Both displays and spatial light modulators (SLMs) form images from electronic signals. In many cases, the technologies used for display are also used for spatial light modulation. Until recently, the easiest way to tell one from the other was size. However, this distinction has disappeared now that several companies are developing microdisplays-high-resolution displays that are too small to be viewed without some form of magnification. A look at two applications for SLMs-optical processing and active diffractive optics-makes clear the differences in performance characteristics required from spatial light modulators compared to those needed for display.
FIGURE 1. Operating curves indicate phase and amplitude relationships of different electro-optic modulators. Typical curves for displays are twisted nematic (a), parallel aligned nematic (b), and binary micromirror or binary ferroelectric liquid crystal (FLC) (c); typical curves for SLMs are twisted nematic (d), deformable mirror or parallel aligned nematic (e), FLC phase modulator (f), FLC bipolar amplitude (g), FLC unipolar amplitude (h), and FLC binary phase modulator (i).
Optical processing
An optical correlator processes data in a manner similar to the way a slide rule processes numbers, by adding exponential terms (logarithms) to multiply numbers. In the case of a propagating wave, the exponential terms are related to the wave`s phase. As the wave`s phase terms slide in relation to each other, the phase terms combine to produce nonlinear effects. A nonlinear interaction is needed for multiplication, modulation, and frequency decomposition. For optical processing, phase is the primary operator within the system. Therefore, the correct phase relationship of the signal components is essential for proper operation.
The eye cannot see phase, only its effect. Therefore, SLM performance can be qualified by observing the far-field diffraction pattern, which is also the Fourier transform of the SLM image. Properly phased signal components are generated by the SLM if the test patterns in the Fourier domain have a limited amount of deviation from ideal. These transform tests verify that the SLM provides good performance in an optical correlator with a minor amount of characterization. The transform tests are conducted at the operating speed of the processor, which verifies that the SLM correctly forms "static" images at a high frame rate. A display does not have to present complete images to the eye even for a short period of time, because the eye does not rely on spatial coherence to form an image. On the other hand, transform tests do not require that every pixel in the array be functional or that the devices have no intensity variation, both of which are important attributes for display.
For microdisplay, it is usually best to suppress phase effects to achieve a clean image. The most obvious of these effects are interference caused by reflecting surfaces within the display and diffraction caused by pixelation. Interference produces intensity variations (fringes) across the display, whereas diffraction produces variations in intensity and color with view angle. These phase effects become more of a problem as the display shrinks in size, because distances between pixels and the various internal surfaces of the display are only a few wavelengths. On this scale, even sunlight has considerable coherence, and coherence is needed for phase to be an issue. Therefore, incoherent illumination is commonly used to eliminate the phase problems.
Typical operating curves for displays and SLMs can be plotted in the complex plane where rotation about the origin represents a phase shift. Operating curves for displays are usually confined to one side of the real axis, which allows voltage and intensity to have a one-to-one correspondence, providing better control of intensity. For SLMs, the operating curves tend to be more distributed over the complex plane or have less phase and amplitude coupling or both (see Fig. 1). These measures allow better control of amplitude and phase within the system.
FIGURE 2. Nyquist sampling makes efficient use of SLM resolution; diagram shows sampling at the frequency plane using pixels with 25% fill factor; to achieve 100% fill factor, the pixel mirrors need to extend to the dotted lines.
With some of the modulators, there is a trade-off between depth of modulation and response time, which is especially true for nematic liquid-crystal devices (see curves a, b, d, and e in Fig. 1). With other modulators, an increase in modulation depth and speed is achieved by adding some complexity to the modulator. This complexity makes the device more difficult to manufacture and control, which increases costs. Therefore, SLM performance comes at a price, literally. Examples of high-speed modulators with increased modulation depth are the deformable mirror (curve e) and the analog FLC modulators (curves f, g, and h in Fig. 1).
There are a variety of methods for producing high-resolution display devices, and the same fabrication technique can be used to produce backplanes for either displays or SLMs. However, there is a significant difference between display and SLM backplanes designed for optical processing. For display, the goal is to use all of the available light by maximizing backplane efficiency. Backplane efficiency increases the operating time for any battery-operated display that does not depend on ambient light for illumination. For projection systems, backplane efficiency increases power handling. In optical processing, efficiency is less critical. With today`s laser diode and CCD technology, it is easy to provide sufficient light at the detection plane. Quality of the signal (instead of quantity) is the more critical requirement. It is important that only correctly processed light arrives at the detection plane, which requires that the light be correctly sampled.
