The mismatched f-number approach is a method to improve diffraction efficiency performance. By utilizing a slower illumination f-number (larger f-number) and faster projection f-number (smaller f-number), the diffraction efficiency increases because more of the diffracted light from the reflected illumination beam is collected into the projection lens aperture. An example case is a system with the 7.56 μm pitch DMD, f/3 illumination and f/2.4 projection optics as shown in Figure 4-8. The matched f/2.4 illumination and f/2.4 projection case has an average diffraction efficiency of 83.9% while the mismatched f/3 illumination and f/2.4 projection case has an average diffraction efficiency of 90.5%. This method works across DMD devices. The margin of improvement depends largely on the selected f-numbers and DMD mirror size being used.

A direct laser system, where larger illumination f-numbers (smaller illumination system etendue) does not significantly lower the projector luminous output, benefits from the mismatched f-number technique. In a slower f-number system with matched illumination and projection f-number, the local minima for a given diffraction efficiency curve is lower as compared to a faster, matched f-number system. This reduced diffraction efficiency can be greatly improved by utilizing the mismatched f-number technique, driving the diffraction efficiency much higher than a matched f-number system would provide. The mismatching of f-number in this way flattens or reduce the peak to valley difference in the diffraction efficiency curves.

The mismatched f-number technique trades off some system contrast for diffraction efficiency. The system contrast lies between the lower matched f-number and the higher matched f-number of those of the projection and illumination path. For example, for a mismatched f-number system in which the illumination is f/3 and projection is f/2.4, the contrast is higher than a f/2.4 matched projection system and lower than a f/3 matched projection system built around the same DMD.