# Adrian Doicu's research while affiliated with German Aerospace Center (DLR) and other places

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## Publications (81)

A stochastic optimization algorithm for analyzing planar central and balanced configurations in the $n$-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to $n=12$. We show some exemplary balanced configurations in the case $n=5$, as well as some balanced configurations wit...

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered. The analysis is performed in a linear-polarization basis and includes (i) a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, (ii) the design...

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specifi...

We consider the scattering of a plane electromagnetic wave obliquely incident on a plane-parallel layer of discrete random medium with non-scattering boundaries. We solve the Lax integral equation for the conditional configuration-averaged exciting field coefficients by assuming a special-form solution, that is, by representing the conditional conf...

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of...

In this paper we apply the Green function formalism and the Wigner transform method to derive the radiative transfer equation for a layer of sparse discrete random medium bounded by scattering rough interfaces. The radiative transfer equation is formulated with respect to the Wigner transform of the dyadic correlation function for the electromagnet...

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scatte...

In this paper, we revisit, with further enhancements and clarifications, the self-consistent first-principles approach developed previously for deriving the vector radiative transfer theory for a discrete random medium with a sparse concentration of particles. We specifically consider the case of a plane-parallel particulate layer embedded in an ot...

For a macroscopically plane-parallel discrete random medium, the boundary conditions for the specific coherency dyadic at a rough interface are derived. The derivation is based on a modification of the Twersky approximation for a scattering system consisting of a group of particles and the rough surface, and reduces to the solution of the scatterin...

The theoretical foundation of the invariant imbedding \(\mathbf {T}\)-matrix method is revised. We present a consistent analysis of the method, show the connection with the superposition \(\mathbf {T}\)-matrix method, and derive new recurrence relations for \(\mathbf {T}\)-matrix calculation. The first recurrence is a numerical method for integrati...

This paper presents the operational cloud retrieval algorithms for the TROPOspheric Monitoring Instrument (TROPOMI) on board the European Space Agency Sentinel-5 Precursor (S5P) mission scheduled for launch in 2017.
Two algorithms working in tandem are used for retrieving cloud properties: OCRA (Optical Cloud Recognition Algorithm) and ROCINN (Ret...

Current and future satellite sensors provide measurements in and around the oxygen A-band on a global basis. These data are commonly used for the determination of cloud and aerosol properties. In this paper, we assess the information content in the oxygen A-band for the retrieval of macrophysical cloud parameters using precise radiative transfer si...

This paper presents a sensitivity study performed for trace gases retrieval from synthetic observations by TELIS (TErahertz and submillimeter LImb Sounder) which is a stratospheric balloon-borne cryogenic heterodyne spectrometer. Issues pertaining to hydroxyl radical (OH) retrieval from the far infrared measurements by the 1.8 THz channel are addre...

This study presents two scientific and one operational retrieval algorithms used to obtain vertical distributions of bromine monoxide (BrO) from observations of the scattered solar light performed by the SCIAMACHY instrument in limb viewing geometry. The study begins with a discussion of the theoretical basis of all algorithms followed by an invest...

In this paper we present several constrained regularization methods for ozone profile retrieval from UV/VIS nadir sounding instruments such as GOME, SCIAMACHY, OMI and GOME-2. These methods extend the Tikhonov regularization and the iteratively regularized Gauss–Newton method with equality and inequality constraints imposed on the vertical column....

In this paper we analyze three methods for computing the total field in the near-zone region. These methods use the expansion of the scattered field outside the minimum circumscribing sphere, an integral representation of the scattered field and a vector spherical wave expansion of the near-zone field. Calculations of the total field within the cir...

In this paper we present several constrained regularization methods for ozone profile retrieval from UV/VIS nadir sounding instruments such as GOME, SCIAMACHY, OMI and GOME-2. These methods extend the Tikhonov regularization and the iteratively regularized Gauss–Newton method with equality and inequality constraints imposed on the vertical column....

Since the foundation of the SCIAMACHY Quality Working Group (SQWG) in a joint inter-agency effort in late 2006 the ESA operational Level 2 processor was significantly improved with respect to data quality and product range. During the last two years the product list was sub-stantially enhanced by new (total columns of SO2, BrO, OClO, H2O, and CO; p...

Novel formulations of the extended boundary condition method for three-dimensional scattering problems are derived by using a system of magnetic and electric dipoles, a system of ‘Mie potentials’ and a system of lowest-order multipoles as complete systems of functions. The key step in these approaches is to use discrete sources located on auxiliary...

