# Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography
## 5 Coherent Noise Suppression  
The laser source, as a coherent illumination, enables the holographic imaging to suffer from the coherent noise, thus reducing the sharpness of the image details and further degrading the imaging quality. The coherent noise or speckle occurs in reconstructed images when there is an incident of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Advantage** & **Limitation** \\ \hline Double exposure & Compensating aberrations in optical components & Recording two holograms \\ method [22; 63; 65] & & \\ \hline Two MOs compensation method & Compensating quadratic phase aberration & Precisely adjusting the distance between MO \\ in two branches [25; 26; 29; 64] & & and CCD \\ \hline Compensation method in & Compensating quadratic phase aberration & precise adjustment of the distance between MO \\ telecentric arrangement [28; 30] & & and collimated lens \\ \hline Phase mask method [22; 26; 60] & Compensating aberrations set by mask & Requiring the sample-free blank region \\ \hline Surface fitting method for a blank & & \\ area [23; 60; 70] & Compensating aberrations set by polynomials & Requiring identical distortion in the total phase \\ \hline Surface fitting method for a total & & \\ reconstructed phase [69; 71; 72] & & \\ \hline Reference conjugated hologram & & \\ method [66; 67; 68] & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of phase aberration compensation methods. coherent light on an object with an optically rough surface. For the reflection, the grain speckle is found when the reflected light irradiates on the sample surface. For a nondiffusing object, such as a transparency, the grain coherent noise is introduced from an undesired diffraction and from multiple reflections, such as the dust particles, scratches, and defects on and in the optical elements. The specimen information affected by the multiplicative coherent noise is expressed as:  
\[O_{0s}(x_{0,}y_{0})=S(x_{0,}y_{0})\cdot N(x_{0,}y_{0})=A_{s}\exp(j\phi_{s}) \cdot A_{N}\exp(j\phi_{N}), \tag{24}\]  
where \(S(x_{0,}y_{0})\) and \(N(x_{0,}y_{0})\) represent the complex amplitude of the specimen and coherent noise, respectively; \(A\) is the amplitude and \(\varphi\) is the phase. There have been a number of approaches to reduce the coherent noise. They may be divided into three categories. The first kind consists of reducing the coherent nature of the laser source by the low spatial or temporal coherent source. In 2004, [PERSON] et al. [77] proposed the method in which a ground glass was placed behind the laser to reduce the spatial coherence of the light source. The method also has been studied by [PERSON] et al. in 2006 [78]. The synthetic aperture of the Fourier holographic optical microscopy, proposed by [PERSON] et al. [79] in 2006, performed a spatial averaging over illumination with various spatial frequencies to reduce the speckle noise. Later in 2013, [PERSON] et al. [80] discussed the speckle noise reduction based on a synthetic Fourier transform light scattering. As a low spatial coherent source, [PERSON] et al. [81] in 2011 and [PERSON] et al. [82] in 2017, employed the dynamic speckle illumination to suppress the speckle noise in DHM, respectively. At the same time, the low temporal coherent source was also applied as an illumination to reduce the source coherence. For example, the femtosecond pulse laser used by [PERSON] et al. [83] in 2005, the Ti-sapphire pulsed laser selected by [PERSON] et al. in 2015 [84], the white light source employed by [PERSON] et al. [85] in 2010, [PERSON] et al. [86] in 2012 and [PERSON] et al. in 2013 [87], the light-emitting diode (LED) adopted by [PERSON] et al. [88] in 2012, [PERSON] [89] in 2013, and [PERSON] et al. [90] in 2017, respectively, have offered immense contributions. These kinds of methods may reduce focal depth and strictly demand the optical path difference between the object and reference beams, thus increasing the adjustment difficulty of the light configuration.