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Root mean square height of rough surface determined by measuring correlation between two scattered radar waves at different frequencies as function of frequency separation
An experimental study of surface roughness effects on bidirectional reflectance of metallic surfaces is presented. Samples consisting of glass, aluminum alloy, and stainless steel materials were roughened using standard grinding techniques and coated with a radiatively opaque layer of pure aluminum. Surface roughness parameters, rms height and rms slope, were evaluated from digitized surface profile measurements and are less than 1.0 micron, and 0.28, respectively. Rough-surface specular, bidirectional, and directional reflectance measurements for selected values of polar angle and wavelength of incident energy within the range from 10 to 80 deg and from 1 to 14 microns, respectively, are reported. The influence of surface roughness is discussed in terms of rms height and rms slope.
An experimental study of surface roughness effects on bidirectional reflectance of metallic surfaces is presented. A facility capable of irradiating a sample from normal to grazing incidence and recording plane of incidence bidirectional reflectance measurements was developed. Samples consisting of glass, aluminum alloy, and stainless steel materials were selected for examination. Samples were roughened using standard grinding techniques and coated with a radiatively opaque layer of pure aluminum. Mechanical surface roughness parameters, rms heights and rms slopes, evaluated from digitized surface profile measurements are less than 1.0 micrometers and 0.28, respectively. Rough surface specular, bidirectional, and directional reflectance measurements for selected values of polar angle of incidence and wavelength of incident energy within the spectral range of 1 to 14 micrometers are reported. The Beckmann bidirectional reflectance model is compared with reflectance measurements to establish its usefulness in describing the magnitude and spatial distribution of energy reflected from rough surfaces.
The Beckmann model is compared with recently reported bidirectional reflectance measurements. Comparisons revealed that monochromatic specular and bidirectional reflectance measurements are not adequately described by corresponding results evaluated from the model using mechanically acquired surface roughness parameters (rms height and rms slope). Significant improvement between measurements and predictions of the model is observed when optically acquired surface roughness parameters are used. Specular reflectance measurements for normal to intermediate polar angles of incidence are adequately represented by the model provided values of optical roughness multiplied by cosine of polar angle of incidence are less than 27 times average optical rms slope.
This paper investigates the potential application of neural network to inversion of soil moisture using polarimetric remote sensing data. The neural network used for the inversion of soil parameters is multi-layer perceptron trained with the back-propagation algorithm. The training data include the polarimetric backscattering coefficients obtained from theoretical surface scattering models together with an assumed nominal range of soil parameters which are comprised of the soil permittivity and surface roughness parameters. Soil permittivity is calculated from the soil moisture and the assumed soil texture based on an empirical formula at C-, L-, and P-bands. The rough surface parameters for the soil surface, which is described by the Gaussian random process, are the root-mean-square (rms) height and correlation length. For the rough surface scattering, small perturbation method is used for the L-band frequency, and Kirchhoff approximation is used for the C-band frequency to obtain the corresponding backscattering coefficients. During the training, the backscattering coefficients are the inputs to the neural net and the output from the net are compared with the desired soil parameters to adjust the interconnecting weights. The process is repeated for each input-output data entry and then for the entire training data until convergence is reached. After training, the backscattering coefficients are applied to the trained neural net to retrieve the soil parameters which are compared with the desired soil parameters to verify the effectiveness of this technique. Several cases are examined. First, for simplicity, the correlation length and rms height of the soil surface are fixed while soil moisture is varied. Soil moisture obtained using the neural networks with either L-band or C-band backscattering coefficients for the HH and VV polarizations as inputs is in good agreement with the desired soil moisture. The neural net output matches the desired output for the soil moisture range of 16 to 60 percent for the C-band case. The next case investigated is to vary both soil moisture and rms height while keeping the correlation length fixed. For this case, C-band backscattering coefficients are not sufficient for retrieving two parameters because the Kirchhoff approximation gives the same HH and VV backscattering coefficients. Therefore, the backscattering coefficients at two different frequency bands are necessary to find both the soil moisture and rms height. Finally, the neural nets are also applied to simultaneously invert soil moisture, rms height, and correlation length. Overall, the soil moisture retrieved from the neural network agrees very well with the desired soil moisture. This suggests that the neural network shows potential for retrieval of soil parameters from remote sensing data.
