# Progress in Phase Calibration for Liquid Crystal Spatial Light Modulators
## 3 Interferometric Phase Calibration Method
### Self-Referenced Method  
The self-referenced method is one of the interferometric phase calibration methods which uses different parts of the SLM's active area to realize interference patterns. In this method, the active area in SLM could be divided into two or more zones, to act as a referenced zone and measured phase-shifted zone, respectively. To generate the measured beam, a series of grayscale patterns are uploaded on the modulated zone and the wave passing through the region will be modulated with a shifted phase related to the addressed grayscale on the SLM pixels. Meanwhile, the addressed grayscale on the referenced zone remains unchanged or changed periodically to realize interference with the measured beam. The shifted phase could be derived from the displacement or deformation of the interference fringes. The earliest experimental arrangement for realizing interference is developed by [PERSON], which inspires the calibration procedure naturally. Nowadays, the most popular phase modulation measurements experimental setup recommended by SLM suppliers in the manual book is based on the division of wavefronts as shown in Figure 3. The wavelength of the light source depends on the working wavelength range of the SLM. A camera is used for capturing the interference fringes. The measurement of the modulated phase could be carried out by remaining the grayscale of one half of the SLM a constant grayscale, while changing the grayscale of the other half of the SLM from 0 to 255 in grayscale gradually. The relatively shifted phase caused by changing the grayscale can be derived from Equation (3) and they could be one to one corresponding to the known grayscales for establishing the grayscale-phase relation. The measured grayscale-phase relation or LUT for the gamma curve could be sent to the driver of SLM by ports according to the manual for better performance of SLM. The setup for the phase measurement of transmissive LC-SLM is shown in reference [13]. In this method, the phase calibration is easy to align for the compact optical structure. However, only the global grayscale-phase relation could be derived. This is because the phase change of the half active area is represented by a beam with the width of a hole on the mask. In addition, the spatial nonuniformity of the SLM could not be characterized by using this method. A good solution for spatial nonuniformity measurement has been proposed [21; 27]. The configuration is shown in Figure 4a. Firstly, the global LUT is measured. The active area on SLM (PLUTO, Holoeye Photonics AG, Germany) is sorted into two zones, the uniform zone and the grating zone. The incident beam hit on both the uniform zone and grating zone. The uniform zone is the uploaded patterns in which the grayscales are uniformly distributed and changed from 0 to 255 at the step of 1. In addition, the grating zone is uploaded with patterns of columns of binary grayscales to form a phase grating. The period of the grating could be chosen according to the optical configuration. The reflected beam from the grating zone could be diffracted into the zeroth order and the first orders. One of the first orders beams interferes with the beam coming from the uniform zone to make the interference fringes. As shown in Figure 4a, the shifted phase of the uniform zone could be derived by the interference fringe's displacement related to the changed grayscales. Figure 3: Configuration of the self-referenced phase calibration method for reflective LCoS (HOLOYE GAEA-2). PS: monochromatic point light source; L1: collimating lens; P: polarizer; MASK: mask with two small holes; L2: Fourier lens; SLM: spatial light modulator; CAM: camera. The fringes move continuously, and the camera used for capturing the fringes is a discrete device, instead. The fringes' displacements smaller than one-pixel size of the camera could be spotted by grayscales changes on the captured image.