Backscattering Direction Research Articles

Enhanced resonant backscattering of light from quantum-well excitons

The angle-dependent resonant Rayleigh scattering of light from excitons in a disordered quantum well is studied theoretically. An enhancement of the scattered intensity peaked on the backscattering direction is predicted, for values of the parameters corresponding to realistic GaAs/AlGaAs heterostructures. It is shown that this effect can be isolated by measuring the differential enhancement between two different scattering directions. An analysis in terms of perturbation theory provides a simple analytical approximation of the measurable quantity.

Magnetic field effects on coherent backscattering of light

We have studied the influence of magneto-optical Faraday rotation on coherent backscattering of light experimentally, theoretically and by computer simulations of Monte-Carlo type. The consistency of these three approaches reveals new aspects of the propagation of vector waves in turbid media with and without Faraday rotation. Experimentally, we have demonstrated that the Faraday rotation may almost completely destroy the reciprocity of light paths. However, as shown by the simulations, the cone of coherent backscattering may not only be destroyed but also shifted off the exact backscattering direction, parallel to the magnetic field, as long as the amount of circular polarization is not completely destroyed by the multiple scattering. The relationship between coherent backscattering, depolarization and Faraday rotation are explained by a simple path model of vector waves. This leads to a new characteristic correlation length required to properly describe the influence of Faraday rotation on multiple light scattering.

Polarimetric bistatic scattering from random rough surfaces along azimuth angle

Electromagnetic wave interaction with random media is a process which needs improved theoretical representations. Existing assumptions and approximations for electromagnetic bistatic scattering from randomly rough surfaces sometimes remain unjustified, since this scattering phenomena is not fully understood. For further understanding the scattering behavior of electromagnetic waves from randomly rough surfaces we need an improved model to predict the bistatic scattering behaviors along different azimuth angle. The model developed for predicting the scattering characteristics from statistically rough surfaces in this paper is based upon the integral equation model with multiple scattering. Its objective is to examine the bistatic scattering characteristics from randomly rough surfaces along the different azimuth angle. For better understanding the scattering behavior from randomly rough surfaces, the information about scattering must be known omnidirectionally, not just in the specular or backscatter direction. Comparisons between the model prediction and the experimental measurements are made for both like and cross polarizations. This model prediction demonstrates good agreement with the experimental data.

View Zenith Angle Effects on the Forest Information Content of Three Spectral Indices

The effects of view zenith angle on the relationship between three spectral vegetation indices (NDVI, SAVI, GEMI) and forest biophysical characteristics is examined. The work uses both simulated reflectance data, derived from a Monte Carlo ray-tracing model, and multiangle Advanced Solid-state Array Spectrometer (ASAS) data. Factorial analysis of variance was applied to the simulated reflectance data set in order to quantify the view angle dependence of the relative sensitivity of an index to independent variations in forest cover, crown leaf-area-index (LAI), stand structure, and background reflectance. Overall, it was found that off-nadir viewing improved the performance of the indices for discriminating cover and LAI, when compared with nadir viewing. The potential of the indices for discriminating forest cover was low either because of strong sensitivity to the other stand characteristics, or because of nonlinear relationships with cover. At low covers, GEMI performed best in the forward-scatter direction, while GEMI had poor sensitivity in the nadir case. The potential for discriminating crown LAI was good; both SAVI and GEMI were found to be sensitive to crown LAI in the backscatter direction. In the plane perpendicular to the solar principal plane, off-nadir viewing gave improved sensitivity to cover (NDVI) and to LAI (GEMI). The results indicate that Sun–sensor geometry may be exploited to improve discrimination of forest characteristics using spectral indices, and further work is needed to test these findings with satellite data. The results are discussed in the context of off-nadir viewing sensors such as the ATSR-2.

Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water

When the face of a finite solid elastic cylinder is ensonified by an acoustic wave, a variety of backscattering contributions associated with acoustic wave coupling into elastic waves are observed. A significant backscattering enhancement is observed for tilts such that the acoustic wave is incident on the face of the cylinder in the vicinity of the coupling angle for launching Rayleigh waves across the face. The observed backscattering indicates that the Rayleigh waves are reflected at the edge of the face and subsequently radiate acoustic waves in the backscattering direction. The measured backscattering is compared to an approximate theoretical prediction. Approximating the focusing of the Rayleigh wave after reflection at the (circular) edge by a Gaussian beam pressure distribution on the cylinder's face yields simple expressions for the amplitude which are consistent with the measurements. In the vicinity of end-on incidence, other backscattering contributions due to the reflection of waves traveling down the length of the cylinder are observed. There is also evidence of a face-traversing longitudinal wave for slightly tilted cylinders.

