Angular distribution of diffuse reflectance from incoherent multiple scattering in turbid media.

The angular distribution of diffuse reflection is elucidated with greater understanding by studying a homogeneous turbid medium. We modeled the medium as an infinite slab and studied the reflection dependence on the following three parameters: the incident direction, optical depth, and asymmetry factor. The diffuse reflection is produced by incoherent multiple scattering and is solved through radiative transfer theory. At large optical depths, the angular distribution of the diffuse reflection with small incident angles is similar to that of a Lambertian surface, but, with incident angles larger than 60°, the angular distributions have a prominent reflection peak around the specular reflection angle. These reflection peaks are found originating from the scattering within one transport mean free path in the top layer of the medium. The maximum reflection angles for different incident angles are analyzed and can characterize the structure of angular distributions for different asymmetry factors and optical depths. The properties of the angular distribution can be applied to more complex systems for a better understanding of diffuse reflection.

Femtosecond-laser-induced shockwaves in water generated at an air-water interface.

We report generation of femtosecond-laser-induced shockwaves at an air-water interface by millijoule femtosecond laser pulses. We document and discuss the main processes accompanying this phenomenon, including light emission, development of the ablation plume in the air, formation of an ablation cavity, and, subsequently, a bubble developing in water. We also discuss the possibility of remotely controlling the characteristics of laser-induced sound waves in water through linear acoustic superposition of sound waves that results from millijoule femtosecond laser-pulse interaction with an air-water interface, thus opening up the possibility of remote acoustic applications in oceanic and riverine environments.

Energy transfer between laser filaments in liquid methanol.

We demonstrate energy exchange between two filament-forming femtosecond laser beams in liquid methanol. Our results are consistent with those of previous works documenting coupling between filaments in air; in addition, we identify an unreported phenomenon in which the direction of energy exchange oscillates at increments in the relative pulse delay equal to an optical period (2.6 fs). Energy transfer from one filament to another may be used in remote sensing and spectroscopic applications utilizing femtosecond laser filaments in water and air.

FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores.

Airborne contaminants, e.g., bacterial spores, are usually analyzed by time-consuming microscopic, chemical, and biological assays. Current research into real-time laser spectroscopic detectors of such contaminants is based on e.g., resonance fluorescence. The present approach derives from recent experiments in which atoms and molecules are prepared by one (or more) coherent laser(s) and probed by another set of lasers. However, generating and using maximally coherent oscillation in macromolecules having an enormous number of degrees of freedom is challenging. In particular, the short dephasing times and rapid internal conversion rates are major obstacles. However, adiabatic fast passage techniques and the ability to generate combs of phase-coherent femtosecond pulses provide tools for the generation and utilization of maximal quantum coherence in large molecules and biopolymers. We call this technique FAST CARS (femtosecond adaptive spectroscopic techniques for coherent anti-Stokes Raman spectroscopy), and the present article proposes and analyses ways in which it could be used to rapidly identify preselected molecules in real time.

Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations.

For single scattering in a turbid medium, the Mueller matrix is the 4 x 4 matrix that multiplies the incident Stokes vector to yield the scattered Stokes vector. This matrix contains all the information that can be obtained from an elastic-scattering system. We have extended this concept to the multiple-scattering domain where we can define an effective Mueller matrix that, when operating on any incident state of light, will yield the output state. We have calculated this matrix using two completely different computational methods and compared the results for several simple two-layer turbid systems separated by a dielectric interface. We have shown that both methods give reliable results and therefore can be used to accurately predict the scattering properties of turbid media.

Light backscattering polarization patterns from turbid media: theory and experiment.

We present both experimental measurements and Monte-Carlo-based simulations of the diffusely backscattered intensity patterns that arise from illuminating a turbid medium with a polarized laser beam. It is rigorously shown that, because of axial symmetry of the system, only seven elements of the effective backscattering Mueller matrix are independent. A new numerical method that allows simultaneous calculation of all 16 elements of the two-dimensional Mueller matrix is used. To validate our method we compared calculations to measurements from a turbid medium that consisted of polystyrene spheres of different sizes and concentrations in deionized water. The experimental and numerical results are in excellent agreement.

