Accepted papers to appear in an upcoming issue
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Achieving ultra-long optical needle with duplex vectoroptical field and parabolic hybrid mask
Peng-Cheng Zhao, Xu-Zhen Gao, Jia-Hao Zhao, Yue Pan, and zhong-xiao man
DOI: 10.1364/JOSAA.442491 Received 03 Sep 2021; Accepted 26 Oct 2021; Posted 26 Oct 2021 View: PDF
Abstract: The optical needle generated by the tightly focusedvector optical field (VOF) has attracted wide attentionand been applied in various areas. In the previousresearches, two typical kinds of VOFs are generallyused to generate optical needles including radially polarized VOF (RP-VOF) and vortex azimuthally polarized VOF (VAP-VOF). Here, we propose a new kindof duplex VOF, which is designed by arranging the RPVOF and VAP-VOF in the concentric belts. With thehelp of the binary phase mask, the optical needle of thetightly focused duplex VOF is much longer than thatgenerated by the two conventional VOFs. Meanwhile,the optical needle has a three-section polarization distribution, as the longitudinal component is dominantat center while the transverse components are at twoends along the longitudinal axis, which is differentfrom pure transversely polarized optical needle andoptical needle with dominant longitudinal component.Furthermore, the parabolic hybrid mask (PHM) is proposed, which can improve the length of the optical needle for the duplex VOF, RP-VOF, and VAP-VOF. Whenapplying the duplex VOF and the PHM simultaneously,the ultra-long optical needle can be achieved. The duplex VOF and the PHM we propose are superior relative to other VOFs and masks in terms of generatingthe ultra-long optical needles, which can be used inareas including optical detection, high-density storage,super-resolution imaging and nano lithography.
The non-linearity that enables theperception of counter-phase flicker
DOI: 10.1364/JOSAA.438897 Received 27 Jul 2021; Accepted 26 Oct 2021; Posted 26 Oct 2021 View: PDF
Abstract: Counter-phase flicker is perceptible consequent on a non-linearity between each retina and binocularfusion. This paper models that non-linearity in terms of the radio reception technology of the earlytwentieth century. The non-linearity is probably realized in the retinal ganglion cells.
FFT-based simulation of hologram-recording processfor light-in-flight recording by holography
Takashi Kakue, Tomoyoshi Inoue, Tomoyoshi Shimobaba, Tomoyoshi Ito, and Yasuhiro Awatsuji
DOI: 10.1364/JOSAA.441585 Received 30 Aug 2021; Accepted 26 Oct 2021; Posted 26 Oct 2021 View: PDF
Abstract: We proposed a numerical simulation method of the hologram-recording process for light-in-flight recording by holography (LIF holography) based on fast Fourier transform to improve the efficiency of the simulation. Because it is crucial to consider the difference in the optical-path length between the object andreference light pulses, we modified a point-spread function by considering the optical-path lengths of theobject and reference light pulses and whether both pulses interfere with each other in LIF holography.The computational time was shortened by 5.5 × 105times for the 4, 096 × 4, 096 resolution of the hologramusing the proposed method. We evaluated the proposed method by calculating the root mean square error(RMSE) of the reconstructed holographic images. The RMSEs were relatively small considering the effectof speckle noise; these results effectively demonstrated the validity of the proposed method. Moreover,we reconstructed the moving pictures of light pulse propagation from the hologram generated by theproposed method. We compared the simulation and experimental results, and succeeded in qualitativelydemonstrating the validity of the proposed method.
Sampling analysis for Fresnel diffraction fields based on phase space representation
Jiasheng Xiao, Wenhui Zhang, and Hao Zhang
DOI: 10.1364/JOSAA.440464 Received 17 Aug 2021; Accepted 24 Oct 2021; Posted 25 Oct 2021 View: PDF
Abstract: Numerical calculation of Fresnel diffraction is widely used in optical applications where wave propagation is needed. Most cases for simulating Fresnel diffraction only consider the sampling of complex amplitude fields, which lacks the comprehensiveness when different diffraction fields are of interest. In this study, from the perspective of phase space optics, we provide a systematical analysis on the sampling of all Fresnel diffraction fields, including the complex amplitude, intensity, amplitude and phase. The space-bandwidth product of each field is illustrated with the aid of phase space diagram, which is further demonstrated from a physical point of view. Such a comprehensive sampling analysis could provide practical suggestions to the numerical calculations of various diffraction fields according to the requirements. Numerical experiments with discrete Fresnel diffraction are implemented to verify the feasibility of the analyses.
