Wavelet transforming characteristic of a lens

Based on the wave-front filtering concept of wavelet optics, which we proposed, here we consider that the wave fronts of a light wave are filtered by the lens when the wave fronts pass through the lens. After filtering, the weight of the light field is redistributed, and a Gaussian frequency-modulated complex-valued wavelet function is introduced with the weight function. Subsequent analysis indicates that the lens has a wavelet-transforming characteristic and that the introduction of a Gaussian frequency-modulated complex-valued wavelet function conforms to the actual lens.