Reconstruction of Digital Hologram by use of the Wavelet Transform

In combination with charge coupled device (CCD) sensor technology and image processing systems, real time dynamic analysis becomes one of the significant advantages of digital holography. In order to achieve the dynamic analysis, lots of holograms should be recorded and every hologram should be numerical reconstructed. The most popular numerical reconstruction methods for digital holography include the well-known Fresnel diffraction integral method, the angular spectrum method and the convolution-based method. In order to filter out the zero-order term, the twin image term and the parasitic interferences, the process of the spatial filtering must be carried out in these methods. When some noises and parasitic interferences are introduced into the hologram, the spectrum of the virtual image would be disturbed by some other spectrum. It brings difficulties to define the spatial filter because of the blurry boundary and non-regular distribution of the spectrum. Manual spatial filters are often employed. However, defining different manual spatial filters would consume plenty of time for dynamic analysis. Therefore, the process of the spatial filtering limits the application of the digital holography for the dynamic and automatic analysis. The wavelet transform, a tool excelling for its multi-resolution and localization in the spacefrequency domains, is applied to the reconstruction of the object wave from the digital hologram in this chapter. Here the one-dimensional (1D) and two-dimensional (2D) Gabor wavelet transform (GWT) are employed for the analysis. By calculating the wavelet coefficients of the hologram at the ridge and the peak automatically, the object wave at the hologram plane can be reconstructed. At the same time the effect of the zero-order and the twin-image terms are eliminated without the process of the spatial filtering. The reconstruction approach for digital holography by use of the GWT is described in theory. And the experimental results are shown.