Micromirror array temperature cannot be measured directly, therefore it must be computed analytically from measurement points on the outside of the package, the package thermal resistance, the electrical power, and the illumination heat load. The following equations show the relationship between array temperature and the reference ceramic temperature, thermal test TP1 Figure 6-1 shown above:

where

• T_ARRAY = Computed array temperature (°C)
• T_CERAMIC = Measured ceramic temperature (°C), TP1 Figure 6-1
• R_{ARRAY–TO–CERAMIC} = Thermal resistance of package specified in Thermal Information from array to ceramic TP1 Figure 6-1 (°C/W)
• Q_ARRAY = Total DMD Power (electrical + absorbed) on array (W)
• Q_ELECTRICAL = Nominal electrical power (W)
• Q_INCIDENT = Incident illumination optical power (W)
• Q_ILLUMINATION = (DMD average thermal absorptivity × Q_INCIDENT (W)
• DMD average thermal absorptivity = 0.44

The electrical power dissipation of the DMD is variable and depends on the voltages, data rates, and operating frequencies. A nominal electrical power dissipation to use when calculating array temperature is 1.4W. The absorbed optical power from the illumination source is variable and depends on the operating state of the micromirrors and the intensity of the light source. The equations shown above are valid for a single chip or multichip DMD system. It assumes an illumination distribution of 83.7% on the active array and 16.3% on the array border.

The sample calculation for a typical projection application is as follows: