# Progress in Phase Calibration for Liquid Crystal Spatial Light Modulators
## 2 Basic Principle of Phase-Only SLM
For linear modulations of the phase described by green lines in Figure 2b, the desired gamma curve can be shown as the green curve in Figure 2a. In this case, a necessary calibration is desired. For the phase modulation of SLM, there is a response time for the molecules in LC cells to be tilted to the orientation needed for modulation. The response could be analyzed from anchoring effects and cell gap effects. The anchoring effects refer to the anisotropic part of the interfacial free energy for the alignment layer [22]. The cell gap refers to the thickness of the LC layer. The response time is  
Figure 2: (**a**) The pre-set ideal gamma curve (red) and the desired gamma curve (green) for linear phase modulation. (**b**) The shifted phase modulated by SLM without calibration (red) and the desired linear shifted phase (green) [21]. proportional to \(d^{x}\), where \(x\) is related to the anchoring energy and \(d\) is the cell gap [23]. Assuming strong anchoring effects, the reflective LCoS could respond four times faster than the transmissive LC-SLM for the same phase retardation. For the LCoS, it takes milliseconds to refresh a grayscale image. The SLMs are pixelated digital devices consisting of millions of pixels (such as the resolution of \(1920\times 1080\)). For each pixel, the pixel size and fill factor are two key parameters. For instance, the pixel size (pixel pitch) of commercial SLM could be \(3.74~{}\upmu\)m \(\times\) 3.74 \(\upmu\)m so that the highest spatial frequency of the image displayed on the SLM is limited. A smaller pixel pitch leads to better resolution and larger diffraction angles. The fill factor influences the intensity of the zeroth order in the modulated diffracted beam [24]. The zeroth order could disturb the image as well as the calibration procedure so that the SLM with a high fill factor is preferred. Even when the fill factor is 100%, the zeroth order cannot be eliminated because of the crosstalk [25]. For high-precision applications of the SLM, the properly polarized incident beam with an illumination angle could lead to a reduction or increase of the phase modulation. Besides, illuminating anisotropic LC with a large angle could lead to multi-reflection on the surface of the layer of LC-SLM or LCoS, in which the condition of the unwanted additional phase related to the addressed grayscale could appear [26]. Hence, normal illumination with proper polarization is the most favorable for phase-only LC-SLM while uploading a grayscale image of complexity, such as the application of holographic display. Alternatively, the incident angle for application could be held as the same as the illumination angle for the calibration procedure if the phase distortion is tolerable. Along with the illumination angle, the power of the incident laser could cause local heating. The phase modulation characteristic could vary with incident power so that the calibration could be carried out under the same incident laser power as the application to minimize the local heating effects [11]. Besides, the threshold of the damage power of the SLM nowadays could be 2 W/cm\({}^{2}\).