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Analysis of numerical diffraction calculationmethods: from the perspective of phase spaceoptics and sampling theorem

Wenhui Zhang, Hao Zhang, Colin Sheppard, and Guofan Jin

DOI: 10.1364/JOSAA.401908 Received 02 Jul 2020; Accepted 21 Sep 2020; Posted 22 Sep 2020  View: PDF

Abstract: Diffraction calculations are widely used in applications that require numericalsimulation of optical wave propagation. Different numerical diffraction calculation methodshave their own transform and sampling properties. In this study, we provide a unified analysiswhere five popular fast diffraction calculation methods are analyzed from the perspective ofphase space optics and the sampling theorem: single-FFT based Fresnel transform, Fresneltransfer function approach, Fresnel impulse response approach, angular spectrum method, andRayleigh-Sommerfeld convolution. The evolutions of an input signal’s space-bandwidthproduct (SBP) during wave propagation are illustrated with the help of a phase space diagram(PSD) and an ABCD matrix. It is demonstrated that all of the above methods cannot makefull use of the SBP of the input signal after diffraction; and some transform properties havebeen ignored. Each method has its own restrictions and applicable range. The reason whydifferent methods have different applicable ranges is explained with physical models. Aftercomprehensively studying and comparing the effect on the SBP and sampling properties ofthese methods, suggestions are given for choosing the proper method for differentapplications and overcoming the restrictions of corresponding methods. The PSD and ABCDmatrix are used to illustrate the properties of these methods intuitively. Numerical results arepresented to verify the analysis; and potential ways to develop new diffraction calculationmethods are also discussed.

The all-dielectric metasurface with multi functions inthe near-infrared band

Xiaodong Zhang, Depeng Kong, Su-Juan Liu, and Haiyan Wang

DOI: 10.1364/JOSAA.398245 Received 29 May 2020; Accepted 17 Sep 2020; Posted 18 Sep 2020  View: PDF

Abstract: This paper presents an approach to design the all-dielectric metasurface with multi-functionin the near-infrared range of 1.5~1.6 μm. Based on the geometric phase principle, the all-dielectricmetasurface is composed of the Si nanopillar and the SiO2 substrate as emitter unit distributed in 21 ×21 array. Under the incidence of the circularly polarized light at 1550 nm, the metasurface works asvortex-beam generator with high performance which generates vortex beam with topological charges of±1 and the mode purity of the vortex beam is 90.66%. Under the incidence of the linearly polarizedlight at 1550 nm, the metasurface also works as the azimuthally/radially polarized beam generator withhigh performance and the purity of the azimuthally and the radially polarized beam is 92.52% and91.02% respectively. Moreover, the metasurface generates different output spots under the differentincident lights which can be applied to optical encryption, and the metasurface with the phase gradientalso can be used as the dual channel encoder/decoder in optical communication. The simulated resultsare in good agreement with the theoretical derivation. The designed metasurface may become apotential candidate as multi-function photon device in the integrated optical system in future.

ARC: Angle-Retaining Chromaticity Diagram for ColorConstancy Error Analysis

Marco Buzzelli, Simone Bianco, and Raimondo Schettini

DOI: 10.1364/JOSAA.398692 Received 27 May 2020; Accepted 13 Sep 2020; Posted 14 Sep 2020  View: PDF

Abstract: Color constancy algorithms are typically evaluated with a statistical analysis of the recovery angular errorand the reproduction angular error between the estimated and ground truth illuminants. Such analysisprovides information about only the magnitude of the errors, and not about their chromatic properties.We propose an Angle-Retaining Chromaticity diagram (ARC) for the visual analysis of the estimatedilluminants and the corresponding errors. We provide both quantitative and qualitative proof of thesuperiority of ARC in preserving angular distances compared to other chromaticity diagrams, making itpossible to quantify the reproduction and recovery errors in terms of Euclidean distances on a plane. Wepresent two case studies for the application of the ARC diagram in the visualization of the ground truthilluminants of color constancy datasets, and the visual analysis of error distributions of color constancyalgorithms.