Virtues of mueller matrix imaging for underwater target detection.

We present a theoretical analysis on use of polarized light in the detection of a model target in a scattering and absorbing medium similar to seawater. Monte Carlo numerical simulations are used in the calculation of the effective Mueller matrix which describes the scattering process. A target in the shape of a disk is divided into three regions, each of which has the same albedo but different reduced Mueller matrices. Contrast between various parts of the target and background is analyzed in the images created by ordinary radiance, by various elements of the Mueller matrix, and by certain suitable combinations of these elements. It is shown that the application of polarized light has distinct advantages in target detection and characterization when compared with use of unpolarized light.

Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium.

We present both experimental and Monte Carlo-based simulation results for the diffusely backscattered intensity patterns that arise from illumination of a turbid medium with a polarized laser beam. A numerical method that allows the calculation of all 16 elements of the two-dimensional Muller matrix is used; moreover, it is shown that only seven matrix elements are independent. To validate our method, we compared our simulations with experimental measurements, using a turbid medium consisting of 2.02-microm -diameter polystyrene spheres suspended in deionized water. By varying the incident polarization and the analyzer optics for the experimental measurements, we obtained the diffuse backscattering Mueller matrix elements. The experimental and the numerical results are in good agreement.

Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium: errata.

In our recent Letter,(1) several typographical errors were present. On p. 487, in Fig. 2, the equations for the following Mueller matrix elements should read as S(14) = (RO - LO), S(22) = (HH + VV) - (HV + VH), S(23) = (PH + MV) - (PV + MH), S(24) = (RH + LV) - (RV + LH), S(32) = (HP + VM) - (HM + VP), S(33) = (PP + MM) - (PM + MP), S(34) = (RP + LM) - (RM + LP), S(41) = (OR + OL), S(42) = (HR + VL) - (HL + VR), S(43) = (PR + ML) - (PL + MR), and S(44) = (RR + LL) - (RL + LR). Also on p. 487, in the left-hand column, line 10 from the top should read as follows: mfp? = 1/[mua + mus(1 - g)], was 0.957 cm.

Theoretical analysis of polarization patterns from incoherent backscattering of light.

Anisotropy in the polarization of the backscattered light from a polarized laser beam incident upon a scattering medium has been observed experimentally. When the beam is viewed through an oriented polarizer, characteristic patterns in the backscattered light are observed. We present here a simple explanation of these patterns, using the theory of incoherent scattering of light by spheres. It appears that the major contribution to the observed patterns comes from the double scattering of light.

Sunset Science. II. A useful diagram.

We present diagrams that show how layers in atmospheric thermal structure are related to the altitudes at which they are seen tangentially. These dip diagrams show that the inferior mirage greatly magnifies the apparent angular size of the lowest few centimeters of atmosphere. Conversely, inversion layers below eye level are compressed-even to zero apparent thickness, in ducts. The diagrams show that, even when distant objects are miraged, the ray crossings occur beyond the lowest point on each ray where the line of sight is tangent to a horizontal surface in the atmosphere. Therefore the apparent altitudes of these tangent points are a monotonic function of their actual heights in the atmosphere. This monotonicity explains an apparent paradox in low-Sun images.

Sunset science. I. The mock mirage.

A previously unrecognized phenomenon, which we call the mock mirage, produces inverted images of the Sun and Moon near the horizon when the observer looks downward through a thermal inversion. No ducting is involved; the rays can be concave toward the Earth throughout their length, with a radius of curvature larger than the radius of the Earth. Quite mild inversions produce surprisingly large effects, which increase with the height of the observer. Although the phenomenon has frequently been photographed, published pictures have been misinterpreted. Finally, we distinguish between features that are due to waves on inversion layers and the larger features that are due to the inversions themselves.

Neutral points in an atmosphere-ocean system. 1: Upwelling light field.

