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Cascaded Diffraction in Optical Systems. PartI: Simulation Model

Herbert Gross

DOI: 10.1364/JOSAA.375526 Received 15 Aug 2019; Accepted 06 Dec 2019; Posted 06 Dec 2019  View: PDF

Abstract: In every real optical system the light beam or ray bundle is laterally limited bydiaphragms or lens boundaries. Therefore, from a rigorous point of view, a diffractioncalculation of the point spread function by assuming a truncation at the exit pupil is asimplification. If several boundaries at different z-positions inside a system truncate the rays,cascaded diffraction occurs and the field in the exit pupil is modified in amplitude and phaseby the edge diffraction effects at all relevant boundaries. A simple model for a fast estimationof these effects and a rule of thumb for real optical systems are worked out in this publication.

Cascaded Diffraction in Optical Systems. Part II: Example Calculations

Herbert Gross

DOI: 10.1364/JOSAA.375533 Received 15 Aug 2019; Accepted 06 Dec 2019; Posted 06 Dec 2019  View: PDF

Abstract: In every real optical system the light beam or ray bundle is laterally limited by diaphragms or lens boundaries. Therefore, from a rigorous point of view, a diffraction calculation of the point spread function by assuming a truncation at the exit pupil is a simplification. If several boundaries at different z-positions inside a system truncate the rays, cascaded diffraction occurs and the field in the exit pupil is modified in amplitude and phase by the edge diffraction effects at all relevant boundaries. A simple model for a fast estimation of these effects for optical systems is presented in an adjacent publication. Some example calculations for real setups and an overview about the order of magnitude of the cascaded diffraction effects are worked out in this publication.

Non-Euclidean symmetries of first-order optical systems

Juan Monzón, Jose Montesinos, and Luis Sanchez-Soto

DOI: 10.1364/JOSAA.378661 Received 23 Sep 2019; Accepted 06 Dec 2019; Posted 06 Dec 2019  View: PDF

Abstract: We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a M\"{o}bius transformation. We examine this action from the perspective of non-Euclidean hyperbolic geometry and resort to the isometric-circle method to decompose it as a reflection followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

Spectra manipulation with photorefractivity effect via spatial–spectral correspondence relationship

Hsun-Ching Hsu and Pin Han

DOI: 10.1364/JOSAA.379536 Received 04 Oct 2019; Accepted 05 Dec 2019; Posted 05 Dec 2019  View: PDF

Abstract: A scheme based on photorefractivity effect to manipulate polychromatic spectra is proposed. Using photorefractive material as a sinusoidal phase grating, the resultant diffracted spatial intensity distribution for monochromatic light is mapped to spectrum distribution for polychromatic light, via the spatial–spectral correspondence relationship for mono-polychromatic light diffraction. Theoretical analyses and numerical examples show that for different detection angles, the diffracted spectrum exhibits different features, and that specific spectral lines selection or lines filter effects can be achieved. We also discuss the possibility of applying this spectral scheme to detect temperature or grating’s period changes.

Time-domain diffuse optical tomographyutilizing truncated Fourier series approximation

Meghdoot Mozumder and Tanja Tarvainen

Doc ID: 376206 Received 26 Aug 2019; Accepted 04 Dec 2019; Posted 04 Dec 2019  View: PDF

Abstract: Diffuse optical tomography (DOT) uses near infrared light for in vivo imagingof spatially varying optical parameters in biological tissues. It is known that time-resolvedmeasurements provides the richest information on soft tissues, among other measurement typesin DOT such as steady state and intensity modulated measurements. Therefore, several integraltransform based moments of the time-resolved DOT measurements has been considered, toestimate spatially distributed optical parameters. However, the use of such moments can resultin low contrast images and cross-talks between the reconstructed optical parameters, limitingtheir accuracy. In this work we propose utilizing a truncated Fourier series approximation intime-resolved DOT. Using this approximation, we obtained optical parameter estimates withaccuracy comparable to using whole time-resolved data, using low computational time andresources. The truncated Fourier series approximation based estimates also displayed goodcontrast and minimal parameter cross-talk, and the estimates further improved in accuracy whenmultiple Fourier frequencies were used.

