Geometric Optics Approximation Method Research Articles

Absorption properties by irregularly shaped particles with inclusions at visible and near-infrared wavelength regions

The absorption properties of snow and ice particles containing impurities such as black carbon (BC) and mineral dust (DS) were investigated using the geometrical optics approximation method (GOM). This study focuses on analyzing the single scattering co-albedo (SSCA) characteristics of non-spherical particles, aiming to enhance the interpretation of radiation observations in snow and ice regions. Particle sizes were varied (rva=50,200 and 500μm) and two types of inclusions (1 ppmw of BC and 100 ppmw DS) were considered. Significant differences in SSCA, ranging from one to two orders of magnitude were observed at λ=0.5μm between the “homogeneous model” with effective medium approximation method (EMA) and the “inhomogeneous model” with 50 BC inclusions. Similarly, differences of a factor of 2 to 4 were found for DS with 100 ppmw at λ=0.5μm and BC with 1 ppmw at λ=0.875μm. To bridge intermediate SSCA values between these models, we propose an “inhomogeneous model with EMA”, introducing two parameters to account for impurity concentration and inclusion aggregation. Our findings highlight the importance of selecting appropriate single scattering calculation methods in the analysis of observation data, particularly when dealing with BC impurity with significant absorption characteristics. This research contributes to a deeper understanding of solar radiation absorption in snow and ice regions, with potential implications for the optical remote sensing of snow and ice and climate modeling studies.

High-frequency backscattering properties of quasi-omnidirectional corner reflector: The great-icosahedral-like reflector

The backscattering of perfectly conducting great-icosahedral-like reflectors is studied in the high-frequency domain. This particular faceted polyhedron, composed of 60 trihedral corner reflectors, is introduced to obtain closer omnidirectional backscattering. Due to the high cost of traditional methods, an estimation method for the full-polarized radar cross section is proposed, which is modified from the geometrical optics approximation method. The validity of the improved method is discussed, and its velocity is determined. The estimated results of the reflectors are studied, which lead to a conclusion that this complex structure has high-frequency properties of quasi-omnidirectivity and depolarization.

Numerical reproduction and explanation of road surface mirages under grazing-angle scattering.

The mirror-like reflection image of the road surface under grazing-angle scattering can be easily observed in daily life. It was suggested that road surface mirages may occur due to a light-enhancing effect of the rough surface under grazing-angle scattering. The main purpose of this work is to explain the light-enhancing mechanism of rough surfaces under grazing-angle scattering. The off-specular reflection from a random rough magnesium oxide ceramic surface is analyzed by using the geometric optics approximation method. Then, the geometric optics approximation method is employed to develop a theoretical model to predict the observation effect of the grazing-angle scattering phenomenon of the road surface. The rough surface is assumed to consist of small-scale rough surface facets. The road surface mirage is reproduced from a large number of small-scale rough surface facets within the eye's resolution limit at grazing scattering angles, as the average bidirectional reflectance distribution function value at the bright location is about twice that of the surface in front of the mirage. It is suggested that the light-enhancing effect of the rough surface under grazing-angle scattering is not proper to be termed as "off-specular reflection," since it has nothing to do with the "specular" direction with respect to the incident direction.

Research on the single scattering albedo of spheroids

Purpose – The purpose of this paper is to discuss the light scattering of nonspherical particles that is very important for the research on the aerosol optical properties. Design/methodology/approach – In this paper, the authors use the spheroid model as the characteristic particle shape to study the single scattering albedo of real nonspherical particles. Meanwhile, the extinction and scattering cross section of spheroids are calculated with the T matrix method combined with the improved geometric optics approximation method (IGOM). Findings – Through this combination, the extinction and scattering cross section of spheroids can be obtained in the larger size range and aspect ratio range. Furthermore, the comparison of the single scattering albedo for the spheroids and their equivalent spheres is conducted in order to investigate the difference of the spherical and nonspherical particles. Originality/value – Simulation experiments indicate that the single scattering albedo of spheroids can be calculated well with this combination, and it has some obvious influence on the variation of the aspect ratio, incident wavelength, and complex refractive index of spheroid particles.

