Coherent sources introduce an additional challenge. Rather than a single homogenous bundle of light, the output is restricted to diffraction orders as noted previously. These orders have the same angular extent as the input bundle. Consequently, a collimated beam, which has virtually no angular extent, results in collimated diffraction orders.

The output aperture sees some number these diffraction orders. If the angular diameter is smaller than sin^-1(λ/d) (where d is the pixel pitch of the DMD), then this is only possible to capture one order in the output aperture as illustrated in the panels of Figure 6.

If the incident illumination angle is fixed, then variations in tilt angle do not cause the diffraction orders to move, but do cause the energy distribution to shift between the orders. Consequently, if the order captured is near a blaze condition, then most of the energy available is captured in this one order, but if the condition is near an anti-blaze point this small aperture only captures a fraction of the output. This is illustrated in Figure 6-6.

To provide tolerance in the system design, TI recommends that the output aperture be expanded to capture four to five orders as shown in Figure 6-7. As per the example previously given, for a 7.56µm pixel pitch DMD with collimated light at 405 nm the minimum angular diameter of about 4.4° captures one or four orders, and 6.2° captures four or five orders. The recommended minimum angular diameter is given by:

Although the orders do not move with variations in tilt angle, the orders do move with changes in the illumination angle. If the illumination is moved by an angle of θ, then the orders at the output move by approximately -θ. Therefore, TI recommends to include a mechanism to adjust the input illumination angle by ± 2°, which allows the four to five orders with the highest intensity to be captured in the output aperture.

As with the incoherent case, the angular diameter of the output aperture sets a practical limit on the de-magnification level that can be achieved. For example, the maximum de-magnification for a 7.68µm pixel pitch DMD using collimated light at 405 nm is about 8.3x. If the incident beam has angular extent, then the diameter needs to be added to the output aperture before determining the de-magnification achievable.

In general, the maximum de-magnification achievable can be determined by the ƒ number of the focusing optics relative to the fabrication surface and then setting the distance to the DMD so that the aperture diameter is the minimum recommended: 2•sin^-1(λ/d) + θ_input. The following formula gives an estimate of the maximum attainable de-magnification:

In summary, coherent sources have the same two limits as incoherent sources. But the minimum aperture is determined by the angular spacing of diffraction orders rather than the tilt tolerance alone, which in turn limits the maximum practical de-magnification.