Fast and robust reconstruction algorithm forfluorescence diffuse optical tomography assuming acuboid target

Chunlong Sun, gen nakamura, Goro Nishimura, yu jiang, Jijun Liu, and Manabu Machida

Doc ID: 377152 Received 16 Sep 2019; Accepted 04 Dec 2019; Posted 04 Dec 2019  View: PDF

Abstract: A fast algorithm for fluorescence diffuse optical tomography is proposed. The algorithm is robust againstthe choice of initial guesses. We identify the location of a fluorescence target by assuming a cuboid(rectangular parallelepiped) for the fluorophore target. The proposed numerical algorithm is verified by anumerical experiment and an experiment with a meat phantom. The target position is reconstructed witha cuboid from measurements in time domain. Moreover, the long-time behavior of the emission light isinvestigated making use of the analytical solution to the diffusion equation.

Level-line moirés by superposition of cylindricalmicro-lens gratings

Thomas Walger, Théophane Besson, Valentin Flauraud, Roger Hersch, and Juergen Brugger

Doc ID: 374132 Received 05 Aug 2019; Accepted 02 Dec 2019; Posted 02 Dec 2019  View: PDF

Abstract: Two superposed layers of transparent cylindrical lenslet gratings create classicalmoiré fringes, when illuminated from behind. We rely on this observation to conceive specialdevices made of superposed lenslet gratings that produce compelling beating shapes, when tiltedagainst the light. Level-line moirés are created by superposing gratings of cylindrical lensletsof the same period on both sides of a substrate and by locally shifting some of the cylindricallenses according to the moiré theory. Depending on the illumination and the viewing conditions,constant light intensities or colors move across graphical elements or faces. Such level-line moirésamples have been fabricated and characterized to determine the optimal fabrication parameters.Thanks to their striking visual appeal and their relatively challenging fabrication, moirés createdby superposition of lenslets have a high potential for document security, art, and decoration.

Characterization of passivity in Mueller matrices

Jose Gil and Ignacio San José

Doc ID: 378752 Received 26 Sep 2019; Accepted 02 Dec 2019; Posted 02 Dec 2019  View: PDF

Abstract: Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming one. This natural passive behavior imposes certain mathematical restrictions on the corresponding Mueller matrices associated to the said transformations. Although the general conditions for passivity in Mueller matrices were presented in a previous paper [J. J. Gil, J. Opt. Soc. Am. A 17, 328-334 (2000)], the demonstration was incomplete. In this paper, the set of two necessary and sufficient conditions for a Mueller matrix to represent a passive medium are determined and demonstrated on the basis of its arbitrary decomposition as a convex combination of nondepolarizing and passive pure Mueller matrices. The procedure followed to solve the problem provides also an appropriate framework to identify the Mueller matrix that, among the family of proportional passive Mueller matrices, exhibits the maximal physically achievable intensity transmittance. Beyond the theoretical interest on the rigorous characterization of passivity, the results obtained, when applied to absolute Mueller polarimetry, also provide a criterion to discard those experimentally measured Mueller matrices that do not satisfy the passivity criterion.

Relating Wavefront Error to Visual Acuity in Pre and Post LASIK Eyes: A Comparison of Methods

Edward DeHoog, Robert Van Dine, Lindsay Fitzgerald-DeHoog, and Jim Schwiegerling

Doc ID: 372984 Received 30 Jul 2019; Accepted 02 Dec 2019; Posted 03 Dec 2019  View: PDF

Abstract: Contrast Threshold and Visual Strehl Ratio methods are used to predict visual acuity from wavefront error for a sample population of pre- and post-LASIK patients. Relative Error (in LogMAR) between predicted and measured visual acuity values are computed for each method and compared using Paired T-tests. Differences in aberration data between pre- and post-LASIK eyes are then evaluated. The Visual acuity prediction using Visual Strehl proved to be more accurate for pre-LASIK patients than Contrast Threshold. However, both methods are comparable for post-LASIK patients.

