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.