Chapter 6 Assessment of optical systems by means of point-spread functions

Braat, Joseph J. M.; Haver, Sven van; Janssen, Ajem Guido; Dirksen, Peter

doi:10.1016/s0079-6638(07)51006-1

Cited by 56 publications

(63 citation statements)

References 64 publications

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“…The plane wave expansion of an electric field is commonly written in terms of the complex amplitudes of the perpendicular (s) and parallel (p) components to the plane of incidence [14]:…”

mentioning

confidence: 99%

Radially Polarized Light for Detection and Nanolocalization of Dielectric Particles on a Planar Substrate

et al. 2015

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A fast noninvasive method based on scattering from a focused radially polarized light to detect and localize subwavelength nanoparticles on a substrate is presented. The technique relies on polarization matching in the far field between scattered and spurious reflected fields. Results show a localization uncertainty of ≈ 10 −4 λ 2 is possible for a particle of area ≈λ 2 =16. The effect of simple pupil shaping is also shown.

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“…The plane wave expansion of an electric field is commonly written in terms of the complex amplitudes of the perpendicular (s) and parallel (p) components to the plane of incidence [14]:…”

mentioning

confidence: 99%

Radially Polarized Light for Detection and Nanolocalization of Dielectric Particles on a Planar Substrate

et al. 2015

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“…The results presented here yield the same limiting value for this special case. Also, in accordance with former results from ENZ analysis (see Appendix D of [36], where a point source at infinity was considered), one can devise a series expansion to quickly obtain accurate values of the integral above that applies to imaging at finite distances. The functions that are used in the expansion and the values of the new expansion coefficients are given in Appendix A.…”

Section: ͑30͒mentioning

confidence: 61%

“…The general expression for an arbitrary field distribution on the exit pupil sphere in image space can be found in [36],…”

Section: ͑27͒mentioning

confidence: 99%

Vectorial aerial-image computations of three-dimensional objects based on the extended Nijboer-Zernike theory

et al. 2009

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We present details of a novel imaging algorithm based on the extended Nijboer-Zernike (ENZ) theory of diffraction. We derive integral expressions relating the electric field distribution in the entrance pupil of an optical system to the electric field in its focal region. The evaluation of these integrals is made possible by means of a highly accurate and efficient series expansion similar to those occurring in standard ENZ theory. Based on these results an ENZ imaging scheme is constructed and evaluated in detail with attention to the convergence properties and computational complexity of the new method.

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“…First we give the definition of the complex Zernike polynomials, in which any pupil function can be decomposed. Then, we explain a result from ENZ-theory [12,14], which relates the pupil Zernike modes Z m n to basic functions V m n in the field in the focal region.…”

Section: Theorymentioning

confidence: 99%

“…It relies on a result of the Extended Nijboer-Zernike theory, as has been suggested by [11]. By exploiting a one-toone correspondence between the Zernike polynomials which compose the pupil function and functions which compose the focal field [12], the number of degrees of freedom reduces to the number of polynomials with which the pupil is constructed, while the computation of the focal field is done by a quick matrix multiplication, rather than a time consuming diffraction integral. In particular, we present in this work an algorithm to find a pupil function which gives rise to an extended depth of focus for the case of a 0.4 numerical aperture, with low loss (less than 40%) of light intensity.…”

Section: Introductionmentioning

confidence: 99%

Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory

Wei¹,

Konijnenberg²,

Kumar³

et al. 2014

Frontiers in Optics 2014

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Abstract:In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM). 145-148 (1965). 6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento 9, 426-438 (1952). 7. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). 8. C. J. R. Sheppard, "Synthesis of filters for specified axial properties," J. Mod. Opt. 43, 525-536 (1996)

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Chapter 6 Assessment of optical systems by means of point-spread functions

Cited by 56 publications

References 64 publications

Radially Polarized Light for Detection and Nanolocalization of Dielectric Particles on a Planar Substrate

Radially Polarized Light for Detection and Nanolocalization of Dielectric Particles on a Planar Substrate

Vectorial aerial-image computations of three-dimensional objects based on the extended Nijboer-Zernike theory

Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory

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