A systematic method is proposed to generate a random image with a known correlation function and the modified Laplace distribution; the modified Laplace distribution includes the one-side exponential distribution and the Laplace distribution as a special case. Several random images with an isotropic correlation and the modified Laplace distribution are generated and displayed in figures.

This paper deals with the scattering of a TE plane wave by an apodised sinusoidal surface. The analysis starts with the extended Floquet solution, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. An integral equation for the amplitude functions is derived and solved by the small perturbation method to get single and double scattering amplitudes. Then, it is found that the beam shape generated by the single scattering is proportional to the Fourier spectrum of the apodisation function, but that generated by the double scattering is proportional to the spectrum of the squared apodisation. As a result, the single scattering beam and the double scattering beam may have different sidelobe patterns. It is demonstrated that the sidelobes are much reduced if Hanning window or Hamming window is used as an apodisation function.

This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking 1 with equal probability. Several mathematical formulas, such as multi-variate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A simple example of orthogonal functional expansion and stationary random seqence generated by the stationary binary sequence are discussed.

A periodic approach introduced previously is applied to the TM wave scattering from a finite periodic surface. A mathematical relation is proposed to estimate the scattering amplitude from the diffraction amplitude for the periodic surface, where the periodic surface is defined as a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . From numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

This paper presents a low-power video A/D conversion technique using features of moving pictures. Neighboring frames in typical video sequences and neighboring pixels in each video frame are highly correlated. This property is effectively used for the video A/D conversion to reduce the number of comparators and the resulting power consumption. A set of reference voltages is given to a comparator array so that the iterative A/D conversion converges in the logarithmic order of the prediction error. Simulation results using standard moving pictures showed that the average number of iterations for the A/D conversion is less than 3 for all the moving pictures tested. In the proposed 12 b A/D converter, the number of comparators can be reduced to about 1/5 compared with that of the two-step flash A/D converters, which are commonly used for video applications. The A/D converter is particularly useful for the integration to CMOS image sensors.

10G-EPON systems have attracted a great deal of attention as a way of exceeding to realize over 10 Gb/s for optical subscriber networking. Rapid burst-mode transmitting/receiving techniques are the key technologies enabling the burst-mode upstream transmission of 10G-EPON systems. In this paper, we have developed a OLT burst-mode 3R receiver incorporating a burst-mode AGC optical receiver and an 82.5 GS/s over-sampling burst-mode CDR and a ONU burst-mode transmitter with high launch power DFB-LD of 1.27 µm wavelength to fully compliant with IEEE802.3av 10G-EPON PR30 standards. The transmitting characteristics of a fast LD turn-on/off time of less than 6ns and a high launch power of more than +8.0 dBm, and the receiving characteristics of receiver sensitivity of -30.1 dBm and the upstream power budget of 38.1 dB are successfully achieved.

We present an 82.5GS/s over-sampling based burst-mode clock and data recovery (BM-CDR) IC chip-set comprising an 82.5GS/s over-sampling IC using 8×10.3GHz multi-phase clocks and a dual-rate data selector logic IC to realize the 10.3Gb/s and 1.25Gb/s dual-rate burst-mode fast-lock operation required for 10-Gigabit based fiber-to-the-x (FTTx) services supported by 10-Gigabit Ethernet passive optical network (10G-EPON) systems. As the key issue for designing the proposed 82.5GS/s BM-CDR, a fresh study of the optimum number of multi-phase clocks, which is equivalent to the sampling resolution, is undertaken, and details of the 10.3Gb/s cum 1.25/Gb/s dual-rate optimum phase data selection logic based on a blind phase decision algorithm, which can realize a full single-platform dual-rate BM-CDR, ate also presented. By using the power of the proposed 82.5GS/s over-sampling BM-CDR in cooperation with our dual-rate burst-mode optical receiver, we further demonstrated that a short dual-rate and burst-mode preamble of 256ns supporting receiver settling and CDR recovery times was successfully achieved, while obtaining high receiver sensitivities of -31.6dBm at 10.3Gb/s and -34.6dBm at 1.25Gb/s and a high pulse-width distortion tolerance of +/-0.53UI, which are superior to the 10G-EPON standard.

