# Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography
## 1 Introduction  
Digital holographic microscopy (DHM) is a topographic measurement technique, which permits full-field, nondestructive, dynamic, quantitative amplitude, and phase-contrast imaging. The DHM, combining holography with microscopy, enables the information of amplitude and phase of the whole object to be recorded by the imaging sensor. The object wavefront is then retrieved by numerical reconstruction. Thus, the object topography can be obtained. Its lateral and longitudinal resolution may reach submicron and subnanometer scale, respectively. The technique has played an important role in different fields of application, such as micro-electro mechanical systems, microintegrated circuits, and the biomedical sciences. In 1997, [PERSON] and [PERSON] [1] applied phase-shifting interferometry to digital holography (DH) and reconstructed an arbitrary cross section of a 3D object, in which the in-line overlapping problem was resolved. In 1998, [PERSON] et al. [2] introduced the phase-shifting DH to microscopic measurement. In 1999, [PERSON] et al. [3] and [PERSON] et al. [4] presented the hybrid DHM and wavelength-scanning DH technique, respectively, which extended the measured to microscopic object. At the same time, [PERSON]'s team [5] realized the DHM configuration by inserting a microscope objective (MO) in the object optical path, thus obtaining an amplified image instead of specimen itself. The adopted off-axis configuration recovered the amplitude and phase information of the resolution chart simultaneously, and its lateral and longitudinal resolution reached submicron and nanometer scale, respectively [5; 6].  
In recent years, scholars have carried out much research on improving the imaging quality of DHM, which is a key step to reconstructing a topographic image with higher precision [7; 8; 9; 10; 11; 12; 13; 14]. In order to suppress the zero-order and the twin-image, the phase-shifting method and frequency filter method provide a notable solution, avoiding the overlapping of the reconstructed image [1; 15; 16; 17; 18; 19; 20; 21]. Due to a phase distortion introduced by the MO, physical or numerical compensation methods may be adopted to eliminate the quadratic phase distortion and other phase distortions [22; 23; 24; 25; 26; 27; 28; 29; 30]. Because the coherent source produces the inherent coherent noise in the reconstructed image, the low-coherent resource, multiplexing holograms methods, and digital processing methods have been studied to improve the imaging quality, respectively [31; 32; 33; 34; 35; 36; 37; 38]. The lateral resolution is related with the wavelength and the MO's numerical aperture. Therefore, the synthetic aperture method [39; 40; 41; 42; 43] and structured illumination approach [44; 45; 46; 47] are utilized to enhance the resolution when the wavelength remains unchanged. In addition, when the specimen's depth change is larger than the optical path of a wavelength, the phase unwrapping algorithms are adopted to obtain the real phase for \(2\pi\) ambiguity problem [48; 49; 50], in which multi-wavelength phase unwrapping methods permit larger synthetic wavelengths to unwrap [51; 52; 53].  
In the paper, imaging quality improvement is performed in DHM, aimed at phase aberration compensation and coherent noise suppression. In Section 2, the basic principle of DHM is introduced. In Section 3, the tilt phase error compensation is provided. In Section 4 the phase aberration compensation is summarized. In Section 5, the coherent noise suppression is presented. The progress and problems of the related methods are analyzed and discussed.