Showing papers on "Physical optics published in 2015"

Polarization Aberrations in Astronomical Telescopes: The Point Spread Function

Abstract: Detailed knowledge of the image of the point spread function (PSF) is necessary to optimize astronomical coronagraph masks and to understand potential sources of errors in astrometric measurements. The PSF for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction but also on those wavefront errors introduced by the physical optics and the polarization properties of reflecting and transmitting surfaces within the optical system. These vector wave aberrations, called polarization aberrations, result from two sources: (1) the mirror coatings necessary to make the highly reflecting mirror surfaces, and (2) the optical prescription with its inevitable non-normal incidence of rays on reflecting surfaces. The purpose of this article is to characterize the importance of polarization aberrations, to describe the analytical tools to calculate the PSF image, and to provide the background to understand how astronomical image data may be affected. To show the order of magnitude of the effects of polarization aberrations on astronomical images, a generic astronomical telescope configuration is analyzed here by modeling a fast Cassegrain telescope followed by a single 90° deviation fold mirror. All mirrors in this example use bare aluminum reflective coatings and the illumination wavelength is 800 nm. Our findings for this example telescope are: (1) The image plane irradiance distribution is the linear superposition of four PSF images: one for each of the two orthogonal polarizations and one for each of two cross-coupled polarization terms. (2) The PSF image is brighter by 9% for one polarization component compared to its orthogonal state. (3) The PSF images for two orthogonal linearly polarization components are shifted with respect to each other, causing the PSF image for unpolarized point sources to become slightly elongated (elliptical) with a centroid separation of about 0.6 mas. This is important for both astrometry and coronagraph applications. (4) Part of the aberration is a polarization-dependent astigmatism, with a magnitude of 22 milliwaves, which enlarges the PSF image. (5) The orthogonally polarized components of unpolarized sources contain different wavefront aberrations, which differ by approximately 32 milliwaves. This implies that a wavefront correction system cannot optimally correct the aberrations for all polarizations simultaneously. (6) The polarization aberrations couple small parts of each polarization component of the light (∼10^(-4)) into the orthogonal polarization where these components cause highly distorted secondary, or “ghost” PSF images. (7) The radius of the spatial extent of the 90% encircled energy of these two ghost PSF image is twice as large as the radius of the Airy diffraction pattern. Coronagraphs for terrestrial exoplanet science are expected to image objects 10^(-10), or 6 orders of magnitude less than the intensity of the instrument-induced “ghost” PSF image, which will interfere with exoplanet measurements. A polarization aberration expansion which approximates the Jones pupil of the example telescope in six polarization terms is presented in the appendix. Individual terms can be associated with particular polarization defects. The dependence of these terms on angles of incidence, numerical aperture, and the Taylor series representation of the Fresnel equations lead to algebraic relations between these parameters and the scaling of the polarization aberrations. These “design rules” applicable to the example telescope are collected in § 5. Currently, exoplanet coronagraph masks are designed and optimized for scalar diffraction in optical systems. Radiation from the “ghost” PSF image leaks around currently designed image plane masks. Here, we show a vector-wave or polarization optimization is recommended. These effects follow from a natural description of the optical system in terms of the Jones matrices associated with each ray path of interest. The importance of these effects varies by orders of magnitude between different optical systems, depending on the optical design and coatings selected. Some of these effects can be calibrated while others are more problematic. Polarization aberration mitigation methods and technologies to minimize these effects are discussed. These effects have important implications for high-contrast imaging, coronagraphy, and astrometry with their stringent PSF image symmetry and scattered light requirements.

Micron-scale light transport decomposition using interferometry

Abstract: We present a computational imaging system, inspired by the optical coherence tomography (OCT) framework, that uses interferometry to produce decompositions of light transport in small scenes or volumes. The system decomposes transport according to various attributes of the paths that photons travel through the scene, including where on the source the paths originate, their pathlengths from source to camera through the scene, their wavelength, and their polarization. Since it uses interference, the system can achieve high pathlength resolutions, with the ability to distinguish paths whose lengths differ by as little as ten microns. We describe how to construct and optimize an optical assembly for this technique, and we build a prototype to measure and visualize three-dimensional shape, direct and indirect reflection components, and properties of scattering, refractive/dispersive, and birefringent materials.

