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Variable magnification in numerical reconstruction of digitally recorded holograms

The numerical reconstruction of digitally recorded holograms can be done via different approaches. Convolution, angular spectrum and Fresnel transform are the most widely used. The size of the reconstruction pixel equals that of the recording device for the two former and for the latter that size is controlled by the experimental parameters; wavelength, number of pixels and reconstruction distance determine the achievable size of the of the reconstructed pitch hence the magnification of the holographic system. It has been a challenge to have a numerical reconstruction method in which the magnification can be chosen at will. In this work, a method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. It is supported on the Fresnel-Bluestein transform that allows for changing the magnification, namely the size of the reconstruction pixel, independent of distances, wavelength and number of pixels. The method is applied to reconstruct holograms recorded in off-axis and in-line setups. The reached magnification is contrasted with that achieved as the holograms are reconstructed with Fresnel transform. Since the proposed method does not modify the number of pixels of the hologram, neither the wavelength nor the reconstruction distance, it suits for application like color digital holography, metrological application among others.