Analytic design of a spherochromatic singlet

Rafael Gonzalez Acuña and Julio Gutierrez-Vega

Doc ID: 377075 Received 05 Sep 2019; Accepted 02 Dec 2019; Posted 03 Dec 2019  View: PDF

Abstract: We derive the analytic formula of the output surface ofa spherochromatic lens. The analytic solution ensuresthat all the rays for a wide range of wavelengths fallinside the Airy disk. So its amount of spherical aberrationis small enough to consider the lens as diffractedlimited. We test the singlet lens using ray tracing methodsand we found satisfactory results including thespot diagram analysis for three different Abbe wavelengths.

Evolution properties of the orbital angular momentumspectrum of twisted Gaussian Schell-model beams inturbulent atmosphere

Mengyao Zhou, Weichen Fan, and Gaofeng Wu

Doc ID: 378974 Received 30 Sep 2019; Accepted 01 Dec 2019; Posted 02 Dec 2019  View: PDF

Abstract: We derive the analytical formula of the energy weight of each orbital angular momentum(OAM) mode oftwisted Gaussian Schell-model(TGSM) beams propagating in weak turbulent atmosphere. The evolutionof its OAM spectrum is studied by the numerical calculation. Our results show that the OAM spectrum ofa TGSM beam changes with the beam propagating in turbulent atmosphere which is completely differentfrom that of the TGSM beam propagating in free space. Furthermore, influences of the source parametersand the turbulence parameters on the OAM spectrum of a TGSM beam in turbulent atmosphere areanalyzed. It is found that the source parameters and turbulence parameters, such as twist factor, coherencelength, beam waist size and structure constant, have significant influences on the OAM spectrum, butthe value of wavelength and inner scale have little influence on that. Increasing the beam waist size ordecreasing the coherence length would lead to the OAM spectrum broadened in the source plane, butwould be robust for the OAM modes of TGSM beam in the turbulent atmosphere. Besides, the bigger thevalue of twist factor is, the more asymmetric the OAM mode of the TGSM beam is, and the better modedistribution can be maintained when it propagates in turbulent atmosphere. Our results have potentialapplications for free-space optical communications and detection.

Field-Only Surface Integral Equations:Scattering from a Dielectric Body

Qiang Sun, Evert Klaseboer, Alex Yuffa, and Derek Chan

Doc ID: 378669 Received 23 Sep 2019; Accepted 01 Dec 2019; Posted 02 Dec 2019  View: PDF

Abstract: An efficient field-only nonsingular surface integral method to solve Maxwell’sequations for the components of the electric field on the surface of a dielectric scatterer isintroduced. In this method, both the vector wave equation and the divergence-free constraintare satisfied inside and outside the scatterer. The divergence-free condition is replaced by anequivalent boundary condition that relates the normal derivatives of the electric field acrossthe surface of the scatterer. Also, the continuity and jump conditions on the electric andmagnetic fields are expressed in terms of the electric field across the surface of the scatterer.Together with these boundary conditions, the scalar Helmholtz equation for the components of theelectric field inside and outside the scatterer is solved by a fully desingularized surface integralmethod. Comparing with the most popular surface integral methods based on the Stratton–Chuformulation or the PMCHWT formulation, our method is conceptually simpler and numericallystraightforward because there is no need to introduce intermediate quantities such as surfacecurrents and the use of complicated vector basis functions can be avoided altogether. Also, ourmethod is not affected by numerical issues such as the zero frequency catastrophe and does notcontain integrals with (strong) singularities. To illustrate the robustness and versatility of ourmethod, we show examples in the Rayleigh, Mie, and geometrical optics scattering regimes.Given the symmetry between the electric field and the magnetic field, our theoretical frameworkcan also be used to solve for the magnetic field.