Modeling physical optics phenomena by complex ray tracing

Abstract: Physical optics modeling requires propagating optical wave fields from a specific radiometric source through complex systems of apertures and reflective or refractive optical components, or even complete instruments or devices, usually to a focal plane or sensor. The model must accurately include the interference and diffraction effects allowed by the polarization and coherence characteristics of both the initial optical wave field and the components and media through which it passes. Like a spherical wave and a plane wave, a Gaussian spherical wave (or Gaussian beam) is also a solution to the paraxial wave equation and does not change its fundamental form during propagation. The propagation of a Gaussian beam is well understood and easily characterized by a few simple parameters. Furthermore, a paraxial Gaussian beam can be propagated through optical systems using geometrical ray-trace methods. The decomposition of arbitrary propagating wave fields into a superposition of Gaussian beamlets is, thus, an alternative to the classical methods of propagating optical wave fields. This decomposition into Gaussian beamlets has been exploited to significant advantage in the modeling of a wide range of physical optics phenomena.

Full wave model of image formation in optical coherence tomography applicable to general samples

Abstract: We demonstrate a highly realistic model of optical coherence tomography, based on an existing model of coherent optical microscopes, which employs a full wave description of light. A defining feature of the model is the decoupling of the key functions of an optical coherence tomography system: sample illumination, light-sample interaction and the collection of light scattered by the sample. We show how such a model can be implemented using the finite-difference time-domain method to model light propagation in general samples. The model employs vectorial focussing theory to represent the optical system and, thus, incorporates general illumination beam types and detection optics. To demonstrate its versatility, we model image formation of a stratified medium, a numerical point-spread function phantom and a numerical phantom, based upon a physical three-dimensional structured phantom employed in our laboratory. We show that simulated images compare well with experimental images of a three-dimensional structured phantom. Such a model provides a powerful means to advance all aspects of optical coherence tomography imaging.

GO/PO and PTD With Virtual Divergence Factor for Fast Analysis of Scattering From Concave Complex Targets

Abstract: Due to simplicity, hybridization of geometrical optics (GO) and physical optics (PO) based on ray tracing has been widely used for fast scattering analyses. However, when targets of curved concavities are discretized by flat facets, the loss of divergence factor (DF) will degrade the simulation accuracy. To remedy this loss, a simple and efficient factor, entitled virtual divergence factor (VDF), is proposed to play the role of DF. To prove the validity of VDF and simulate the scattering of concave complex targets, a hybrid method of GO/PO and physical theory of diffraction (PTD) is elucidated. With VDF correction, several typical targets, including a S-shape cavity, are simulated by this hybrid method. In comparison to multilevel fast multipole algorithm (MLFMA) or measurements, the validaty of VDF is fully demonstrated by good agreements and the excellent performance relative to DF on canonical surfaces, where the great efficiency and flexibility of this hybrid method are also shown. Moreover, one interesting and important issue, the dependance of field convergence on the maximum number of ray reflections, is also investigated for the first time.

Application of complex geometrical optics to determination of thermal, transport, and optical parameters of thin films by the photothermal beam deflection technique

Abstract: In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO2, N- and C-doped TiO2, or TiO2/SiO2 composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature.

High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

Abstract: Explicit closed form solutions are presented for the high-frequency evaluation of the electromagnetic field produced inside and outside an acute-angled lossless penetrable wedge. Both cases of $E$ - and $H$ -polarized incident plane waves are addressed in the study. The problem is tackled and solved in the framework of the uniform theory of diffraction, so that the total field at the observation point is determined by adding the geometrical optics contributions and the diffraction one. This last is obtained by performing a uniform asymptotic evaluation of the radiation integrals arising from a physical optics approximation for the equivalent electric and magnetic surface currents lying on the infinite wedge boundaries. No limitation exists on the refractive index of the structure. The accuracy of the solution is assessed by comparisons with data produced by numerical tools. The physical optics approximation gives rise to inaccuracies when using the solution at grazing incidence and in correspondence of the dielectric interfaces.

