Fan Hong-Yi, Liu Shu-Guang, Hu Li-Yun
Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui, China.
Opt Lett. 2009 Mar 1;34(5):551-3. doi: 10.1364/ol.34.000551.
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.
与量子光学菲涅耳变换相关的辛小波变换被发展为辛伸缩混合小波变换（SDWT）。SDWT既涉及实变量伸缩变换又涉及复变量辛变换，并且具有诸如帕塞瓦尔定理和反演公式等良好性质。纠缠相干态表示不仅是SDWT的基础，而且有助于推导相应的量子变换算符，其在经典光学中的对应物是透镜 - 菲涅耳混合变换。