Spectral density of light waves on scattering from a collection of semi-soft boundary particles
Qihang Dai, Zhenfei Jiang, Hange Wang, Xiaoling Ji, and Tao Wang
DOI: 10.1364/JOSAA.442902 Received 13 Sep 2021; Accepted 22 Oct 2021; Posted 22 Oct 2021 View: PDF
Abstract: The scattering behavior of light waves from a collection of semi-soft boundary particles is discussed. It is shown that the structural information of the medium, i.e., the position distribution of the particles, the effective width of each particle, and the boundary conditions of each particle, may play an important role in the distribution of the far zone scattered spectral density. This result may have potential applications in the manipulation of scattered field and in the measurement of structural information of particulate media.
Destroying and recovering spiral vortex beams due to figured perturbations
Alexander Volyar, Eugeny Abramochkin, Yana Akimova, and Mikhail Bretsko
DOI: 10.1364/JOSAA.440756 Received 20 Aug 2021; Accepted 21 Oct 2021; Posted 21 Oct 2021 View: PDF
Abstract: Using asymptotic approaches and an experiment supported by a computer simulation, we examined transforming spiral vortex (SV) beams caused by affecting figured hard-edged apertures. By the example of a tetragonal beam, we considered three perturbation scenarios: 1) asymmetric perturbation, when an opaque screen covers the caustic only on one side of the tetragon, 2) symmetric perturbation, when the figured aperture covers the entire beam except for a narrow caustic region, and 3) symmetric perturbation when the figured aperture screens only the caustic region without affecting the rest of the beam. At the same time, we have carried out asymptotic calculations for all types of polygonal beams. It was found that the beam can partially restore its original state if the aperture does not touch the caustic region. Otherwise, the former SV beam structure is destroyed, but a new stable state appears in a far diffraction zone
Blazed grating pupil remapping and rotationalsynthesis with computational phasecorrection for a two-aperture system
Sarah Krug and David Rabb
DOI: 10.1364/JOSAA.431363 Received 21 May 2021; Accepted 18 Oct 2021; Posted 18 Oct 2021 View: PDF
Abstract: Multi-aperture imaging systems can be used to decrease the size, weight, and cost ofan imaging system while retaining a resolution related to the diameter of the aperture gain. Onesolution for phasing apertures in an array uses anamorphic pupil remapping and acomputational phase correction algorithm. It is shown that using blazed gratings to remap theaperture fields reduces FDC and leads to piston corrections for partially coherent illumination.Additionally, rotational aperture synthesis is used to combine two piston corrected images andcreate an image with resolution increases in more than just the axis of aperture gain.
Electron Holography by Planar Electron Backscattered Diffraction Patterns
Matthias Gianfelice and Carsten Westphal
DOI: 10.1364/JOSAA.442927 Received 09 Sep 2021; Accepted 14 Oct 2021; Posted 15 Oct 2021 View: PDF
Abstract: Since Dennis Gabor introduced holography in 1948, it is of interest to apply it to atomar scales. Electrons with high kinetic energies may indeed be used for electron holography. We describe the holographic process with electron backscatter diffraction as a non-invasive surface structure analysis. We show that typical parameters of current experiments already provide the requirements to collect sufficient data for a successful holographic reconstruction. As a first example we describe how holography may be applied to planar EBSD patterns. Furthermore, we discuss the influence of experimental parameters in order to improve the quality of the reconstruction.