Inversion of COSMIC atmospheric open-loop radio occultation data

The GPS open-loop receiver has been used in COSMIC GPS radio occultation to improve the data quality of the troposphere occultation and the ability of tracking the rising occultation events. The open-loop data are affected by the navigation data modulations. This effect must be removed in the post-data processing to get the high quality scientific inversion results. Two methods for removing the effect, one using the external navigation data modulation bit information and the other method using the internal relationship of the atmospheric excess phase data between adjacent epochs, were investigated. For a case study, the above methods were applied in the data processing of one COSMIC radio occultation event s atmospheric excess phase data to remove the navigation data modulation effect and to output the corrected atmospheric excess phase data. By using the corrected atmospheric excess phase data, the ray bending angles were estimated with the geometric optics approximation method and the full spectrum inversion method. The estimated bending angles with the full spectrum inversion method and the corresponding retrieved temperatures agree excellently with those provided by the COSMIC data center. The agreement suggests that our algorithms for open-loop data processing work efficiently.

Extraction methods of phase information for X-ray diffraction enhanced imaging

X-ray diffraction enhanced imaging (DEI) is one of X-ray phase-contrast imaging methods, which is applied to inspect internal structures of weakly absorbing low- Z samples. The key problem of the DEI is how to extract phase information which is expressed by refraction-angle images from a series of DEI images measured in different positions of the rocking curve of the analyzer. Three effective extraction methods are presented in this paper: the statistical geometric-optics-approximation method, the maximum refraction-angle method and the Gaussian curve fitting method. They are compared with the existing methods, such as the D. Chapman's geometric optics approximation method and the multiple-images statistical method. A 2D computer simulation experiment is performed to draw comparisons of these methods. The experimental results prove that the above three methods have more precision of refraction-angle values than existing methods.

Directional hemispherical radiative properties of random dielectric rough surfaces

In this paper the directional hemispherical reflectivity and transmissivity of one-dimensional, randomly rough, dielectric surfaces are determined by the use of the integral method. This method is derived from electromagnetic theory without any restrictive hypotheses. Since this exact approach is computationally very intensive, a geometric optics approximation method is also developed. Curves displaying radiative properties versus the correlation length for a constant mean square deviation of the surface from flatness are presented. In this respect, the influence on the validity of the approximate method of multiple scattering, the shadowing effect and the real index of refraction of the dielectric have been investigated. Transverse electric and transverse magnetic polarized incident plane waves are considered. For the latter, our interest is focused on the influence of roughness on the reflected and transmitted intensities for an angle of incidence close to the Brewster angle.

2 × 2 propagation matrix for electromagnetic waves propagating obliquely in layered inhomogeneous uniaxial media

A 2 × 2 propagation-matrix formalism for finding the obliquely propagating electromagnetic fields in layered inhomogeneous uniaxial structures is presented. The 2 × 2 propagation matrix was produced by our generalized geometrical-optics approximation method. A 2 × 1 field vector for the transverse electric field is defined together with a 2 × 2 propagation matrix, which describes the spatial propagation of the 2 × 1 field vector. Eight different equivalent forms for the propagation matrix are presented. The propagation matrix depends on the dielectric parameter and other optical parameters of the medium, the thickness of the medium, and the propagation vector of the incident light. The inhomogeneous medium is divided into sublayers, and the problem is then solved as if each layer has spatially invariant optical parameters. The propagation matrix for the inhomogeneous medium is equal to the matrix product of the propagation matrices for any complete series of layers that subdivide the inhomogeneous medium. The 2 × 2 propagation matrix reduces to the conventional Jones matrix for the case of normally incident light. The results are applied in studying the electro-optics of various liquid-crystal displays. The computation results are the same as those produced by the generalized geometrical-optics approximation and are in good agreement with those computed by the 4 × 4 propagation matrix and with experimental results.