A signification characteristic is found by analyzing lensless Fourier digital hologram and synthetic aperture holography
that is the imaging surface of reconstructed image of lensless Fourier digital hologram just is focus plane of positive lens
that is unrelated with wavelength of restruction and recording and their ratio. The nature is propitious to resolve the
problem of DMD display caused by unstable holographic imaging surface. Zero order diffraction image is focused on
nearby center of focal surface and imaging zone is rapidly contracted that largely improved quality of reconstructed
image. Meanwhile, position of holographic reconstructed image is not to be altered when parallel moving lensless
Fourier digital holography on the holographic image plane that is easier to improve hologram duty cycle, DMD
availability and quality of reconstructed image with theory of synthetic aperture that attained by single illumination.
According to this analysis, a new method is proposed that combine lensless Fourier digital holography with synthetic
aperture that could improve quality of DMD reconstructed image. We provided laboratory results and verified all theory
analysis that totally proved the method is available and feasible.