This paper deals with the singular behavior of the diffraction of transverse magnetic (TM) waves by a perfectly conductive triangular periodic surface at a low grazing limit of incidence. The wave field above the highest excursion of the surface is represented as a sum of Floquet modes with modified diffraction amplitudes, whereas the wave field inside a triangular groove is written as a sum of guided modes with unknown mode amplitudes. Then, two sets of equations are derived for such amplitudes. From the equation sets, all the amplitudes are analytically shown to vanish at a low grazing limit of incidence. From this fact, it is concluded analytically that no diffraction takes place and only reflection occurs at a low grazing limit of incidence for any period length and any triangle height. This theoretical result is verified by a numerical example.

As a method of analyzing the wave scattering from a finite periodic surface, this paper introduces a periodic approach. The approach first considers the wave diffraction by a periodic surface that is a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . It is pointed out that the Floquet solution for such a periodic case becomes an integral representation of the scattered field from the finite periodic surface when the period goes to infinity. A mathematical relation estimating the scattering amplitude for the finite periodic surface from the diffraction amplitude for the periodic surface is proposed. From some numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

This paper deals with the scattering of a cylindrical wave by a perfectly conductive periodic surface. This problem is equivalent to finding the Green's function G(x,z|xs,zs), where (x,z) and (xs,zs) are the observation and radiation source positions above the periodic surface, respectively. It is widely known that the Green's function satisfies the reciprocity: G(x,z|xs,zs)=G(xs,zs|x,z), where G(xs,zs|x,z) is named the reversal Green's function in this paper. So far, there is no numerical method to synthesize the Green's function with the reciprocal property in the grating theory. By combining the shadow theory, the reciprocity theorem for scattering factors and the average filter introduced previously, this paper gives a new numerical method to synthesize the Green's function with reciprocal property. The reciprocity means that any properties of the Green's function can be obtained from the reversal Green's function. Taking this fact, this paper obtains several new formulae on the radiation and scattering from the reversal Green's function, such as a spectral representation of the Green's function, an asymptotic expression of the Green's function in the far region, the angular distribution of radiation power, the total power of radiation and the relative error of power balance. These formulae are simple and easy to use. Numerical examples are given for a very rough periodic surface. Several properties of the radiation and scattering are calculated for a transverse magnetic (TM) case and illustrated in figures.

This paper deals with the diffraction of a monochromatic plane wave by a periodic grating. We discuss a problem how to obtain a numerical diffraction efficiency (NDE) satisfying the reciprocity theorem for diffraction efficiencies, because diffraction efficiencies are the subject of the diffraction theories. First, this paper introduces a new formula that decomposes an NDE into two components: the even component and the odd one. The former satisfies the reciprocity theorem for diffraction efficiencies, but the latter does not. Therefore, the even component of an NDE becomes an answer to our problem. On the other hand, the odd component of an NDE represents an unwanted error. Using such the decomposition formula, we then obtain another new formula that decomposes the conventional energy error into two components. One is the energy error made by even components of NDE's. The other is the energy error constructed by unwanted odd ones and it may be used as a reciprocity criterion of a numerical solution. This decomposition formula shows a drawback of the conventional energy balance. The total energy error is newly introduced as a more strict condition for a desirable solution. We point out theoretically that the reciprocal wave solution, an approximate solution satisfying the reciprocity for wave fields, gives another solution to our problem. Numerical examples are given for the diffraction of a TM plane wave by a very rough periodic surface with perfect conductivity. In the case of a numerical solution by the image integral equation of the second kind, we found that the energy error is much reduced by use of the even component of an NDE as an approximate diffraction efficiency or by use of a reciprocal wave solution.

A transverse magnetic (TM) plane wave is diffracted by a periodic surface into discrete directions. However, only the reflection and no diffraction take place when the angle of incidence becomes a low grazing limit. On the other hand, the scattering occurs even at such a limit, if the periodic surface is finite in extent. To solve such contradiction, this paper deals with the scattering from a perfectly conductive sinusoidal surface with finite extent. By the undersampling approximation introduced previously, the total scattering cross section is numerically calculated against the angle of incidence for several corrugation widths up to more than 104 times of wavelength. It is then found that the total scattering cross section is linearly proportional to the corrugation width in general. But an exception takes place at a low grazing limit of incidence, where the total scattering cross section increases almost proportional to the square root of the corrugation width. This suggests that, when the corrugation width goes to infinity, the total scattering cross section diverges and the total scattering cross section per unit surface vanishes at a low grazing limit of incidence. Then, it is concluded that, at a low grazing limit of incidence, no diffraction takes place by a periodic surface with infinite extent and the scattering occurs from a periodic surface with finite extent.