Vectorial ray-based diffraction integral.

Abstract: Laser interferometry, as applied in cutting-edge length and displacement metrology, requires detailed analysis of systematic effects due to diffraction, which may affect the measurement uncertainty. When the measurements aim at subnanometer accuracy levels, it is possible that the description of interferometer operation by paraxial and scalar approximations is not sufficient. Therefore, in this paper, we place emphasis on models based on nonparaxial vector beams. We address this challenge by proposing a method that uses the Huygens integral to propagate the electromagnetic fields and ray tracing to achieve numerical computability. Toy models are used to test the method's accuracy. Finally, we recalculate the diffraction correction for an interferometer, which was recently investigated by paraxial methods.

Wave Optics in Black Hole Spacetimes: Schwarzschild Case

Abstract: We investigate the wave optics in the Schwarzschild spacetime. Applying the standard formalism of wave scattering problems, the Green function represented by the sum over the partial waves is evaluated using the Poisson sum formula. The effect of orbiting scattering due to the unstable circular orbit for null rays is taken into account as the contribution of the Regge poles of the scattering matrix and the asymptotic form of the scattering wave is obtained in the eikonal limit. Using this wave function, images of the black hole illuminated by a point source are reconstructed. We also discuss the wave effect in the frequency domain caused by the interference between the direct rays and the winding rays.

The GO4 Model in Near-Nadir Microwave Scattering From the Sea Surface

Abstract: We introduce a practical and accurate model, referred to as “GO4,” to describe near-nadir microwave scattering from the sea surface, and at the same time, we address the issue of the filtered mean square slope (mss) conventionally used in the geometrical optics model. GO4 is a simple correction of this last model, taking into account the diffraction correction induced by the rough surface through what we call an effective mean square curvature (msc). We evaluate the effective msc as a function of the surface wavenumber spectrum and the radar frequency and show that GO4 reaches the same accuracy as the physical optics model in a wide range of incidence and frequency bands with the sole knowledge of the mss and msc parameters. The key point is that the mss entering in GO4 is not the filtered but the total slope. We provide estimation of the effective msc on the basis of classical sea spectrum models. We also evaluate the effective msc from near-nadir satellite data in various bands and show that it is consistent with model predictions. Non-Gaussian effects are discussed and shown to be incorporated in the effective msc. We give some applications of the method, namely, the estimation of the total sea surface mss and the recalibration of relative radar cross sections.

Instrument transfer function of slope measuring deflectometry systems.

Abstract: Slope measuring deflectometry (SMD) systems are developing rapidly in testing freeform optics. They measure the surface slope using a camera and an incoherent source. The principle of the test is mainly discussed in geometric optic domain. The system response as a function of spatial frequency or instrument transfer function (ITF) has yet to be studied thoroughly. Through mathematical modeling, simulation, and experiment we show that the ITF of an SMD system is very close to the modulation transfer function of the camera used. Furthermore, the ITF can be enhanced using a deconvolution filter. This study will lead to more accurate measurements in SMD and will show the physical optics nature of these tests.

Effect of slope errors on the performance of mirrors for x-ray free electron laser applications

Abstract: In this work we point out that slope errors play only a minor role in the performance of a certain class of x-ray optics for X-ray Free Electron Laser (XFEL) applications. Using physical optics propagation simulations and the formalism of Church and Takacs [Opt. Eng. 34, 353 (1995)], we show that diffraction limited optics commonly found at XFEL facilities posses a critical spatial wavelength that makes them less sensitive to slope errors, and more sensitive to height error. Given the number of XFELs currently operating or under construction across the world, we hope that this simple observation will help to correctly define specifications for x-ray optics to be deployed at XFELs, possibly reducing the budget and the timeframe needed to complete the optical manufacturing and metrology.

