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We demonstrate analytically and numerically that the transverse spatial coherence (the spectral degree of coherence) of the field radiated by two partially correlated electromagnetic sources oscillates as a function of propagation distance in free space. In particular, it is possible for its magnitude to completely collapse to zero on propagation, and then return again to unity at a further distance. Our results are a direct demonstration of the wave character of the optical correlation functions. A similar oscillatory effect occurs for the degree of polarization.

© 2021 Optical Society of America.The superposition of two partially correlated waves is shown to produce fields with drastically altered coherence properties. It is demonstrated, both theoretically and experimentally, that two strongly correlated sources may generate a field with practically zero correlation between certain pairs of points. This anomalous change in coherence is a general phenomenon that takes place in all cases of wave superposition, including Mie scattering, as is shown. Our results are particularly relevant to applications in which it is assumed that highly coherent radiation maintains its spatial coherence on propagation, such as optical systems design and the imaging of extended sources.

JOSA A Editor-in-Chief P. Scott Carney, Feature Editor Johannes Courtial, and members of the 2020 Emerging Researcher Best Paper Prize Committee announce the recipient of the 2020 prize for the best paper published by an emerging researcher in the Journal.

We demonstrate that two strongly correlated sources may generate a field with practically zero correlation between certain pairs of points. We argue that this is a general phenomenon in radiation and scattering.

When light that is spatially partially coherent, such as sunlight, is incident on a sphere, the scattered field exhibits surprising coherence properties. The observed oscillatory behavior with deep minima means that the field in certain pairs of directions is highly correlated, whereas in others, it is essentially uncorrelated, and can even have correlation singularities. Because any subsequent scattering event is strongly affected by the state of coherence, these results are particularly important for multiple scattering in discrete disordered media.

The latest combustion model-validation experiments are presented using a time-, space-, and polarization-resolved subframe-burst gating Raman spectroscopy system. A modification to the original subframe-burst gating diagnostics system enables parallel detection of both polarized and depolarized Raman components for the first time in a high-pressure flame tube, which permits signal detection with reduced background noise, and consequently more precise determination of temperature and species in optically harsh flames. This technique is applied to the measurement of mass fractions of the major species and temperature in a swirl-stabilized hydrogen-methane flame at an elevated pressure of 15.5 bar. The single-shot linear Raman spectra are reduced to provide quantitative multiscalar information throughout the primary reaction zone. The experimental dataset is plotted along with the laminar flamelet calculations for different Lewis numbers and strain rates to allow better interpretation. Time-dependent analysi...

Preventing fires in spacecraft and other remote platforms is an important facet of avoiding fires that potentially compromise missions, hardware, and crew. If a fire occurs, the objective is to detect the associated fire signatures at the earliest possible time from inception, thus minimizing propagation and collateral damage while providing maximal margin for suppression. The goal is to provide detection sensitivity without introducing spurious false alarms that compromise operations and trigger responsive abatement and containment provisions. A related issue in sealed, self-contained environments is post-fire clean up, and sensors to evaluate the environmental suitability in crewed quarters. In both situations, knowledge of the particulate and/or gaseous fire signatures as they occur under the unique combination of a reduced-gravity environment and materials typical of spaceflight applications is essential for the design of spacecraft fire detectors and habitat sensors. This paper describes recent ground and spaced-based data on fire signatures, and the response of a novel multi-channel optical scattering sensor. This detector, known as the Multi-Parameter Aerosol Scattering Sensor (MPASS), determines multiple moments of the aerosol distributions. The methodology for designing a sensor with the desired response function is discussed, as well as test results that demonstrate the performance of prototype devices.

We report an experimental study and thermochemical analysis of high-pressure swirl-stabilized combustion utilizing subframe burst gating (SBG) Raman spectroscopy. SBG Raman spectroscopy is a novel diagnostic technique that provides increased accuracy of quantitative scalar measurements in a single-shot pointwise manner. A recent modification of our original system allows parallel detection of both Stokes and anti-Stokes spectral components (hence the term dual SBG). We begin by briefly describing the experimental construction of a Raman calibration matrix, which allows us to reduce spectral cross-talk in the measurements. Next we describe the application of dual-SBG Raman spectroscopy to simultaneous single-shot measurement of temperature and species mass fractions in a turbulent flame stabilized over a lean-direct-injection (LDI) burner using gaseous methane fuel at elevated pressure of 17 atm. Our discussion includes the practical challenges of Raman spectroscopy in a pressurized combustion rig. Statist...

