Causes of the reconstructed cross appearing in lensless Fourier transform digital holography

Causes of the bright cross appearing in the reconstructed field of lensless Fourier transform digital hologram (LFDH) are presented. Firstly, as LFDH's reconstruction was directly performed by Fourier transform algorithm, the intensity distribution of reconstructed image plane was just LFDH's spectrum, and three parts of the reconstructed field are imaged in the spectral plane. Meanwhile their intensities were almost the same. Hence, the ratio of signal to noise of the reconstructed image was obviously lower than that of the conventional digital hologram. Further, non-uniformity of the background intensity and random noises usually existed in a practical LFDH. Meanwhile their spectra spread through the central and the edge areas; this also led to decrease in the ratio of signal to noise of the reconstructed image. Specially, as the two-dimensional Fourier transform algorithm was performed row by row, and then column by column, the low-frequency spectrum induced by the non-uniformity of the background and random noises along the directions of rows and columns would concentrate on the central column and row, respectively, and what is gotten looked like a cross. Therefore, the cross appearing in LFDH's reconstructed field should be attributed to the combination of the background and the Fourier transform algorithm itself.