Effect of Unknown Emitter Intensities on LocalizationAccuracy in Stochastic Optical Localization NanoscopyUsing Single Frames
Yi Sun and Yue Guan
DOI: 10.1364/JOSAA.429996 Received 27 Apr 2021; Accepted 13 Oct 2021; Posted 15 Oct 2021 View: PDF
Abstract: Cramer-Rao lower bound (CRLB) indicates the inherent power of stochastic optical localization nanoscopy in spatiallyresolving emitters. The CRLB for a known and identical intensity of emitters is obtained previously. In practice, intensitiesof emitters at times are unknown and must be estimated along with emitter localization. To study effect of unknownemitter intensities on localization accuracy, we analyze Fisher information and CRLB and obtain their formulas in threeextended cases: emitter intensities are (i) known and arbitrary, (ii) known to be identical with an unknown value, and(iii) all unknown. The effect of unknown emitter intensities on CRLB is then numerically investigated in three scenarios:2D emitters on a line with an Airy point spread function (PSF), 2D randomly distributed emitters with a Gaussian PSF, and3D randomly distributed emitters with an astigmatic PSF. In all three scenarios it is shown that in comparison with thecase of a known and identical emitter intensity, cases (i) and (ii) slightly increase CRLB; however, case (iii) significantlyincreases CRLB no matter whether the emitter intensities are identical or not. These results imply that in practice theemitter intensities, which are known a prior to have an identical value, incur little penalty on localization accuracy. Incontrast, the emitter intensities, which are all unknown, significantly lower localization accuracy unless the emitterdensity is so low as to have little chance of overlapped PSFs. The analytical and numerical results can be extensivelyapplied to set up an experiment, develop localization algorithms, and benchmark localization algorithms.
On the sampling requirements for ptychography
DOI: 10.1364/JOSAA.430548 Received 04 May 2021; Accepted 13 Oct 2021; Posted 19 Oct 2021 View: PDF
Abstract: We investigate how the distance between probe positions and the resolution ofmeasured diffraction patterns affects the iterative ptychographic reconstruction. The ptychographicphase retrieval problem where both the object and probe are reconstructed is analyzed theoretically,by introducing a 4D object to describe the 4D ptychopgraphical data set. This is similar tointroducing the 3D Ewald sphere to describe the field in a 3D focal volume. Conclusions that aredrawn on the basis of the theoretical analysis are verified using simulations with a simplified2D ptychographic problem where the probe and object are 1D. Though the 2D problem is asimplification compared to the typical 4D ptychography problem of lensless imaging, it still haspractical applications for pulse reconstruction.
Electrodynamic Solution for Polarized Reflectivity and Wide-FieldOrientation Imaging of Uniaxial Metals
Brian Hoover, Jonathan Turner, and Cesar Ornelas-Rascon
DOI: 10.1364/JOSAA.435617 Received 01 Jul 2021; Accepted 13 Oct 2021; Posted 13 Oct 2021 View: PDF
Abstract: The polarized reflectivity of an ideally-smooth metal with uniaxial anisotropic complex refractive index,for instance metals with hexagonally close-packed (HCP) symmetry, is derived from the electromagneticwave equation for normal incidence and arbitrary crystal orientation. The resulting orientation-dependentMueller matrices of the surface are applicable to c-axis orientation-imaging of metals including beryllium,magnesium, titanium, cobalt, zinc, zirconium, tin, and most of their alloys, as well as other uniaxialcompounds. Comparing orientation images recorded with a generalized polarized-light microscope (PLM),in this case an original coherent laser PLM, with orientation images obtained by electron backscatterdiffraction (EBSD) enables imaging ellipsometry (IE) at near-normal incidence and increases confidence inellipsometric refractive-index measurements. In this initial study, without modeling oxides, the resultingc-axis orientation images of several titanium alloys are still verified to better than 11% against EBSD mapsof the same samples over instantaneous FOVs exceeding 1cm2and FOVs approaching 1in2obtained bystitching several such images together.
Image Reconstruction Approach for HighSpace-Bandwidth Product Structured IlluminationMicroscopy System
Krishnendu Samanta and Joby Joseph
DOI: 10.1364/JOSAA.432840 Received 31 May 2021; Accepted 12 Oct 2021; Posted 13 Oct 2021 View: PDF
Abstract: Conventional structured illumination microscopy(SIM) utilizes a sinusoidal excitation pattern of frequency within the detection passband and providesa maximum of 2-fold resolution enhancement overthe diffraction limit. A transmission approach proposed in an earlier publication  to further improvethe lateral resolution requires sequential higher frequency illumination patterns. However, the existingreconstruction algorithms fail to deliver appropriatereconstruction when the excitation frequency lies farfrom the passband boundary. Here, we present acorrelation-based SIM reconstruction approach for sequential high-frequency illumination patterns even ifthe pattern frequency lies far from the passband limit.The scheme can be suitably implemented in a varietyof custom-built systems where illumination frequencylies beyond the passband support (e.g.non-linear SIM,plasmonic SIM and so on).