DIRECT OBSERVATIONS OF THE SURFACE ATOMIC STRUCTURE OF THE Si(111)-(7 × 7) RECONSTRUCTED SURFACE WITH KIKUCHI ELECTRON HOLOGRAPHY

More than 50 symmetry-inequivalent emitter–scatterer (E–S) pairs were observed for the Si (111)-(7 × 7) surface using Kikchi electron holography (KEH) with various incident/detection configurations. For different configurations, the E–S pairs in the backscattering direction are preferentially enhanced. Thus, one can obtain detailed structural information by changing the incident/detection direction, which will be helpful in sorting out the correct surface structure model.

Micro-interferometric backscatter detection using a diode laser

Micro-interferometric backscatter detection (MIBD) is performed with a simple, folded optical train based on the interaction of a diode laser beam and a fused silica capillary tube allowing for refractive index (RI) determinations and detection of optically active molecules in small volumes. Side illumination of the capillary by a laser produces a 360° fan of scattered light that contains two sets of high contrast interference fringes. These light and dark spots are viewed on a flat plane in the direct backscatter configuration. Signal interrogation for polarimetry is based on quantifying the relative intensities (depth of modulation (DOM)) of adjacent high frequency (HF) interference fringes for polarimetry and relative fringe position for RI detection. Positional changes of the interference pattern extrema (fringes) allow for the determination of Δ n at the 10 −7 level or 5.3 pmol or 0.48 ng of solute. The MIBD-RI detection volume is just 5.0 nl. DOM changes allow for optical activity detection limits of 5.7 × 10 −5° (mandelic acid, [α] 23 = −153°, and D-glucose, [α] 25 = +52.5°), and a 2 σ detection limit of 7.5 × 10 −4 M (D-glucose) and 1.14 × 10 −3 M (R-mandelic acid). The probe volume of MIBD-polarimetry was 38 nl, and within the probed volume at the limit of detection, about 28.7 pmol of mandelic acid or about 43.7 pmol of D-glucose is present. Furthermore, DOM (polarimetry signal) is unchanged when a non-optically active solute is interrogated by the MIBD-polarimeter. Finally, an optical model was derived and used to evaluate the advantages and pitfalls of using diode laser for MIBD.

The effects of aspect ratio and surface roughness on satellite retrievals of ice-cloud properties

This study investigates the effects of non-sphericity on satellite retrievals of ice-cloud properties including optical thickness and particle sizes. Ray-tracing technique is used to calculate single scattering phase function and single scattering albedo for both smooth and rough surfaces of hexagonal columns and plates at visible and near-infrared wavelengths. Two parameters, aspect ratio and distortion parameter, are used to simulate different, randomly oriented, ice crystal shapes and surface roughnesses in the ray-tracing process. A wide range of aspect ratio and distortion parameter is explored in the calculations. The resultant phase functions and single scattering albedos are used to compute bidirectional reflection functions by a radiative transfer model with adding–doubling technique. The results show that in a direct backscattering regima (Θ>150°), if no information of particle shape is available, the uncertainties in the retrieved optical thickness (a factor of more than ten) would make the retrieval meaningless. For images with viewing geometry outside of this region, the typical range of uncertainty of retrieved optical thickness is less than a factor of about two. Using averaged phase function will cut this uncertainty in half. That is, the uncertainty in the retrieved optical thickness is about 40%. Sensitivity tests show that aspect ratios are critical in reducing the uncertainties of the retrieved optical thickness using satellite data. The uncertainties in the retrieved ice particle sizes are also estimated in a similar way. It is found that using an averaged aspect ratio and roughness, the uncertainty of retrieved particle size is about 30% for small particles and 10% for large particles at λ=3.7 μ m. The corresponding uncertainties are about 70% for small particles and 35% for large particles if data at λ=1.6 or 2.2 μ m are used in the retrieval. However, at λ=1.6 and 2.2 μ m, retrieval of particle size may encounter even larger uncertainties for thin ice-clouds ( τ<3).