Computation of light scattering from particles deposited upon a surface is of great interest in the simulation, development and calibration of surface scanners for wafer inspection [1]. More recent applications include laser cleaning [2], scanning near-field optical microscopy (SNOM) [3] and plasmon resonances effects in surface-enhanced Raman spec...

In this paper we consider electromagnetic wave scattering by aggregated fibres using a multiple scattering approach. Scattering by particles of complex shape such as concave particles, torus, or clusters of fibres can not normally be computed using the T-matrix method. In this paper we are proposing a decompositioning approach to handle this scatte...

This paper is devoted to an intercomparison of ozone vertical profiles retrieved from the measurements of scattered solar radiation performed by the SCIAMACHY instrument in the limb viewing geometry. Three different inversion algorithms including the prototype of the operational Level 1 to 2 processor to be operated by the European Space Agency are...

For the interpretation of satellite limb observations we investigate the linearization capability of spherical radiative transfer in the ultraviolet and visible part of the solar spectrum, where multiple scattering of light complicates the model simulations. From plane-parallel radiative transfer it is known that the forward-adjoint perturbation th...

Light Scattering by Systems of Particles comprehensively develops the theory of the null-field method, while covering almost all aspects and current applications. The Null-field Method with Discrete Sources is an extension of the Null-field Method (also called T-Matrix Method) to compute light scattering by arbitrarily shaped dielectric particles....

The T-matrix method, which is also known as the null field method (NFM) or extended boundary condition method (EBCM), has established itself as a well known and highly regarded method for calculating light scattering by non-spherical particles. Its biggest advantage is the possibility to obtain all information about the scattering characteristics o...

Simulation of light scattering gets more and more important; topics of interest are for example characterization of the shape of particles, detection of airborne fibers, determination of spherical and non-spherical particles, etc. To develop advanced methods for optical particle characterization corresponding light scattering theories and simulatio...

In this paper we present a retrieval algorithm for atmospheric remote sensing. The algorithm combines the Tikhonov regularisation and the iteratively Gauss-Newton method and is devoted to the solution of multi-parameter inverse problems with simple bounds on the variables. The basic features of the algorithm: the solution of the bound-constrained m...

The problem of light scattering by a particle on or near a surface is treated using the field decomposition method and the free-field T-matrix method. The model takes into account that the incident field strikes the particle either directly or after interacting with the surface, while the fields emanating from the particle may also reflect off the...

The electromagnetic scattering by a three-dimensional uniaxial anisotropic particle is studied. Electromagnetic fields in a uniaxial medium are expressed in terms of a system of vector functions which are similar to the system of regular spherical vector wave functions. The scattering problem is solved by using the null-field method. Numerical simu...

The surface Green's function belonging to the non-spheri-cal exterior boundary value problem of Helmholtz's equation in spher-ical coordinates is derived. This is performed in two ways, first by applying the Separation of Variables method, and, second, by using the Method of Lines as a special Finite-Difference technique. With this Green's function...

The surface Green's function belonging to the non‐spherical exterior boundary value problem of Helmholtz's equation in spherical coordinates is derived. This is performed in two ways, first by applying the Separation of Variables method, and, second, by using the Method of Lines as a special Finite‐Difference technique. With this Green's function w...

A novel formulation for improving the numerical stability of the null-field method for highly flattened particles is presented. The key step in this approach is to approximate the surface current density by circularly distributed spherical vector wave functions. The circularly distributed spherical vector wave functions are obtained by integrating...

A novel formulation for improving the numerical stability of the null-field method for highly elongated and flattened layered scatterers is presented. The key step in this approach is to approximate the surface current densities by the lowest-order multipoles located in the complex plane. The accuracy of the proposed method is investigated from a n...

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some nume...

In this paper we analyse the scattering by a
spherical particle with multiple spherical inclusions. Our
analysis is focused on the equivalence between the
inhomogeneous sphere and a homogeneous sphere with an equivalent
refractive index. The equivalent sphere reproduces the
differential scattering cross section of the inhomogeneous
sphere reasonabl...

A novel formulation for improving the numerical stability of the null-field method for highly elongated and flattened composite scatterers is presented. The key step in this approach is to approximate the surface current densities by the lowest-order multipoles located in the complex plane. The accuracy of the proposed method is investigated from a...

