The image formation and the point-spread function of an optical system are analyzed by use of the wavelet basis function. The image described by a wavelet is no longer an indivisible whole image. It is, rather, a complex image consisting of many wavelet subimages, which come from the changes of different parameters (scale)a andc, and parametersb andd show the positions of wavelet subimages under different scales. A Gaussian frequency-modulated complex-valued wavelet function is introduced to express the point-spread function of an optical system and used to describe the image formation. The analysis, in allusion to the situation of illumination with a monochromatic plain light wave, shows that using the theory of wavelet optics to describe the image formation of an optical system is feasible.
© 2005 Optical Society of America
Fourier Optics and Optical Signal Processing
Original Manuscript: July 2, 2004
Manuscript Accepted: September 16, 2004
Published: December 1, 2005
Liying Tan, Jing Ma, and Guangming Wang, "Imaging system of wavelet optics described by the Gaussian linear frequency-modulated complex wavelet," J. Opt. Soc. Am. A 22, 2668-2671 (2005)