Starlet transform applied to digital Gabor holographic microscopy

In this paper, we show how the starlet transform can be used to process holograms from a digital Gabor holographic microscope. The starlet transform is an undecimated wavelet transform with the property that when performing reconstruction, we only need to add all scales without the use of a synthesis filter bank. When the starlet transform is applied to a hologram, we divide the hologram into a certain number of scales, process them separately, and propagate each one using a numerical diffraction method. After diffraction propagation, we perform processing on complex amplitudes that correspond to individual scales. With the aforementioned procedure, it is possible to reduce the background and effects of parasitic fringes caused by high coherence of a laser, enhance the contrast, and reduce the effects of the twin image. Experimental results confirming the method are presented.