Image reconstruction with the use of fresnel holograms: relationship between the longitudinal and transverse scales of images

We study the Fresnel holography, one of the main methods used for recording three-dimensional images in medicine, biology, and machine building. It is shown that, in using the Fresnel holograms, the transverse and longitudinal scales of reconstructed images change, which leads to the inaccurate reconstruction of the three-dimensional structure of the object and affects the quality of analysis and interpretation of the obtained data. It is indicated that, for the classical quadratic relationship between longitudinal and transverse dimensions of the image, it is impossible to change the scale of the image without distortions. The method for changing the classical relationship between transverse and longitudinal scales of optical images is theoretically justified. An optical scheme of the device aimed at the realization of this method is proposed. The optimal conditions for recording and reconstruction of the Fresnel holograms guaranteeing more accurate high-quality reconstruction of three-dimensional images are determined. The scaling transformations of the image are analyzed for the optical schemes of Fresnel holography with the use of spatially incoherent radiation. The condition for reconstruction of the undistorted images is obtained in the form of the relationship determined by the parameters of the optical scheme of recording of the holograms. It is shown that the recorded Fresnel hologram makes it possible to vary the relationship between the transverse and longitudinal scales of the reconstructed image within fairly wide ranges. The accumulated results can be used in the fields of science and technology, where it is required to create images reproducing the objects of real world with the maximum possible accuracy (without distortions), e.g., in the field of medical visualization.