Advances in direct and diffraction methods for surface structural determination

I describe recent advances in low-energy electron diffraction holography and photoelectron diffraction holography. These are direct methods for determining the surface structure. I show that for LEED and PD spectra taken in an energy and angular mesh, the relative phase between the reference wave and the scattered wave has a known geometric form if the spectra are always taken from within a small angular cone in the near backscattering direction. By using data in the backscattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamic factors. I also describe the use of a convergent iterative method of PD and LEED. The computation time of this method scales as N 2, where N is the dimension of the propagator matrix, rather than N 3 as in conventional Gaussian substitutional methods. Both the Rehr–Albers separable-propagator cluster approach and the slab-type non-separable approach can be cast in the new iterative form. With substantial savings in computational time and no loss in numerical accuracy, this method is very useful in applications of multiple scattering theory, particularly for systems involving either very large unit cells (>300 atoms) or where no long-range order is present.

Parameterization of surface polarized reflectance derived from POLDER spaceborne measurements

Two months of spaceborne POLDER polarization measurements have been used to generate empirical surface bidirectional polarization distribution functions (BPDFs). Eleven surface classes have been defined based on a surface classification and a vegetation index. Within each class, the surface polarized reflectance was found rather homogeneous. The surface polarized reflectance is highly anisotropic and varies between 0 close to the backscattering direction, and a few percent in the forward scattering direction. For a given observation geometry, the polarization is about twice as large over the pixels classified as "desert" than over vegetated surfaces. An empirical function with two parameters fits the estimated surface polarized reflectance with a residue on the order of 10/sup -3/ in reflectance units. An analysis of top-of-the-atmosphere (TOA) polarized reflectance over specific sunphotometer sites where the atmospheric contribution is well characterized confirms the estimated accuracy of 10/sup -3/.

Ion Analysis Using Capillary Electrophoresis with Refractive Index Detection

An optically simple, inexpensive, microvolume refractive index detector has been applied to capillary electrophoresis, allowing universal solute detection at the subpicogram level. The micro-interferometric backscatter detector employs direct side illumination of an unmodified capillary by a He–Ne laser, producing a 360° fan of scattered light that contains a set of high-contrast interference fringes. Positional changes of the interference pattern extrema (backscattered light) are directly related to the refractive index (RI),n,of the fluid in the tube, and allow for the determination of Δnat the 10−7level. These light and dark spots are viewed on a flat plane in the direct backscatter configuration. Signal interrogation is accomplished by a simple slit–photodetector assembly that is capable of monitoring the time-dependent fringe shifts produced or imparted by RI changes. Nanoliter detector volumes (0.27 × 10−9liter) are produced by this unique optical train that requires no modification of the separation capillary. The system's utility is demonstrated by the separation and quantitation of a mixture of cations (K+, Ba2+, Na+, and Li+) that are separable and detectable at the parts-per-million level, using no active thermal stabilization.

Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces

We study theoretically the generation and scattering of second harmonic light at randomly rough metallic interfaces. For surfaces with relatively large roughness and slopes, we find that the angular distribution of the scattered light at the harmonic frequency displays well-defined minima in the backscattering direction. Using an iterative procedure to solve the scattering equations, we show that the observed features are due to destructive interference between waves that have been multiply scattered in the valleys of the surface.

Measurement of Coherent Backscattering Phenomena in Emulsion

Coherent backscattering measurement was applied for the study of microstructures in emulsified liquids. An enhanced component towards the backscattering direction emerges superimposed on the diffuse light scattering from a sample with randomly dispersed scatterers, giving evidence of the weak localization of light in random systems. Accurate measurement of the coherent backscattering peak gives us information on the optical transport mean free path in the sample, which leads to an estimation of the droplet size in emulsion. A new measurement system was developed and the clear backscattering peaks were successfully observed for various kinds of emulsions. The key technique of the present experiment was to decrease the laser speckle by stirring the liquid. The result obtained for heptane/AOT/water emulsion was qualitatively related to the droplet size which could be controlled by changing the amount of added salt. The effect of excluded volume on the scattering mean free path was discussed.

