## 3 Phase Modulation Characteristic Calibration and Compensation of LCoS-SLM  
In the model of Section 2.2, the LCoS-SLM is seen as an ideal phase compensator. However, due to the cutting and polishing operation in the LCoS-SLM manufacture procedure, some deformation remains on its backplane, which could affect the configuration of liquid crystal molecules and bring in an initial wavefront residual error. Moreover, the environment would also impact phase modulation effectiveness. Hence the LCoS-SLM have certain nonlinear and nonuniform phase modulation character. It is necessary to calibrate the character and compensate for the initial wavefront error. There have been some methods to measure the nonlinear modulation character of LCoS-SLM. For example, to calculate the relative displacement of the interference fringes on the LCoS-SLM or the intensity contrast of diffraction methods and find the curve of \"grayscale-phase\" of an LCoS-SLM, so that a global lookup table for the nonlinear character of LCoS-SLM can be established. On the other hand, LCoS-SLM is an array device, which leads to a nonuniform phase modulation problem, which has been reported in the research literature [21; 22]. For the proposed optical system of Figure 5, the phase of LCoS-SLM can be directly measured by the interferometer. The electrical addressing sequence of SLM [23; 24] has been set to \"5-5\" to get a proper phase fluctuation stability performance. \"5-5\" means the duty cycle of the LCoS-SLM driving voltage, which makes the liquid crystal molecules tilted to modify the phase of the extraordinary light. A special phase pattern to measure the phase modulation character is shown in Figure 6. There are three areas on the phase pattern. Its central rectangle with four corners E, F, G and H (called rectangle EFGH) is given as the designed phase value, and the area outside the rectangle of ABCD is set as the reference phase of zero. Between these two areas are the transition area. The dimensions  
Figure 5: Optical system configuration based on LCoS-SLM. in LCoS pixels are \(1920\times 1080\), with a pixel size of 8 \(\upmu\)m. The inner EFGH area is used to set a change phase value from 0 to \(2\uppi\), and the other area of the LCoS-SLM is set to zero as the reference to measure the phase response of the LCoS-SLM. Figure 7 presents the LCoS-SLM configuration of calibration, which contains an interferometer, a polarizer, the LCoS-SLM and adjustment mounts; the wavelength is \(\uplambda=632.8\) nm. It is true that the phase modulation ability of the LCoS-SLM would be changed under oblique incidence [25; 26]. Moreover, the phase modulation change between normal incidence and oblique incidence has been measured. The modulation difference is small, with an oblique angle within 5 degrees. Moreover, this has also been measured by other researchers such as [PERSON] et al. [27] and [PERSON] et al. [28]. The angle's influence is very small within 5 degrees, and in the proposed optical configuration, the angle is 3 degrees. With the consideration of the incidence angle, we use a cosine function in the phase calculation to compensate for the phase modulation difference, and this method is a common method when using an interferometer to measure the phase in an off axis optical configuration. In the calibration experiment, a series of phase patterns with 18 grayscale intervals (total gray range of 0-255, and every single gray step is 15) are loaded on the LCoS-SLM, and the phase response is measured sequentially. Each measured phase data is subtracted with the first phase with the grayscale of zero to remove the tilt of phase data. The value in the designed phase area of _EFGH_ is calculated and subtracted with the phase value of the reference area. The phase steps are presented in Figure 8. Figure 9a shows the curve of the measured value with the given grayscale image on the LCoS-SLM, and the straight line is the theoretical value. Figure 9b shows the error of them.