Micromirror array temperature cannot be measured directly, therefore it must be computed analytically using one or more of these conditions:

• Thermal test point location (see Figure 8-3 or Figure 8-4)
• Package thermal resistance
• Electrical power dissipation
• Illumination heat load

The relationship between the micromirror array and the case temperature is provided by the following equations:

where

• T_Array = Computed micromirror array temperature (°C)
• T_Ceramic = Ceramic case temperature (°C), located at TP1
• Q_Array = Total (electrical + absorbed) DMD array power (W)
• R_{Array-to-Ceramic} = Thermal resistance of DMD package from array to TP1 (°C/W)
• Q_Elec = Nominal electrical power (W)
• Q_Illum = Absorbed illumination heat (W)
• C_L2W = Lumens-to-watts constant, estimated at 0.00293 W/lm, based on array characteristics. It assumes a spectral efficiency of 300 lm/W for the projected light, illumination distribution of 83.7% on the active array, and 16.3% on the array border and window apertureP_D = Illumination power density
• SL = Screen lumensA = Illumination area on DMD

An example calculation is provided in Equation 4 and Equation 5. DMD electrical power dissipation varies and depends on the voltage, data rates, and operating frequencies. The nominal electrical power dissipation is used in this calculation with nominal screen lumens of 200 lm and a ceramic case temperature at TP1 of 55°C with a power density of 2 W/cm², an illumination area of 0.725 cm², and a ceramic case temperature at TP1 of 55°C. The DMD absorption constant of 0.42 assumes nominal operation with an illumination distribution of 83.7% on the active array, 11.9% on the array border, and 4.4% on the window aperture. A system aperture may be required to limit power incident on the package aperture since this area absorbs much more efficiently than the array. Using these values in the previous equations, the following values are computed: