During a given period of time, the landed duty cycle of a given pixel depends on the image content being displayed by that pixel.

In the simplest case for example, when the system displays pure-white on a given pixel for a given time period, that pixel operates very close to a 100/0 landed duty cycle during that time period. Likewise, when the system displays pure-black, the pixel operates very close to a 0/100 landed duty cycle.

Between the two extremes (ignoring for the moment color and any image processing that may be applied to an incoming image), the landed duty cycle tracks one-to-one with the gray scale value, as shown in Table 7-1.

To account for color rendition (and continuing to ignore image processing for this example) requires knowing both the color intensity (from 0% to 100%) for each constituent primary color (red, green, and/or blue) for the given pixel as well as the color cycle time for each primary color, where color cycle time describes the total percentage of the frame time that a given primary must be displayed in order to achieve the desired white point.

During a given period of time, the nominal landed duty cycle of a given pixel can be calculated as follows:

where

• Red_Cycle_% represents the percentage of the frame time that red displays to achieve the desired white point
• Green_Cycle_% represents the percentage of the frame time that green displays to achieve the desired white point
• Blue_Cycle_% represents the percentage of the frame time that blue displays to achieve the desired white point

For example, assume that the ratio of red, green and blue color cycle times are as listed in Table 7-2 (in order to achieve the desired white point) then the resulting nominal landed duty cycle for various combinations of red, green, blue color intensities are as shown in Table 7-3.

The last factor to consider when estimating the landed duty cycle is any applied image processing. In the DLPC34xx controller family, the two functions which influence the actual landed duty cycle are Gamma and IntelliBright™, and bitplane sequencing rules.

Gamma is a power function of the form Output_Level = A × Input_Level^Gamma, where A is a scaling factor that is typically set to 1.

In the DLPC34xx controller family, gamma is applied to the incoming image data on a pixel-by-pixel basis. A typical gamma factor is 2.2, which transforms the incoming data as shown in Figure 7-2.

Figure 7-2 Example of Gamma = 2.2

As shown in Figure 7-2, when the gray scale value of a given input pixel is 40% (before gamma is applied), then gray scale value is 13% after gamma is applied. Because gamma has a direct impact on the displayed gray scale level of a pixel, it also has a direct impact on the landed duty cycle of a pixel.

The IntelliBright algorithms content adaptive illumination control (CAIC) and local area brightness boost (LABB) also apply transform functions on the gray scale level of each pixel. But while amount of gamma applied to every pixel (of every frame) is constant (the exponent, gamma, is constant), CAIC and LABB are both adaptive functions that can apply a different amounts of either boost or compression to every pixel of every frame. Be sure to account for any image processing which occurs before the controller.