An adjustable magnification method of lensless Fourier holography based on the equivalent spatial frequency

The equivalent spatial frequency is defined according to the characteristic of lensless Fourier hologram. It is found from the theoretical analysis that the adjustable magnification without aberration can be achieved only if the relation of the equivalent spatial frequency is satisfied. This process can be regarded as numerical magnification of the real object. Meanwhile, its corresponding reconstruction algorithm is given. To testify the method, a transmission setup and a reflection setup are used to record lensless Fourier holograms of a small object and a large object, respectively. Magnification and de-magnification of the reconstructions with improved image quality demonstrate the effectiveness of the proposed method. In addition, the effects of the under-sampling problem in phase-unwrapping are minimized.