## 3 Results  
### Uncertainty Analysis  
We analyzed the measurement uncertainty \(u(L_{m})\) on the DGGE. Different grayscales are generated from the unique light source by DLP in the sequence algorithm as described in Section 2.3; the uncertainty of grayscale (relative luminance) generation of DGGE is related to the stability of the light source \(\Delta L_{r}\) and the uniformity of the luminance screen \(\Delta L_{u}\). Furthermore, the grayscale must be traced to luminance by photometer, so the uncertainty of the photometer measurement result \(\Delta L_{P}\) should be considered. Thus, the uncertainty model of grayscale (No., n) \(\Delta L_{n}\) from DGGE can be described by:  
\[\Delta L_{n}=\frac{n}{N}\Delta L_{r}+\frac{n}{N}\Delta L_{u}+\frac{n}{N}\Delta L _{P}, \tag{3}\]  
where \(N\) means the maximum grayscale number (corresponding to bit depth). This means there are three main sources of uncertainty; \(u(S_{r})\) is the uncertainty from the stability of the light source \(\Delta L_{r}\), \(u(S_{u})\) is the uncertainty from the uniformity of the luminance screen \(\Delta L_{u}\), and \(u(L_{p})\) is the uncertainty from the photometer measurement result \(\Delta L_{P}\). (1) \(u(S_{r})\)--The uncertainty from the stability of the light source \(\Delta L_{r}\)  
According to the digital control mode of the equipment, the light source works at a fixed working current, and its emission degree is also determined. We set all control bits of the DMD to \"1\", that is, the luminance of the light source projected onto the whiteboard is the maximum, and the grayscale corresponds to 255 (8-bit precision). The amount of change in the luminance of the projection whiteboard at 1 h was measured as the stability of the light source. The measurement interval is 5 min, and the measurement results are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time (min)** & **0** & **5** & **10** & **15** & **20** & **25** & **30** \\ \hline Luminance (cd/m\({}^{2}\)) & 3996 & 3998 & 3994 & 3999 & 4004 & 4002 & 3998 \\ \hline
**Time (min)** & **35** & **40** & **45** & **50** & **55** & **60** & \\ \hline Luminance (cd/m\({}^{2}\)) & 4003 & 4005 & 3995 & 4001 & 3996 & 4000 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stability of the light source. Figure 6: PC control interface. (**a**)Main interface of the program; (**b**)Grayscale preview interface. The stability of the light source calculated according to [PERSON]'s formula is:  
\[u(S_{r})=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{(L_{i}-\overline{L})}^{2}}}}{n-1}}=3.55 cd/m^{2}, \tag{4}\]  
where \(L_{i}\) represents each luminance measurement result, \(\overline{L}\) represents the average of the results, and \(n\) is the number of measurements (which is 13). (2) \(u(S_{u})\)--The uniformity of the luminance screen \(\Delta L_{u}\)  
According to the field of view and distance of the calibrated photometer, the size of the luminance area can be estimated. The whiteboard on the projection surface is a circular area with a diameter of 100 mm. Considering the influence of aberrations, an area with a diameter of 30 mm is selected as the calibration plane. As shown in Table 4, the uncertainty of the luminance uniformity of the screen of \(\Phi\)30 mm when measuring the 255 th gray level was taken as the result. The position mark on the luminance screen is shown in Figure 7.  
The uniformity calculation formula can be expressed as:  
\[u(S_{u})=L_{i}-L_{0}, \tag{5}\]  
where \(L_{i}\) represents the luminance of the i-th position (position 2 is selected here), and \(L_{0}\) represents the luminance at the center of the measurement area (corresponding to position 9). It can be calculated as:  
\[u(S_{u})=22 cd/m^{2}, \tag{6}\]  
(3) \(u(L_{p})\)--The uncertainty from the photometer measurement result \(\Delta L_{p}\)  
Both the output of the digital grayscale generation equipment and the display curve of the calibrated image are characterized by luminance.