Digital micromirror device

A digital micromirror device (DMD) is a binary spatial light modulator: a silicon memory chip covered by an array of square aluminium mirrors, each on a torsion hinge, that in most chips tilt about their diagonal to one of two stops. In the "on" state a pixel reflects the illumination into the projection or imaging optics; in the "off" state it reflects into a beam dump. Mirror pitches are typically about 5–14 µm, arrays range from under a million to several million mirrors, and a mirror switches in a few microseconds, so full binary frames can be loaded at up to tens of kilohertz depending on the chip and controller. The DMD was developed by Larry Hornbeck at Texas Instruments from 1987 and is widely known by its projector brand name, DLP.

Geometry of the on and off beams

With mirrors tilting ±12°, switching a mirror changes its angle by 24° and the reflected beam by twice that, so the on and off beams leave the chip 48° apart. The illumination is brought in at 24° from the array normal, in the plane perpendicular to the tilt axis, so that "on" light leaves along the normal. Because the tilt axis runs along the mirror diagonal, that plane of incidence is at 45° to the chip edges, which is why DMD optical layouts look rotated relative to the package. Some chips use ±17° tilt, which separates the beams further and eases the optical design at higher étendue.

Grey levels and timing

A DMD pixel is either on or off; grey levels come from time multiplexing. For 8-bit intensity at 60 frames per second, binary-weighted bit planes are displayed for durations in the ratio 1:2:4:...:128, and the shortest (least significant) bit lasts

$$t_\text{LSB} = \frac{1}{60 \times 255} \approx 65\ \mu\text{s}.$$

A detector or camera that integrates for less than a frame, or a pulsed laser that fires during a single bit plane, records individual bit planes; the grey level appears only when averaged over a whole frame. For scientific use the controller is usually run in a pattern mode that displays pre-loaded binary images at the highest rate the chip supports, with a trigger output for synchronizing cameras.

The DMD as a diffraction grating

Under incoherent illumination the array behaves as a set of tilted mirrors. Under laser light it is a two-dimensional diffraction grating with period equal to the mirror pitch, blazed by the mirror tilt. At 532 nm and 7.56 µm pitch the orders are spaced by about $\lambda/p = 70$ mrad (4.0°), and the fraction of light in any one order depends on how closely the specular direction of the tilted mirrors coincides with an order direction (the blaze condition). Efficiency into the wanted order can therefore change markedly with wavelength and incidence angle, and coherent setups choose the angle of incidence to satisfy the blaze condition at the laser wavelength.

A DMD can also display binary amplitude holograms. With a Lee-type hologram, a binary grating whose local shift and duty cycle encode phase and amplitude, the ideal first-order efficiency of a 50% duty binary amplitude grating is $1/\pi^2 \approx 10.1\%$. The low efficiency is accepted in exchange for switching rates of kilohertz, beyond what liquid-crystal devices reach; the Fourier optics of the setup, with a spatial filter passing only the first order, is the same as for a phase SLM.

Applications

• Projection displays and cinema projectors, the original application.
• Maskless photolithography, 3D printing by photopolymerization and laser direct imaging of circuit boards.
• Structured illumination and patterned photostimulation in microscopy, and programmable pinhole arrays in confocal microscopy.
• Single-pixel and compressive imaging, where a sequence of patterns is projected and a single photodiode records the total light for each.
• Programmable spectral filtering in the focal plane of a spectrometer.

Pitfalls

The standard window coating covers the visible band; ultraviolet and near-infrared use requires chips with suitable windows, and the aluminium mirrors and hinge limit the power density the array tolerates. Mirrors in the "off" state send considerable light into the system, so the off beam needs a well-placed dump. In coherent systems the gaps between mirrors and the diffraction orders produce ghost spots, and the flatness of the chip can add wavefront error across a large aperture. Mirrors held in one state for long periods can develop hinge memory, which is why controllers balance on and off times.

Common questions

How is a DMD different from a liquid-crystal SLM?

A DMD modulates amplitude in binary steps, is polarization-independent and switches in microseconds. An LCoS SLM modulates phase continuously and with higher diffraction efficiency, but refreshes tens to hundreds of times more slowly.

Why is the mirror tilt axis diagonal?

The hinge runs along the diagonal beneath the mirror, with an address electrode under each half, so the hinge and electronics are hidden from the light and the fill factor stays high.

References: L. J. Hornbeck, Proc. SPIE 3013, 27 (1997); J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017); W.-H. Lee, Appl. Opt. 18, 3661 (1979).