Viewing Angle Effect on the Remote Sensing Monitoring of Wheat and Rice Crops

Bidirectional reflectance characteristics of a wheat and a rice canopy were studied using radiometric measurements over the two canopies with an Exotech Radiometer Model 100AX. For both rice and wheat, the measurements exhibited significant variations in reflectance amplitude for varying viewing zenith angles and their values decreased from backward to forward scattering direction. Reflectance obtained its maximum value in the backscatter direction for the viewing angle that corresponds approximately to the solar zenith angle at the time of measurements. Canopy background condition (irrigated or non‐irrigated) was an important determining factor of canopy reflectance particularly in the near‐infrared region of the solar spectrum. Furthermore, bidirectional response characteristics of a vegetation canopy were influenced by the amount of vegetation cover.

An optical technique for the detection of surfacedefects in ferromagnetic samples

We discuss the details of a new optical technique developed for the detection of defects in ferromagnetic materials or components, using a ferrofluid emulsion. This new flux leakage probe consists of a monodispersed ferrofluid either confined between two thin transparent sheets or in a cuvette, and a white light source for illumination. By employing ferrofluid droplets of suitable size and surfactant concentration, and mounting the cell on the test specimen surface, one can detect the region where the defect is located in the test specimen by visually observing a colour change in the ferrofluid cell, in the vicinity of the defect. The origin of this colour change in the backscattering direction is Bragg scattering from the droplet chains, which are formed by the leaked magnetic flux in the presence of a defect. The details of the defect detection procedure and typical experimental results obtained in a ferromagnetic specimen with a rectangular slot (i.e. an artificial defect) are presented.

Ray analysis of low-grazing scattering from a breaking water wave

Low-grazing-angle backscattering from a modeled breaking-wave surface profile has been calculated using a ray-optical approach and compared with reference scattering found using an extended moment method. The calculations show that interference between the direct backscatter from the breaking plume and multipath scattering between the plume and wave face can lead to the HH-to-VV polarization-backscattering ratios of greater than 9 dB that characterize sea-spike events. The multipath effects can be accurately predicted from simple reflection from the front face at the smallest grazing angles. At higher angles, diffraction from rapid changes in the surface curvature must also be considered.

Universal detection in capillary electrophoresis with a micro-interferometric backscatter detector

An optically simple, inexpensive, micro-volume refractive index detector was applied to capillary electrophoresis (CE), allowing universal solute detection at the sub-picogram level. The micro-interferometric backscatter detector (MIBD) employs direct, side illumination of an unmodified capillary by an He–Ne laser, producing a 360° fan of scattered light that contains a set of high contrast interference fringes. These light and dark spots are viewed on a flat plane in the direct backscatter configuration. A slit–photodetector assembly accomplishes signal interrogation of the time-dependent fringe shifts, produced or imparted by refractive index (RI) changes. Using an unfocused laser beam to prove the unmodified separation capillary produces a detector volume of 4.7 × 10–9 L. The separation and quantification of a mixture of organic dyes and simple sugars demonstrate the system’s utility. Submicromolar concentration detection limits of 0.46, 1.1 and 0.72 µM for Bromothymol Blue, Thymol Blue and Bromocresol Green, respectively, are achievable with CE-MIBD in the simplest configuration. The 3ς RI concentration detection limits are 2.5 times superior to those obtained by UV/VIS detection performed under the same conditions. Several carbohydrates (maltose, lactose and D-ribose) are separable and detectable at the ppm level, using no active thermal stabilization. Further demonstrating the utility of MIBD for universal detection with CE.

Biomass burning aerosol size distribution and modeled optical properties

Satellite remote sensing of smoke aerosol and estimates of aerosol forcing of climate require knowledge of the aerosol optical properties. A smoke aerosol physical and optical model is developed from a database of over 800 volume size distributions inverted from sky radiance data measured by the AERONET radiometer network in Brazil over a 3‐year period. The model represents total column, ambient conditions during the burning season in the Amazon Basin and cerrado region of Brazil. The mean volume size distributions are bimodal and can be represented by two lognormals. Accumulation mode modal radius is 0.13±0.02 μm with σ = 0.60 ± 0.04, and coarse‐mode modal radius ranges from 6 to 40 μm, with a mean of 11.5 μm and σ = 1.26 ± 0.23. The volume of each mode varies with optical thickness, causing the ratio of accumulation mode and coarse mode to vary as well, but the effect on the optical properties is negligible. Refractive index is taken to be 1.43‐0.0035i, and single scattering albedo is assumed to be 0.90, which is modeled with an external mixing of black carbon. The optical properties in the visible are dominated by the accumulation mode. Accumulation mode characteristics do not vary from year to year, from forest to cerrado region, with optical thickness or with precipitable water vapor. At one test location, accumulation mode characteristics do vary with air mass trajectory origin. The model is tested with independent data and can accurately predict the scattering phase function and path radiance in the backscattering direction that determines remote sensing properties and is responsible for scattering sunlight back to space.

