Numerical reference plane algorithm for effectively solving tilt distortion of a phase image in digital off-axis holography

Abstract

It is a simple and commonly-used approach to use an inclined plane reference wave to remove zero-order diffraction and conjugated image in digital off-axis holography. However, this method is encountering a difficulty, since an additional carrier frequency is incorporated into the inclined reference wave and it is difficult to accurately obtain this additional carrier frequency via experimental measurement, a certain tilt distortion of the phase image will occur in the hologram reconstruction. In this paper, a numerical reference plane algorithm is proposed to solve this problem. This method innovatively constructs a numerical reference plane which is able to exactly characterize the tilt of the phase image by choosing three different points from a local flat of the reconstructed image, and establishes a mathematical relation between the plane parameters and the carrier frequency of the reference wave, which is used as a criterion of correcting the tilt distortion of the phase image in the subsequent iterative computation. The procedures of the algorithm are as follows. 1) Input the nominal carrier frequencies, (fx', fy') of the plane reference wave and reconstruct the hologram. 2) Unwrap the phase with PUMA algorithm and suppress the noise using bilateral filtering and short time Fourier transform with wavelet shrinkage. 3) Construct the numerical reference plane reflecting the image inclination and establish the mathematical relation between the plane parameters and the carrier frequencies of the reference wave. 4) Perform the iterative computation to correct the nominal carrier frequencies, (fx', fy') by using the differential coefficients, (a, b) of the reference plane equation as the criterion. 5) Output the computation result and the corrected phase image. The algorithm is simple and effective. It is able not only to achieve accurate correction to the tilt phase distortion, but also to exactly obtain the additional carrier frequency of the inclined plane reference wave. Since in the phase unwrapping reconstruction, the proposed approach combines with bi-lateral filtering processing, wavelet shrinking and short time Fourier transform to remove the noise influence while the image details are preserved, the method would still be valid under the influences of environmental and system noise. The experimental result supports the theoretical prediction very well.