Probability of Error for Detecting a Change in aParameter and Bayesian Fisher Information

Eric Clarkson

Doc ID: 376001 Received 21 Aug 2019; Accepted 30 Nov 2019; Posted 02 Dec 2019  View: PDF

Abstract: The van Trees inequality relates the Ensemble Mean Squared Error of an estimatorto a Bayesian version of the Fisher Information. The Ziv-Zakai inequality relates the EnsembleMean Squared Error of an estimator to the Minimum Probability of Error for the task of detectinga change in the parameter. In this work we complete this circle by deriving an inequality thatrelates this Minimum Probability of Error to the Bayesian version of the Fisher Information.We discuss this result for both scalar and vector parameters. In the process we discover thatan important intermediary in the calculation is the Total Variation of the posterior probabilitydistribution function for the parameter given the data. This total variation is of interest in its ownright since it may be easier to compute than the other figures of merit discussed here.

Signal magnitude nonlinearity to an absorptioncoefficient in Photoacoustic imaging

Dongyel Kang

Doc ID: 376555 Received 28 Aug 2019; Accepted 30 Nov 2019; Posted 02 Dec 2019  View: PDF

Abstract: We investigate photoacoustic (PA) signal magnitude variation to an absorption coefficient of localized absorbingobjects measured by spherically focused ultrasound (US) transducers (TDs). For this investigation, we develop thePA simulation method that directly calculates Green function solutions of the Helmholtz PA wave equationconsidering grid-like elements on absorbing objects and US TDs. The simulation results show that the PA signalamplitude in the PA imaging is nonlinearly varied to the absorption coefficient of localized objects, which aredistinct from the known PA saturation effect. For spherical objects, especially, the PA amplitude increases up to acertain absorption coefficient showing a maximum value, and decreases even though an absorption coefficientfurther increases. We suggest conceptual and mathematical interpretations for this phenomenon by analyzing thecharacteristics of PA spectra combined with US TD transfer functions, which indicates that the combined effect ofUS TD spatial and temporal filtering is the significant role on the PA signal magnitude nonlinearity.

Pixel reassignment in image scanning microscopy: are-evaluation

Colin Sheppard, Marco Castello, Giorgio Tortarolo, Takahiro Deguchi, Sami Koho, Giuseppe Vicidomini, and Alberto Diaspro

Doc ID: 375804 Received 19 Aug 2019; Accepted 29 Nov 2019; Posted 02 Dec 2019  View: PDF

Abstract: Image scanning microscopy is a technique based on confocal microscopy, in which the confocal pinholeis replaced by a detector array, and the resulting image is reconstructed, usually by the process of pixelreassignment. The detector array collects most of the fluorescent light, so the signal-to-noise ratio is muchimproved compared with confocal microscopy with a small pinhole, while the resolution is improvedcompared with conventional (wide-field) microscopy. In previous studies it has usually been assumedthat pixels should be reassigned by a constant factor, to a point midway between the illumination anddetection spots. Here it is shown that the peak intensity of the effective point spread function can befurther increased by 4% by a new choice of the pixel reassignment factor. For an array of 2 Airy units, thepeak of the effective PSF is 1.90 times that of a conventional microscope, and the transverse resolutionis 1.53 times better. It is confirmed that image scanning microscopy gives identical optical sectioningstrength to that of a confocal microscope with a pinhole equal to the size of the detector array. However,it is shown that image scanning microscopy exhibits superior axial resolution than a confocal microscopewith a pinhole the same size as the detector array. For a 2 Airy unit array, the axial resolution is 1.34 timesbetter than in a conventional microscope for the standard reassignment factor, and 1.28 times better forthe new reassignment factor. The axial resolution of a confocal microscope with a 2 Airy unit pinhole isonly 1.04 times better than conventional microscopy. We also examine the signal to noise ratio of a pointobject in a uniform background (called the detectability), and show that it is 1.6 times higher than in aconfocal microscope.

Theoretical analysis of quantum random walks withstress-engineered optics

Kevin Liang, Ashan Ariyawansa, Omar Magana Loaiza, and Thomas Brown

Doc ID: 376425 Received 29 Aug 2019; Accepted 24 Nov 2019; Posted 25 Nov 2019  View: PDF

Abstract: Quantum random walks (QRWs) are random processes in which the resulting probability density of the"walker" state, whose movement is governed by a "coin" state, is described in a non-classical manner.Previously, Q-plates have been used to demonstrate QRWs with polarization and orbital angular momentumplaying the role of coin and walker states, respectively. In this theoretical analysis, we show howstress-engineered optics can be used to develop new platforms for complex QRWs through relative simpleoptical elements. Our work opens up new paths to speed up classical-to-quantum transitions in robustphotonic networks.

CIE Self-luminous Gray-scale Calculation:inflections, parameters and high-contrastlimiting behavior

Robert Carter

Doc ID: 372076 Received 08 Jul 2019; Accepted 23 Nov 2019; Posted 25 Nov 2019  View: PDF

Abstract: Wide generalizability of the CIE-recommended gray scale calculation for selfluminousdevices suggests that its parameters, the extrema of the calculation’s derivatives andits limiting behavior are fundamental. The calculation has a negative-contrast point ofinflection not predicted by any other gray-scale calculation, but that is consistent with dataand with the terrestrial luminance histogram. The parameters of the calculation are analyzedand their significance is explained. High-positive-contrast behavior of the calculation isshown and related to scientific literature. This knowledge represents a clearer understandingof daylight suprathreshold vision, and it enables optimal luminance-coding of contemporaryhigh-resolution, high-contrast, high-luminance displays.

Focused and defocused retinal images with Bessel andAxicon pupil functions

Gerald Westheimer

Doc ID: 376356 Received 27 Aug 2019; Accepted 21 Nov 2019; Posted 27 Nov 2019  View: PDF

Abstract: Retinal image light distributions in a standard optical model of a diffraction-limited eye with roundpupils are presented for several patterns of amplitude and phase modulation of the light admitted into the eye. Ofspecial interest are circularly symmetrical configurations of truncated Bessel amplitude transmission functions, andof light subjected to axicon deviation. It is shown by several examples that this kind of beam shaping allowsgeneration of retinal imagery which can be more robust to defocus while maintaining minimal image degradationand it points to situations of two separate zones simultaneously in sharp focus, several diopters apart.

Subtraction method via phase mask enables contrastenhancement in scanned Bessel light-sheetmicroscopy

Suhui Deng, Peng Wang, Yulong Zhang, Huilin Zhou, Jianzhong Yang, and Mingping Liu

Doc ID: 367860 Received 17 May 2019; Accepted 19 Nov 2019; Posted 19 Nov 2019  View: PDF

Abstract: We report on the generation of a hollow Bessel beam with a hole along the direction of propagation by using aneasy-to-implement phase mask and investigate its effectiveness to reduce the out-of-focus background in lightsheetfluorescence microscopy (LSFM) with scanned Bessel beams by subtraction imaging. Overlaying 􀫈-phaseretardation between the two equal parts of the Bessel beam across the entrance pupil of the objective lens, ahollow Bessel beam with zero-intensity at the focal plane can be achieved. By optimizing the numerical aperture ofthe annular mask applied in the hollow Bessel beam, matched distributions of the ring system between the hollowBessel beam and the conventional Bessel beam is achieved. By subtraction between the two LSFM images, the outof-focus blur caused by the ring system of the Bessel beam can be significantly reduced. Comparison withconventional Bessel LSFM images exhibits a better sectioning capability and higher contrast.