Passive scintillometer: Theory and field measurements
DOI: 10.1364/JOSAA.438401 Received 20 Jul 2021; Accepted 11 Oct 2021; Posted 13 Oct 2021 View: PDF
Abstract: We propose design of a low-cost passive scintillometer that measures the strength of optical turbulence by analyzing scintillation in the image a straight edge between the two areas of uniform, but distinct brightness. Theory for scintillations variance is developed based on the rigorous path integral propagation model. We propose approximations that cover the most promising conditions for the passive scintillometer applications, and describe the image processing technique that separates the target characteristics from the turbulence scintillations. Results of the proof-of-concept field experiment where images of the target were taken by a consumer grade camera equipped with an inexpensive telephoto lens are presented.
A method with high accuracy for phase retrieval inFourier FPP based on the modified FCM andvariational image decomposition
Qi zhao, Chen Tang, Min Xu, and Zhenkun Lei
DOI: 10.1364/JOSAA.435345 Received 28 Jun 2021; Accepted 11 Oct 2021; Posted 15 Oct 2021 View: PDF
Abstract: Phase retrieval with high accuracy remains one of the most challenging problems in Fourier fringe projectionprofilometry(FPP). The variational image decomposition TV-Hilbert-L2 model has been proved to be a powerfultool for phase retrieval. In this paper, we first propose a modified fuzzy c-means (FCM) clustering algorithm toremove background from fringe projection patterns. In order to further improve the accuracy, we combine themodified FCM and the variational image decomposition TV-Hilbert-L2 model and propose a new method to get thefringe part from the single frame fringe projection pattern. We evaluate the performance of this method viaapplication to two simulated and one experimental fringe projection patterns and comparison with the Fouriertransform (FT), morphological operation-based bi-dimensional empirical mode decomposition (MOBEMD) andvariational image decomposition TV-Hilbert-L2 model. The experiment results show that our method improves theaccuracy of phase retrieval for TV-Hilbert-L2 model and can achieve the similar accuracy to the phase-shiftingmethod.
A Convergent Numerical Method for the Reflector Antenna Problem via Optimal Transport on the Sphere
Brittany Froese and Axel Turnquist
DOI: 10.1364/JOSAA.439679 Received 04 Aug 2021; Accepted 06 Oct 2021; Posted 07 Oct 2021 View: PDF
Abstract: We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left\Vert x - y \right\Vert$. At each point on the sphere, we replace the surface PDE with a generalized Monge-Amp\`ere type equation posed on the local tangent plane. We then utilize a provably convergent finite difference scheme to approximate the solution and construct the reflector. The method is easily adapted to take into account highly nonsmooth data and solutions, which makes it particularly well adapted to real-world optics problems. Computational examples demonstrate the success of this method in computing reflectors for a range of challenging problems including discontinuous intensities and intensities supported on complicated geoemtries.
Formulation of diffraction efficiencies ofbinary phase gratings for array illuminationwith ultrashort pulse beams
Jun Amako and Hidetoshi Nakano
DOI: 10.1364/JOSAA.439269 Received 30 Jul 2021; Accepted 05 Oct 2021; Posted 13 Oct 2021 View: PDF
Abstract: We present simple formulas for the diffraction efficiencies of a binary phasegrating that performs array illumination with ultrashort pulse beams. Using scalar diffractiontheory, we formulated the efficiencies as a function of pulse spectral width by Fouriertransforming the complex-modulated frequency spectra of diffracted pulses in the far-fieldregion. From the analytical simulations, we found that pulse array uniformity departs fromunity as the spectral width increases, or the pulse duration decreases, thereby limiting theattainable split counts. This finding can be considered in the design of gratings for deliveringcontrolled amounts of pulse energies to diffraction orders of interest.