Soil roughness strongly influences processes like erosion, infiltration, moisture and evaporation of soils as well as growth of agricultural plants. An approach to soil roughness based on active-passive microwave covariation is proposed in order to simultaneously retrieve the vertical RMS height (s) and horizontal correlation length (l) of soil surfaces from simultaneously measured radar and radiometer microwave signatures. The approach is based on a retrieval algorithm for active-passive covariation including the improved Integral Equation Method (I2EM). The algorithm is tested with the global active-passive microwave observations of the SMAP mission. The developed roughness retrieval algorithm shows independence of permittivity for > 10 [-] due to the covariation formalism. Results reveal that s and l can be estimated simultaneously by the proposed approach since surface patterns of non-vegetated areas become evident on global scale. In regions with sandy deserts, like the Sahara or the outback in Australia, determined and confirm rather smooth to semi-rough surface roughness patterns with small vertical RMS heights and corresponding higher horizontal correlation lengths.
The sources of scattering of artificial sea ice were determined, backscatter measurements semi-quantitatively were compared with theoretical predictions, and inexpensive polarimetric radars were developed for sea ice backscatter studies. A brief review of the dielectric properties of sea ice and of commonly used surface and volume scattering theories is presented. A description is provided of the backscatter measurements performed and experimental techniques used. The development of inexpensive short-range polarimetric radars is discussed. The steps taken to add polarimetric capability to a simple FM-W radar are considered as are sample polarimetric phase measurements of the radar. Ice surface characterization data and techniques are discussed, including computation of surface rms height and correlation length and air bubble distribution statistics. A method is also presented of estimating the standard deviation of rms height and correlation length for cases of few data points. Comparisons were made of backscatter measurements and theory. It was determined that backscatter from an extremely smooth saline ice surface at C band cannot be attributed only to surface scatter. It was found that snow cover had a significant influence on backscatter from extremely smooth saline ice at C band.
In an earlier study, an empirical model was developed to infer soil moisture and surface roughness from radar data. The inversion technique was extensively tested over bare surfaces by comparing the estimated soil moisture to in situ measurements. The overall root mean square (RMS) error in the soil moisture estimate was found to be about 3.5% and the RMS error in the RMS height estimate was less than 0.35 cm absolute for bare or slightly vegetated surfaces. However, inversion results indicate that significant amounts of vegetation cause the algorithm to underestimate soil moisture and overestimate RMS height. Among the areas over which the inversion cannot be applied, the areas with intermediate vegetation cover are of particular interest as both the vegetation and the underlying bare surface affect the backscatter. This paper concentrates mostly on these areas. Using the full polarimetric information and the Cloude target decomposition approach, three different components of the target backscattering can be isolated. One of these three components can be identified as the surface component in the case of intermediate vegetation cover. Once the surface component of the scattering is isolated, the bare surface inversion can then be applied.
In an earlier study, an empirical model was developed to infer soil moisture and surface roughness from radar data. The inversion technique was extensively tested over bare surfaces by comparing the estimated soil moisture to in situ measurements. The overall RMS error in the soil moisture estimate was found to be 3.5% and the RMS error in the RMS height estimate was less than 0.35 cm absolute for bare or slightly vegetated surfaces. However, inversion results indicate that significant amounts of vegetation cause the algorithm to underestimate soil moisture and overestimate RMS height. Among the areas over which the inversion cannot be applied, the areas with intermediate vegetation cover are of particular interest as both the vegetation and the underlying bare surface affect the backscatter. This paper concentrates mostly on these areas. Using the full polarimetric information and the Cloude target decomposition approach. Three different components of the target backscattering can be isolated. One of these three components can be identified as the surface component in the case of intermediate vegetation cover. Once the surface component of the scattering is isolated, the bare surface inversion can then be applied.
