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Hebri D, Rasouli S. Theoretical study on the diffraction-based generation of a 2D orthogonal lattice of optical beams: physical bases and application for a vortex beam multiplication. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2022; 39:1694-1711. [PMID: 36215638 DOI: 10.1364/josaa.459929] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 08/02/2022] [Indexed: 06/16/2023]
Abstract
A comprehensive theoretical study on the generation of a 2D orthogonal lattice of optical beams based on the near-field diffraction and Talbot effect is presented. First we investigate the near-field diffraction of an optical beam with a finite lateral extension from an infinite 2D orthogonal grating. It is shown that the resulting diffraction patterns over the Talbot planes depend on the following parameters: the period and opening ratio (OR) of the grating, wavelength and spatial spectral bandwidth of the incident beam, and the propagation distance. In terms of these parameters, we find multiplication conditions: the certain conditions under which a 2D orthogonal lattice of the Fourier transform of the incident beam is generated on the Talbot planes. Therefore, if the incident beam is Fourier-invariant and all the established multiplication conditions are fulfilled, the intensity profile of each of the individual Talbot images resembles the intensity profile of the incident beam. We consider the Laguerre-Gaussian beams having zero radial index as an important class of the vortex beams. We explicitly show that these beams are Fourier-invariant and we calculate their spatial spectral bandwidth. As a result, in the illumination of a 2D orthogonal binary grating with this kind of vortex beam, a 2D orthogonal lattice of the incident optical vortex is generated at the Talbot planes. Considering the obtained multiplication conditions, for the first time, to our knowledge, we determine a multiplication interval. This interval covers the propagation distances at which the vortex beam multiplication occurs. Moreover, we obtain the maximum possible value of the grating's OR for the realizations of the vortex multiplication. It is shown that both the multiplication interval and the maximum value of the OR depend on the topological charge (TC) of the incident beam. With the aid of some practical examples and defining a multiplication quality factor, the mentioned results are verified quantitatively. In addition to the vortex beam multiplication effect, we consider another interesting phenomenon that results from the interference of the grating's first diffraction orders. We call this phenomenon the first diffraction orders interference (FDOI) effect. We show that both the multiplication and the FDOI effects occur simultaneously but at different propagation distances. It is also shown that the multiplication and FDOI intervals separate and distance from each other by increasing the TC of the incident beam.
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Nghiem J, Jaeck J, Primot J, Coudrain C, Derelle S, Huard E, Caes M, Bernhardt S, Haidar R, Christol P, Ribet-Mohamed I. MTF measurements of a type-II superlattice infrared focal plane array sealed in a cryocooler. OPTICS EXPRESS 2018; 26:11034-11045. [PMID: 29716031 DOI: 10.1364/oe.26.011034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Accepted: 03/21/2018] [Indexed: 06/08/2023]
Abstract
In operational electro-optical systems, infrared focal plane arrays (IR FPA) are integrated in cryocoolers which induce vibrations that may strongly affect their modulation transfer function (MTF). In this paper, we present the MTF measurement of an IR FPA sealed in its cryocooler. The method we use to measure the MTF decorrelates operational constraints and the technological limitations of the IR FPA. The bench is based on the diffraction properties of a continuously self imaging grating (CSIG). The 26 µm pixel size extracted from the MTF measurement is in good agreement with the expected value.
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Liang C, Mi C, Wang F, Zhao C, Cai Y, Ponomarenko SA. Vector optical coherence lattices generating controllable far-field beam profiles. OPTICS EXPRESS 2017; 25:9872-9885. [PMID: 28468366 DOI: 10.1364/oe.25.009872] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We introduce partially coherent vector sources with periodic spatial coherence properties, which we term vector optical coherence lattices (VOCLs), as an extension of recently introduced scalar OCLs. We derive the realizability conditions and propagation formulae for radially polarized VOCLs (i.e., a typical kind of VOCLs). We show that radially polarized VOCLs display nontrivial propagation properties and generate controllable intensity lattices in the far zone of the source (or in the focal plane of a lens). By adjusting source coherence, one can obtain intensity lattices with bright or dark nodes. The latter can be employed to simultaneously trap multiple particles or atoms as well as in free-space optical communications. We also report the experimental generation of radially polarized VOCLs and we characterize VOCLs propagation properties.