The paper is devoted to the application of a rigorous approach for analyzing the evanescent wave scattering by sensor tip near a plane surface. On the basis of the discrete sources method a numerical schemes was developed and implemented in computer program. Numerical results related to the influence of the position of the sensor tip on the scatter...

The paper is devoted to semi-analytical approaches for analyzing the evanescent wave scattering by penetrable scatterers on a plane surface. On the basis of the discrete sources method and the T-matrix method numerical schemes were developed and implemented in computer programs. Numerical results related to the influence of the plane surface on the...

This chapter presents the fundaments of the null-field method (NFM) for solving the Dirichlet and Neumann boundary-value problems. The chapter begins by showing that the scattering problem reduces to the approximation problem of the surface densities by convergent sequences. It then presents convergent projection methods for the general null-field...

This chapter introduces the basic concepts of the discrete sources method (DSM) for solving electromagnetic scattering problems. In the acoustic case, the electromagnetic scattering problem reduces to the approximation problem of the boundary value of the incident field in the “L2”-norm. The technical aspect of the acoustic case is not repeated. An...

This chapter discusses the fundamental results of functional analysis. It firstly presents the notion of a Hilbert space and discusses some basic properties of the orthogonal projection operator. It then introduces the concept of closeness and completeness of a system of elements that belong to a Hilbert space. The completeness of the system of ele...

This chapter presents the mathematical justification of the discrete sources method (DSM). Only the exterior Dirichlet, Neumann and impedance boundary value problems are discussed in detail as the basic concepts are fully represented in these cases. A description of the smoothing procedure developed by Yasuura and Ikuno is included in analysis. In...

The chapter discusses the analysis of complete and linear independent systems of functions for the Maxwell equations. The analysis begins by presenting some fundamental results on the completeness of the localized spherical vector wave functions. The completeness properties of the systems of discrete sources are of primary interest as they provide...

This chapter discusses the Maxwell Equations. Up until now, the direct obstacle scattering problems for time-harmonic acoustic waves was considered. Analysis on acoustic scattering begins by recalling the fundaments of the Maxwell equations. After a brief discussion of the physical background of electromagnetic waves propagation, the boundary-value...

This chapter discusses the analysis of complete and linear independent systems of functions for the Helmholtz equation. As complete systems of functions, the systems of discrete sources will be discussed in the chapter. There is a close relation between the properties of the fields of discrete sources and the structure of their support. In particul...

This chapter discusses the analysis of electromagnetic scattering using the null-field method (NFM) with discrete sources. The chapter focuses on the exterior and the transmission boundary-value problems. It begins by constructing projection methods for the general null-field equations. Next, it presents the conventional null-field method with disc...

This chapter is devoted to presenting the foundations of obstacle scattering problems for time-harmonic acoustic waves. The chapter provides brief discussion of the physical background of the scattering problem, and then formulates the boundary-value problems for the Helmholtz equation. It will synthetically recall the basic concepts as they were p...

This chapter describes the use of the fundamental theorem of discrete approximation to construct projection schemes for a category of variational problems in the Hilbert spaces. The results of these problems are then used to construct approximate solutions to the boundary-value problems for the Maxwell equations.

The communication is devoted to semi-analytical approaches for analyzing the scattering by a non-axisymmetric structure consisting of a nonspherical particle and a plane surface. On the basis of the discrete sources method and the T-matrix method, numerical schemes were developed and implemented in computer programs. Numerical results related to th...

The T-matrix method and a new projection method for the impedance boundary value problem in electromagnetic scattering theory are presented. The new method is called the D-matrix method since the matrix of the linear system of equations is dissipative. The dissipativity is established as a consequence of the conservation law of energy. The converge...

One of the fastest and most powerful numerical tools for computing nonspherical light scattering using spherical vector wave functions expansions is the null-field method. In the null-field method, the particle is replaced by a set of surface-current densities, so that in the exterior region the sources and fields are exactly the same as those exis...

Three-dimensional problems of electromagnetic scattering have been a subject of intense investigation and research in various scientific and engineering fields such as astronomy, optics, meteorology, remote sensing, optical particle sizing, and electrical engineering. These efforts have led to a development of a large number of analytical tools and...

The problem of computing the transition matrix (T matrix) in the framework of the null-field method with discrete sources is treated. Numerical experiments are performed to investigate the symmetry property of the T matrix when localized and distributed vector spherical functions are used for solution construction.