Polarimetric radar measurements were conducted for bare soil surfaces under a variety of roughness and moisture conditions at L-, C-, and X-band frequencies at incidence angles ranging from 10 to 70 deg. Using a laser profiler and dielectric probes, a complete and accurate set of ground truth data were collected for each surface condition, from which accurate measurements were made of the rms height, correlation length, and dielectric constant. Based on knowledge of the scattering behavior in limiting cases and the experimental observations, an empirical model was developed which was found to yield very good agreement with the backscattering measurements of this study, as well as with measurements reported in other investigations. An inversion technique for predicting the rms height of the surface and its moisture content from multipolarized radar observations is developed on the basis of the model.
In summer 1988 an intensive field experiment was conducted in the vicinity of the Pisgah lava flow in the Mojave Desert. Physical properties such as microtopography, composition, soil moisture, and dielectric constant were measured at five sites representing surfaces with rms heights varying from less than one centimeter to tens of centimeters. In addition, polarimetric radar images at P-band, L-band, and C-band were acquired at three different incidence angles with the NASA/JPL airborne imaging radar polarimeter. Using trihedral corner reflectors deployed in the area prior to imaging, the L- and C-band images were calibrated to provide sigma0 values for each resolution element in the scene. The results of inferring geophysical parameters such as rms surface height and correlation length of the measured surfaces by fitting the observed signatures with those predicted by the small-perturbation model are presented: for smoother surfaces, the rms height values inferred are in good agreement with in situ measurements.
A thermal oxide patterning method has proven to be effective for correcting coating-stress-induced distortion on flat silicon wafers. We report progress on developing this method for correcting curved silicon mirrors distorted by front-side iridium coatings. Owing to the difference in geometry, a finite element model has been established to calculate the appropriate duty cycle maps in thermal oxide hexagon patterns used for compensation. In addition, a photolithographic process, along with three-dimensional printed equipment, has been developed for creating patterns precisely on the back side of curved mirrors. The developed method has been used to recover the original surface shape of two silicon mirrors which are 100-mm long, 0.5-mm thick, having 312-mm radius of curvature, and 30 deg in azimuthal span (Wolter-I geometry). These mirrors’ front sides are sputter-coated by 20-nm iridium layers with ∼-70 N∕m integrated stress. Measurement results show that the developed method can mitigate coating-induced distortion by a factor of ∼5 in RMS height and ∼4 in RMS slope error, corresponding to ∼0.5 arc sec RMS slope error. Residual errors after correction are dominated by midfrequency ripples created during the annealing process, which will be resolved in the future. The presented method is precise and inexpensive and a potential candidate for resolving the coating stress issue for Lynx optics in the future.
An active-passive microwave retrieval algorithm for simultaneous determination of soil surface roughness parameters [vertical root-mean-square (RMS) height (s) and horizontal correlation length (l)] is presented for bare soils. The algorithm is based on active-passive microwave covariation, including the improved Integral Equation Method (I²EM), and is tested with global soil moisture active passive (SMAP) observations. The estimated retrieval results for s and l are overall consistent with values in the literature, indicating the validity of the proposed algorithm. Sensitivity analyses showed that the developed roughness retrieval algorithm is independent of permittivity for εₛ > 10 [-]. Furthermore, the physical model basis of this approach (I²EM) allows the application of different autocorrelation functions (ACF), such as Gaussian and exponential ACFs. Global roughness retrieval results confirm bare areas in deserts such as Sahara or Gobi. However, the type of ACF used within roughness parameter estimation is important. Retrieval results for the Gaussian ACF describe a rougher surface than retrieval results for the exponential ACF. No correlations were found between roughness results and the amount of precipitation or the soil texture, which could be due to the coarse spatial resolution of the SMAP data. The extension of this approach to vegetated soils is planned as an add-on study.
