# Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography
## 4 Phase Aberration Compensation
The Zernike fitting results of the total phase reflected the slow distribution of phase distortion for the sample with high-spatial-frequency content. The experimental micro-holes were estimated as high as 550 nm and its corresponding height standard derivation reached 19 nm. The method is immune to topographic distribution due to the application for sample with high-spatial-frequency content. It reduces the difficult of precisely adjusting the distance in the telecentric arrangement and improves the imaging quality in construction. A reference conjugated hologram approach was presented by [PERSON] et al. [67] in 2006. The reference conjugated hologram was produced by means of a sample hologram to correct the phase distortion. Subsequently, [PERSON] et al. [66] in 2008 and [PERSON] et al. [68] in 2010 carried out the corresponding research, respectively. The method can be applied for dynamic measurement only by one hologram, but it demands that there exists a blank region in proximity to the sample. In 2013, [PERSON] et al. [74] proposed a numerical phase aberration compensation method based on the principal component analysis (PCA). By means of a singular value decomposition, the phase aberration function \(Q\) was determined as:  
\[\xi_{2}(x,y)=\exp\biggl{[}-\frac{jk}{2f_{1}M_{0}}\biggl{(}x^{2}+y^{2}\biggr{)} \biggr{]}. \tag{19}\]1  
where \(l_{x}\) and \(l_{y}\) were the parameters to describe the spherical phase curvature. Its conjugate multiplied with the filtered hologram, leads to a new aberration-free hologram. The experiments of two cells were performed, in which the subcellular features as well as the thin borders of the cells were clearly observed without any curved or tilted background. Despite this, the approach improves the compensation efficiency by transferring 2D phase unwrapping and 2D surface fitting into a 1D procedure on two orthogonal directions. The PCA itself is the time-consuming task due to its processing time. To ensure efficiency, an optimal PCA-based method, proposed by [PERSON] et al. [75] in 2016, only extracted the reduced-sized aberration spectrum to compensate the phase aberration, thus improving the computational efficiency. In 2017, [PERSON] et al. [76] proposed an automatic phase aberration compensation method that combines a supervised deep learning technique with a convolutional neural network (CNN) and the Zernike polynomial fitting. The deep learning CNN was implemented to detect the background region automatically, which resolved the problem of aberration and the speckle noise that existed in other segmentation techniques. In addition, the Zernike polynomial was allowed to compute the self-conjugated phase to compensate for most aberrations. The approach can perform the real-time and automatic phase aberration compensation in DHM. The comparison of the phase aberration compensation methods are shown in \[\xi_{2}(x,y)=\exp\biggl{[}-\frac{jk}{2f_{1}M_{0}}\biggl{(}x^{2}+y^{2}\biggr{)} \biggr{]}. \tag{19}\]2 The advantages and limitations of the physical and digital compensation methods are listed. These methods can compensate for the different phase aberrations. The physical compensation methods are mainly restricted by adjustment or two holograms recording, while the limitations of the numerical compensation methods focus in the fitted region and the fitting model.