co2amp: A software program for modeling the dynamics of ultrashort pulses in optical systems with CO_2 amplifiers

Abstract: A computer code for simulating the amplification of ultrashort mid-infrared laser pulses in CO2 amplifiers and their propagation through arbitrary optical systems is described. The code is based on a comprehensive model that includes an accurate consideration of the CO2 active medium and a physical optics propagation algorithm, and takes into account the interaction of the laser pulse with the material of the optical elements. The application of the code for optimizing an isotopic regenerative amplifier is described.

Computing low‐frequency radar surface echoes for planetary radar using Huygens‐Fresnel's principle

Abstract: Radar echoes from planetary sounders often contain ambiguities between surface echoes -clutter- and subsurface reflections. Such problems severely constrain quantitative data analysis especially for rough terrains. We propose a physical optics approach to simulate planetary sounding radar surface echoes to address this specific issue. The method relies on the Huygens-Fresnel's principle which permits the recasting of Maxwell's equations in a surface integral formulation. To compute this integral, we describe the surface through a mesh composed of adjacent triangular elements for which we provide an analytical expression of the scattered electromagnetic fields. The main contribution of this work lies in the use analytical integrals over triangular facet elements much larger than the wavelength of the electromagnetic field. Hence, the advantage of the proposed approach is its computation efficiency which reduces the computational requirements while maintaining the physical optics accuracy. This allows a systematic analysis of the continuously growing planetary sounding radar database. Equations and implementation are detailed in this paper as well as illustrations of obtained results for different instruments (namely SHARAD, LRS and STM). Our simulation results suggest that the method is able to accurately reproduce the observed clutter in both rough and smooth terrains of the planetary cases discussed in this paper.

Parametric analysis of extended hemispherical dielectric lenses fed by a broadband connected array of leaky-wave slots

Abstract: In this study, the authors examine the properties of a broadband array of leaky-wave slots located in the focal plane of an extended hemispherical dielectric lens, to generate several independent beams for imaging applications. The array performance is investigated over a 4:1 band. Parametric analyses are performed by varying the extension length of the lens and the off-axis distance of the feed point. The results of these analyses provide useful guidelines for the lens design. A spectral domain approach is used to characterise the field generated by the array, while a numerically efficient physical optics algorithm is employed for the analysis of the lens. Simulations performed with Computer Simulation Technology Microwave Studio are used for the validation of the combined analysis methods.

Quantum physics and the beam splitter mystery

Abstract: Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including "which-way" determination of light particles, N. Bohr's complementarity principle, or the EPR paradox and all their measurement apparatus. Although they look as common optical components at first glance, their behaviour remains somewhat mysterious since they apparently exhibit stand-alone particle-like features, and then wave-like characteristics when inserted into a Mach-Zehnder interferometer. In this communication are examined and discussed some basic properties of these beamssplitters, both from a classical optics and quantum physics point of view. Herein some convergences and contradictions are highlighted, and the results of a few emblematic experiments demonstrating photon existence are discussed. An alternative empirical model in wave optics is also proposed in order to shed light on some remaining questions

Limits to applicability of geometrical optics approximation to light backscattering by quasihorizontally oriented hexagonal ice plates

Abstract: Quasihorizontally oriented ice crystals of cirrus clouds became an object of active study in recent times. Experimental observations are made with the use of multiwavelength and polarization lidars; their signals are interpreted on the basis of solutions obtained in the approximation of physical or geometrical optics. In this work, we compare these approximations for solution of the problem of light backscattering by quasihorizontally oriented hexagonal ice plates. Special attention is paid to the limits to applicability of geometrical optics approach to solution of such problems.

Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering

Abstract: It has been previously shown that a Pancharatnam phase device with a dual-twist structure can deflect light up to 60° with nearly perfect efficiency. This was beyond the limits previously assumed for these types of devices, which were considered to be optically similar to Raman-Nath gratings. In this paper we first consider the range of parameters that will allow for high efficiency and show the results for a structure that demonstrates 80° deflection. We then explore the light propagation through these devices to point out interesting intensity variations in the deflected mode of light as it traverses the deflecting layer. Finally, we explain the key to understanding the efficiency of these devices, which is not the typical parameters that are important for traditional diffractive devices, but rather the control of the polarization state of light. We provide a simple design approach for optimizing the twist angle and retardation for high efficiency.

Coherence and polarization of polarization speckle generated by a rough-surfaced retardation plate depolarizer

Abstract: The coherence and polarization of polarization speckle, arising from a stochastic electromagnetic field with random change of polarization, modulated by a depolarizer are examined on the basis of the coherence matrix. The depolarizer is a rough-surfaced retardation plate with a random function of position introducing random phase differences between the two orthogonal components of the electric vector. Under the assumption of Gaussian statistics with zero mean, the surface model for the depolarizer of the rough-surfaced retardation plate is obtained. The propagation of the modulated fields through any quadratic optical system is examined within the framework of the complex ABCD matrix theory to show how the degree of coherence and polarization of the beam changes on propagation, including propagation in free space.

Electromagnetic scattering from a PEC object above a dielectric rough sea surface by a hybrid PO–PO method

Abstract: In this paper, the electromagnetic scattering from a perfectly electric conducting object above a dielectric sea surface is investigated by an efficient hybrid method combining physical optics (PO) with physical optics (PO). Both the scatterings of an object and the underlying sea surface are calculated by the PO method and the mutual couplings between them are solved by the equivalence principle and multi-path scattering strategy. In numerical simulations, the monostatic and bistatic normalized radar cross-section of the composite model is computed by the proposed method and is compared with that by the conventional method of moments. The results show the hybrid PO–PO method has a good accuracy, presence of PO and can greatly reduce the computational time and memory requirement.

TD-UAPO diffracted field evaluation for penetrable wedges with acute apex angle.

Abstract: This study deals with the time domain (TD) diffraction phenomenon related to a penetrable acute-angled dielectric wedge. The transient diffracted field originated by an arbitrary function plane wave is evaluated via a convolution integral involving the TD diffraction coefficients, which are determined here in closed form, starting from the knowledge of the frequency domain counterparts. In particular, the inverse Laplace transform is applied to the uniform Asymptotic physical optics diffraction coefficients valid for the internal region of the wedge and the surrounding space. Diffraction by penetrable wedges in the TD framework is a challenging problem from the analytical point of view, and no other expressions are available in closed form for the diffraction coefficients associated with the considered problem.

Geometrical Optics Reloaded

Abstract: Ray optics has constituted the fundament of optical modeling and design for more than 2000 years. In recent decades, the introduction of ray tracing software has brought a powerful optical design technology to everybody dealing with optics and photonics. However, with the development and availability of advanced light sources, the capability to produce micro and nano structures, and a boost in the variety of applications and related demands on optical functions, the limitations of ray optics become obvious more often. Optical modeling based on physical optics is required and is the logical next step in the development of optical design. This requires a generalization of ray tracing and its connection with diffractive modeling techniques.

Nonlinear optics: Anti-diffraction of light

Abstract: Using an electro-optic effect, submicrometre-sized beams have been shown to exhibit non-paraxial propagation over 1,000 Rayleigh lengths. The discovery does not require inhomogeneous or lossy media like plasmon waveguiding.

Fourier theory of linear gain media

Abstract: The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit), separately. For gain media, we demonstrate that these two limits generally do not commute; for example, one order may lead to a diverging field, while the other order leads to a finite field. Moreover, the plane wave limit may be dependent on whether it is realized with a rect function excitation or gaussian excitation of infinite widths. We consider wave propagation in gain media by a Fourier--Laplace integral in time and space, and demonstrate how the correct monochromatic limit or plane wave limit can be taken, by deforming the integration surface in complex frequency--complex wavenumber space. We also give the most general criterion for absolute instabilities. The general theory is applied in several cases, and is used to predict media with novel properties. In particular, we show the existence of isotropic media which in principle exhibit simultaneous refraction, meaning that they refract positively and negatively at the same time.

