A separable two-dimensional discrete Hartley transform

Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed

Surfaces roughness effects on the transmission of Gaussian beams by anisotropic parallel plates

Influence of the plate surfaces roughness in precise ellipsometry experiments is studied. The realistic case of a Gaussian laser beam crossing a uniaxial platelet is considered. Expression for the transmittance is determined using the first order perturbation theory. In this frame, it is shown that interference takes place between the specular transmitted beam and the scattered field. This effect is due to the angular distribution of the Gaussian beam and is of first order in the roughness over wavelength ratio. As an application, a numerical simulation of the effects of quartz roughness surfaces at normal incidence is provided. The interference term is found to be strongly connected to the random nature of the surface roughness.Comment: 18 pages, Journal of Physics D: Applied Physics, volume 36, issue 21, pages 2697 - 270

Carte des deux Florides et de la Louisiane inférieure

dressée pour les voyages de Mr. Robin dans les années 1802, 1803, 1804, 1805 et 1806https://digitalcommons.usf.edu/fl_maps_collection/1050/thumbnail.jp

Appearance of colored patterns: pattern-color separability

We have measured how color appearance of square-wave bars varies with stimulus strength and spatial frequency. Observers adjusted the color of a uniform patch to match the color appearance of the bars in squarewave patterns. We used low-to-moderate square-wave patterns, from 1 to 8 cycles per degree (c/deg). The matches are not photoreceptor matches but rather are established at more central neural sites. The signals at the putative central sites obey several simple regularities. The cone contrast of the uniform patch is proportional to square-wave stimulus strength (color homogeneity) and additive with respect to the superposition of equal-frequency square waves containing different colors (color superposition). We use the asymmetric matches to derive, from first principles, three pattern-color-separable appearance pathways. The matches are explained by two spectrally opponent, spatially low-pass mechanisms and one spectrally positive, spatially bandpass mechanism. The spectral mechanisms that we derive are similar to luminance and opponent mechanisms that are derived with entirely different experimental methods. 1