An active–passive microwave retrieval algorithm for simultaneous determination of soil surface roughness parameters [vertical root-mean-square (RMS) height ( s ) and horizontal correlation length ( l )] is presented for bare soils. The algorithm is based on active–passive microwave covariation, including the improved Integral Equation Method (I(exp 2) EM), and is tested with global soil moisture active passive (SMAP) observations. The estimated retrieval results for s and l are overall consistent with values in the literature, indicating the validity of the proposed algorithm. Sensitivity analyses showed that the developed roughness retrieval algorithm is independent of permittivity for E(sub s) > 10 [-]. Furthermore, the physical model basis of this approach (I(exp 2) EM) allows the application of different autocorrelation functions (ACF), such as Gaussian and exponential ACFs. Global roughness retrieval results confirm bare areas in deserts such as Sahara or Gobi. However, the type of ACF used within roughness parameter estimation is important. Retrieval results for the Gaussian ACF describe a rougher surface than retrieval results for the exponential ACF. No correlations were found between roughness results and the amount of precipitation or the soil texture, which could be due to the coarse spatial resolution of the SMAP data. The extension of this approach to vegetated soils is planned as an add-on study.
A technique is presented for registering polarimetric SAR data to other aircraft and spaceborne data sets. Resampling is done on the full Stokes matrix, allowing full polarization synthesis on the coregistered data set. Analysis of data acquired over Pisgah Crater in the Mojave Desert, CA, as part of the Mojave Field Experiment shown that the resampling does not seriously affect the pedestal heights of polarization signatures or affect estimates of RMS heights for smooth to moderately rough surfaces.
This paper presents radar-altimeter scattering models for each of the diagenetic zones of the Greenland ice sheet. AAFE radar- altimeter waveforms obtained during the 1991 and 1993 NASA multi-sensor airborne altimetry experiments over Greenland reveal that the Ku-band return pulse changes significantly with the different diagenetic zones. These changes are due to varying amounts of surface and volume scattering in the return waveform. In the ablation and soaked zones, where surface scattering dominates the AAFE return, geophysical parameters such as rms surface height and rms surface slope are obtained by fitting the waveforms to a surface-scattering model. Waveforms from the percolation zone show that the sub-surface ice features have a much more significant effect on the return pulse than the surrounding snowpack. Model percolation waveforms, created using a combined surface- and volume-scattering model and an ice-feature distribution obtained during the 1993 field season, agree well with actual AAFE waveforms taken in the same time period. Using a combined surface- and volume-scattering model for the dry-snow-zone return waveforms, the rms surface height and slope and the attenuation coefficient of the snowpack are obtained. These scattering models not only allow geophysical parameters of the ice sheet to be measured but also help in the understanding of satellite radar-altimeter data.
Topographic profiles at 25- and 5-cm horizontal resolution for three sites along a lava flow on Kilauea Volcano are presented, and these data are used to illustrate techniques for surface roughness analysis. Height and slope distributions and the height autocorrelation function are evaluated as a function of varying lowpass filter wavelength for the 25-cm data. Rms slopes are found to increase rapidly with decreasing topographic scale and are typically much higher than those found by modeling of Magellan altimeter data for Venus. A more robust description of the surface roughness appears to be the ratio of rms height to surface height correlation length. For all three sites this parameter falls within the range of values typically found from model fits to Magellan altimeter waveforms. The 5-cm profile data are used to estimate the effect of small-scale roughness on quasi-specular scattering.
The interaction between wind and desert surfaces has important implications for sediment transport on Earth, Mars, and Venus, and for understanding the relationship between radar backscatter and aerodynamic roughness. Here, researchers report results from measurements of atmospheric boundary layer profiles, assessment of radar backscatter at P, L, and C wavelengths, and surface roughness in Death Valley, the Mojave Desert, and Lunar Lake, NV, and discuss the implications for aeolian process. The sites include playas, gravel and sand regs, alluvial fans, and lava flows. Boundary layer wind profiles were measured using anemometers at heights of 0.75, 1.25, 2.07, 3.44, 5.72, and 9.5 m; temperature sensors at heights of 1.3 and 9.6 m; and wind vanes at 9.7 and 1.5 m. Microtopographic measurements were made using a template and a laser-photo device to obtain RMS height. This study demonstrates that radar backscatter coefficients obtained from airborne and perhaps orbiting instruments could permit the derivation of aerodynamic roughness values for large areas. Such values, when combined with wind frequency data, could enable assessment of aeolian processes on a regional scale.