Paraxial ray optics cloaking

Abstract: Despite much interest and progress in optical spatial cloaking, a three-dimensional (3D), transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. Here we experimentally demonstrate such a cloak using ray optics, albeit with some edge effects. Our device requires no new materials, uses isotropic off-the-shelf optics, scales easily to cloak arbitrarily large objects, and is as broadband as the choice of optical material, all of which have been challenges for current cloaking schemes. In addition, we provide a concise formalism that quantifies and produces perfect optical cloaks in the small-angle (`paraxial') limit.

The Contour Deformation Method for Calculating the High-Frequency Scattered Field by the Fock Current on the Surface of the 3-D Convex Cylinder

Abstract: In this paper, the high-frequency diffracted waves like the creeping waves are comprehensively analyzed by the Fock currents. On invoking the contour deformation method, the highly oscillatory Fock currents are efficiently calculated. Furthermore, the workload for the calculation of Fock currents is frequency-independent. To capture the high-frequency wave physics phenomenon, the Fock current is separated into the classical physical optics (PO) current and the nonuniform (NU)-Fock current along the shadow boundary and in the deep shadow region. To calculate the highly oscillatory scattered wave fields from the Fock current, quadratic approximations of the phase functions in the integrand are adopted. On invoking the numerical steepest descent path (NSDP) method, the scattered wave fields are efficiently calculated with frequency-independent computational effort and error controllable accuracy in each frequency-independent segment. Meanwhile, the high-frequency creeping wave coming from the NU-Fock current is efficiently captured by the NSDP method. Numerical results for the Fock currents, the high-frequency NU-diffracted and scattered far fields on the convex cylinders are given to validate the efficiency of the proposed method. Furthermore, the contour deformation method for computing the Fock currents offers a clear physical picture for the high-frequency wave fields on the convex scatterer.

Geometric optics for a coupling model of the electromagnetic and gravitational fields

Abstract: The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics are invalid in the usual spacetime. By introducing an effective spacetime, we find that the wave vector can be casted into null and then it obeys the geodesic equation, the polarization vector is perpendicular to the rays, and the number of photons is conserved. That is to say, the laws of geometric optics are still valid for the modified theory in the effective spacetime. We also show that the focusing theorem of light rays for the modified theory in the effective spacetime takes the same form as usual.

Multistep Cylindrical Structure Design for Wideband Radar Cross Section Reduction at Normal Incidence

Abstract: A wideband radar cross section (RCS) reduction measure applicable to rod-like targets is proposed. This technique uses the differences in radii among multistep cylindrical structures to create a phase reversal for backscattering cancelation. In order to broaden the reduction bandwidth, a simple one-step design is evolved into a multistep one using the binomial expansion method. Its superior performance is verified via numerical simulations based on the physical optics (PO) and full-wave method. Under normal incidence, a 2.45:1 bandwidth ratio is achieved for more than 20-dB RCS reduction with a five-step design. Effects of critical design parameters such as the number of steps and the cylinder displacement order are examined. This approach can be employed on rod-like defense targets. A series of simulations that emulate a periscope protruding from the sea surface is conducted to demonstrate the applicability of the proposed technique.

Comparison of microfacet BRDF model elements to diffraction BRDF model elements

Abstract: A popular class of BRDF models is the microfacet model, where geometric optics is assumed, but where physical optics effects such as accurate wavelength scaling, important to Hyperspectral Imagery, are lost More complex physical optics models may more accurately predict the BRDF, but the calculation is time-consuming These seemingly disparate approaches are compared in detail The linear systems direction cosine space is compared to microfacet coordinates, and the microfacet models Fresnel reflection in microfacet coordinates is compared to diffraction theory’s Fresnel-like term Similarities and differences between these terms are highlighted to merge these two approaches to the BRDF