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Patorski K, Trusiak M, Pokorski K. Diffraction grating three-beam interferometry without self-imaging regime contrast modulations. OPTICS LETTERS 2015; 40:1089-1092. [PMID: 25768189 DOI: 10.1364/ol.40.001089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Achromatic grating shearing interferometry method for wave front sensing is developed. Two Fresnel diffraction patterns formed by grating three lowest diffraction orders are recorded. The beam-splitter grating is displaced laterally by half its period between exposures. Calculating the sum of two patterns results in a two-beam interferogram free of inherent light propagation direction and observation plane contrast modulations imposed by the self-imaging phenomenon (Talbot effect). Single-frame automatic fringe pattern processing provides the interferogram phase distribution. The technique enables continuous shear variations suitable for dynamic range sensing. Experimental works corroborate enhanced capabilities of the proposed approach.
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Piponnier M, Druart G, Horisaki R, Guérineau N, Primot J, Mugnier L, Goudail F. Three-dimensional imaging using continuously self-imaging gratings. OPTICS LETTERS 2013; 38:4058-4061. [PMID: 24321922 DOI: 10.1364/ol.38.004058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this Letter, we propose a method to perform 3D imaging with a simple and robust imaging system only composed of a continuously self-imaging grating (CSIG) and a matrix detector. With a CSIG, the intensity pattern generated by an object source is periodic and propagation invariant, apart from a dilatation factor that depends on the distance of the object. We demonstrate, theoretically and experimentally, how to exploit this property to analyze a scene in three dimensions. Such an imaging system can be used, for example, for tomographic applications.
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Rizzi J, Mercère P, Idir M, Silva PD, Vincent G, Primot J. X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer. OPTICS EXPRESS 2013; 21:17340-51. [PMID: 23938580 DOI: 10.1364/oe.21.017340] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
In this paper we present some quantitative measurements of X-ray phase contrast images and noise evaluation obtained with a recent grating based X-ray phase contrast interferometer. This device is built using a single phase grating and a large broadband X-ray source. It was calibrated using a reference sample and finally used to perform measurements of a biological fossil: a mosquito trapped in amber. As phase images, noise was evaluated from the measured interferograms.
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Affiliation(s)
- J Rizzi
- ONERA, The French Aerospace Laboratory, Chemin de la Hunière, 91761 Palaiseau, France.
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Horisaki R, Piponnier M, Druart G, Guérineau N, Primot J, Goudail F, Taboury J, Tanida J. Regularized image reconstruction for continuously self-imaging gratings. APPLIED OPTICS 2013; 52:3802-3811. [PMID: 23736336 DOI: 10.1364/ao.52.003802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Accepted: 04/23/2013] [Indexed: 06/02/2023]
Abstract
In this paper, we demonstrate two image reconstruction schemes for continuously self-imaging gratings (CSIGs). CSIGs are diffractive optical elements that generate a depth-invariant propagation pattern and sample objects with a sparse spatial frequency spectrum. To compensate for the sparse sampling, we apply two methods with different regularizations for CSIG imaging. The first method employs continuity of the spatial frequency spectrum, and the second one uses sparsity of the intensity pattern. The two methods are demonstrated with simulations and experiments.
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Affiliation(s)
- Ryoichi Horisaki
- Department of Information and Physical Sciences, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, Japan.
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Piponnier M, Horisaki R, Druart G, Guérineau N, Kattnig A, Primot J. Relevance of continuously self-imaging gratings for noise robust imagery. OPTICS LETTERS 2012; 37:3492-3494. [PMID: 22940926 DOI: 10.1364/ol.37.003492] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We have designed miniaturized, simple, and robust cameras composed of a single diffractive optical element (DOE) that generates a continuously self-imaging (CSI) beam. Two different DOEs are explored: the J0 Bessel transmittance, characterized by a continuous optical transfer function (OTF) and the CSI grating (CSIG), characterized by a sparse OTF. In this Letter, we will analyze the properties of both DOEs in terms of radiometric performances. We will demonstrate that the noise robustness is enhanced for a CSIG, thanks to the sparsity of its OTF. A camera using this DOE has been made and experimental images are presented to illustrate the noise robustness.