Projection schemes for constructing an approximate solution to the exterior Maxwell boundary problem are presented. The methods are derived in the context of the null field approach by using the fundamental theorem of discrete approximation. We established the convergence and unique solvability of the linear system of equations for any system of fu...

Convergence of the T-matrix approach for analyzing the scattering light from a particle located on a smooth surface is investigated. Numerical experiments are performed for oblate spheroids by choosing the discrete source method as reference. The results show that instability and convergence problems occur when the sphere enclosing the singularitie...

Mathematical tools are provided for the computation of the scattered field produced by non-spherical particles moving through the measurement volume of a phase Doppler anemometer. The phase distribution of a spheroid with random orientation is computed by using the rigorous extended boundary condition method and the ray theory. In a phase Doppler e...

In this paper the extended boundary condition method with discrete sources (DS) is introduced for the electromagnetic scattering problem of a conducting axisymmetric particle. The approximate solution is constructed as a linear combination of “Mie-potentials” with different origins. In order to take advantage of the rotational symmetry the DS are d...

The influence of agglomerates of solid conducting spheres on the response of a phase-Doppler anemometer (PDA) is described for a two-sphere system by using a ray theory model. First- and second-order reflection and diffraction are considered for far-field calculations of the PDA phase difference. The numerical simulations are accompanied and suppor...

The problem of light scattering by a particle on or near a surface is treated using the extended boundary condition method's solution for scattering by a particle in a homogeneous medium and the integral representation of spherical vector wave functions over plane waves for the calculation of the reflection of the scattered field by the surface. An...

The influence of the surface roughness of solid conducting spheres on the response of a phase-Doppler anemometer (PDA) is described by using a ray theory model. A rough particle surface is modeled as an ensemble of distorted spheres. First- and second-order reflection and diffraction are considered for far-field calculations of the PDA phase differ...

The accuracy of various formulations of the extended boundary condition method (EBCM) for solving the scattering problem of a cone-sphere particle is investigated. We compare the standard EBCM, the multiple miltipole EBCM, the lowest-order multipole EBCM and the EBCM with sub-domain bases. For this pusposes we choose the residual of the total elect...

A novel formulation for improving the numerical stability of the extended boundary condition method for highly elongated and flattened dielectric objects is presented. The key step in this approach is to approximate the surface currents by using lowest-order multipoles located in the complex plane. The accuracy of the proposed method for strongly d...

The generalized Lorenz-Mie theory describes the electromagnetic scattering of a Gaussian laser beam by a spherical particle. The most intensive computational aspect of the theory concerns the evaluation of the beam-shape coefficients in the general case of an off-axis location of the scatterer. These beam-shape coefficients can be computed starting...

Novel formulations for improving the numerical stability of the extended boundary conditions method and extending its application to highly elongated dielectric objects illuminated by a Gaussian beamare described. The derived formulations are obtained as special cases of a general approach, which considers arbitrary complete system functions on the...

A novel formulation for improving the numerical stability of the extended boundary condition method for highly elongated dielectric objects is presented. The surface currents are approximated by using the lowest-order multipoles located inside the particle surface. Calculations are presented for prolates with an aspect ratio of 20:1.

A plane wave spectrum method of Gaussian beams can be derived by using Davis' approximations for the vector potential. An equivalent vector potential is introduced by considering the inverse Fourier transform of the spectrum function of the original vector potential in a given plane. The electromagnetic field, which corresponds to the equivalent ve...

Mathematical tools are provided for the computation of the scattered field produced by a non-spherical particle moving through the measurement volume of a phase Doppler anemometer. The Doppler signal is modeled by using the rigorous extended boundary condition method and an approximate ray theory. The region of applicability of ray theory is discus...

The Scattering of focused laser beams by arbitrarily shaped dielectric bodies is investigated theoretically. The beam description is based on Davis third-order beam approximation for the field components. The scattering problem can be solved on a spherical basis by the extended boundary condition method or by the so-called modified version of the e...

Final report, June 2003, EC Project EVG1-CT-1999-00015.

In this paper we consider electromagnetic wave scatter- ing by aggregated fibres using a multiple scattering ap- proach. Scattering by particles of complex shape such as concave particles, torus, or clusters of fibres can not nor- mally be computed using the T-matrix method. In this paper we are proposing a decompositioning approach to handle this...