Nyquist sampling makes the most efficient use of the SLM`s resolution. For Nyquist sampling, the envelopes of the different frequency components overlap (see Fig. 2). For the SLM to correctly sample the optical data, the sample area of the pixel must be kept small to avoid crosstalk. Ideally, the sample area is confined to the area where the envelopes from adjacent frequency components drop to zero. However, this reduces the optical throughput of the SLM to zero. Therefore, the sample area must be extended to increase efficiency at the cost of increasing crosstalk. The percentage of sample area to the total pixel area is commonly referred to as the fill factor. For optical processing, a 25%-50% fill factor is a good compromise, whereas the trend in display is to obtain a 100% fill factor to maximize efficiency, which also maximizes crosstalk.
Active diffractive optics
Active diffractive optics are programmable high-resolution devices that emulate mechanically moving optical elements. Two uses for this type of device are beamsteering and adaptive wavefront control. Techniques for steering a beam without mechanical movement are being developed to eliminate the inertia or radar signature generated by a fast-moving mirror. Adaptive wavefront control is currently being used to correct atmospheric-induced aberrations in astronomy imaging systems. Also under consideration are high-resolution wavefront controllers for medical-imaging systems, where body fluids distort the image, or laser beam shaping for precision cutting and welding systems, where thermal effects distort the beam`s profile.
Active diffractive optical elements need an optical modulator that changes the optical path length of the light without changing its amplitude. Systems using active diffractive optical elements also need the backplanes to be very efficient (as is needed for display), but the pixel must be optically flat to prevent intra-pixel phase distortion that is not correctable by modulating the pixel.
In addition to these characteristics, this application uses resolution to achieve effective modulation depth in the same manner as a pivoting mirror that linearly phase shifts light by thousands of waves over its surface. It is the linear phase shift that steers light to a new location through the Fourier transform relationship of phase and position. A large phase shift is not practical using nonmechanical or micromechanical phase shifters unless we spatially divide the phase shift across the aperture into small phase ramps having modulo 2? resets.
As the effective stroke (phase shift) increases, so do the number of phase ramps. This shortens the width of each ramp. For large angles, the ramps become very narrow. Producing narrow phase ramps requires pixels spaced only a few microns apart. On this scale, it is difficult to produce pixels with a 100% fill factor. As discussed above, if the pixel fill factor is not 100%, then the efficiency of the backplane is reduced. To fabricate fully programmable, highly reflective backplanes that have spatial resolution on the order of a wavelength, the SLM manufacturer has to resort to techniques that have little to do with display.
The problem becomes more interesting when the light being steered is broadband. Diffractive elements are dispersive. That is, the diffraction angle is a function of wavelength, l. In the far field, the first-order diffraction angle, q, is given by sinq = l/L, where L is the period of the diffractive pattern. According to this equation, blue light is diffracted at a smaller angle than red light. This dispersion is useful for spectrally sorting energy as in a grating spectrometer. However, there is another effect that prevents grating dispersion from correctly sorting the light energy if the device has limited modulation depth.
If the phase profile is an ideal linear ramp with modulo 2? resets, then at the design wavelength of 650 nm, most of the energy is diverted into the first diffracted order. However, at 550 and 450 nm, more energy is scattered into higher spatial frequencies (see Fig. 3). This increases the sidelobe amplitudes and produces a nondiffracted component, which results in interference.
To prevent wavelength-dependent interference, a nondispersive phase shifter is needed where the modulator produces the same phase shift independent of wavelength. In this manner, red, green, and blue light are shifted by the same fraction of a wavelength with the same modulator setting. This type of phase shifter is possible by manipulating circular polarization. Boulder Nonlinear Systems has developed a nondispersive phase shifter that is useful for any high-resolution multispectral application, because it decouples the dispersion of the diffractive pattern from the phase modulation. For routing spectrally encoded signals, its nondispersive nature prevents crosstalk between channels. For manipulating chromatic light in an imaging system, the modulator cleanly separates the spectral components; this allows the grating dispersion to be corrected separately using an achromatic Fourier transform lens. However, if the phase shifter is dispersive, the only method for correcting the problem is to limit the diffraction to very small angles (that is, to limit the resolution of the adaptive optics).
FIGURE 3. Wavelength-dependent phase modulation from a nematic liquid-crystal diffractive optical element designed for operation at 650 nm is shown for three different frequencies; as the light`s wavelength varies from the design wavelength, the phase ramp becomes increasingly distorted by modulator resets.
The need for different SLMs is driven by the disparate requirements of applications such as those described here. There is also a dramatic increase in the types of microdisplays being developed, but because of the differences in the application requirements, it is not likely that the microdisplay industry will produce devices that completely satisfy the needs of the SLM market.
STEVEN SERATI is president and KIPP BAUCHERT is project manager of optical processing systems at Boulder Nonlinear Systems, 450 Courtney Way, Lafayette, CO 80026; e-mail: [email protected].