...
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Journal Article•DOI•

Relationship between refractive error and monochromatic aberrations of the eye.

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Xu Cheng¹, Arthur Bradley, Xin Hong, Larry N. Thibos•Institutions (1)

Indiana University¹

01 Jan 2003-Optometry and Vision Science

TL;DR: A reduced-eye model of myopia assuming fixed optical parameters and variable axial length is not tenable because it is found that the optical system of the eye is uncorrelated with the degree of ametropia.

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Abstract: Purpose. To examine the relationship between ametropia and optical aberrations in a population of 200 normal human eyes with refractive errors spanning the range from +5.00 to −10.00 D. Methods. Using a reduced-eye model of ametropia, we tested the hypothesis that the optical system of the eye is uncorrelated with the degree of ametropia. These predictions were evaluated experimentally with a Shack-Hartmann aberrometer that measured the monochromatic aberrations across the central 6 mm of the dilated pupil in well-corrected, cyclopleged eyes. Results. Optical theory predicted, and control experiments on a model eye verified, that Shack-Hartmann measurements of spherical aberration will vary with axial elongation of the eye even if the dioptric components of the eye are fixed. Contrary to these predictions, spherical aberration was not significantly different from emmetropic eyes. Root mean square of third-order aberrations, fourth-order aberrations, and total higher aberrations (third to 10th) in myopic and hyperopic eyes were also uncorrelated with refractive error. Astigmatic eyes tended to have larger total higher-order aberrations than nonastigmatic eyes. Conclusions. We conclude that a reduced-eye model of myopia assuming fixed optical parameters and variable axial length is not tenable.

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211 citations

Cites methods from "Aberration Theory Made Simple"

...Indiana reduced-eye model(24) for a source located at the eye’s far point using the method of optical path differences.(25) This model was configured with three different levels of asphericity (conic constant values p 0....
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Journal Article•DOI•

High-quality computational imaging through simple lenses

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Felix Heide¹, Mushfiqur Rouf¹, Matthias B. Hullin¹, Björn Labitzke², Wolfgang Heidrich¹, Andreas Kolb² - Show less +2 more•Institutions (2)

University of British Columbia¹, University of Siegen²

08 Oct 2013-ACM Transactions on Graphics

TL;DR: This article estimates per-channel, spatially varying point spread functions, and performs nonblind deconvolution with a novel cross-channel term that is designed to specifically eliminate color fringing.

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Abstract: Modern imaging optics are highly complex systems consisting of up to two dozen individual optical elements. This complexity is required in order to compensate for the geometric and chromatic aberrations of a single lens, including geometric distortion, field curvature, wavelength-dependent blur, and color fringing.In this article, we propose a set of computational photography techniques that remove these artifacts, and thus allow for postcapture correction of images captured through uncompensated, simple optics which are lighter and significantly less expensive. Specifically, we estimate per-channel, spatially varying point spread functions, and perform nonblind deconvolution with a novel cross-channel term that is designed to specifically eliminate color fringing.

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187 citations

Cites background from "Aberration Theory Made Simple"

...The common way to correct for these effects in optical systems is to design increasingly complex systems with larger and larger numbers of individual lens elements [Mahajan 1991]....
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...Optical aberrations include effects such as geometric distortions, chromatic aberration (wavelength-dependent focal length), spherical aberration (focal length depends on the distance from the optical axis), and coma (angular dependence on focus) [Mahajan 1991]....
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...Optical aberrations include effects such as geometric distortions, chromatic aberration (wavelength-dependent focal length), spherical aberration (focal length depends on the distance from the optical axis), and coma (angular dependence on focus) [Mahajan 1991]. All single lens elements with spherical surfaces suffer from these artifacts, and as a result cannot be used in high-resolution, high-quality photography. Instead, modern optical systems feature a combination of different lens elements with the intent of canceling out aberrations. For example, an achromatic doublet is a compound lens made from two glass types of different dispersion, thay is, their refractive indices depend on the wavelength of light differently. The result is a lens that is (in the first order) compensated for chromatic aberration, but still suffers from the other artifacts mentioned before. Despite their better geometric imaging properties, modern lens designs are not without disadvantages, including a significant impact on the cost and weight of camera objectives, as well as increased lens flare. In this article, we propose an alternative approach to high-quality photography: instead of ever more complex optics, we propose to revisit much simpler optics used for hundreds of years (see, e.g., Rashed [1990]), while correcting for the ensuing aberrations computationally. While this idea is not entirely new (see, e.g., Schuler et al. [2011]), our approach, which exploits crosschannel information, is significantly more robust than other methods that have been proposed....
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...Optical aberrations include effects such as geometric distortions, chromatic aberration (wavelength-dependent focal length), spherical aberration (focal length depends on the distance from the optical axis), and coma (angular dependence on focus) [Mahajan 1991]....
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...The common way to correct for these effects in optical systems is to design increasingly complex systems with larger and larger numbers of individual lens elements [Mahajan 1991]....
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References

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Open Access

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Journal Article•DOI•

Introduction to Fourier Optics

[...]

Joseph W. Goodman, Mary E. Cox

01 Apr 1969-Physics Today

TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.

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Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.

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12,159 citations

Book•

Introduction to Fourier optics

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Joseph W. Goodman

01 Jan 1968

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9,800 citations

Journal Article•DOI•

Strehl ratio for primary aberrations in terms of their aberration variance

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Virendra N. Mahajan¹•Institutions (1)

Charles Stark Draper Laboratory¹

01 Jun 1983-Journal of the Optical Society of America

TL;DR: In this paper, the authors considered the Strehl ratio for imaging systems with circular and annular pupils aberrated by primary aberrations and compared the actual numerical results with the approximate ones.

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Abstract: The Strehl ratio for imaging systems with circular and annular pupils aberrated by primary aberrations is considered in terms of the variance σΦ2 of the phase aberration across the pupil. Classical as well as balanced (Zernike) aberrations are considered. By comparing the actual numerical results with the approximate ones, we find that exp(−σΦ2) gives a better approximation for the Strehl ratio than does the Marechal formula. Whereas the Marechal formula underestimates the Strehl ratio, exp(−σΦ2) generally overestimates it, especially for annular pupils with a large obscuration.

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223 citations

On the Diffraction of an Object-glass with Circular Aperture

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George Biddell Airy

01 Jan 1835

185 citations

Journal Article•DOI•

Strehl ratio for primary aberrations: some analytical results for circular and annular pupils.

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Virendra N. Mahajan¹•Institutions (1)

Charles Stark Draper Laboratory¹

01 Sep 1982-Journal of the Optical Society of America

TL;DR: In this paper, a closed-form solution for the Strehl ratio was derived for imaging systems with circular and annular pupils aberrated by primary aberrations, except in the case of coma, for which the integral form was used.

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Abstract: Imaging systems with circular and annular pupils aberrated by primary aberrations are considered. Both classical and balanced (Zernike) aberrations are discussed. Closed-form solutions are derived for the Strehl ratio, except in the case of coma, for which the integral form is used. Numerical results are obtained and compared with Marechal’s formula for small aberrations. It is shown that, as long as the Strehl ratio is greater than 0.6, the Marechal formula gives its value with an error of less than 10%. A discussion of the Rayleigh quarter-wave rule is given, and it is shown that it provides only a qualitative measure of aberration tolerance. Nonoptimally balanced aberrations are also considered, and it is shown that, unless the Strehl ratio is quite high, an optimally balanced aberration does not necessarily give a maximum Strehl ratio.

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175 citations