Correlated imaging with partially coherent light for remote sensing

Based on the extended Huygens–Fresnel integral and the theory of coherence of light field, we have investigated the correlated imaging by using the transverse normalized second-order intensity fluctuation correlation function with partially coherent light radiation. The imaging for a reflected object with relative long distance is determined by the feature of speckle-to-speckle correlation. By using the correlation function, we study the effects of imaging distance, the sizes of object lens and reference lens, the source’s transverse coherent width and its transverse size on the quality of correlated imaging. Numerical results show that the parameters of imaging system and the properties of partially coherent light source have significant influences on the imaging resolution and visibility. For an object lens with large enough diameter, the resolution is determined by the transverse coherent width of light source. On the contrary, it depends on the aperture of object lens. The magnification of the system depends only on the propagation distance. This speckle-to-speckle correlated imaging with unbalanced arms have potential applications in remote sensing due to its unique features.     

Three-dimensional imaging by partially coherent light under nonparaxial condition

In this paper, we present the theory of three-dimensional (3D) imaging using partially coherent light under the nonparaxial condition. Using the linear system approach, we derive the image intensity in terms of the 3D nonparaxial transmission cross coefficient (TCC) and the transmission function defined in this paper. We present that the 3D TCC can be calculated by multiple applications of the 3D fast Fourier transform instead of the six-dimensional integral in the original formula. Using the simplified formula, we simulate phase contrast and Nomarski differential interference contrast (DIC) imaging of a transparent 3D object. Within our knowledge, the 3D model for the DIC based on the 3D nonparaxial TCC is the most rigorous approach that has been suggested. It demonstrates clearly the optical sectioning effect of DIC.     

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.     

Coincidence fractional Fourier transform implemented with partially coherent light radiation

We introduce the coincidence fractional Fourier transform (FRT) implemented with incoherent and partially coherent light radiation. Optical systems for implementing the coincidence FRT are designed. The results show that the visibility and quality of the coincidence FRT of an object are closely related to the light source's transverse size, coherence, and spectral width. As an example, we numerically study the coincidence FRT of a single slit.     

Performance of diffractive optical elements for homogenizing partially coherent light

The effectiveness of different types of diffractive optical element (DOE) for homogenizing partially coherent beams is analyzed, both analytically and numerically. The effectiveness is described by the homogenizing parameter, defined as the inverse of the normalized variance of the dose distribution. For an important class of DOEs designed with common discrete-Fourier-transform methods, it is found that the homogenizing parameter is only of the order of the number of coherence cells in the illuminating beam. However, for a different type of DOE that produces distinct beams under coherent illumination, the homogenizing parameter can be an order of magnitude higher. The inherent dehomogenizing effect caused by the limited temporal duration of the beam, a phenomenon sometimes referred to as dynamic speckle, is also considered.     

Uniform theory of the Talbot effect with partially coherent light illumination

A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.     

General transfer-matrix method for optical multilayer systems with coherent,partially coherent,and incoherent interference

The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 x 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the Fresnel coefficients, so as to include incoherent (thick layers) and partially coherent (rough surface or interfaces) reflection and transmission. The method is integrated by use of models for refractive-index depth profiling. The utility of the method is illustrated with various multilayer structures formed by ion implantation into Si, including buried insulating and conducting layers, and multilayers with a thick incoherent layer in an arbitrary position.     

Generalized Gouy phase for focused partially coherent light and its implications for interferometry

The Gouy phase, sometimes called the phase anomaly, is the remarkable effect that in the region of focus a converging wave field undergoes a rapid phase change by an amount of π, compared to the phase of a plane wave of the same frequency. This phenomenon plays a crucial role in any application where fields are focused, such as optical coherence tomography, mode selection in laser resonators, and interference microscopy. However, when the field is spatially partially coherent, as is often the case, its phase is a random quantity. When such a field is focused, the Gouy phase is therefore undefined. The correlation properties of partially coherent fields are described by their so-called spectral degree of coherence. We demonstrate that this coherence function does exhibit a generalized Gouy phase. Its precise behavior in the focal region depends on the transverse coherence length. We show that this effect influences the fringe spacing in interference experiments in a nontrivial manner.     

Axial intensity distribution of partially coherent light focused by a lens with spherical aberration

Abstract

The focusing of partially coherent light by a lens with spherical aberration (SA) is studied. The numerical calculation results are given, showing that the axial intensity distribution not only depends on the SA, but also on the coherence of partially coherent light and the Fresnel number of the lens. As the coherence decreases, the influence of the SA on the axial intensity distribution decreases, and the positions of maximum axial intensity shift towards the lens.     

Spectral switches of partially coherent light focused by a filter-lens system with chromatic aberration

It is shown that when partially coherent polychromatic light is focused by a filter-lens system with chromatic aberration, a spectral shift exists in the focused field, and a spectral switch that is defined as a sharp transition of the spectral shift also takes place at some positions of the focused field. The influence of the chromatic aberration of the lens, the coherence of the partially coherent light in the filter (a circular aperture), the radius of the aperture, and the spectral width of the partially coherent light in the aperture on the spectral shift and the spectral switch are investigated in detail. The numerical results show that these parameters affect the spectral shift and the spectral switch significantly. Potential applications of the spectral shift and the spectral switch of the partially coherent light are discussed.     