We have developed a Monte Carlo code that utilizes the complete Stokes vector to examine the structure of the degree of linear polarization in the complete observable solid angle at any level in an atmosphere-ocean system. By performing these calculations we are able to compute the positions of neutral points in the upwelling light above and beneath the ocean surface. The locations of these points in a single-scatter calculation and a Monte Carlo treatment are shown for various conditions. The presence of aerosols in the atmosphere and hydrosols in the ocean was found to have an effect on the location of these neutral points.

Unique temperature profiles for the atmosphere below an observer from sunset images.

We were able to transform the usual refraction equations for an observer within a spherically symmetric atmosphere into an Abel integral equation that has a unique inverse. It is now possible to extract accurate temperature profiles of the atmosphere below an observer over the marine boundary layer with use of simple edge-finding software on solar images at sunset. Several examples are presented demonstrating the efficiency of the method.

Multiple scattering effects on the remote sensing of the speed of sound in the ocean by Brillouin scattering.

Monte Carlo calculations have been performed to investigate the effect of multiple scattering on the frequency spectra caused by Brillouin scattering in the ocean. It is shown that the use of the frequency spectra to determine the speed of sound profile and the hydrosol backscattering probability is stable under multiple scattering because the problem is limited to single backscattering events.

Filling in of Fraunhofer lines in the ocean by Brillouin scattering.

We have investigated the relative contribution of Brillouin scattering to the filling in of both narrow and wide Fraunhofer lines in the ocean. The spectral behavior of the filling in was studied in two ways. First we studied Fraunhofer lines of variable width, such as the 455-nm Ba line with full-width at half-maximum (FWHM) = 0.02 nm, the 486-nm H(ß) line (FWHM = 0.08 nm), and the 518-nm Mg line (FWHM = 0.11 nm). We then used the 455-nm Ba line as a narrow-line model to calculate the spectral dependence of the filling in. We found that Brillouin scattering can play a significant role in the filling in of narrow Fraunhofer lines in the ocean. We have also shown that, compared with the filling in caused by Raman scattering, the filling in caused by Brillouin scattering has less dependence on both the wavelength and ocean depth but is strongly dependent on the linewidth of the Fraunhofer line.

Exact spread function for a pulsed collimated beam in a medium with small-angle scattering.

A solution has been obtained for the spatial and temporal distribution function for a pulsed fully collimated beam propagating through a homogeneous medium with Gaussian small-angle scattering. The solution was obtained first by separation of the general problem into two plane problems, which results in a partial differential equation in three variables. A Fourier transform on two projected variables (one angular and one spatial) and a Laplace transform on the projected temporal variable yielded a set of nonlinear differential equations, which were solved. A recursion relation for the moments of the distribution function was also obtained, and the software MATHEMATICA was used to evaluate these moments to high orders. The contractions on certain variables are also presented; they correspond to the solutions of less-general problems contained in the main problem. A change in the definition of the time-delay produces a remarkable change in the structure of the equations. These solutions should be quite useful for lidar studies in atmospheric and oceanic optics, x-ray and radio-wave scattering in the atmosphere and interstellar medium, and in medical physics.

Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system.

We have developed a Monte Carlo program that is capable of calculating both the scalar and the Stokes vector radiances in an atmosphere-ocean system in a single computer run. The correlated sampling technique is used to compute radiance distributions for both the scalar and the Stokes vector formulations simultaneously, thus permitting a direct comparison of the errors induced. We show the effect of the volume-scattering phase function on the errors in radiance calculations when one neglects polarization effects. The model used in this study assumes a conservative Rayleigh-scattering atmosphere above a flat ocean. Within the ocean, the volume-scattering function (the first element in the Mueller matrix) is varied according to both a Henyey-Greenstein phase function, with asymmetry factors G = 0.0, 0.5, and 0.9, and also to a Rayleigh-scattering phase function. The remainder of the reduced Mueller matrix for the ocean is taken to be that for Rayleigh scattering, which is consistent with ocean water measurement.