# Speckle Noise Reduction in Digital Holography Using a DMD and Multi-Hologram Resampling
## 6 Results and Discussion
### Synthetic Holograms  
We evaluated our numerical strategy to obtain synthetic holograms in combination with the plane wave holograms experimentally recorded. To simplify the analysis, we fixed the number of holograms generated using this strategy to \(h_{s}=20\), matching the number \(h\) of holograms experimentally recorded. We evaluated the quality of the final reconstruction for different patch sizes \(G\). Figure 6 contains the results, which were selected as exact divisions of \(2048\times 2048\), the size of the registered holograms.  
Figure 5: Results in reduction of speckle noise for the three methodologies. First row: single hologram reconstruction. Second row: Average of reconstructed intensities.  
The curves of the speckle coefficient indicate that there is a significant improvement in comparison to the results obtained by the optical strategy, yet not a significant variation among different \(G\) values. In contrast, the size of the patch significantly decreases the resolution as it is presented in the profiles plot. For \(G=512\), we observe the best resolution since the edges are more defined in comparison to smaller patch sizes, from prior knowledge about the physical attributes of our dice object, we know that the cavity in the center, where the profile crosses, has vertical edges. From Figure 6 we can see that the profile corresponding to \(G=512\) presents the more vertical transition from the light region to the dark center. Moreover we can observe that the specular reflection in the center of the cavity of the dice, presents a higher intensity value, indicating a larger efficiency of diffraction in the reconstruction, which implies more fidelity. Therefore, we consider this to be the optimal value.  
In the third column of Figure 5, we present an individual reconstruction along with the average reconstruction for \(G=512\). The individual reconstruction presents an increase in speckle in comparison to the ones obtained by the originally recorded registers. This indicates the random 3D resampling effect. The averaged intensity has a better image quality in comparison to the one obtained by the original holograms. In Figure 7 the correlation coefficient matrix in the third column indicates smaller values, as well as a loss in the regularity that is present in the plane wave strategy, thus further indicating that the new speckle obtained by the resampling is more uncorrelated than the one in the recorded holograms. Similarly, the speckle coefficient plot, clearly demonstrates the improvement gained by the resampling strategy.  
Figure 6: Comparison of speckle reduction and image quality for different cell sizes. (**Left**): speckle coefficient. (**Right**): Line profile for the final averaged images corresponding with different values of patch sizes \(G\). The profiles have been vertically shifted by subtracting each corresponding mean.  
Figure 7: Behavior of the speckle metrics for the three methodologies. First row: speckle coefficient for the square region indicated in Figure 6. Second row: correlation coefficients for every image pair.