# Progress in Phase Calibration for Liquid Crystal Spatial Light Modulators
## 1 Introduction  
Liquid Crystal Spatial Light Modulator (LC-SLM) and Digital Micro-Mirror device (DMD) are two of the most successful SLMs. For phase manipulation, the LC-SLM has been widely used in many fields: holographic display [1; 2; 3], precision metering [4; 5], optical tweezers [6; 7], lithography [8], beam shaping [9; 10], etc. In the listed fields, the accurate phase manipulation is essential, especially for deploying SLM as a programmable diffractive device. The shifted phase could be modulated by the addressed grayscale or pixel voltage for an electric-addressed SLM. Ideally, the transfer from the uploaded grayscale to the shifted phase of the light wave is the same as the look up table (LUT) shown in the startup manual of the SLM. However, in practice, due to the nonlinear optical response of liquid crystal as well as manufacturing defects, the grayscale-phase response could be different for every single SLM device, even varying on sections of an SLM panel.  
The performance reduction of SLM is due to two kinds of static errors: the global grayscale-phase mismatch and spatial nonuniformity. The global grayscale-phase mismatch comes from the application of the unsuitable pre-set LUT of the SLM. The spatial nonuniformity of SLM's active area (on the panel to modulate incident beam) comes from the nonuniform electric drive [11], the curvature of the backplane of the SLM [12], or the aberration induced by the thickness variations of the LC layer. Besides, the accuracy of the applied electric field transferred from the uploaded grayscale for the pixels could lead to errors. For different illuminating wavelengths, the response will be different. Along with the static errors, there could be fluctuations of the phase modulation caused by the dynamic errors, including the local heating caused by an incident laser beam and the changes of environmental condition, such as temperature or humidity. Besides, performance reduction could happen as the SLM is aging. Therefore, the phase modulation of the SLM will not be the same as the way it is designed, and phase modulation calibration is needed for improving the performance of the SLM involvedsystem, especially the static calibration [13]. For instance, with spatially calibrated SLM, the control of the trapping intensities could increase in the holographic optical trapping system [11].  
The key point of the SLM calibration process is to acquire the phase corresponding to the grayscale. The main task is to measure the modulated phase of the SLM efficiently and accurately. All of the phase calibration methods are aiming to transfer the indirectly detectable phase distributions to detectable intensities such as interference fringes that could be used for analysis. A diverse array of calibration methods have been proposed and could be sorted into two categories: the interferometric phase calibration method and the diffractive phase calibration method. Both these methods provide solutions for transforming the phase to intensities, which are also widely applied in the measurements of all kinds of phase objects, such as the quantitative phase imaging for biological sample characterization.  
In this work, the LC-SLM and LCoS are investigated for instance to review the progress in the calibration methods. The interferometric methods are firstly discussed, which contain the self-referenced and out-referenced calibration methods. The diffractive methods are then described, which contain the diffraction pattern analysis method, optical elements generated method and polarization analyzed method. The advantages of these methods are analyzed and compared. The potential methods for different applications are suggested. The suggestions could be a reference for the calibrations of any SLM for its applications.