Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.     

Influence of forward and multiple light scatter on the measurement of beam attenuation in highly scattering marine environments

Using three-dimensional Monte Carlo radiative transfer simulations, we examine the effect of beam transmissometer geometry on the relative error in the measurement of the beam-attenuation coefficient in an aquatic environment characterized by intense light scattering, especially within submerged bubble clouds entrained by surface-wave breaking. We discuss the forward-scattering error associated with the detection of photons scattered at small angles (< 1 degrees) and the multiple-scattering error associated with the detection of photons scattered more than once along the path length of the instrument. Several scattering phase functions describing bubble clouds at different bubble void fractions in the water are considered. Owing to forward-scattering error, a beam-attenuation meter (beam transmissometer) with a half-angle of receiver acceptance of 1.0 degrees and a path length of 0.1 m can underestimate the true beam attenuation within the bubble cloud by more than 50%. For bubble clouds with a beam attenuation of as much as 100 m(-1), the multiple-scattering error is no more than a few percent. These results are compared with simulations for some example phase functions that are representative of other scattering regimes found in natural waters. The forward-scattering error for the Petzold phase function of turbid waters is 16% for a typical instrument geometry, whereas for the Henyey-Greenstein phase function with the asymmetry parameter of 0.7 and 0.9 the error range is 8-28%.     

Size distribution of mineral aerosol: using light-scattering models in laser particle sizing

The size distribution of semitransparent irregularly shaped mineral dust aerosol samples is determined using a commonly used laser particle-sizing technique. The size distribution is derived from intensity measurements of singly scattered light at various scattering angles close to the forward-scattering direction at a wavelength of 632.8 nm. We analyze the results based on various light-scattering models including diffraction theory, Mie calculations for spheres with various refractive indices, and T-matrix calculations for spheroidal particles. We identify systematic errors of the retrieved size distribution when the semitransparent and nonspherical properties of the particles are neglected. Synthetic light-scattering data for a variety of parameterized size distributions of spheres and spheroids are used to investigate the effect of simplifying assumptions made when the diffraction model or Mie theory is applied in the retrieval.     

Comparison of two methods for obtaining quantitative mass concentrations from aerosol time-of-flight mass spectrometry measurements

Aerosol time-of-flight mass spectrometry (ATOFMS) measurements provide continuous information on the aerodynamic size and chemical composition of individual particles. In this work, we compare two approaches for converting unscaled ATOFMS measurements into quantitative particle mass concentrations using (1) reference mass concentrations from a co-located micro-orifice uniform deposit impactor (MOUDI) with an accurate estimate of instrument busy time and (2) reference number concentrations from a co-located aerodynamic particle sizer (APS). Aerodynamic-diameter-dependent scaling factors are used for both methods to account for particle transmission efficiencies through the ATOFMS inlet. Scaling with APS data retains the high-resolution characteristics of the ambient aerosol because the scaling functions are specific for each hourly time period and account for a maximum in the ATOFMS transmission efficiency curve for larger-sized particles. Scaled mass concentrations obtained from both methods are compared with co-located PM(2.5) measurements for evaluation purposes. When compared against mass concentrations from a beta attenuation monitor (BAM), the MOUDI-scaled ATOFMS mass concentrations show correlations of 0.79 at Fresno, and the APS-scaled results show correlations of 0.91 at Angiola. Applying composition-dependent density corrections leads to a slope of nearly 1 with 0 intercept between the APS-scaled absolute mass concentration values and BAM mass measurements. This paper provides details on the methodologies used to convert ATOFMS data into continuous, quantitative, and size-resolved mass concentrations that will ultimately be used to provide a quantitative estimate of the number and mass concentrations of particles from different sources.     

Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation

This study is devoted to the examination of scattering of waves by a slab containing randomly located cylinders. For the first time to our knowledge, the complete transmission problem has been solved numerically. We have compared the radiative transfer theory with a numerical solution of the wave equation. We discuss the coherent effects, such as forward-scattering dip and backscattering enhancement. It is seen that the radiative transfer equation can be used with great accuracy even for optically thin systems whose geometric thickness is comparable with the wavelength. We have also shown the presence of dependent scattering.     

Near-Field Gain Correction for Transmission between Horn Antennas

When the gain of a horn antenna is to be measured from the power transmission loss between it and a standard horn, the Friis transmission formula must be corrected if the horn separation is not considerably greater than 2d2/?. Expressions for the correction between a pyramidal horn and a conical horn, and between dissimilar pyramidal horns, are presented with sample results. A method of applying these corrections to minimize the errors in the horn gain measurements is described.     

Inverse scattering with diffusing waves.

We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are used to illustrate these results in model systems.     

Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition

We continue our study of the inverse scattering problem for diffuse light. In particular, we derive inversion formulas for this problem that are based on the functional singular-value decomposition of the linearized forward-scattering operator in the slab, cylindrical, and spherical geometries. Computer simulations are used to illustrate our results in model systems.     

Light-scattering measurements of optical thin-film components at 157 and 193 nm

An instrument for total backscattering and forward-scattering measurements of optical coating components at 157 and 193 nm is described. The system is operated in both vacuum and nitrogen purge gas. An excimer laser as well as a deuterium lamp can be used as a radiation source. Suppression of the background signal level to 1 part in 10(6) permits measurements even of low-scatter samples such as superpolished substrates and antireflection coatings. Results of investigations of antireflective and highly reflective multilayers and CaF2 substrates reveal scattering from surface and interface roughness as well as from the volume of the substrate material. First steps to extend the instrument for angle-resolved scatter, transmittance, and reflectance measurements are described.     

Minicomputers and Microprocessors in Optical Systems

A periodic variation of the angular field of view of the receiver during transmittance measurements in dense fogs allowed some scattering characteristics of the medium to be monitored continuously. In addition, the extinction coefficient was evaluated and compared with the width of the forward-scattering curve.     

Edge contribution to forward scattering by spheres

Edge functions T1 and T2, which describe the polarization-dependent edge contribution to forward scattering by spheres, are derived from the exact Mie solution. All the relative refractive indices and the 64 < x < 2048 size parameter range are considered. The edge functions significantly improve the approximation methods that can be used to calculate forward-scattering patterns. For m close to 1, an asymptotic approximation is used. Otherwise, the familiar geometrical optics approximation and the similar physical optics approximation for glory rays are used. Both geometrical and physical optics equations can be deduced from the above-mentioned asymptotic approximation.     

Simultaneous retrieval of aerosol refractive index and particle size distribution from ground-based measurements of direct and scattered solar radiation

Ground-based sunphotometer observation of direct and scattered solar radiation is a traditional tool for providing data on aerosol optical properties. Spectral transmission and solar aureole measurements provide an optical source of aerosol information, which can be inverted for retrieval of microphysical properties (particle size distribution and refractive index). However, to infer these aerosol properties from ground-based remote-sensing measurements, special numerical inversion methods should be developed and applied. We propose two improvements to the existing inversion techniques employed to derive aerosol microphysical properties from combined atmospheric transmission and solar aureole measurements. First, the aerosol refractive index is directly included in the inversion procedure and is retrieved simultaneously with the particle size spectra. Second, we allow for real or effective instrumental pointing errors by including a correction factor for scattering angle errors as a retrieved inversion parameter. The inversion technique is validated by numerical simulations and applied to field data. It is shown that ground-based sunphotometer measurements enable one to derive the real part of the aerosol refractive index with an absolute error of 0.03-0.05 and to distinguish roughly between weakly and strongly absorbing aerosols. The aureole angular observation scheme can be refined with an absolute accuracy of 0.15-0.19 deg. Offset corrections to the scattering angle error are generally found to be small and consistently of the order of -0.17. This error magnitude is deduced to be due primarily to nonlinear field-of-view averaging effects rather than to instrumental errors.     

Simultaneous Measurement of Complex Permittivity and Permeability in the Millimeter Region by a Frequency-Domain Technique

A frequency-domain techique based on the measurement of scattering parameters has been described for the simultaneous measurement of complex permittivity ?* and permeability ?* in the millimeter region. The technique can be easily adapted for broad-band measurements. Results are given for teflon, plexiglas, fiberglass, and FGM-40, a magnetic absorber in the X band. Reflection and transmission error parameters corrections can be implemented to improve the accuracy.     

Radiative transfer. I. Atmospheric transmission monitoring with modeling and ground-based multispectral measurements

Existing solar radiative codes such as lowtran allow us to model the radiative properties of the atmosphere and its constituents for standard atmospheric conditions. The increase in urbanization and air pollution has led to changes in the distribution, type, and concentration of the atmospheric constituents, affecting spectral atmospheric transmission and modifying weather and climate. This requires knowledge of the real optical properties of atmospheric transmission. We have developed a model for the radiative properties of atmospheric transmission, with ground-based multispectral measurements of direct solar radiation in the 310-830-nm range. An application of this model to Athens' urban atmosphere is described. The radiative properties of a U.S. Standard Atmosphere are also simulated by use of the lowtran 7 code; simulations and calculations are compared. The total ozone retrieval scheme and the algorithm for retrieving the spectral transmission function and optical thickness, considering multiple scattering, are given. Results for the spectral atmospheric transmission and aerosol and gas transmission functions as well as optical-thickness measurements for the Athens area are also presented as an application of the proposed methodology.     

