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Hai-Liang Lu

Publications and source records attributed to Hai-Liang Lu.

4 recordsLinked to original sources
PubMed2006

Symplectic wavelet transformation.

Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi(*)(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi(*)(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version.

Journal Article↗
PubMed2006

Collins diffraction formula studied in quantum optics.

We find that the Collins diffraction formula in cylindrical coordinates is just the transformation matrix element of a three-parameter two-mode squeezing operator in the deduced entangled state representation. This is a new tie connecting the unitary transform in quantum optics to the generalized Hankel transform in Fourier optics. The group multiplication rule of the squeezing operators maps to the Collins formula related to two successive Hankel transforms.

Journal Article↗
PubMed2006

General formula for finding mother wavelets by virtue of Dirac's representation theory and the coherent state.

The admissibility condition of a mother wavelet is explored in the context of quantum optics theory. By virtue of Dirac's representation theory and the coherent state property we derive a general formula for finding qualified mother wavelets. A comparison between a wavelet transform computed with the newly found mother wavelet and one computed with a Mexican hat wavelet is presented.

Journal Article↗