# Pursuing High Quality Phase-Only Liquid Crystal on Silicon (LCoS) Devices
## 5 Phase Precision  
Besides the linear phase response in all gray scales, another issue is the phase precision over the entire active area. Phase precision has been discussed in many different forms, such as \"spatially varying phase response\" (SVPR) [46], \"spatially resolved phase response\" (SRPR) [47], \"multipoint phase modulation\" [48; 49; 50; 51], \"uniformity metrology\" [52; 53; 54; 55], \"wavefront distortion\" [56], \"optical flatness\", etc. The phase precision quality of an LCoS-SLM panel can be defined by using the above-mentioned evaluation methods. The current four major LCoS SLM manufacturers provide the following phase precision standards: (1) the latest 4K2K GAEA-2 from Holoeye Photonics--the optical flatness can be adjusted from \(\lambda/6.6\) to \(\lambda/10\) (RMS) after phase compensation; (2) the high phase precision LCoS panel from Hamamatsu Photonics--the phase precision has to be \(\lambda/50\) mean standard deviations (mSTD) after phase compensation; (3) the latest HSP1920 from Meadowlark Optics--the phase precision can be adjusted from \(\lambda/7\) to \(\lambda/20\) (RMS); and (4) the latest SLM-200 from Santec Corp.--its wavefront distortion is greater than \(\lambda\), but can be reduced to \(\lambda/40\) after compensation. We adopt the mSTD from 256 (8 bits) gray scales to evaluate the phase precision before compensation, defined as:  
\[mSTD(x,y)=\frac{\sum\limits_{GL=0}^{GL=255}\sqrt{\frac{\sum\limits_{mxy-1}^{ mxy-max}\left(\delta mxy(LUT_{global}(GL)\right)x,y\right)-\overline{mxy}\left(LUT_{global}(GL),x,y \right)}^{2}}}{Total\ mxy} \tag{4}\]  
where \(\delta\) is the phase measurement based on the LUT at different gray levels, and \(x\) and \(y\) refer to the specific area measured over the whole panel as shown in Figure 5. Fewer or more sections of mxy is dependent on the beam size or characterization method. The following formula represents various factors that affect phase modulation:  
\[\delta_{\rm total}(V,\ T,\ x,\ y)=\Delta\delta(T,\ V,\ x,\ y)+\delta_{o}(x,y) \tag{5}\]  
Factors that can affect the output wavefront (\(\delta_{\rm total}\)) of an SLM can be attributed to modulated terms (\(\Delta\delta\)) and non-modulated terms (\(\delta_{o}\)). The modulated terms (\(\Delta\delta\)) can be rewritten as follows to specify the effects on LC birefringence (\(\Delta\)n) and cell gap (d):  
\[\delta_{\rm total}(V,\ T,\ x,\ y)=\Delta n(T(x,\ y),V(x,y))d(x,y)+\delta_{o}(x,y) \tag{6}\]  
In the non-modulated term, unevenness may arise due to the surface flatness of LCoS IC-backplane after the chemical mechanical polishing (CMP) process [57], the surface flatness of LC alignment layer, or other components like Indium Tin Oxide (ITO)cover glass. The main source of imprecision of the SLM phase is the modulation term. The three factors can be recognized across the entire LCoS panel (\(x,y\)) as following: (1) the cell gap uniformity (d); (2) the temperature effect (T) of the SLM panel, and (3) the voltage uniformity (V) from pixels. The uniformity of the LC layer is the most important parameter for the output wavefront. It requires a high assembly precision to control the cell gap uniformity error of \(\sim\)1% over the entire active area in the liquid crystal assembly (LCA) process (assuming no internal damage to the IC backplane during LCA). This becomes more difficult if the cell gap is below 1.6 \(\upmu\)m. The problem of rising temperature may be caused by either a high-power light source or the thermal effect from IC backplane. The output wavefront unevenness could result from non-uniform backplane temperature due to poor heat dissipation design in the optical system. This effect can be minimized if the operating temperature of the LCoS-SLM backplane can be evenly controlled at a constant temperature. Most of the problems that affect the phase precision of the panel are mainly due to the non-uniform LC cell gap and the uneven output voltage at each pixel.