Airborne spectral measurements of surface anisotropy during SCAR‐B

During the Smoke, Clouds, and Radiation‐Brazil (SCAR‐B) deployment, angular distributions of spectral reflectance for vegetated surfaces and smoke layers were measured using the scanning cloud absorption radiometer (CAR) mounted on the University of Washington C‐131A research aircraft. The CAR contains 13 narrowband spectral channels between 0.3 and 2.3 μm with a 190° scan aperture (5° before zenith to 5° past nadir) and 1° instantaneous field of view. The bidirectional reflectance is obtained by flying a clockwise circular orbit above the surface, resulting in a ground track ∼3 km in diameter within about 2 min. Although the CAR measurements are contaminated by minor atmospheric effects, results show distinct spectral characteristics for various types of surfaces. Spectral bidirectional reflectances of three simple and well‐defined surfaces are presented: cerrado (August 18, 1995) and dense forest (August 25, 1995), both measured in Brazil under nearly clear‐sky conditions, and thick smoke layers over dense forest (September 6 and 11, 1995). The bidirectional reflectances of cerrado and dense forest revealed fairly symmetric patterns along the principal plane, with varying maximal strengths and widths spectrally in the backscattering direction. In the shortwave‐infrared region the aerosol effect is very small due to low spectral optical depth. Also, these backscattering maxima can be seen on the bidirectional reflectance of smoke layer over dense forest. These detailed measurements of the angular distribution of spectral reflectance can be parameterized by a few independent variables and utilized to retrieve either surface characteristics or aerosol microphysical and optical properties (e.g., size distribution and single‐scattering parameters), if proper physical and radiation models are used. The spectral‐hemispherical albedo of these surfaces is obtained directly by integrating all angular measurements and is compared with the measured nadir reflectance. Using CAR nadir reflectance as a surrogate for spectral‐hemispherical albedo can cause albedos to be underestimated by 10–60%, depending on solar zenith angle.

Influence of Subpixel-Scale Cloud-Top Structure on Reflectances from Overcast Stratiform Cloud Layers

Recent observational studies have shown that satellite retrievals of cloud optical depth based on plane-parallel model theory suffer from systematic biases that depend on viewing geometry, even when observations are restricted to overcast marine stratus layers, arguably the closest to plane parallel in nature. At moderate to low sun elevations, the plane-parallel model significantly overestimates the reflectance dependence on view angle in the forward-scattering direction but shows a similar dependence in the backscattering direction. Theoretical simulations are performed that show that the likely cause for this discrepancy is because the plane-parallel model assumption does not account for subpixel-scale variations in cloud-top height (i.e., “cloud bumps”). Monte Carlo simulations comparing 1D model radiances to radiances from overcast cloud fields with 1) cloud-top height variations but constant cloud volume extinction, 2) flat tops but horizontal variations in cloud volume extinction, and 3) variations in both cloud-top height and cloud extinction are performed over a ≈4 km × 4 km domain (roughly the size of an individual GAC AVHRR pixel). The comparisons show that when cloud-top height variations are included, departures from 1D theory are remarkably similar (qualitatively) to those obtained observationally. In contrast, when clouds are assumed flat and only cloud extinction is variable, reflectance differences are much smaller and do not show any view-angle dependence. When both cloud-top height and cloud extinction variations are included, however, large increases in cloud extinction variability can enhance reflectance differences. The reason 3D–1D reflectance differences are more sensitive to cloud-top height variations in the forward-scattering direction (at moderate to low sun elevations) is because photons leaving the cloud field in that direction experience fewer scattering events (low-order scattering) and are restricted to the topmost portions of the cloud. While reflectance deviations from 1D theory are much larger for bumpy clouds than for flat clouds with variable cloud extinction, differences in cloud albedo are comparable for these two cases.