A New 'Analytic' Method for Computing the Optical Transfer Function
TL;DR: Using a series expansion in Zernike polynomials to express the pupil function of an optical system, a means for computing the Optical Transfer Function has been found which avoids explicit numerica as discussed by the authors.
Abstract: Using a series expansion in Zernike polynomials to express the pupil function of an optical system, a means for computing the Optical Transfer Function has been found which avoids explicit numerica...
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TL;DR: A powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0=OTFperfect is applied.
Abstract: We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0=OTFperfect. To this end, we apply a powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems. Here we depart from Legendre polynomials for the particular case of rotationally symmetric OTF and from spherical harmonics for the general case. Numerical experiments with different examples show that the number of terms necessary to obtain an accurate linear expansion of the OTF mainly depends on the image quality. In the rotationally symmetric case we obtained a reasonable accuracy with approximately 10 basis functions, but in general, for cases of poor image quality, the number of basis functions may increase and hence affect the efficiency of the method. Other potential applications, such as new image quality metrics are also discussed.
9 citations
TL;DR: The light energy in the Point Spread Function (PSF) enclosed within a circle of specified radius centred on the gaussian image point was calculated analytically from an orthogonal series representation for the PSF.
Abstract: The light energy in the Point-Spread Function (PSF) enclosed within a circle of specified radius centred on the gaussian image point may be calculated analytically from an orthogonal series representation for the PSF.
7 citations
TL;DR: In this paper, an off-axis optical transfer function (OTF) can be represented as a linear combination of analytical functions where the weighting terms are directly related to the wavefront error coefficients and apodization of the complex pupil function.
Abstract: The Optical Transfer Function (OTF) and its modulus the Modulation Transfer Function (MTF) are metrics of optical system performance However in system optimization, calculation times for the OTF are often substantially longer than more traditional optimization targets such as wavefront error or transverse ray error The OTF is typically calculated as either the autocorrelation of the complex pupil function or as the Fourier transform of the Point Spread Function We recently demonstrated that the on-axis OTF can be represented as a linear combination of analytical functions where the weighting terms are directly related to the wavefront error coefficients and apodization of the complex pupil function Here, we extend this technique to the off-axis case The expansion technique offers a potential for accelerating OTF optimization in lens design, as well as insight into the interaction of aberrations with components of the OTF
7 citations
01 May 2019
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01 May 2019
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References
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Book•
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01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
[...]
01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
Book•
01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.
9,584 citations
TL;DR: In this paper, ausammenfassung auf Grundlage der A b b eschen Beugungstheorie der optischen Abbildung wird das Aussehen eines Hohlspiegels mit willkurlich verlaufenden kleinen Abweichungen beim Foucaul tschen Schneidenverfahren and beim neuen Phasenkontrastverfhren berechnet.
967 citations