Collimation and finite-size effects in suspended resonant guided-mode gratings
Christian Toft-Vandborg, Alexios Parthenopoulos, Ali Akbar Darki, and Aurelien Dantan
DOI: 10.1364/JOSAA.440215 Received 10 Aug 2021; Accepted 05 Oct 2021; Posted 13 Oct 2021 View: PDF
Abstract: The optical transmission of resonant guided-mode gratings patterned on suspended silicon nitridethin films and illuminated at normal incidence with a Gaussian beam are investigated both experimentally and theoretically. Effects due to the beam focusing and its finite size are accounted for bya phenomenological coupled mode model whose predictions are found to be in very good agreementwith the experimentally measured spectra for various grating structures and beam sizes, and whichallow for a detailed analysis of the respective magnitude of these effects. These results are highlyrelevant for the design and optimization of such suspended structured films which are widely usedfor photonics, sensing and optomechanics applications.
Measurement of Chromatic Aberrations Using Phase Retrieval
Matthew Bergkoetter, Brian Kruschwitz, Seung-Whan Bahk, and James Fienup
DOI: 10.1364/JOSAA.431117 Received 05 Jul 2021; Accepted 04 Oct 2021; Posted 07 Oct 2021 View: PDF
Abstract: We explore the feasibility of measuring chromatic aberrations using a techniquebased on phase retrieval, primarily for the purpose of diagnostics on the OMEGA EP laser. A computational model and optimization strategy is described,issues of numerical efficiency are addressed, and the potential limitations of the method are studied using mathematical analysis and Monte Carlo simulations. The algorithm performs well in simulation and yields encouraging results in a small-scale laboratory experiment.
Pearcey Beams Tuning and Caustics Evolution
DOI: 10.1364/JOSAA.438792 Received 02 Aug 2021; Accepted 02 Oct 2021; Posted 07 Oct 2021 View: PDF
Abstract: Based on the principle of catastrophe theory, we add a phase factor to adjust the Pearcey beams,which has more flexible and controllable topological structure.The basic optical structure and the transmission characteristics of caustics are also researched. Theoretical and computer simulation results found that the caustics remain unchanged and lateral shift during the transmission process in free space with special parameter values. This special phenomenon has potential application value in the field of optical manipulation.
Optimal efficiency for passively coupling partially coherent light into mode-limited optical waveguides
Yousef Chahine, Sarah Tedder, Jeremy Staffa, and Brian Vyhnalek
DOI: 10.1364/JOSAA.439666 Received 05 Aug 2021; Accepted 01 Oct 2021; Posted 01 Oct 2021 View: PDF
Abstract: In this paper we examine the problem of coupling partially coherent light from a telescope into an optical fiber within the framework of phase space optics using Wigner distributions. Specifically, we consider the optimization of the coupling efficiency for passive optical systems under constraints in the number of spatial modes guided by the optical fiber as are often imposed by the limitations of fiber devices or detectors employed later in the optical chain. As our primary example we consider in detail the case of monochromatic plane wave optical fields distorted by random phase perturbations caused by propagation through atmospheric turbulence. By analyzing the Wigner distribution function for a plane wave in atmospheric turbulence we develop an expression for the coupling efficiency as a function of the number of fiber modes and the ratio of the telescope diameter to Fried's atmospheric coherence diameter.
The δ-𝑆𝑃𝑁 approximation for numerical modeling of directional sources and scattering
Nishigandha Patil and Naren Naik
DOI: 10.1364/JOSAA.436141 Received 08 Jul 2021; Accepted 26 Sep 2021; Posted 01 Oct 2021 View: PDF
Abstract: We propose the 𝛿-𝑆𝑃𝑁 approximation for the coupled radiative transfer equations modeling fluorescence with collimated incident beams and present its numerical implementation using the Finite Element Method. The performance of the proposed model is investigated with respect to Monte Carlo simulations and the standard 𝑆𝑃𝑁 approximation over sub-centimeter domains for various optical properties. We find that the 𝛿-𝑆𝑃𝑁 approximation is more accurate than the 𝑆𝑃𝑁 in the near-source region, and provides improved estimates of phase and partial currents, at both excitation and emission wavelengths, over wider range of optical properties. Increasing approximation order improves accuracy of the 𝛿-𝑆𝑃𝑁 model for normally incident beams.