## 3 Results
### Applications in Coherent Imaging  
The characterization with this new method can also be tested using the SLM in coherent imaging. [PERSON] et al. showed that arbitrary complex-valued fields could be retrieved through aperture-plane modulation [26; 27]. In Reference [26], a phase plate was used as the wave-front modulator. By shifting the plate, the authors recorded a set of diffractograms with different modulations and used them to retrieve the complex-valued fields by using an iterative retrieval technique. Here, we used SLM as the modulator, and different modulations were produced by loading different images on the SLM. The experimental setup is referred to in Reference [26]. For simplicity, only a pure modulus-type specimen was used in the experiment as a prototype. A map with a transparent character J surrounded by a translucent background was treated as the specimen, and its size was about 3 \(\times\) 3 mm (Figure 5a). The specimen is fixed on a glass by the lighttight taps. The monitor used here was a COMS camera (MER-131-210U3M, Beijing Daheng Corp) with a pixel size of 4.8 \(\upmu\)m \(\times\) 4.8 \(\upmu\)m. In the experiment, the distance between the SLM and specimen and that between the specimen and the digital receiver were about 7 and 207 mm, respectively. Because the phase modulation of the SLM may be affected by the environment, the phase added might have had a slight deviation from what we expected. To reduce the effect, we use random grid-like masks (Figure 5b). Only two gray scales are in the masks; one was 0 and the other was 110, corresponding to 0.440\(\uppi\) according to our characterization. We took six different masks to adjust the diffractograms. A typical diffractogram can be seen in Figure 5c. The specimen is then retrieved using the iterative method, the details of which are referred to in Reference [26]. This process spends about 6 s for about 100 iterations. Figure 5d shows the retrieved modulus of the specimen. From the figure, not only character J, but also the background with poor transmittance and the lighttight area around the specimen were retrieved. This confirms that the characterization was available in practice. Figure 4: Sketch of the process of the traditional method. (a) Figure 3b after being rotated slightly and properly cut; the curves beside the pattern represent the intensity along the dashed lines at the left and right parts, respectively; (**b**) comparison of the troughs of the light intensities of the dashed lines. It is possible that a value of \(\theta\) in a range around \(0.44\pi\) can lead to successful retrieval. During the retrieval process, we set different values of \(\theta\) to investigate how they affected the retrieval. One-hundred iterations were taken for all the \(\theta\). Figure 6 shows part of the results. When \(\theta\) is set to be \(0.439\pi\), it seems that the modulus is retrieved with little loss of the quality (Figure 6a). The specimen cannot be retrieved when \(\theta\) equals \(0.437\pi\) or \(0.443\pi\), as shown in Figure 6b,c. To quantitatively evaluate the retrieval, we introduced parameter \(E_{I}\). It is defined as:  
\[E_{I}=\frac{\sum\limits_{i}\sqrt{\sum\bigl{(}|I_{\text{cal},i}|-|I_{\text{ exp},i}|\bigr{)}^{2}}}{N_{\text{mask}}N_{\text{pixel}}} \tag{10}\]  
Here, \(I_{\text{cal},i}\) and \(I_{\text{exp},i}\) are the intensities of the calculated and the experimental diffractograms for the \(i\)th mask, respectively. \(N_{\text{mask}}\) and \(N_{\text{pixel}}\) are the total number of masks and the total pixels in a diffractogram, respectively. Considering that a pure amplitude sample was used in the experiment, \(I_{\text{cal},i}\) was calculated by the retrieved modulus instead of the complex amplitude. Obviously, a smaller \(E_{I}\) means a more accurate retrieval. The relationship of the \(E_{I}\) and \(\theta\) values can be seen in Figure 6d. For Figure 6a-c, the \(E_{I}\) values are \(0.0117\), \(0.0133\) and \(0.0245\), respectively.