Numerical evaluation of a class of integrals for image assessment.
TL;DR: A new quadrature technique is presented that obviates the need for knowledge of derivatives of the argument of the exponential integrand in the calculation of image assessment critiera.
Abstract: The calculation of image assessment critiera, eg, the Strehl ratio, the point spread function, or the optical transfer function, involves the evaluation of an integral where the integrand is highly oscillatory over a large range of integration Prefaced with a brief description of the well-known numerical quadrature methods adopted for the purpose, this paper presents a new quadrature technique that obviates the need for knowledge of derivatives of the argument of the exponential integrand Some illustrative numerical results are presented
Citations
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Dissertation•
21 Mar 2016
TL;DR: In this paper, a chromatisch-kon-fokale system is described, in which the spektralen Kompenenten of the system are modelled.
Abstract: Chromatisch-konfokale Systeme fokussieren die spektralen Kompenenten eines
polychromatischen Signals auf unterschiedliche raumliche Positionen, an
denen sie mit Hilfe von Blenden gefiltert werden. Auf diese Weise konnen
Informationen einerseits in der Spektralverteilung eines optischen Signals
gespeichert werden. Anderseits kann auch die Spektralverteilung eines
polychromatischen Signals ermittelt werden. Chromatisch-konfokale Systeme
werden haufig zur beruhrungslosen Abstandsmessung und fur die
ortsaufgeloste Spektroskopie eingesetzt. In dieser Arbeit werden
Designstrategien fur chromatisch-konfokale Systeme entwickelt. Ein
Schwerpunkt liegt auf der systematischen Modellierung der Signalentstehung
unter Berucksichtigung der physikalischen Eigenschaften des optischen
Systems, der Abbildungsfehler und der Eigenschaften des Detektionssystems.
Hierbei werden insbesondere auch inkoharente Lichtquellen und raumlich
ausgedehnte Beleuchtungsgeometrien berucksichtigt. Schnelle numerische
Implementationen dieser Modelle erlauben in allen Stadien des
Designprozesses eine Vorhersage des spektralen Filterverhaltens. Das
spektrale Filterverhalten wird als primares Bewertungskriterium fur die
Leistungsfahigkeit des optischen Systems verwendet und wird zur Ableitung
effektiver Designstrategien herangezogen. Die Designstrategien umfassen
sowohl die Entwicklung von Startsystemen als auch den nachfolgenden
Optimierungsprozess, bei dem monochromatische Abbildungsfehler
berucksichtigt werden. Der Fokus liegt hierbei insbesondere auf der
nachtraglichen Korrektur der Abbildungsfehler wahrend der Signalverabeitung
und auf ihrer automatischen Kompensation durch bestimmte Systemanordnungen.
In Kombination mit den neu entwickelten Signalerzeugungsmodellen ermoglicht
dieser Ansatz die Entwicklung optimierter, kompakter und gunstiger
Sensorsysteme, die auf die Anforderungen des jeweiligen Anwendungsgebietes
zugeschnitten sind und auf kostengunstigen Lichtquellen wie Leuchtdioden
basieren. Die vorgestellten Designstrategien werden fur die Entwicklung
verschiedener Demonstrator- und kommerzieller Sensorsysteme eingesetzt.
24 citations
01 Jan 2008
TL;DR: In this article, the role of amplitude-, phase-, and polarization distribution on the tightly focused structure of the optical beams is reviewed. And some applications in which tight focusing is desired are briefly discussed.
Abstract: Complex amplitude and polarization distribution of an optical beam plays a dominant role in shaping the focused structure of the beam. It is therefore possible to engineer the focal spot using the pupil function manipulation. Helical phase structure arising due to phase singularity in the wave front plays an important role in shaping the focal spot. Tight focusing of an optical beam produces intensity distribution in the focal volume different from the well-known results based on scalar theory, and polarization distribution shows space variant characteristics. In the present paper, roles of the amplitude-, phase-, and polarization distribution on the tightly focused structure of the optical beams are reviewed. Impact of the helical phase structure in the pupil function engineering and subsequently on the focused structure is discussed with special reference to the authors' investigations at IIT Delhi. Certain applications in which tight focusing is desired are briefly discussed. Some miscellaneous investigations are also mentioned.
7 citations
Cites background or methods from "Numerical evaluation of a class of ..."
...…1980, Hopkins and Yzuel 1970, Matsui et al 1976 [398-402]), (Yzuel and Arlegui 1980, Gravelsaeter and Stamnes 1982, Stamnes and Spjelkavik 1983, Hazra 1988, Mendlovic et al 1997 [403-407]), (Stamnes and Heier 1998, Cooper et al 2002, Cooper and Sheppard 2003, Engelberg and Ruschin 2004,…...
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...Hence numerical methods are preferred for their evaluation, and a fair amount of literature is available on the subject (Hopkins 1957, Barakat 1964, 1980, Hopkins and Yzuel 1970, Matsui et al 1976 [398-402]), (Yzuel and Arlegui 1980, Gravelsaeter and Stamnes 1982, Stamnes and Spjelkavik 1983, Hazra 1988, Mendlovic et al 1997 [403-407]), (Stamnes and Heier 1998, Cooper et al 2002, Cooper and Sheppard 2003, Engelberg and Ruschin 2004, Leutenegger et al 2006 [408-412]), (Xin et al 2007, Kaddour et al 2008, Shimobaba et al 2008 [413-415])....
