The symplectic wavelet transform, which is related to the quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable dilation-transform and a complex-variable symplectic transform and possesses well-behaved properties such as the Parseval theorem and the inversion formula. The entangled-coherent state representation not only underlies the SDWT but also helps to derive the corresponding quantum transform operator whose counterpart in classical optics is the lens-Fresnel mixed transform.
© 2009 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: September 19, 2008
Revised Manuscript: November 15, 2008
Manuscript Accepted: December 3, 2008
Published: February 18, 2009
Hong-yi Fan, Shu-guang Liu, and Li-yun Hu, "Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics," Opt. Lett. 34, 551-553 (2009)