Enhancement of low-quality reconstructed digital hologram images based on frequency extrapolation of large objects under the diffraction limit

During the reconstruction of a digital hologram, the reconstructed image is usually degraded by speckle noise, which makes it hard to observe the original object pattern. In this paper, a new reconstructed image enhancement method is proposed, which first reduces the speckle noise using an adaptive Gaussian filter, then calculates the high frequencies that belong to the object pattern based on a frequency extrapolation strategy. The proposed frequency extrapolation first calculates the frequency spectrum of the Fourier-filtered image, which is originally reconstructed from the +1 order of the hologram, and then gives the initial parameters for an iterative solution. The analytic iteration is implemented by continuous gradient threshold convergence to estimate the image level and vertical gradient information. The predicted spectrum is acquired through the analytical iteration of the original spectrum and gradient spectrum analysis. Finally, the reconstructed spectrum of the restoration image is acquired from the synthetic correction of the original spectrum using the predicted gradient spectrum. We conducted our experiment very close to the diffraction limit and used low-quality equipment to prove the feasibility of our method. Detailed analysis and figure demonstrations are presented in the paper.