When a monochromatic electromagnetic plane wave is incident on an infinitely extending surface with the translation invariance property, a curious phenomenon often takes place at a low grazing angle of incidence, at which the total wave field vanishes and a dark shadow appears. This paper looks for physical and mathematical reasons why such a shadow occurs. Three cases are considered: wave reflection by a flat interface between two media, diffraction by a periodic surface, and scattering from a homogeneous random surface. Then, it is found that, when a translation invariant surface does not support guided waves (eigen functions) propagating with real propagation constants, such the shadow always takes place, because the primary excitation disappears at a low grazing angle of incidence. At the same time, a shadow form of solution is proposed. Further, several open problems are given for future works.

This paper deals with the diffraction of TM plane wave by a perfectly conductive periodic surface. Applying the Rayleigh hypothesis, a linear equation system determining the diffraction amplitudes is derived. The linear equation is formally solved by Cramer's formula. It is then found that, when the angle of incidence becomes a low grazing limit, the amplitude of the specular reflection becomes -1 and any other diffraction amplitudes vanish for any perfectly conductive periodic surfaces with small roughness and gentle slope.

The energy conservation law and the optical theorem in the grating theory are discussed: the energy conservation law states that the incident energy is equal to the sum of diffracted energies and the optical theorem means that the diffraction takes place at the loss of the specularly reflection amplitude. A mathematical relation between the optical theorem and the energy conservation law is given. Some numerical examples are given for a TM plane wave diffraction by a sinusoidal surface.

This paper deals with the scattering and diffraction of a plane wave by a randomly rough half-plane by three tools: the small perturbation method, the Wiener-Hopf technique and a group theoretic consideration based on the shift-invariance of a homogeneous random surface. For a slightly rough case, the scattered wavefield is obtained up to the second-order perturbation with respect to the small roughness parameter and represented by a sum of the Fresnel integrals with complex arguments, integrals along the steepest descent path and branch-cut integrals, which are evaluated numerically. For a Gaussian roughness spectrum, intensities of the coherent and incoherent waves are calculated in the region near the edge and illustrated in figures, in terms of which several characteristics of scattering and diffraction are discussed.

This paper deals with the scattering of a transverse magnetic (TM) plane wave from a perfectly conductive sinusoidal surface with finite extent. By use of the undersampling approximation and a rectangular pulse approximation, an asymptotic formula for the total scattering cross section at a low grazing limit of incident angle is obtained explicitly under conditions such that the surface is small in roughness and slope, and the corrugation width is sufficiently large. The formula shows that the total scattering cross section is proportional to the square root of the corrugation width but does not depend on the surface period and surface roughness. When the corrugation width is not large, however, the scattered wave can be obtained by a single scattering approximation, which gives the total scattering cross section proportional to the corrugation width and the Rayleigh slope parameter. From the asymptotic formula and the single scattering solution, a transition point is defined explicitly. By comparison with numerical results, it is concluded that the asymptotic formula is fairly accurate when the corrugation width is much larger than the transition point.

This paper deals with a new formulation for the diffraction of a plane wave by a periodic grating. As a simple example, the diffraction of a transverse magnetic wave by a perfectly conductive periodic array of rectangular grooves is discussed. On the basis of a shadow hypothesis such that no diffraction takes place and only the reflection occurs with the reflection coefficient -1 at a low grazing limit of incident angle, this paper proposes the scattering factor as a new concept. In terms of the scattering factor, several new formulas on the diffraction amplitude, the diffraction efficiency and the optical theorem are obtained. It is newly found that the scattering factor is an even function due to the reciprocity. The diffraction efficiency is defined for a propagating incident wave as well as an evanescent incident wave. Then, it is theoretically found that the 0th order diffraction efficiency becomes unity and any other order diffraction efficiencies vanish when a real angle of incidence becomes low grazing. Numerical examples of the scattering factor and diffraction efficiency are illustrated in figures.

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.