Diffraction by ruled gratings with variable spacing: fundamental method of intensity calculation.

A regular diffraction grating produces intensity patterns that combine waves coming through equispaced slits, so that the waves emerging from any two neighboring slits have identical phase differences. In this paper, we calculate the degradation in the intensity pattern when the grating has irregular spacing. The model of randomness considers the grating spacing and openings as being created by a "random walk." The resolving power of the grating is evaluated in relation to the D lines of sodium. It is shown that as the number of rulings increases, the uniformity of their spacing becomes more important in precision spectroscopic measurements, such as in astrophysical spectroscopy.

DECT evaluation of noncalcified coronary artery plaque.

PURPOSE: Composition of the coronary artery plaque is known to have critical role in heart attack. While calcified plaque can easily be diagnosed by conventional CT, it fails to distinguish between fibrous and lipid rich plaques. In the present paper, the authors discuss the experimental techniques and obtain a numerical algorithm by which the electron density (ρ(e)) and the effective atomic number (Z(eff)) can be obtained from the dual energy computed tomography (DECT) data. The idea is to use this inversion method to characterize and distinguish between the lipid and fibrous coronary artery plaques. METHODS: For the purpose of calibration of the CT machine, the authors prepare aqueous samples whose calculated values of (ρ(e), Z(eff)) lie in the range of (2.65 × 10(23) ≤ ρ(e) ≤ 3.64 × 10(23)/cm(3)) and (6.80 ≤ Z(eff) ≤ 8.90). The authors fill the phantom with these known samples and experimentally determine HU(V1) and HU(V2), with V1,V2 = 100 and 140 kVp, for the same pixels and thus determine the coefficients of inversion that allow us to determine (ρ(e), Z(eff)) from the DECT data. The HU(100) and HU(140) for the coronary artery plaque are obtained by filling the channel of the coronary artery with a viscous solution of methyl cellulose in water, containing 2% contrast. These (ρ(e), Z(eff)) values of the coronary artery plaque are used for their characterization on the basis of theoretical models of atomic compositions of the plaque materials. These results are compared with histopathological report. RESULTS: The authors find that the calibration gives ρ(e) with an accuracy of ±3.5% while Z(eff) is found within ±1% of the actual value, the confidence being 95%. The HU(100) and HU(140) are found to be considerably different for the same plaque at the same position and there is a linear trend between these two HU values. It is noted that pure lipid type plaques are practically nonexistent, and microcalcification, as observed in histopathology, has to be taken into account to explain the nature of the observed (ρ(e), Z(eff)) data. This also enables us to judge the composition of the plaque in terms of basic model which considers the plaque to be composed of fibres, lipids, and microcalcification. CONCLUSIONS: This simple and reliable method has the potential as an effective modality to investigate the composition of noncalcified coronary artery plaques and thus help in their characterization. In this inversion method, (ρ(e), Z(eff)) of the scanned sample can be found by eliminating the effects of the CT machine and also by ensuring that the determination of the two unknowns (ρ(e), Ze(ff)) does not interfere with each other and the nature of the plaque can be identified in terms of a three component model.

Intensity profile of light scattered from a rough surface.

We present in this paper, approximate analytical expressions for the intensity of light scattered by a rough surface, whose elevation ξ(x,y) in the z-direction is a zero mean stationary Gaussian random variable. With (x,y) and (x',y') being two points on the surface, we have 〈ξ(x,y)〉=0 with a correlation, 〈ξ(x,y)ξ(x',y')〉=σ2g(r), where r=[(x-x')2+(y-y')2]1/2 is the distance between these two points. We consider g(r)=exp[-(r/l)ß] with 1≤ß≤2, showing that g(0)=1 and g(r)→0 for r≫l. The intensity expression is sought to be expressed as f(vxy)={1+(c/2y)[vx2+vy2]}-y, where vx and vy are the wave vectors of scattering, as defined by the Beckmann notation. In the paper, we present expressions for c and y, in terms of σ, l, and ß. The closed form expressions are verified to be true, for the cases ß=1 and ß=2, for which exact expressions are known. For other cases, i.e., ß≠1, 2 we present approximate expressions for the scattered intensity, in the range, vxy=(vx2+vy2)1/2≤6.0 and show that the relation for f(vxy), given above, expresses the scattered intensity quite accurately, thus providing a simple computational methods in situations of practical importance.

Scattering of light by a periodic structure in the presence of randomness. V. Detection of successive peaks in a periodic structure.

We address the problem of detecting periodic structures hidden behind roughness. We have shown that if r(0) is the coherence length of the scattered radiation, due to the random part of the surface, and Lambda is the wavelength of the periodic part of the surface, then with a matched filtering method that we introduce, and by using simple computations with the intensity data, it is possible to detect the hidden first-order peak even when (r(0)/Lambda) approximately 0.11. Here we advance the method to bring out very weak second-order peaks, which we demonstrate for what we believe is the first time. The unmistakable presence of both the first- and second-order peaks, which have identical shapes as the zeroth-order peak, is strong evidence of the hidden periodicity and serves as a novel method for the detection of weak periodicities hidden behind strong randomness.