Monochromatic electromagnetic wavelets and the huygens principle

Description of the transfer function of an optical system with wavelet transforms

According to the wavefront filtering idea of wavelet optics, the transfer function of an optical system is described with a wavelet scale function. In the transfer function described with a wavelet scale function, different scale parameters a,c and shift parameters b,d correspond to different subtransfer functions, which correspond to different situations of the optical system. According to the request of the optical system, by adjusting all these scale parameters, not only can we obtain the optical images under different conditions, but we can also obtain the singular points under this scale parameter; hence a more ideal output can be obtained by such processing. The transfer function described with a wavelet scale function can be adjusted according to the request of the optical system, which makes the described transfer function self-adjustable. According to all types of disturbing effects to the system, by adjusting the scale and shift parameters, the practical form of the transfer function of an optical system can be confirmed, which satisfies the request of the self-adjustability of the optical imaging system. The result of our analysis shows that describing the transfer function of an optical system with a wavelet scale function is not only feasible but also satisfies the request of the self-adjustability of the optical imaging system, and different optical systems can be described by different wavelet scale parameters. This work breaks from the formal additional describing mode of the transfer function of an optical system and makes description of the transfer function of an optical system convenient.

Continuous-scale-invariant pattern recognition with adaptive-wavelet-matched filters

We designed and implemented a composite-wavelet-matched filter that is invariant to continuous-scale changes of the input and is useful for correlation-based pattern recognition of objects whose size is not known exactly. We optimize the adaptive wavelet to extract sparse image features and use the scale-space analysis to determine the wavelet scale for the scale invariance. Experimental results obtained by use of a programmable optical correlator with three liquid-crystal spatial light modulators are demonstrated.