We study the Gouy phase of a scalar wavefield that is focused by a lens suffering from primary spherical aberration. It is found that the Gouy phase has different behaviors at the two sides of the intensity maximum. This results in a systematic increase of the successive wavefront spacings around the diffraction focus. Since all lenses have some amount of spherical aberration, this observation has implications for optical calibration and metrology. © 2013 Optical Society of America.

The structural information carried by the homogeneous and evanescent components of the scattered field is investigated for the case of a single plane wave, either homogeneous or evanescent, incident on a weakly scattering three-dimensional medium. For homogeneous plane wave incidence, it is shown that, unlike the one-to-one mapping that exists in the case of scattering from thin (i.e. two-dimensional) structures, the evanescent components of the scattered field are related to the three-dimensional Fourier transform of the dielectric susceptibility through a generalized Radon transform. For evanescent plane wave incidence, a reciprocal relationship exists between the homogenous components of the scattered field and the three-dimensional Fourier transform of the susceptibility. Inversion techniques are outlined for these two cases, as well as other experimental modalities, which explicitly require, except for separable media, complete (i.e. multiple view) measurement data. These results have direct...

The theory of diffraction tomography is generalized to random media. A relationship between the two-point spatial correlation function of the dielectric susceptibility and the cross-spectral density of the scattered field is derived, and the reconstruction of the two-point spatial correlation function from measurements of the cross-spectral density in two planes, on different sides and at finite distances from the medium, is investigated. It is shown that the two-point spatial correlation function cannot be determined uniquely, in general, from scattered field measurements, except for a class of random media known as quasi-homogeneous random media.

The theory of diffraction tomography is extended to the reconstruction of quasi-homogeneous random objects. It is shown that a low-pass filtered version of the degree of spatial correlation of the scattering potential of such an object can be determined from measurements of the cross-spectral density of the scattered field in two planes, one on each side of the scatterer.

A method is presented for reconstructing the normalized second moment of the dielectric susceptibility of a quasihomogeneous random medium. The method involves illuminating the medium with plane-wave pulses and measuring the intensity of the scattered field in the far zone for various directions of incidence. We illustrate our analysis by computer simulation.

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 ?, 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. © 2012 Optical Society of America.

An important indicator of health status is hematocrit (HCT), the fractional volume of red blood cells. As such, a noninvasive, real-time means of its measurement is highly desirable in a space flight situation. We propose to exploit ultrasound technology to provide such a capability. We introduce a specific measurement concept including the hardware and requisite processing algorithms, and discuss progress towards realization of such a measurement capability.

We present a method of using an unmodified differential interference contrast microscope to acquire quantitative information on scatter and absorption of thin tissue samples. A simple calibration process is discussed that uses a standard optical wedge. Subsequently, we present a phase-stepping procedure for acquiring phase gradient information exclusive of absorption effects. The procedure results in two-dimensional maps of the local angular (polar and azimuthal) ray deviation. We demonstrate the calibration process, discuss details of the phase-stepping algorithm, and present representative results for a porcine skin sample.

We present an analysis of the accuracy and information content of three-dimensional reconstructions of the dielectric susceptibility of a sample from noisy, near-field holographic measurements, such as those made in scanning probe microscopy. Holographic measurements are related to the dielectric susceptibility via a linear operator within the accuracy of the first Born approximation. The maximum-likelihood reconstruction of the dielectric susceptibility is expressed as a linear combination of basis functions determined by singular value decomposition of the weighted measurement operator. Maximum a posteriori estimates based on prior information are also discussed. Semianalytical expressions are given for the likely error due to measurement noise in the basis function coefficients, resulting in effective resolution limits in all three dimensions. These results are illustrated by numerical examples.

We discuss the use of a DIC microscope for characterization of the scatter and absorption properties of thin tissue samples. We demonstrate the calibration process, illustrate phase-stepping approaches, and show representative results.

Source masking by a cosine amplitude grating is shown to render possible the reconstruction of the intensity distribution associated with globally incoherent optical sources from spectral measurements performed with a Young's two-pinhole fixed-baseline interferometer. The effect of the mask is to map the low spatial frequencies of the source intensity onto accessible optical frequencies. The permissible parameter regimes are studied, and the feasibility of the technique is demonstrated by numerical simulations.