Measurements of spatial coherence of partially coherent light with and without orbital angular momentum

We study the spatial coherence of a partially coherent beam before and after being transmitted through a spiral phase plate that changes the overall orbital angular momentum of the field. The two-point coherence function is measured and directly visualized on a CCD through interference in a Mach-Zehnder interferometer equipped with an image rotator. We show, in particular, how the coherence singularities associated with Airy rings are strongly affected by the spiral phase plate.     

Anisotropic pure-phase plates for quality improvement of partially coherent,partially polarized beams

From a theoretical point of view, the use of anisotropic pure-phase plates (APP) is considered in order to improve the quality parameter of certain partially coherent, partially polarized beams. It is shown that, to optimize the beam-quality parameter, the phases of the two Cartesian components of the field at the output of the APP plate should be identical and should exhibit a quadratic dependence on the radial polar coordinate.     

Topology optimization for optical microlithography with partially coherent illumination

This article revisits a topology optimization design approach for micro‐manufacturing and extends it to optical microlithography with partially coherent illumination. The solution is based on a combination of two technologies, the topology optimization and the proximity error correction in microlithography/nanolithography. The key steps include (i) modeling the physical inputs of the fabrication process, including the ultraviolet light illumination source and the mask, as the design variables in optimization and (ii) applying physical filtering and heaviside projection for topology optimization, which corresponds to the aerial image formulation and the pattern development processes, respectively. The proposed approach results in an effective source and a binary design mask, which can be sent directly to fabrication without additional post‐processing steps for proximity error correction. Meanwhile, the performance of the device is optimized and robust with respect to process variations, such as dose/photo‐resist variations and lens defocus. A compliant micro‐gripper design example is considered to demonstrate the applicability of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Method of direction-of-arrival estimation for uncorrelated, partially correlated and coherent sources

A new direction-of-arrival estimation method is proposed when uncorrelated, partially correlated and coherent sources coexist. These sources are estimated at two different stages. The uncorrelated and partially correlated sources are first estimated using conventional subspace methods. By exploiting the property of oblique projection, the contributions of uncorrelated and partially correlated sources are then eliminated from the covariance matrix and only the coherent sources remain. Finally, the coherent sources are estimated by the technique of spatial smoothing. The new method need not estimate the partially correlated sources repeatedly but can resolve more sources than the array elements. Simulation results demonstrate the effectiveness and efficiency of the new method.     

Analytic diffraction analysis of a 32-m telescope with hexagonal segments for high-contrast imaging

Large segmented telescopes cannot be modeled accurately with fast-Fourier-transform techniques since small features such as gaps between the segments will be inadequately sampled. An analytic Fourier-transform method can be used to model any pupil configuration with straight edges, including tolerance analysis and some types of apodization. We analytically investigated a 32-m segmented primary with 18 hexagonal segments for high-contrast imaging. There are significant regions in the image in which extrasolar planets could be detected. However, the hexagonal profile of the pupil was not as useful as expected. The gaps between the segments, the secondary obscuration, and the secondary spiders must be as small as possible and their edges must be apodized. Apodizing the edges of the individual segments reduced the useful regions in the image since the gaps appeared to be wider.     

Near-infrared laser tomographic imaging with right-angled scattered coherent light using an optical heterodyne-detection-based confocal scanning system

We demonstrate, what is to the best of our knowledge, a novel optical tomographic method for the visualization of the inner structure of scattering media such as biological tissue in the near-infrared region. We constructed a scanning confocal imaging system with a cross-axes arrangement using optical fibers. This system is based on the optical heterodyne technique and enables the detection of very weak coherence photons that are generated in the spatially restricted confocal region and scattered laterally (90 degrees ) against an incident beam. To evaluate the fundamental imaging capabilities of the system, we assessed measurements from scattering phantoms composed of an Intralipid suspension with varying volume concentrations. The results of this study demonstrate that the right-angled scattered light adheres to the Lambert-Beer law and that the present system can detect light propagating through a distance of approximately 31l of the mean free path. An inclusion as small as 100 microm can be discriminated in a scattering media with an optical thickness of 4. We investigated the potential of the proposed system for imaging biological tissues in preliminary experiments using samples of chicken breast tissue.     

Reflection and transmission properties of holographic mirrors and holographic Fabry-Perot filters. II. Holographic mirrors with partially coherent light

The reflection and transmission properties of holographic mirrors (HM's) under partially coherent illumination are investigated with emphasis on the properties of reflected light. The effects of a HM on the spectrum and on the coherence properties of partially coherent incident light are studied. We show that within angular and frequency-selectivity ranges of HM's (where their reflectivities are nearly uniform), the changes in the spectrum and in the coherence properties are negligible. Yet changes are expected when the spectrum of the incident light falls beyond frequency-selectivity ranges of the HM's or when the spectrum of the reflected light is observed beyond the angular-selectivity ranges of the mirrors. We illustrate the results by considering in detail the performance of HM's when the incident light is produced by planar secondary Gaussian Schell-model sources. Some computed curves are presented.     

Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics

We report the experimental observation of the fractional Fourier transform (FRT) for a partially coherent optical beam with Gaussian statistics [i.e., partially coherent Gaussian Schell-model (GSM) beam]. The intensity distribution (or beam width) and the modulus of the square of the spectral degree of coherence (or coherence width) of a partially coherent GSM beam in the FRT plane are measured, and the experimental results are analyzed and agree well with the theoretical results. The FRT optical system provides a convenient way to control the properties, e.g., the intensity distribution, beam width, spectral degree of coherence, and coherence width, of a partially coherent beam.