Optical realization of wavelet transform for a one-dimensional signal

Characterization of a liquid crystal microlens array using multiwalled carbon nanotube electrodes

Reconfigurable liquid crystal microlenses employing arrays of multiwalled carbon nanotubes (MWNTs) have been designed and fabricated. The cells consist of arrays of 2 microm high MWNTs grown by plasma-enhanced chemical vapor deposition on silicon with a top electrode of indium tin oxide coated glass positioned 20 microm above the silicon and the gap filled with the nematic liquid crystal BLO48. Simulations have found that, while its nematic liquid crystal aligns with MWNTs within a distance of 10nm, this distance is greatly enhanced by the application of an external electric field. Polarized light experiments show that light is focused with focal lengths ranging from approximately 7 microm to 12 microm.

Optical implementation of the continuous wavelet transform

A simple optical implementation for the one-dimensional wavelet transform (WT) is proposed. In contrast with previous WT optical implementations, the obtained WT is continuous along both axes (dilation and shift). An optical implementation to the inverse WT is proposed as well. Thus an optical continuous WT processor can be implemented.

Continuous two-dimensional on-axis optical wavelet transformer and wavelet processor with white-light illumination

The wavelet transform can be expressed mathematically as a convolution between the input function and a continuous set of scaled wavelet mother functions. Optics has managed to implement only the hybrid wavelet transform in which the set of scaled wavelet mother functions is discrete but the shift is continuous. White-light illumination is used to obtain a two-dimensional, fully continuous, on-axis wavelet transformer. When the illumination source is also spatially incoherent, a complete wavelet processor may be constructed.

Fractional wavelet transform

The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform. Optical implementation of this transform is briefly discussed.

Two-dimensional wavelet processor

An optical implementation of the two-dimensional (2-D) wavelet transform and inverse wavelet transform is performed in real time by the exploitation of a new multichannel system that processes the different daughter wavelets separately. The so-coined wavelet-processor system relies on a multichannel replication array generated that uses a Dammann grating and is able to handle every wavelet function. All channels process in parallel using a conventional 2-D correlator. Experimental results applying the Mexican-hat wavelet-decomposition technique are presented.

Wavelet filter: pure-intensity spatial filters that implement wavelet transforms

Saloma [Opt. Lett. 20, 1943 (1995)] proposed the concept of mirrors with point-spread functions that exhibit wavelet-related characteristics. We propose novel filters with wavelet point-spread functions. The mirrors are suggested to reform not only the phases of optical waves, but also the filters for amplitude. The transmittance functions of the filters, which are real and positive under some conditions, are given. Optical wavelet transforms can easily be made with these filters, and computer simulations for edge and corner extractions are given.

Power distribution in two-dimensional optical network channels

The power distribution in two-dimensional optical network channels is analyzed. The maximum number of allowable channels as determined by the characteristics of optical detector is identified, in particular, for neural-network and wavelet-transform applications.

Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material

An optical system that employs holographic recording in a photorefractive material is proposed and experimentally demonstrated for the implementation of a wavelet transform of two-dimensional mages. A scaling operation, to derive the family of wavelet filters from a mother wavelet filter, is performed by the use of an optical feedback loop. The selection of a desired wavelet filter from the family and the correlation for a wavelet transformation are made by the use of a holographic recording in a photorefractive material. The principle of operation of the system relies on the frequency detuning introduced inside the loop and the subsequent variation in the holographic grating diffraction. Experimental results on wavelet-filter selection and wavelet transformation are presented. This nonlinear optical wavelet-transform system is advantageous for pattern recognition applications.

Optical wavelet matched filter

A shift-invariant optical continuous wavelet transform is used for pattern recognition. We propose an Voptical wavelet matched filter that performs optical wavelet transforms for edge enhancement and the correlation between two wavelet transforms in a single step. This new bandpass matched filter shows improved discrimination capability with respect to the conventional matched filter and improved signal-to-noise ratio with respect to the phase-only matched filter. The wavelet matched filter provides flexibility of an adaptive choice of the scale factors of the wavelets that permit the selection of size and orientation of the smoothing function used in edge enhancement and the optimization of the performance of the filter. Optical experimental results are shown.

Short-time Fourier transform and wavelet transform with Fourier-domain processing

We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processing, which is suitable for optical implementation. We also systematically analyze the selection of the window functions, especially those based on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inverse STFT and the inverse WT. A couple of optical architectures based on Fourier-domain processing for the STFT and the WT, by which real-time signal processing can be realized, are proposed.

Optoelectronic wavelet processors based on Smartt interferometry

Optoelectronic wavelet-processor implementations based on Smartt interferometry are described for both one-dimensional (1-D) and two-dimensional (2-D) wavelet transforms. The 1-D processor study focuses on the processor's capability to perform the wavelet transform when the wavelets are defined in the time domain. The experimental results indicate that the system preserves all the phase information of the selected mother wavelets and thus delivers the true wavelet transform. The 2-D version of the processor is designed for the implementation of the complex wavelet transform. This processor will be valuable for applications, such as image coding-decoding, for which the preservation of phase information is necessary. A pair of prototype processors that incorporates.the 1-D and the 2-D systems has been built and tested to mechanical vibrations. High-quality reconstructed images were also obtained from the experimental data. The proposed systems have great potential for many practical applications.

Two-dimensional optical wavelet transform in space domain and its performance analysis

A new architecture of an optical wavelet transform system with a lenslet array is proposed, and its optical performance and optical limits are analyzed.

Generation of optical Haar wavelets by zone plates

Optical Haar wavelets are generated by zone plates that are designed to realize the bipolar nature of Haar wavelets. We present a circular Haar wavelet in two-dimensional space, which can extract the edge and corner features simultaneously, and characterize its properties with computer simulations. A comparison with rectangular Haar wavelets is also given.

Joint transform correlator that uses wavelet transforms

A joint transform correlation system based on wavelet transforms is introduced. The selection of wavelets and the optical wavelet transform of images enables this optical correlator to identify the specific features and distinguish similar characters. Preliminary experimental results are given.