Optical orthogonal codes obtained from conics on finite projective planes

AbstractOptical orthogonal codes can be applied to fiber optical code division multiple access (CDMA) communications. In this paper, we show that optical orthogonal codes with auto- and cross-correlations at most 2 can be obtained from conics on a finite projective plane. In addition, the obtained codes asymptotically attain the upper bound on the number of codewords when the order q of the base field is large enough

Tracking the apparent location of targets in interpolated motion

AbstractUnder appropriate conditions, a target moving in discrete steps can appear to move smoothly and continuously even within the portions of the path where no physical stimulus is present. We investigated the nature of this interpolated motion in attentive tracking displays as well as apparent motion. The results showed that the apparent location of the target moved smoothly through space between the two discrete locations and the judgements of interpolated motion for attentive tracking and apparent motion were comparable to those for continuous motion in both the perceived path and the precision of the judgements. There were few, if any, differences between judgements for real and interpolated motion. An alignment procedure showed that the smooth change in location judgements was real and not a consequence of averaging across discrete locations actually seen on each trial. We also found that the slowest alternation rate which supported accurate location judgements corresponded to a critical SOA of about 500 ms, similar to the longest SOA which supported a subjective impression of motion in the display. Deviations from a constant velocity which were shorter than 200 ms did not register in the judged motion path, suggesting a fairly long time constant for the integration of velocity information into the perceived motion. These results suggest a specialized motion analysis which provides an accurate, explicit model of the interpolated motion path

Desingularization of matrix equations employing hypersingular integrals in boundary element methods using double nodes

In boundary element methods, the method of using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations (CBIE) become singular under certain combinations of double node boundary conditions. In this paper, we analyze the singular conditions of the CBIE formulation for cases where the boundary conditions at the double node are imposed by combinations of Dirichlet, Neumann, Robin, and interface conditions. To address this singularity we propose the use of hypersingular integral equations (HBIE) for wave propagation problems that obey Helmholtz equation. To demonstrate the applicability of HBIE, we compare three types of simultaneous equations: (i) CBIE, (ii) partial-HBIE in which HBIE is only applied to the double nodes at corners while CBIE is applied to the other nodes, and (iii) full-HBIE in which HBIE is applied to all nodes. Based on our numerical results, we observe the following results. The singularity of the matrix equations for problems with any combination of boundary conditions can be resolved by both full-HBIE and partial-HBIE, and partial-HBIE exhibits better accuracy than full-HBIE. Furthermore, the computational cost of partial-HBIE is smaller than that of full-HBIE.Comment: 14 pages, 10 figures, accepted manuscript submitted to Engineering Analysis with Boundary Elemen

Wavefront restoration from lateral shearing data using spectral interpolation

Although a lateral-shear interferometer is robust against optical component vibrations, its interferogram provides information about differential wavefronts rather than the wavefronts themselves, resulting in the loss of specific frequency components. Previous studies have addressed this limitation by measuring four interferograms with different shear amounts to accurately restore the two-dimensional wavefront. This study proposes a technique that employs spectral interpolation to reduce the number of required interferograms. The proposed approach introduces an origin-shift technique for accurate spectral interpolation, which in turn is implemented by combining two methods: natural extension and least-squares determination of ambiguities in uniform biases. Numerical simulations confirmed that the proposed method accurately restored a two-dimensional wavefront from just two interferograms, thereby indicating its potential to address the limitations of the lateral-shear interferometer.Comment: 11 pages, 6 figure