High-speed range and velocity measurementusing frequency scanning interferometry withadaptive delay lines

Christos Pallikarakis, Jonathan Huntley, and Pablo Ruiz

DOI: 10.1364/JOSAA.403858 Received 28 Jul 2020; Accepted 08 Sep 2020; Posted 10 Sep 2020  View: PDF

Abstract: Range (i.e., absolute distance), displacement and velocity of a moving target havebeen measured with a Frequency Scanning Interferometer that incorporates a 100,000 scan s-1VCSEL laser with 100-nm tuning range. An Adaptive Delay Line in the reference beam,consisting of a chain of switchable exponentially-growing optical delays, reduced modulationfrequencies to sub-GHz levels. Range, displacement and velocity were determined from thephase of the interference signal; fine alignment and linearization of the scans was achievedfrom the interferogram of an independent reference interferometer. Sub-nm displacementresolution, sub-100-nm range resolution, and velocity resolution of 12 μm s-1 have beendemonstrated over a depth measurement range of 300 mm.

High Étendue Fourier Transform Spectroscopy byQuadratic Off Axis Path Difference Error Cancellation

Selene Routley, Jamie Flynn, Antony Martin, and William Palmer

DOI: 10.1364/JOSAA.396748 Received 04 May 2020; Accepted 08 Sep 2020; Posted 08 Sep 2020  View: PDF

Abstract: Instrumentation design for Fourier transform spectroscopy has until now been hindered by a seeminglyfundamental tradeoff between the étendue of the analyzed light source on the one hand and the spectralresolution on the other. For example, if a freespace scanning Michelson interferometer is to achieve aspectral resolution of 4cm−1, it can have a maximum angular field of view of roughly 1◦for of wavelengthsin the neighborhood of λ = 800nm wavelength, where the general tradeoff for this instrument can bestated that the quotient θ2m/∆k of the square of the angular field of view θm and the minimum resolvablewavenumber difference ∆k is a constant. This paper demonstrates a method to increase the angular fieldof view allowable for a given resolution by a full order of magnitude, and thus to increase the étendue and,with it, the potential power gathered from an extended source and potential measurement signal to noiseratio, by two orders of magnitude relative to the performance of a freespace Michelson interferometer.Generalizing this example, we argue that there may be no fundamental thermodynamic grounds for thetradeoff and that a scanning Fourier transform spectrometer can accept an arbitrarily high étendue fieldand still, in theory, achieve an arbitrarily narrow spectral resolution.

An investigation of the characteristics of a fibre opticgas-liquid two-phase flow sensor

Yu Ma, Xu Zhang, Yangrui Zhang, Song Li, Weimin Sun, and Elfed Lewis

DOI: 10.1364/JOSAA.401823 Received 02 Jul 2020; Accepted 08 Sep 2020; Posted 10 Sep 2020  View: PDF

Abstract: A laboratory prepared wedge shaped fibre probe using stepindex multi-mode plastic optical fibre was described and tested in alab-scale gas-liquid flow generator. A three-dimensional model wasestablished in order to fully simulate the process of bubble piercing bythe optical fibre probe. A theoretical analysis of the luminous intensitydistribution of the light transmission in the process of bubble piercingwas undertaken under conditions of different relative positionsbetween the fibre probe and the bubble axis. Using this analyticalmethod, it was possible to accurately define the range of the centralregion of bubble where the pre-signal appeared.

Toric lens analysis as a focal ring and Bessel beamgenerator

Mireille Quemener, Jason Guenette, Jeck Borne, and Simon Thibault

DOI: 10.1364/JOSAA.402378 Received 09 Jul 2020; Accepted 07 Sep 2020; Posted 10 Sep 2020  View: PDF

Abstract: We propose an analytical solution of the focal ring generated at the focus of a toric lens. The analyticalfield of the focal ring is used with a Fourier transform lens to generate a Bessel beam. A comparativeanalysis between the use of an illuminated annular aperture, an axicon and a toric lens to generate aBessel beam is performed and the benefits and drawbacks of each is discussed. This highlights the advantages of using a toric lens with a Gaussian beam to produce a focal line of increasing intensity, whichis advantageous for applications such as high depth-of-field microscopy. ©

Structure-Preserving Spectral Reflectance Estimationusing Guided Filtering

Frank Sippel, Jürgen Seiler, Nils Genser, and André Kaup

DOI: 10.1364/JOSAA.400485 Received 16 Jun 2020; Accepted 07 Sep 2020; Posted 10 Sep 2020  View: PDF

