ABSTRACT
The Maggi-Rubinowicz method (MRM) is a useful tool to compute diffraction patterns from opaque planar objects. We adapted the MRM to planar rectangles. In the first part of this study, differences between diffraction patterns, both the intensity and the phase distributions, from a tilted rectangle and from the square having the same orthogonal projection on the observation plane, have been analyzed. In the second part, we compared results obtained with the MRM to those obtained with angular spectrum theory (AST) coupled to fast Fourier transform (FFT). The main novelty of this work is the fact that MRM is particularly well suited for evaluating anti-aliasing procedures applied to AST-FFT calculations.
ABSTRACT
A regularized algorithm that has the potential to improve the quality of Raman lidar data processing is presented. Compared to the conventional scheme, the proposed algorithm has the advantage, which results from the fact that it is based on a well-posed procedure. That is, the profile of the aerosol backscatter coefficient is computed directly, using the explicit relationships, without numerical differentiation. Thereafter, the profile of the lidar ratio is retrieved as a regularized solution of a first-kind Volterra integral equation. Once these two steps have been completed, the profile of the aerosol extinction coefficient is computed by a straightforward multiplication. The numerical simulations demonstrated that the proposed algorithm provides good accuracy and resolution of aerosol profile retrievals. The error analysis showed that the retrieved profiles are continuous functions of the measurement errors and of the a priori information uncertainties.
ABSTRACT
We present what we believe to be the first results of a light-scattering analysis on several Chebyshev particles characterized by higher orders. Chebyshev particles of comparatively lower orders were used in the past to study the effects of nonspherical but concave geometries in remote sensing applications. We will show that, based on the developed methodology, accurate results can also be obtained for particles of higher orders exhibiting a more pronounced surface waviness. The achieved results demonstrate that higher-order Chebyshev particles can be used to estimate the influence of a weak surface roughness on the light-scattering behavior of the underlying smooth scatterer. The effects obtained correspond with the results of other approaches and with the theoretical expectations of a weak surface roughness. In contrast to what is known for regular particles, there can be observed an essential difference between the phase functions of the underlying spherical scatterer and the corresponding higher-order Chebyshev particle if a higher absorptivity of the scattering medium is considered. This paper demonstrates additionally that Chebyshev polynomials can be simply combined with smooth geometries other than spheres.
ABSTRACT
An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height-dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height-dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well.
