This paper deals with a probabilistic formulation of the diffraction and scattering of a plane wave from a periodic surface randomly deformed by a binary sequence. The scattered wave is shown to have a stochastic Floquet's form, that is a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then represented in terms of a harmonic series representation similar to Fourier series, where `Fourier coefficients' are mutually correlated stationary processes rather than constants. The mutually correlated stationary processes are written by binary orthogonal functionals with unknown binary kernels. When the surface deformations are small compared with wavelength, an approximate solution is obtained for low-order binary kernels, from which the scattering cross section, coherently diffracted power and the optical theorem are numerically calculated and are illustrated in figures.

This paper studies the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent by the small perturbation method. We obtain the first and second order perturbed solutions explicitly, in terms of which the differential scattering cross section and the total scattering cross section per unit surface are calculated and are illustrated in figures. By comparison with results by a numerical method, it is concluded that the perturbed solution is reasonable even for a critical angle of incidence if the surface is small in roughness and gentle in slope and if the corrugation width is less than certain value. A brief discussion is given on multiple scattering effects.

This paper proposes a second order auto-regressive equation with discrete-valued random coefficients. The auto-regressive equation transforms an independent stochastic sequence into a binary sequence, which is a special case of a stationary Markov chain. The power spectrum, correlation function and the transition probability are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.

The Communications Research Laboratory (CRL), the National Astronomical Observatory (NAO), the Institute of Space and Astronoutical Science (ISAS), and the Telecommunication Network Laboratory Group of Nippon Telegraph and Telephone Corporation (NTT) have developed a very-long-baseline-connected-interferometry array, maximum baseline-length was 208 km, using a high-speed asynchronous transfer mode (ATM) network with an AAL1 that corresponds to the constant bit-rate protocol. The very long baseline interferometry (VLBI) observed data is transmitted through a 2.488-Gbps [STM-16/OC-48] ATM network instead of being recorded onto magnetic tape. By combining antennas via a high-speed ATM network, a highly-sensitive virtual (radio) telescope system was realized. The system was composed of two real-time VLBI networks: the Key-Stone-Project (KSP) network of CRL (which is used for measuring crustal deformation in the Tokyo metropolitan area), and the OLIVE (optically linked VLBI experiment) network of NAO and ISAS which is used for astronomy (space-VLBI). These networks operated in cooperation with NTT. In order to realize a virtual telescope, the acquired VLBI data were corrected via the ATM networks and were synthesized using the VLBI technique. The cross-correlation processing and data observation were done simultaneously in this system and radio flares on the weak radio source (HR1099) were detected.

This paper deals with the scattering of a transverse magnetic (TM) plane wave from a perfectly conductive surface with a finite periodic array of rectangular grooves. By use of the method in a previous paper [IEICE TRANS. ELECTRON. VOL.E90-C, no.4, pp.903-906, APRIL 2007], the total scattering cross section is numerically calculated for several different numbers of grooves at a low grazing angle of incidence. It is newly found that, when the corrugation width becomes thousands times of wavelength, the total scattering cross section slightly depends on the groove depth and the period, and becomes almost proportional to square root of the corrugation width with a small correction.

In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the $m$th order scattering factor is an even function with respect to a symmetrical axis depending on the order $m$ of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.

This paper deals with the wave scattering from a periodic surface with finite extent. Modifying a spectral formalism, we find that the spectral amplitude of the scattered wave can be determined by the surface field on only the corrugated part of the surface. The surface field on such a corrugated part is then expanded into Fourier series with unknown Fourier coefficients. A matrix equation for the Fourier coefficients is obtained and is solved numerically for a sinusoidally corrugated surface. Then, the angular distribution of the scattering, the relative power of each diffraction beam and the optical theorem are calculated and illustrated in figures. Also, the relative powers of diffraction are calculated against the angle of incidence for a periodic surface with infinite extent. By comparing a finite periodic case with an infinite periodic case, it is pointed out that relative powers of diffraction beam are much similar in these of diffraction for the infinite periodic case.

This paper deals with the scattering of a TM plane wave from a periodic grating with single defect, of which position is known. The surface is perfectly conductive and made up with a periodic array of rectangular grooves and a defect where a groove is not formed. The scattered wave above grooves is written as a variation from the diffracted wave for the perfectly periodic case. Then, an integral equation for the scattering amplitude is obtained, which is solved numerically by use of truncation and the iteration method. The differential scattering cross section and the optical theorem are calculated in terms of the scattering amplitude and are illustrated in figures. It is found that incoherent Wood's anomaly appears at critical angles of scattering. The physical mechanisms of Wood's anomaly and incoherent Wood's anomaly are discussed in relation to the guided surface wave excited by the incident plane wave. It is concluded that incoherent Wood's anomaly is caused by the diffraction of the guided surface wave.