Abstract: Light spectra are a very important source of information for diverse classification problems, e.g., for discrimination of materials. To lower the cost for acquiring this information, multispectral cameras are used.Several techniques exist for estimating light spectra out of multispectral images by exploiting properties about the spectrum. Unfortunately, especially when capturing multispectral videos, the images areheavily affected by noise due to the nature of limited exposure times in videos. Therefore, models thatexplicitly try to lower the influence of noise on the reconstructed spectrum are highly desirable. Hence, anovel reconstruction algorithm is presented. This novel estimation method is based on the guided filtering technique which preserves basic structures, while using spatial information to reduce the influenceof noise. The evaluation based on spectra of natural images reveals that this new technique yields better quantitative and subjective results in noisy scenarios than other state-of-the-art spatial reconstructionmethods. Specifically, the proposed algorithm lowers the mean squared error and the spectral angle up to46% and 35% in noisy scenarios, respectively. Furthermore, it is shown that the proposed reconstructiontechnique works out-of-the-box and does not need any calibration or training by reconstructing spectrafrom a real-world multispectral camera with nine channels.

Image scanning microscopy with multiphotonexcitation or Bessel beam illumination

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

DOI: 10.1364/JOSAA.402048 Received 06 Jul 2020; Accepted 02 Sep 2020; Posted 02 Sep 2020  View: PDF

Abstract: Image scanning microscopy is a technique of confocal microscopy in which the confocal pinhole is replaced by a detector array, and the image reconstructed, most straightforwardly by pixel reassignment.In the fluorescence mode, the detector array collects most of the fluorescent light, so the signal-to-noiseratio is much improved compared with confocal microscopy with a small pinhole, while the resolutionis improved compared with conventional fluorescence microscopy. Here, we consider two cases whenthe illumination and detection point spread functions are dissimilar: illumination with a Bessel beam,and multiphoton microscopy. It has been shown previously that for Bessel beam illumination in imagescanning microscopy with a large array, the imaging performance is degraded. On the other hand, it isalso known that the resolution of confocal microscopy is improved by Bessel beam illumination. Here,we analyze image scanning microscopy with Bessel beam illumination together with a small array, andshow that an improvement in transverse resolution (width of point spread function) by a factor of 1.78compared with a conventional fluorescence microscope can be obtained. We also examine the behavior ofimage scanning microscopy in two- or three-photon fluorescence, and for two-photon excitation also withBessel beam illumination. The combination of the optical sectioning effect of image scanning microscopywith multiphoton microscopy reduces background from the sample surface, which can increase penetration depth. For a detector array of size two Airy units, the resolution of two-photon image scanningmicroscopy is a factor 1.85 better and the peak of the point spread function 2.84 times higher than in nonconfocal two-photon fluorescence. The resolution of three-photon image scanning microscopy is a factor2.10 better and the peak of the point spread function 3.77 times higher than in nonconfocal three-photonfluorescence. The resolution of two-photon image scanning microscopy with Bessel beam illuminationis a factor 2.13 better than in standard two-photon fluorescence. Axial resolution and optical sectioningin two-photon or three-photon fluorescence are also improved by using the image scanning modality.

Simplification Method for 3D Terracotta WarriorFragments Based on Local Structure and Deep Neuralnetworks

Guohua Geng, jie liu, Xin Cao, yangyang liu, Wei Zhou, Fengjun Zhao, Linzhi Su, kang li, and Mingquan Zhou

DOI: 10.1364/JOSAA.400571 Received 17 Jun 2020; Accepted 02 Sep 2020; Posted 02 Sep 2020  View: PDF

Abstract: The emergence of 3D scanner has benefited the archeology a lot, which can store the cultural heritage artifacts incomputers and present them on the Internet. As many Terracotta Warriors have been predominantly found infragments, the pre-processing of these fragments is very important. The raw point cloud of the fragments has lots ofredundant points, it requires excessively large storage space and lots of time for post-processing. Thus, an effectivemethod for point cloud simplification is proposed for 3D Terracotta Warriors fragments. Firstly, an algorithm forextracting feature points is proposed, which is based on local structure. By constructing a k-dimension tree (kd-tree)to establish k-nearest neighborhood of the point cloud, and comparing the feature discriminant parameter andcharacteristic threshold, the feature points, as well as the non-feature points, are separated. Secondly, a deep neuralnetwork is constructed to simplify the non-feature points. Finally, the feature points and simplified non-feature pointsare merged to form the complete simplified point cloud. Experiments with the public point cloud data and the realworld Terracotta Warrior Fragments data are designed and conducted. Excellent simplification results have beenobtained, while the geometric feature can be preserved very well.

