David G. Fischer

INVERSE PROBLEMS WITH QUASI-HOMOGENEOUS RANDOM MEDIA

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.

Monte Carlo modeling of spatial coherence: free-space diffraction.

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.

The information content of weakly scattered fields : implications for near-field imaging of three-dimensional structures

Abstract 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 bearing on total internal reflection microscopy (TIRM), and they yield insight into the limitations of more general near-field imaging techniques.

CHASER: An Innovative Satellite Mission Concept to Measure the Effects of Aerosols on Clouds and Climate

The formation of cloud droplets on aerosol particles, technically known as the activation of cloud condensation nuclei (CCN), is the fundamental process driving the interactions of aerosols with clouds and precipitation. The Intergovernmental Panel on Climate Change (IPCC) and the Decadal Survey indicate that the uncertainty in how clouds adjust to aerosol perturbations dominates the uncertainty in the overall quantification of the radiative forcing attributable to human activities. Measurements by current satellites allow the determination of crude profiles of cloud particle size, but not of the activated CCN that seed them. The Clouds, Hazards, and Aerosols Survey for Earth Researchers (CHASER) mission concept responds to the IPCC and Decadal Survey concerns, utilizing a new technique and high-heritage instruments to measure all the quantities necessary to produce the first global survey maps of activated CCN and the properties of the clouds associated with them. CHASER also determines the activated CCN...

Coherence effects in Mie scattering

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.

Inverse Problems with Quasihomogeneous Random Media Utilizing Scattered Pulses

Abstract 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.

Monte Carlo Green's function formalism for the propagation of partially coherent light

We present a Monte Carlo-derived Greens function for the propagation of partially spatially coherent fields. This Greens 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.

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.

Interfacial shape and contact-angle measurement of transparent samples with confocal interference microscopy

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.

Multiscalar Analyses of High-Pressure Swirl-Stabilized Combustion via Single-Shot Dual-SBG Raman Spectroscopy

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. Statistical analyses of the single-shot thermochemical data provide insights into the nature of the partial-premixing process and its impact on the subsequent combustion process.