## 3 An On-Line Monitor System for OASLM Modulation  
The optical setup in Figure 5 is constructed for on-line monitoring of the phase modulation of the OASLM. A CCD with a spatial resolution of 512 pixels \(\times\) 512 pixels is used to monitor the OASLM phase modulation and a WFS is used to detect the actual wave-front after the OASLM. In order to achieve phase-only modulation, the relative angle of the optical axis direction between the polarizer and the OALCLV is set to 0\({}^{\circ}\) for WFS measurement. The transmittance is measured by the CCD, when the relative angle of the optical axis direction between the polarizer and the OALCLV is set to 45\({}^{\circ}\), and the polarizer and the analyzer are perpendicular to each other. Figure 6a shows the transmittance when the OASLM is subjected to a current of write light of 400 mA and \(V_{AC}\) of 14 V at 200 Hz. The red curve in the legend is the transmittance of a single-value grayscale modulation, from which we obtain the phase-change function shown in Figure 6b with a PV value of 1\(\lambda\). After 8-order polynomial fitting, this function is expressed as follows. \[\mathrm{y}=p_{1}x^{8}+p_{2}x^{7}+p_{3}x^{6}+p_{4}x^{5}+p_{5}x^{4}+p_{6}x^{3}+p_ {7}x^{2}+p_{8}x+p_{9} \tag{4}\]  
Figure 4: (**a**) Drive current of the write light affects the peak-to-valley (PV) value of the phase change when the OALCLV is at a \(V_{AC}\) value of 14 V at 100 Hz. (**b**) The voltage on the LC layer of the OALCLV as determined by the drive current of the write light. The values of the fitting coefficients \(p_{1}-p_{9}\) are:  
\[p_{1}=661.1715,\ p_{2}=-2101.2010,\ p_{3}=2600.9500,\ p_{4}=-1532.0300,\]  
\[p_{5}=401.8500,\ p_{6}=-28.0760,\ p_{7}=0.8321,\ p_{8}=0.2068,\ p_{9}=-0.0002.\]  
In order to further prove that the modulation results of the multi-value grayscale still satisfy the aforementioned relationship, we designed a gray-level ramp image and loaded it onto the OASLM to modulate the laser beam. The black curve in Figure 6a shows the corresponding one-dimensional (1D) transmittance distribution of the central row measured by the CCD, which has good consistency with the red curve. Figure 5: Optical setup used to measure the modulated wave-front. 1, 1055 nm continuous-wave Laser; 2, expander; 3, polarizer; 4, OASLM; 5, lens1, f1 = 150 mm; 6, lens2, f2 = 100 mm; 7, partially reflective mirror; 8, analyzer; 9, filter; 10, CCD; 11, filter; 12, wave-front sensor (WFS) (Physics Co., France, the spatial resolution is 29.6 \(\upmu\)m). Figure 6: (**a**) Transmittance as a function of the grayscale. (**b**) Phase change as a function of the grayscale. If we design a wave-front using Equation (4) and the actual modulation of the SLM loading the corresponding grayscale image is consistent with it, then we can assume that the transmittance measured by the CCD can monitor the phase-modulation result because the phase function in Equation (4) is directly derived from the transmittance. Figure 7a depicts a phase distribution designed with Equation (4), Figure 7b is the actual wave-front directly measured by the WFS and Figure 7c is a comparison of the 1D distribution of their central row. The modulated result is in good agreement with our designed wave-front. Spatial resolution is also a key parameter of the monitoring system. In Figure 6a, the gray values corresponding to the maximum and minimum values are 0.25 and 0.45, respectively. Therefore, in order to demonstrate the accuracy of the system, we designed binary grayscale images with these two values, and the modulation results obtained by the CCD and WFS are compared with their theoretical values. Figure 8 shows modulation results of the OASLM loading Figure 9a (a binary image with a gray-value mutation). Figure 8a is a comparison between the 1D wave-front results obtained from the WFS and the theoretical distribution.