Digital holography has been widely applied in quantitative phase imaging (QPI) for monolayer objects within a limited depth. For multilayer imaging, compressive sensing is employed to eliminate defocused images but with missing phase information. A phase iteratively enhanced compressive sensing (PIE-CS) algorithm is proposed to achieve phase imaging and eliminate defocused images simultaneously. Linear filtering is first applied to the off-axis hologram in Fourier domain, and an intermediate reconstructed complex image is obtained. A periodic phase mask is then superimposed on the intermediate reconstructed image to iteratively eliminate the defocused images and recover the object with phase information. The experimental recovery of amplitude and phase of a two-layer sample with as little as 7% random measurement is demonstrated. The average phase error of the PIE-CS algorithm is analyzed, and the results show the feasibility for QPI.
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