Spectral Intensity Correlations of Backscattereddiffuse light: the effect of scattering anisotropy

Angel Duran Ledezma, Hugo de la Cruz, and Luis Rojas-Ochoa

DOI: 10.1364/JOSAA.400379 Received 18 Jun 2020; Accepted 01 Sep 2020; Posted 02 Sep 2020  View: PDF

Abstract: In this work, we report experiments and a theoretical scheme of photon transport in the frequency domain of rigidturbid media. We have employed spectral multi-speckle intensity correlations to estimate optical properties as thetransport mean free path and the absorption length of turbid systems. We propose a scheme based on the photondiffusion model using an effective path-length distribution in the backscattering configuration and takes explicitlyinto account the particles scattering anisotropy parameter ࢍ .By studying rigid Teflon slabs and polymer matricesdoped with polystyrene particles of different degrees of scattering anisotropy, we find that the proposed modeladequately describes our experimental results. Our hypothesis for the diffuse transport of backscattered photonsin the weak multiple scattering regime is further validated using a numerical simulation scheme of specklesdynamics, based on the Copula method.

Orbital angular momentum and topological charge of a multi-vortex Gaussian beam

Alexey Kovalev, Victor Kotlyar, and Alexey Porfirev

DOI: 10.1364/JOSAA.401561 Received 13 Jul 2020; Accepted 31 Aug 2020; Posted 17 Sep 2020  View: PDF

Abstract: We report on a theoretical and numerical study of a Gaussian beam modulated of several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. Topological charge (TC) of such multi-vortex beam equals the sum of topological charges of all optical vortices. If OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the optical vortices to appear at the infinity of such combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of the said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time and we obtained TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) TC is unchanged, while the OAM changes less than by 10%, if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

Machine Learning-Aided Classification of Beams Carrying OrbitalAngular Momentum Propagated in Highly Turbid Water

Svetlana Avramov-Zamurovic, Abbie Watnik, james lindle, Kyle Judd, and Svetlana esposito

DOI: 10.1364/JOSAA.401153 Received 24 Jun 2020; Accepted 18 Aug 2020; Posted 26 Aug 2020  View: PDF

Abstract: A set of laser beams carrying Orbital Angular Momentum (OAM) is designed with the objective ofestablishing an effective underwater communication link. Messages are constructed using unique Laguerre-Gaussbeams which can be combined to represent four bits of information. We report on the experimental results wherethe beams are transmitted through highly turbid water, reaching approximately twelve attenuation lengths. Wemeasured the signal-to-noise ratio in each test scenario to provide characterization of the underwater environment. Aconvolutional neural network was developed to decode the received images with the objective of successfullyclassifying messages quickly. We demonstrate near perfect classification in all scenarios provided the training setincludes some images taken under the same underwater conditions.

Flash X-ray diffraction imaging in 3D: aproposed analysis pipeline

Jing Liu, Stefan Engblom, and Carl Nettelblad

DOI: 10.1364/JOSAA.390384 Received 11 Feb 2020; Accepted 29 Jul 2020; Posted 24 Aug 2020  View: PDF

Abstract: Modern Flash X-ray diffraction Imaging (FXI) acquires diffraction signals fromsingle biomolecules at a high repetition rate from X-ray Free Electron Lasers (XFELs), easilyobtaining millions of 2D diffraction patterns from a single experiment. Due to the stochasticnature of FXI experiments and the massive volumes of data, retrieving 3D electron densitiesfrom raw 2D diffraction patterns is a challenging and time-consuming task.We propose a semi-automatic data analysis pipeline for FXI experiments, which includes foursteps: hit finding and preliminary filtering, pattern classification, 3D Fourier reconstruction, andpost analysis. We also include a recently developed bootstrap methodology in the post-analysisstep for uncertainty analysis and quality control. To achieve the best possible resolution, we furthersuggest using background subtraction, signal windowing, and convex optimization techniqueswhen retrieving the Fourier phases in the post-analysis step.As an application example, we quantified the 3D electron structure of the PR772 virus using theproposed data-analysis pipeline. The retrieved structure was above the detector-edge resolutionand clearly showed the pseudo-icosahedral capsid of the PR772.

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