# Aberration Theory Made Simple

##### Citations

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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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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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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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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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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