A numerical compensation technique is proposed to enhance the quality of reconstruction of phase-shifting lensless Fourier digital holographic microscopy. Introducing phase-shifting technique into the in-line lensless Fourier digital holographic microscopy is widely used, because this system possesses high resolution and is able to suppress the zero-order of diffraction and the twin image in reconstruction. Practically, it is likely to suffer from the lower resolution due to the blurred image in reconstruction plane in respect that the normal of object plane is not perpendicular to the CCD plane or the distance between the source of reference wave and the CCD plane is not equal to the distance between the object plane and the CCD plane accurately. Mechanical adjustment has difficulty in achieving high accuracy of adjustment and needs a great deal of time. Based on the theories of Fresnel diffraction and holography, it is found that numerical compensation can complete adjustment in high accuracy. It uses chirp function as compensation factor. The values of the three compensating parameters in three directions are obtained by repeatedly applying the numerical reconstruction procedure through gradual approach until the best in-focus image is obtained. The precisions of the three compensating parameters are decided by requirement. The main advantages are: (1) the accuracy of adjustment is high, (2) the quality of reconstruction can be greatly improved. In order to testify the feasibility of the numerical compensation technique, experiment is carried out. Its results show that fine numerical compensation is necessary to advance the quality and resolution of reconstruction.
In the interference phase measurement of slow-changing process, by use of the phase-shifting technology in the initial state, the background and amplitude of interference fringes can be obtained, and a novel phase unwrapping method based on cosine function is proposed. The holograms of the changing process are recorded, and then the phase cosine functions can be obtained by removing the background and amplitude from the holograms. The arccosine functions of phase cosine functions, which are called phase cosine wrapping function in this paper, can be unwrapped by utilizing the additional normal orientation information. The experimental analyses show that the residual noise and the phase-shifting errors have great influence on the accuracy of unwrapped phase. The tangent wrapping phase can’t be filtered by traditional method due to the π phase jumps, and the existing phase unwrapping algorithms are very complex. The phase-shifting errors can only influence the positions of phase jump points in the tangent wrapping phase. It is difficulty to optimize the tangent wrapping phase further. Compared with tangent wrapping phase, the phase cosine wrapping function is consecutive and can be filtered, and the unwrapping process is easier than that of tangent wrapping phase. The influence of phase-shifting errors on phase cosine function is not only positions but values of the wave crest and wave trough. The more precise the phase-shifting is, the closer the values of cosine function to ±1 at wave crest and wave trough are. The Experiment results show that cosine unwrapping method has the equivalent precision with tangent unwrapping method.