# Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography
## 5 Coherent Noise Suppression
The filter process was repeated \(n\) times by means of shifting a bandpass filter and the resulting intensities were averaged to obtain the speckle-reduced image. Despite only one hologram, the method losses the spatial resolution of the reconstructed image and is suitable for an in-axis optical arrangement. At the same year, [PERSON] et al. [113] presented an effective method using the windowed holograms to reduce the speckle noise, which was a window function with a value of one in a small region of the whole hologram area and a value of zero in the rest. The windowed hologram was obtained by a multiplication of the window function by the complex amplitude of the original hologram. By moving the window, many phase-difference values of the reconstructed images obtained with different windows were averaged with weights. The method using phase-shifting DH provided a very high-resolution displacement measurement, in which the standard deviation of error reached 88 pm. But the speckle-reduced image exhibits a lower spatial resolution. A single-shot speckle reduction approach was proposed by [PERSON] et al. [114] in 2015. The principle is identical with that of the method presented by [PERSON] [113]. The \(S=T\times T\) different sub-holograms were the results of the original hologram times a binary dynamic mask containing a movable window, as shown in Figure 7, in which \(T\) denoted the sub-hologram number in one dimension. They may be considered as having been recorded by CCD at \(S\) different locations. Each sub-hologram yielded a reconstructed image with the same sample information, but with a different speckle pattern. The experimental results of the speckle noise reduction were shown in Figure 8. These results showed a reduction to 0.28 from 1.0 in the contrast \(C\) of speckle noise as the value of \(S\) increased from 1 to 16, in which C is the ratio between the standard deviation and the mean value of the intensity of the reconstructed image. But the precondition of the approach was that the sub-holograms cannot be overlapped. Therefore, the relationship between the speckle reduction effect and the loss of spatial resolution is a trade-off. Compared to the approach proposed by [PERSON] [114], the speckle reduction by spatial-domain mask, presented by [PERSON] et al. [115] in 2016, permitted the spatial-domain mask to overlap, which released the limit of the available number of the images to be synthesized. A number of reconstructed images were obtained by shifting a digital aperture in the original hologram. Each spatial frequency of the reconstructed image was distributed in the whole area of hologram, thus each spatial frequency of these sub-holograms was uniformly distributed. As a result, the shifting aperture could be overlapped and many different speckle patterns were produced. The average of the amplitudes of multiple reconstructed images meant that the speckle suppression was achieved. The experimental results showed that the image contrast and the spatial resolution were decreased with the smaller aperture  
Figure 8: Results of the single-shot speckle reduction approach. (**a**) \(S=1\) sub-hologram; (**b**) \(S=4\) sub-holograms; (**c**) \(S=9\) sub-holograms; (**d**) \(S=16\) sub-holograms. (Reproduced with permission from [114], Copyright OSA publishing, 2015). Figure 7: Schematic of the generation of sub-holograms in the single-shot speckle reduction approach. (Reproduced with permission from [114], Copyright OSA publishing, 2015). size, respectively. Moreover, the larger number of the synthesized images also obtained the improved speckle contrast at the same aperture size. The method may be applied to the dynamic measurement only by one hologram. However, the spatial resolution of the reconstructed images also depended on the aperture size, even if the sub-holograms were allowed to overlap each other.