Numerical reconstruction of digital holograms

This thesis presents a new method for the numerical reconstruction of digital holograms recorded in the off-axis configuration using a CCD camera. The propagation of the reconstructed wave front, from the hologram plane to an observation plane, is achieved by a calculation of scalar diffraction in the Fresnel approximation. An image representing the distribution of intensity at the surface of the object can be obtained by calculating the intensity of the reconstructed wave front. The focusing of this image is performed digitally by adjusting a parameter which defines the distance between the hologram and the observation plane. A second image representing the phase distribution at the surface of the object can be obtained from the same hologram by calculating the argument of the reconstructed wave front. We show here that for getting a phase distribution that represents only the contribution of the object wave, the hologram or the reconstructed wave front must be multiplied by a computed replica of the complex conjugate of the wave used as reference during the recording. For a plane reference wave, the reconstruction of the phase distribution requires a precise adjustment of two digital parameters defining its propagation direction. An application to surface profilometry has demonstrated the quantitative nature of the obtained phase distribution which gives access to the topography of the object. A vertical resolution of λ/100 has been estimated on the basis of a preliminary study. The introduction of a microscope objective along the optical path of the object wave enhances the transverse resolution of the method. In this case, the wave front deformation produced by the microscope objective can be digitally compensated. Under the assumption of a paraboloidal deformation, we show that the wave front curvature can be numerically corrected by multiplication with an array of complex numbers computed using the complex conjugate of the analytical expression describing the defocusing aberration. A preliminary study indicates that the transverse resolution of the method approaches that of classical optical microscopy (diffraction limit). The application of a digital technique of spatial filtering allows for the elimination of the zero order of diffraction and of the twin image. This operation enhances the signal to background ratio. We show also that the influence of diffraction effects associated to the numerical reconstruction method can be reduced by apodization of the hologram aperture. This operation is performed digitally by means of a procedure which defines the transmission of the hologram aperture using a cubic spline interpolation.