Preventing fires in spacecraft or remote habitats is always the first line of defense to avoid a fire that compromises the missions, hardware, and crew. If a fire occurs, the objective is to detect the associated fire signatures at the earliest possible time from inception, thus minimizing propagation and collateral damage while providing maximal margin for suppression. Knowledge of the particulate and/or gaseous fire signatures as they occur under the unique combination of a reduced-gravity environment and materials typical of spaceflight applications is essential for the design of spacecraft fire detectors. This paper describes how recent experiments conducted on the ISS have guided the design and development of a unique two-moment smoke particulate detector. This detector, known as the Multi-Parameter Aerosol Scattering Spectrometer (MPASS) determines both the total surface area and mass of the aerosol, corresponding to the second and third moments of the distributions, respectively. These quantities can be correlated with the specific materials being pyrolyzed, and potentially the spatial/temporal evolution as the aerosol ages. The methodology for designing a sensor with the desired response function is discussed, as well as test results that demonstrate the performance of prototype devices.

We describe an architecture for spontaneous Raman scattering utilizing a frame-transfer CCD sensor operating in a subframe burst-gating mode to realize time-resolved combustion diagnostics. The technique permits all-electronic optical gating with microsecond shutter speeds (

Stochastic Huygens describes a method of propagating a partially coherent source by sampling the Huygens wavelets that evolve from each point of the wavefront. The amplitude and phase of each wavelet is tracked as the light passes through the optical system. We have previously described how a partially coherent wavefront may be simulated by propagating an ensemble of wavefronts with specified first and second-order statistics through simple optical systems. In this work we extend the modeling effort to include an ensemble of phase (or scattering) screens that characterize thin microscope tissue samples in the optical path.

The propagation of light through complex structures, such as biological tissue, is a poorly understood phenomenon. Typically the tissue is modeled as an effective medium, and Monte Carlo techniques are used to solve the radiative transport equation. In such an approach the medium is characterized in terms of a limited number of physical scatter and absorption parameters, but is otherwise considered homogeneous. For exploration of propagation phenomena such as spatial coherence, however, a physical model of the tissue medium that allows multiscale structure is required. We present a particularly simple means of establishing such a multiscale tissue characterization based on measurements using a differential interference contrast (DIC) microscope. This characterization is in terms of spatially resolved maps of the (polar and azimuthal) angular ray deviations. With such data, tissues can be characterized in terms of their first and second order scatter properties. We discuss a simple means of calibrating a DIC microscope, the measurement procedure and quantitative interpretation of the ensuing data. These characterizations are in terms of the scatter phase function and the spatial power spectral density

Analysis of the first and second order statistical properties of light is a powerful means of establishing the properties of a medium with which the light has interacted. In turn, the first and second order statistical properties of the medium dictate the manner in which light interacts with the medium. The former is the inverse problem and the latter is the forward problem. Towards an understanding of the propagation of light through complex structures, such as biological tissue, one might choose to explore either the inverse or the forward problem. Fundamental to the problem, however, is a physical parametric model that relates the two halves; a model that allows prediction of the measured effect or prediction of the parameters based on measurements. This is the objective of our study. As a means of characterizing the first and second order properties of tissue, we discuss measurements with differential interference contrast microscopy using a phasestepping approach. First and second order properties are characterized respectively in terms of scatter phase functions and spatial power spectral densities. Results are shown for representative tissue.

We study the effects of spatial coherence of the incident beam on the scattering by a sphere. Strong modifications of the radiant intensity are predicted.

We present a Monte Carlo-derived Green's function for the propagation of partially spatially coherent fields. This Green's function, which is derived by sampling Huygens-Fresnel wavelets, can be used to propagate fields through an optical system and to compute first- and second-order field statistics directly. The concept is illustrated for a cylindrical f/1 imaging system. A Gaussian copula is used to synthesize realizations of a Gaussian Schell-model field in the pupil plane. Physical optics and Monte Carlo predictions are made for the first- and second-order statistics of the field in the vicinity of the focal plane for a variety of source coherence conditions. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. This formalism can be generally employed to treat the interaction of partially coherent fields with diffracting structures.

The classic "Ewald-sphere construction" for determining the structure of crystalline objects from x-ray and neutron diffraction experiments is generalized to determine the correlation functions of scattering potentials of stationary random media from scattering experiments.