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TL;DR: This paper dwells upon the inverse problem of global optimization of the pupil function by phase filtering in accordance with the desired PSF.
Abstract: Resolution capability of any optical imaging system is limited by residual aberrations as well as diffraction effects. Overcoming this fundamental limit is called super-resolution. Several new paradigms for super-resolution in optical systems use ‘a posteriori’ digital image processing. In these ventures the three-dimensional point spread function (PSF) of the lens plays a key role in image acquisition. A straightforward tailoring of the PSF can be performed by appropriate pupil plane filtering. With a brief review of the state-of-art in this research area, this paper dwells upon the inverse problem of global optimization of the pupil function by phase filtering in accordance with the desired PSF.
6 citations
TL;DR: The use of phase annuli as pupil filters in tailoring of both transverse and axial resolution is explored, with results reported on an application of evolutionary programming in solving this problem to obtain globally or quasi-globally optimum solutions.
Abstract: Pupil plane filtering provides a convenient technique for modifying the point spread function. Such modifications are
used in many practical applications that require enhancement of selective frequency band in images. Also, in many new
imaging paradigms, acquisition of 3D image information calls for tailoring of the 3D point spread function. This can be
achieved by suitable pupil plane filtering, preferably by phase filters. By using a pupil plane filter with an array of
concentric annuli, the point spread function can be tailored in a fashion such that a narrow central lobe is surrounded by
neighboring lobes of low amplitude, with one or more lobes of high amplitude spaced far away from the center. In our
study we intend to explore the use of phase annuli as pupil filters in tailoring of both transverse and axial resolution.
Determination of such phase filters in accordance with a set of prespecified requirements for amplitude/intensity
distribution around the focus constitutes a problem of nonlinear optimization. This paper reports some results of our
preliminary investigations on an application of evolutionary programming in solving this problem to obtain globally or
quasi-globally optimum solutions.
6 citations
Cites background from "Numerical evaluation of a class of ..."
...0 = = ∫ rdr F (31) The normalized amplitude ( ) b FN is given by, ( ) ( ) ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = = b b J F b F b FN 1 2 0 ) ( (32) Now considering a phase filter with M concentric equal area of annular zones, let, ( ) ∑ = = M m m r f r f 1 ) ( m B (33) where, ( ) r m B are zero-one or Walsh Block functions as defined earlier in equation (18)....
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References
More filters
TL;DR: A new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency is outlined.
Abstract: We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using fast Fourier transforms. The new algorithm offers advantages in speed and substantial advantages in storage requirements over conventional methods for evaluating Hankel transforms with large numbers of points.
293 citations
TL;DR: The diffraction integral for the disturbance produced in the image plane normal to the optical axis by an extra-axial pencil has been shown to lead to a Fourier transform provided the exit pupil surface is taken to be that of the reference sphere as discussed by the authors.
Abstract: The diffraction integral for the disturbance produced in the image plane normal to the optical axis by an extra-axial pencil has been shown to lead to a Fourier transform provided the exit pupil surface is taken to be that of the reference sphere. It has been shown also that, except for small aperture and field sizes, the effect on the wave-front aberration of a shift of the image plane is not represented with sufficient accuracy merely by a term proportional to the aperture squared. Both of these results have been respected in formulating a numerical technique for the calculation of point spread functions. The diffraction integral is evaluated in polar coordinates, and is such that no error is made in approximating the domain of the exit pupil in cases where this may be represented by an ellipse. A study of the accuracy obtained has shown that, if each quadrant of the pupil is divided into a 20 × 20 mesh of elementary areas, the error in the intensity is not expected to exceed 0·8 per cent of the intensi...
93 citations
01 Oct 1957
TL;DR: A die for use in a food chopper downstream of the coarse-cut die is formed with an array of like small-diameter holes and on each of its faces with an arrays of grooves having a width substantially greater than the diameter of the through-going holes extending at an angle to the blade which sweeps over the upstream face of this die.
Abstract: A die for use in a food chopper downstream of the coarse-cut die is formed with an array of like small-diameter holes and on each of its faces with an array of grooves having a width substantially greater than the diameter of the through-going holes and extending at an angle to the blade which sweeps over the upstream face of this die. Particles which have passed through the upstream die and which are unable to pass through the small-diameter holes in the downstream die are caught in the grooves and cut between the downstream edge of the grooves and the cutter blade. These grooves are arrayed such that the cutter blade conducts the food along the grooves, and the grooves may be of decreasing depth in the direction of travel of the material therealong so as to allow the material to be reduced to very small size. At the inner ends the grooves may terminate in large-diameter throughgoing holes which are connected to an arrangement for carrying unchoppable particles out of the chopper.
90 citations
TL;DR: In this article, the sampling theorem is applied to optical diffraction theory as a computational tool and formulas are developed in terms of sampled values of the point spread function for the transfer function, total illuminance, line spread function and cumulative line spread functions.
Abstract: The sampling theorem is applied to optical diffraction theory as a computational tool. Formulas are developed in terms of sampled values of the point spread function for the transfer function, total illuminance, line spread function and cumulative line spread function. Typical numerical examples are presented. The theory is presented for general point spread functions for slit and square apertures, but only for rotationally symmetric point spread functions for circular apertures. In the case of the slit aperture, the following question is answered: Given the real part of the incoherent transfer function, determine its imaginary part and vice versa. The theory of conjugate Fourier series and finite Hilbert transforms is introduced in order to answer this question.
59 citations
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...
45 citations