Objective This work presents an improved phase vibration minimization (PVM)-based method for fast compensating phase aberrations in digital holographic microscopy. Polynomials are used to fit the aberrations, and the quasi-Newton optimization procedure is applied to find their coefficients. During the optimization procedure, gradients of the merit function value related to the coefficients are offered. The results of simulations and experiments show that this treatment makes the procedure fast and more reliable. Furthermore, the sampling technique is used to improve the processing speed even further. The analysis and experimental results reveal the improved method that can meet the demand for robustness to noise in everyday use. With high speed and accuracy, this method is suitable for dynamic holographic microscopic imaging.
Methods This work presents an improved PVM-based method for fast compensating phase aberrations in digital holographic microscopy. We use polynomials, such as standard and Zernike polynomials, to fit the phase aberration φa. To further improve the optimization speed, formula (4) is rewritten. The rewritten formula is shown in formula (7). It is more convenient to use software such as MATLAB to compute the derivative of the optimization coefficient and then use the fminunc function in MATLAB to carry out the optimization process using the quasi-Newton method and evaluation function (7). The obtained aberration coefficient {ai} can expand the formula (2) to obtain the compensated phase. In addition, this method can conveniently use sampling technology to increase the processing speed further.
Results and Discussions Simulative methods are used to verify the gradient-offered PVM-based method. This method is more accurate than the original method (Table 1). The main reason is that the maximum number of iterations set by MATLAB is 900. When the derivative of the optimized function with respect to the parameter to be optimized is not provided, the original method’s calculation process fails to converge. The improved method in this paper completes the optimization process in about 2.00 s (approximately 100 iterations), whereas the original method takes about 10.60 s to complete 900 iterations (Figs.1 and 2). This demonstrates that the improved PVM method can significantly speed up the calculation. Moreover, we used experimental methods to test the improved PVM method (Fig.3). However, the original method takes about 2.544 s to complete the optimization, whereas the improved method takes about 0.536 s. The latter method is more efficient. The improved PVM method with sampling processing can save the processing time (Fig.4). Compared to the improved PVM method without sampling, sampling saves 84% and 81% of the processing time.
Conclusions The PVM-based method can accomplish phase compensation without the need for specimen-free areas. In this paper, we introduce the gradients of the merit function value M related to {ai} in the method’s nonlinear optimization process by properly processing the merit function. It becomes faster and more reliable with this treatment, according to simulation and experimental results. Furthermore, sampling can be used to reduce processing time even further. Analysis and experimental results show that the improved PVM method and that with the sampling can meet the demand for noise robustness in common use. With high speed and accuracy, the improved PVM-based methods can be used in dynamic holographic microscopic imaging.