Reflectance of pigmented polymer coatings: comparisons between measurements and radiative transfer calculations

Solar reflectance spectra of pigmented coatings have been obtained from spectroscopic measurements involving integrating sphere attachments. We demonstrate that measured and computed reflectances of an extended four-flux model [Appl. Opt. 37, 2615 (1998)] whose average path-length parameters (APP's) and forward-scattering ratios (FSR's) are explicitly evaluated from a multiple-scattering approach at the front or back interface of the particulate coatings display fairly good agreement. The agreement of these properties in a standard four-flux model [Appl. Opt. 23, 3353 (1984)], which neglects the spectral dependence of the APP and FSR, is found in the near infrared. Good agreement between these two four-flux approaches over the solar spectral range is obtained when the mean values of the APP's and FSR's are used in the standard model.     

Extinction and scattering of a guided beam in a hollow dielectric waveguide.

We present a theoretical approach to the problem of mode scattering by a spherical object that is placed inside a circular dielectric waveguide. This approach is based on the separation-of-variables method for each subsystem, namely, the spherical inclusion and the circular dielectric cylinder, and on the concept of the generalized recursive T-matrix algorithm for multilayered structures. We apply the technique to the backward and the forward scattering of a quasi-optical beam in the form of the fundamental HE11 mode by a sphere inside a circular hollow dielectric waveguide. The results calculated for the perfectly conducting spherical objects inside the circular hollow dielectric waveguide are compared with corresponding measured data of the backward-and the forward-scattering characteristics at the 4-mm wave band.     

Optical properties and size distribution of aerosols derived from simultaneous measurements with lidar, a sunphotometer, and an aureolemeter

A new method is proposed to derive the optical properties and size distribution of aerosol in an air column from simultaneous measurements of the backscattering coefficient, the optical thickness, and the solar aureole intensity with lidar, a sunphotometer, and an aureolemeter. Inasmuch as the backscattering properties and the optical thickness depend on both the complex refractive index and the size distribution, whereas the forward-scattering properties depend mainly on the size distribution, real and imaginary indices of refraction and size distributions of aerosol are retrieved from these measurements. The real and the imaginary parts of the complex refractive index of an aerosol at a wavelength of 500 nm during the period from November 1991 to March 1992 obtained in Tsukuba, Japan, were estimated to be 1.46-1.48 and 0.005-0.014, respectively. It is inferred from the size distribution and an optical thickness fraction of stratospheric aerosols in the total columnar aerosols that these results reflect the influences of stratospheric aerosols that originated from the Mt. Pinatubo eruption.     

Characterization of intersubband devices combining a nonequilibrium many body theory with transmission spectroscopy experiments

In this paper we apply a microscopic nonequilibrium many body Keldysh Green′s functions approach to an analysis of complex intersubband optical materials and devices. The calculated absorption/gain spectra are in very good agreement with transmission spectroscopy measurements of quantum cascade laser structures operating in the mid-infrared (midIR). The very good agreement reached between theoretical results and experimental measurements benchmarks the predictive power of our algorithms and its potential as a design tool for efficient intersubband designs.     

Primary Thermometry in the Intermediate Coulomb Blockade Regime

We investigate Coulomb blockade thermometers (CBT) in an intermediate temperature regime, where measurements with enhanced accuracy are possible due to the increased magnitude of the differential conductance dip. Previous theoretical results show that corrections to the half width and to the depth of the measured conductance dip of a sensor are needed, when leaving the regime of weak Coulomb blockade towards lower temperatures. In the present work, we demonstrate experimentally that the temperature range of a CBT sensor can be extended by employing these corrections without compromising the primary nature or the accuracy of the thermometer.     

Corrections of size-of-source effect and distance effect in radiometric measurements of radiance

Many optical instruments used in quality control of the optical radiation emission level of several devices are limited by the so-called size-of-source effect (SSE) as well as the distance effect (DE) when we are dealing with very accurate measurements. Different authors have studied the SSE and DE and have proposed experimental methods that provide corrections for them. We describe a general method based on the partial coherence theory that allows us to describe and calculate the SSE and DE in any radiometric system with circular apertures. We show some experimental results that verify our proposal. Additionally, as a practical example, we present the corresponding DE and SSE correction factors for a particular geometry.