## Citations

... The interference of this kind manifests itself in the mutual shadowing and may considerably influence the opposition effects . While the description of the light scattering by densely packed media in terms of the ladder and cyclic diagrams has been considerably improved in recent years [see Doicu and Mishchenko, 2019b;Doicu and Mishchenko, 2019c) and references therein], the contribution of the diagrams corresponding to the interference of waves of different scattering orders has not been taken into account yet. ...

... The interference of this kind manifests itself in the mutual shadowing and may considerably influence the opposition effects . While the description of the light scattering by densely packed media in terms of the ladder and cyclic diagrams has been considerably improved in recent years [see Doicu and Mishchenko, 2019b;Doicu and Mishchenko, 2019c) and references therein], the contribution of the diagrams corresponding to the interference of waves of different scattering orders has not been taken into account yet. ...

... and that, when considering only one type of particle, the above reduces to an equation which is found in much of the literature [38,18,56,41,15,28]. 12) and the angles θ p and φ p can be complex numbers, meaning that we may have |k p | = 1, but we do have thatk p ·k p = 1 for the real inner product. ...

... In this paper we consider five models of a discrete random densely-packed medium (from A to E below), which differ by both the scattering characteristics of a volume element and the behavior of the extinction in a medium. The medium is considered as a semi-infinite layer, and the incident radiation is assumed to propagate perpendicularly to its boundary, since the theory for a more general case of the obliquely incident radiation is still at an early stage of development [see, e.g., Doicu and Mishchenko, 2019a)]. We compare the results of these models to each other and to the simulation results reported by Penttilä et al. (2021). ...

... This is a self-consistent system Green's function equation analogous to the Dyson equation of quantum field theory [74][75][76][77]. After slightly rearranging Eq. (13) and converting back to standard representation [78,79], we obtain ...

... However, the implementation of radiative transfer theory often involves some approximations even in one dimension (after already assuming a "plane-parallel atmosphere"; see, e.g., [10]) and requires more sophisticated assumptions and techniques in three dimensions when horizontal homogeneity cannot be assumed (see, e.g., [11,12]). In fact, radiative transfer theory itself is based on an approximation; as Mishchenko [13], Doicu and Mishchenko [14], and Doicu et al. [15] show, the radiative transfer equation can be derived from Twersky's approximation, according to which photons (scattered waves) do not loop through the same scattering center more than once during their trajectories (see, e.g., Twersky [16,17], Ishimaru [18], and Haspel and Sela [19]), whereas a full first-principles calculation would account for all scattered wave paths in the medium. Thus, though it has been shown that radiative transfer theory should be a good approximation in the case of a large and sparsely spaced collection of spherical scatterers (see, e.g., [7,15]), with modern computational capabilities, a first-principles-based calculation, if feasible, may actually present some advantages over radiative transfer theory in such a case. ...

... As there are many particles in a particulate medium, the scattered photon from a particle may interact with those from other particles. This means incident beams can be scattered more than one time and they can be scattered again by the nearby particles (Mishchenko et al., 1999;Dai and Haussener, 2018;Doicu and Mishchenko, 2018;Mishchenko and Dlugach, 2018). ...

... Similarly, the Q matrix can also be transformed into a block diagonal matrix. According to the IIM T-matrix theory, the Q matrix is calculated using the U matrix with the following equation: Because the matrix element of g(r n , r n ) is independent of the azimuthal mode m [20,22,31], we can rearrange the layout of the matrix element of g(r n , r n ) into an N-block diagonal matrix according to the arrangement rule of the U matrix [20,22], as shown in Figure 5. ...

... The passive atmospheric composition sensors (ACS) detect and record the radiance reflected by the Earth atmosphere in the ultraviolet (UV), visible (VIS), and thermal infrared (IR) regions. The information about the atmosphere is then retrieved from the spectral data by using the so called atmospheric processors, i.e. codes which are specifically designed to invert ACS measurements [1]. Extracting the information about geophysical parameters (level-2 data) from spectral radiance distributions (level-1 data) turns out to be a major computational challenge and requires high performance computing (HPC) [2]. ...

... In practice, we usually apply a scheme in which the regularization strength is gradually decreased during the iterative process, i.e. q ≥ 0.8. Doicu et al. [2002Doicu et al. [ , 2003 analyzed the numerical performances of this algorithm for nonlinear ill-posed problems without/with bound-constraint by means of simulated infrared spectra. ...