The propagation of light through complex structures, such as biological tissue, is a poorly understood phenomenon. Current practice typically ignores the coherence of the optical field. Propagation is treated by Monte Carlo implementation of the radiative transport equation, in which the field is taken to be incoherent and is described solely by the first-order statistical moment of the intensity. Although recent Monte Carlo studies have explored the evolution of polarization using a Stokes vector description, these efforts, too are single-point statistical characterizations and thus ignore the wave nature of light. As a result, the manner in which propagation affects coherence and polarization cannot be predicted. In this paper, we demonstrate a Monte Carlo approach for propagating partially coherent fields through complicated deterministic optical systems. Random sources with arbitrary spatial coherence properties are generated using a Gaussian copula. Physical optics and Monte Carlo predictions of the first and second order statistics of the field are shown for coherent and partially coherent sources for a variety of imaging and non-imaging configurations. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Finally, we discuss convergence criteria for judging the quality of the Monte Carlo predictions. Ultimately, this formalism will be utilized to determine certain properties of a given optical system from measurements of the spatial coherence of the field at an output plane. Although our specific interests lie in biomedical imaging applications, it is expected that this work will find application to important radiometric problems as well.

We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions.

A model has been developed that predicts the effective optical path through a thick, refractive specimen on a reflective substrate, as measured with a scanning confocal interference microscope equipped with a high-numerical-aperture objective. Assuming that the effective pinhole of the confocal microscope has an infinitesimal diameter, only one ray in the illumination bundle (the magic ray) contributes to the differential optical path length (OPL). A pinhole with finite diameter, however, allows rays within a small angular cone centered on the magic ray to contribute to the OPL. The model was incorporated into an iterative algorithm that allows the measured phase to be corrected for refractive errors by use of an a priori estimate of the sample profile. The algorithm was validated with a reflected-light microscope equipped with a phase-shifting laser-feedback interferometer to measure the interface shape and the 68 degrees contact angle of a silicone-oil drop on a coated silicon wafer.

The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the Spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas. © 2006 Optical Society of America.

The information content of the near-zone scattered field, for the case of a holographic measurement geometry, is examined using the variance of the least squares estimate of the susceptibility. Several examples will be presented.

We demonstrate the use of phase-shifting interferometry in OCT to determine the optical phase and fringe visibility within the coherence envelope. Phase-shifting algorithms provide both the optical phase and visibility from a series of intensity measurements corresponding to controlled phase shifts. In addition to providing phase information which supplements the visibility or envelope data which is traditionally obtained in OCT, this technique will provide an independent, highly sensitive measurement of the coherence envelope which may be used for a precise determination of the source power spectrum.

An overview of a novel new form of near-field microscopy known as total internal reflection tomography (TIRT), which allows for true three-dimensional sub-wavelength optical imaging, will be presented.

The structural information carried by the evanescent components of the scattered field is discussed for the case of a single homogeneous plane wave incident on a weakly scattering three-dimensional medium. It is shown that, unlike the homogeneous components of the scattered field, the evanescent components are related to the three-dimensional Fourier transform of the dielectric susceptibility through a generalized Radon transform. The region of the three- dimensional Fourier space that is accessible from evanescent wave measurements is discussed, as well as the spatial resolution attainable in a typical multiple-view scattering experiment.

We have developed a model that predicts the effective optical path length (OPL) through a thick, refractive specimen on a reflective substrate as measured with a high numerical aperture, confocal interference microscope. Assuming an infinitesimal pinhole, only one 'magic ray' contributes to the measured OPL. It is possible to correct for the refractive errors and to unambiguously interpret the data. We present a comparison of our model predictions with experimental measurements of a fluid drop on a silicon substrate, obtained with a phase shifting laser feedback microscope.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Calibration of the axial response of interference microscopes has received considerable attention in the past two decades. In addition to systematic errors which could be caused by components in the microscope or measurement technique, a numerical correction factor associated with imaging at high apertures must be determined. Unfortunately, the cost of reference height standards increases sharply with their spatial homogeneity and calibration accuracy and these standards may be easily contaminated and therefore require sophisticated cleaning and re-calibration. To address these problems, we have investigated the interferometric measurement of the equilibrium shape of static fluid drops on coated substrates. For drops with small Bond number (the Bond number is a ratio of gravitational to capillary forces), the surface of the drop forms a spherical cap. It appears that nature forms a highly smooth, curved surface. By varying the surface energy, it is possible to obtain a wide range of static contact angles. For example, silicone oil [polydimethylsiloxane (PDMS)] on glass forms a contact angle of about 5 degrees, while it forms an angle of 38 degrees on Teflon and 68 degrees on a fluorinated silicon surface. We have measured contact angles as large as 68 degrees for PDMS on a single crystal silicon wafer with a 50 X/0.8 NA objective using a custom-made phase-shifted, laser feedback microscope. The method for preparing these static drops is simple and we envision that microscopists will be able to prepare easily disposable calibration standards in their laboratories.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The scattering of a partially coherent beam by a deterministic, spherical scatterer is studied. In particular, the Mie scattering by a Gaussian Schell-model beam is analyzed. Expressions are derived for (a) the extinguished power, (b) the radiant intensity of the scattered field, and (c) the encircled energy in the far field. It is found that the radiant intensity and the encircled energy in the far field depend on the degree of coherence of the incident beam, whereas the extinguished power does not. (C) 2011 Optical Society of America