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Piponnier M, Druart G, Guérineau N, de Bougrenet JL, Primot J. Optimal conditions for using the binary approximation of continuously self-imaging gratings. OPTICS EXPRESS 2011; 19:23054-23066. [PMID: 22109185 DOI: 10.1364/oe.19.023054] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Diffractive Optical Elements (DOE), that generate a propagation-invariant transverse intensity pattern, can be used for metrology and imaging application because they provide a very wide depth of focus. However, exact implementation of such DOE is not easy, so we generally code the transmittance by a binary approximation. In this paper, we will study the influence of the binary approximation of Continuously Self-Imaging Gratings (CSIG) on the propagated intensity pattern, for amplitude or phase coding. We will thus demonstrate that under specific conditions, parasitic effects due to the binarization disappear and we retrieve the theoretical non-diffracting property of CSIG's.
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Arrizón V, Sánchez-de-la-Llave D, Ruiz U, Méndez G. Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation. OPTICS LETTERS 2009; 34:1456-1458. [PMID: 19412304 DOI: 10.1364/ol.34.001456] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report a highly efficient method for generation of any high-order nondiffracting Bessel beam employing a phase hologram whose transmittance coincides with the phase modulation of such a beam. It is remarkable that the Bessel beam generated by this hologram, at the plane of this device, has peak amplitude higher than the amplitude of the beam employed to illuminate it.
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Affiliation(s)
- Víctor Arrizón
- Instituto Nacional de Astrofísica, Optica y Electrónica, Apdo. Postal 51 y 216, Puebla PUE 72000, Mexico.
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Druart G, Guérineau N, Haïdar R, Primot J, Chavel P, Taboury J. Nonparaxial analysis of continuous self-imaging gratings in oblique illumination. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2007; 24:3379-87. [PMID: 17912335 DOI: 10.1364/josaa.24.003379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Tolerance in angles of continuously self-imaging gratings (CSIGs) is explored. The degradation in angle of the shape of the point-spread function is theoretically investigated and illustrated by simulations and experiments. The formalism presented is inspired by the one used for classical lenses and can be easily generalized to diffraction gratings. It turns out that well-designed CSIGs could be used for scanning optical systems requiring a large field of view.
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Affiliation(s)
- Guillaume Druart
- Office National d'Etudes et de Recherches Aérospatiales, Chemin de Hunière, 91761 Palaiseau Cedex, France.
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Mínguez-Vega G, Fernández-Alonso M, Tajahuerce E, Lancis J, Jaroszewicz Z, Andrés P. Chromatic compensation in the near-field region: shape and size tunability. APPLIED OPTICS 2005; 44:6933-9. [PMID: 16294969 DOI: 10.1364/ao.44.006933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We report a diffractive-lens triplet with which to achieve wavelength compensation in the near field diffracted by any aperture. On the one hand, the all-diffractive triplet allows us to tune, in a sequential way, the Fresnel-irradiance shape to be achromatized by changing the focal length of one diffractive lens. On the other hand, we can adjust the scale of the chromatically compensated Fresnel diffraction field by shifting the aperture along the optical axis. Within this framework, we present an extremely flexible white-light Fresnel-plane array illuminator based on the kinoform sampling filter. A variable compression ratio and continuous selection of the output pitch are the most appealing features of this novel application.
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Affiliation(s)
- G Mínguez-Vega
- Departament de Ciències Experimentals, Universitat Jaume I, 12080 Castelló, Spain
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di Mambro E, Haïdar R, Guérineau N, Primot J. Sharpness limitations in the projection of thin lines by use of the Talbot experiment. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2004; 21:2276-2282. [PMID: 15603062 DOI: 10.1364/josaa.21.002276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Studying the limitations of sharpness in self-images of the Talbot effect leads us to abandon the use of the paraxial assumption. In this respect, we will clarify the self-image concept and show experimentally and theoretically the influence of "nonparaxial effects" on the self-image. The boundary between paraxial and nonparaxial scalar theory is also clarified in this context. The Rayleigh criterion in aberration diffraction theory is adapted for explicit estimations of this boundary and the maximum sharpness of lines projected by use of the Talbot effect.
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Affiliation(s)
- Emmanuel di Mambro
- Office National d'Etudes et de Recherches Aérospatiales, 29 rue de la division Leclerc, 92322 Châtillon Cedex, France.
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Saastamoinen T, Tervo J, Vahimaa P, Turunen J. Exact self-imaging of transversely periodic fields. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2004; 21:1424-1429. [PMID: 15330469 DOI: 10.1364/josaa.21.001424] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Conditions for exactly self-imaging nonparaxial fields that are periodic also in the transverse direction are introduced. The theory is first derived by assuming full coherence and then extended into the domain of partial coherence. Different types of solutions are discussed, and some illustrations of the existence of solutions and intensity distributions of the fields are presented.
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