Gaussian pulsed beam decomposition for propagationof ultra-short pulses through optical systems

Norman Girma Worku and Herbert Gross

Doc ID: 377655 Received 13 Sep 2019; Accepted 18 Nov 2019; Posted 19 Nov 2019  View: PDF

Abstract: Many applications of ultra-short laser pulses require manipulation and control of the pulse parametersby propagating them through different optical components before the target. This requires methods ofsimulating the pulse propagation taking into account all effects of dispersion, diffraction and systemaberrations. In this paper we propose a method of propagating ultra-short pulses through real opticalsystem by using the Gaussian pulsed beam decomposition. An input pulse with arbitrary spatial andtemporal (spectral) profiles is decomposed into a set of elementary Gaussian pulsed beams in the spatiospectraldomain. The final scalar electric field of the ultra-short pulse after propagation is then obtainedby performing the phase correct superposition of the electric fields all Gaussian pulsed beams which arepropagated independently through the optical system. We demonstrate the application of the method bypropagating an ultra-short pulse through a focusing aspherical lens with large chromatic aberration anda Bessel-X pulse generating axicon lens.

Twisted elliptical muti-Gaussian Schell-modelbeams and their propagation properties

Haiyun Wang, Xiaofeng Peng, Lin Liu, Fei Wang, and Yangjian Cai

Doc ID: 377796 Received 16 Sep 2019; Accepted 18 Nov 2019; Posted 19 Nov 2019  View: PDF

Abstract: We introduce a new kind of partially coherent sources whose cross spectral density(CSD) function is described as the incoherent superposition of elliptical twisted GaussianSchell-model (TGSM) sources with different beam widths and transverse coherence widths,named as twisted elliptical multi-Gaussian Schell-model (TEMGSM) beam. Analyticalexpression for the CSD function propagating through a paraxial ABCD optical system isderived with the help of generalized Collins formula. Our results show that the TEMGSMbeam is capable of generating flat-topped elliptical beam profile in the far field, and the beamspot during propagation exhibits the clockwise/anti-clockwise rotation with respect to itspropagation axis. In addition, the analytical expressions for the orbital angular momentum(OAM) and the propagation factor are also derived by means of Wigner distribution function(WDF). The influences of the twisted factor and the beam index on the OAM and thepropagation factor are studied and discussed in detail.

Glens combinations that satisfy theedge-imaging condition of transformation optics

Tomas Tyc, Jakub Belin, Stephen Oxburgh, Chris White, Euan Cowie, and Johannes Courtial

Doc ID: 378040 Received 16 Sep 2019; Accepted 06 Nov 2019; Posted 14 Nov 2019  View: PDF

Abstract: We recently introduced the edge-imaging condition, a necessary condition on allgeneralised lenses (glenses) [Chaplain et al., J. Opt. Soc. Am. A 33, 962 (2016)] in a ray-opticaltransformation-optics (RTO) device that share a common edge [Courtial et al., Opt. Express26, 17872 (2018)]. The edge-imaging condition states that, in combination, such glenses mustimage every point to itself. Here we start the process of building up a library of combinations ofglenses that satisfy the edge-imaging condition, starting with all relevant combinations of up tothree glenses. As it grows, this library should become increasingly useful when constructinglens-based RTO devices.

Relativistic photography with a wide aperture

Norman Gray, Ruaridh O'Donnell, Ross MacSporran, Stephen Oxburgh, and Johannes Courtial

Doc ID: 377476 Received 10 Sep 2019; Accepted 04 Nov 2019; Posted 06 Nov 2019  View: PDF

Abstract: We discuss new effects related to relativistic aberration, which is the apparent distortion of objects moving at relativistic speeds relative to an idealised camera. Our analysis assumes that the camera lens is capable of stigmatic imaging of objects at rest with respect to the camera, and that each point on the shutter surface is transparent for one instant, but different points are not necessarily transparent synchronously. We pay special attention to the placement of the shutter. Firstly, we find that a wide aperture requires the shutter to be placed in the detector plane to enable stigmatic images. Secondly, a Lorentz-transformation window [Oxburgh et al., Proc. SPIE 9193, 91931K (2014)] can correct for relativistic distortion. We illustrate our results, which are significant for future spaceships, with ray-tracing simulations.

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