A technique is presented for determining the two-point spatial correlation function of the dielectric susceptibility of a quasi-homogeneous random medium.1

In the analysis of light scattering on a sphere it is implicitly assumed that the incident field is spatially fully coherent. However, under usual circumstances the field is partially coherent. We generalize the partial waves expansion method to this situation and examine the influence of the degree of coherence of the incident field on the radiant intensity of the scattered field in the far zone. We show that when the coherence length of the incident field is comparable to, or is smaller than, the radius of the sphere, the angular distribution of the radiant intensity depends strongly on the degree of coherence. The results have implications, for example, for scattering in the atmosphere and colloidal suspensions. © 2010 The American Physical Society.

In a series of papers [1], it has been claimed that evanescent waves contribute to the far field of a radiating dipole, i.e. that the amplitude of the sum of the evanescent waves decreases as 1/r with increasing distance, r, from the dipole. In spite of the fact that three recent papers [2] have demonstrated that these claims are incorrect and that they contradict well-established results relating to the farzone behavior of the angular spectrum representation of wavefields [3], the author continues to repeat this claim, most recently in a note with the title ‘Evanescent waves do contribute to the field’. It is the purpose of this note to point out an error in the previous publications [1] which has led to this erroneous conclusion.

Inversion formulas are presented for determining the second-order correlation properties of spatially random media of a certain class, namely, quasihomogeneous media,1 from the knowledge of the spectra of the scattered field. In general, the far zone spectra of the scattered field must be known for all directions of incidence and all directions of scattering. The solution yields a low-pass filtered version of the cross-correlation function of the scattering potential.

We investigate the spatial coherence properties in the focal region of a converging, spatially partially coherent wave field. In particular, we find that, depending on the effective coherence length of the field in the aperture, the longitudinal and transverse coherence lengths in the focal region can be either larger or smaller than the corresponding width of the intensity distribution. Also, the correlation function is shown to exhibit phase singularities. © 2004 Optical Society of America.

Limits on the effective resolution of many optical near-field experiments are investigated. The results are applicable to variants of total-internal-reflection microscopy (TIRM), photon-scanning-tunneling microscopy (PSTM), and near-field-scanning-optical microscopy (NSOM) in which the sample is weakly scattering and the direction of illumination may be controlled. Analytical expressions for the variance of the estimate of the complex susceptibility of an unknown two-dimensional object as a function of spatial frequency are obtained for Gaussian and Poisson noise models, and a model-independent measure is examined. The results are used to explore the transition from near-zone to far-zone detection. It is demonstrated that the information content of the measurements made at a distance of even one wavelength away from the sample is already not much different from the information content of the far field.

A generalized Radon transform is presented that relates, for the case of an evanescent wave that is incident upon a weakly scattering medium, the homogeneous components of the scattered field to the three-dimensional Fourier transform of the dielectric susceptibility. This relationship is used within the context of total internal reflection microscopy to reconstruct the depth structure of the dielectric susceptibility from simulated scattered field data.

Formulas are derived for determining low-pass filtered versions of the two constituent factors of the two-point spatial correlation function of a quasi-homogeneous random medium from knowledge of the cross-spectral density of the scattered field in the far zone. The results are illustrated by an example. When the scale lengths of variation of these quantities are greater than approximately half of the mean wavelength of the incident light, the reconstructions are found to be practically exact.