Inflation symmetry is one of the peculiar features of the diffraction pattern of a quasicrystal. However, it is not an exclusive property of quasicrystalline structures and it may be present in incommensurately modulated structures, as shown recently in the Al-Mg system (Donnadieu P et al 1996 J. Physique I 6 1153-64). The conditions that a single modulation parameter of an incommensurate structure must fulfil in order to have inflation symmetry are determined. Although the number of possible distinct inflation-symmetric quasilattices is infinite, from physical/experimental arguments it can be concluded that, in practice, only a few of them can be experimentally observed, the reported phase of the Al-Mg system being one of these particular cases. A quantitative criterion to classify the modulation parameters that give rise to quasilattices with observable inflation symmetry is proposed. The generalization of the analysis of incommensurate structures with more than one single modulation parameter is also discussed. Finally, the inflation parameters of diffraction patterns with rotational point groups of finite order, C N , are compared with the parameters of the one-dimensional case.
A spatial light modulator (SLM) may be used to variably tap and weight an acousto-optic (AO) delay line. This SLM application occurs in the optical signal processing of multipath delays from radar or other communication sources, as has been demonstrated with various electro-optic processing architectures1.2,3. These multipath delays signal must be estimated and suppressed to ensure optimal system performance. In the architecture presented here, the SLM must accurately select and weight various delays of a signal that propagate across an acousto-optic modulator. This paper reports the relative performance characteristics of the following spatial light modulators used in this application: an AO deflector used as an SLM (AOSLM), a liquid crystal television display (LCD) and a magneto-optic SLM (MOSLM).
We designed a programmable delay line using laser diodes to tap an acousto-optic cell. The laser diodes optically tap the Bragg cell at vaxying distances from the transducer to create delayed versions of the input signaL We describe the optical architecture that uses heterodyne detection to collect delayed versions of the input signal. We present experimental results that veiify system perfonnance. Applications for the delay line include radar and signal processing systems.
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