Reducing unwanted intensity fluctuations in laser-projected images

Compared to typical display projectors based on incandescent lamps, laser sources have several advantages. Among them are directionality, miniaturization potential, multiplexing possibilities, improved color gamut, higher contrast, deeper focus, and higher brightness. However, laser light is coherent—it has a well-defined wavefront—which creates constructive and destructive interference in the observer's eye. This manifests as a grainy, noiselike pattern over the image,¹ called speckle. The main challenge with laser projectors is to reduce the presence of speckle to an acceptable level. However, existing methods are often expensive, cause loss of power, or degrade the image.

One common approach to speckle reduction is to place a diffuser in the light path, between the light source and imaging system. Making a small alteration to the surface of the diffuser changes the wavefront of the beam and, consequently, the speckle pattern. Summing the resulting speckle patterns in the eye during its exposure time diminishes the unwanted intensity fluctuations in the image. A challenge is to find a suitable way of changing the speckle pattern. Here, we present a novel method² based on discrete rotation of a diffraction pattern on a diffuser, where the stationary zeroth-order diffraction maximum is extinguished without losing overall power.

Imagine that a beam of coherent light is passed through a sinusoidal phase grating and diffracted into a line of spots on a diffuser (see Figure 1). Rotating the grating causes the spots to cover different areas of the diffuser and produce different speckle patterns. However, the zeroth-order maximum will remain stationary. A sinusoidal phase grating with a peak-to-peak phase delay of 4.8 radians cancels out the zeroth order without losing beam power.^{2, 3} The continuous nature of the phase modulation caused by the sinusoid makes this speckle-reduction method appropriate for implementation by novel microelectromechanical systems (MEMS)-controlled gratings.

Figure 1. Diffraction from a sinusoidal phase grating with a peak-to-peak phase delay of 4.8 radians produces a pattern with a vanishing zeroth order. Rotation of the diffraction pattern onto new areas on the diffuser creates independent speckle patterns.

For the proof-of-concept we used two spatial light modulators (SLMs) in series to implement a sinusoidal grating without coupling between phase and amplitude. Figure 2 shows a schematic of the setup. We passed an expanded beam of wavelength 532nm through the SLMs, which caused the beam to diffract. We then subjected it to Fourier transform, and magnified it. We used a filter to block unwanted maxima before passing the light through a stationary diffuser. The maxima were intentionally unfocused on the diffuser to obtain a more uniform light distribution. Finally, the light was reflected off a screen and imaged onto a CCD.

Figure 2. A sketch of the speckle contrast measurement setup. Ap.: Aperture. Beam exp.: Beam expander. Micr. obj.: Microscope objective. Pol: Polarizer. SLM: Spatial light modulator.

When the diffraction patterns are displayed at N non-overlapping positions on the diffuser, the speckle patterns are uncorrelated and the speckle contrast is given by . To compare the measurements with theory and to investigate the performance of our modulation principle, we present a mathematical model for the speckle contrast of N correlated patterns. We made three assumptions. First, the imaging system is a mapping of intensities from diffuser to screen. Second, diffraction spots have constant amplitude across the diffuser. And finally, diffraction spots have radially dependent phase distributions.

From these assumptions we obtain the formula

Here, J_q² is the relative power of the ±qth order, and A_rq^(p) is the relative overlap area between two positions of the ±qth order, p incremental rotations apart. A full explanation is provided elsewhere.²

Figure 3 shows the speckle contrasts obtained for two measurement series, together with our theoretical model and the contrast from independent speckle patterns. The experimental data follow the trend of the theoretical model quite well. However, measured speckle contrast is higher due to limitations in the setup, especially the modulators. By increasing the number of incremental rotations N, decreasing the spot diameter, or increasing the radii of trajectories shown in Figure 1, we can achieve a lower speckle contrast.

Figure 3. Speckle contrast as a function of the number of averaged images. The dashed line shows the measured contrast, the solid line shows the contrast found by the theoretical model, and the dotted line shows the contrast of the sum of N independent speckle patterns. Triangles and circles correspond to grating periods of 12 and 24 pixels, respectively (with 32μm pixel pitch). px: Pixels.

In summary, to use lasers as the light source in display projectors, the presence of speckle must be reduced. We have proposed a modulation principle based on rotation of a diffraction pattern on a diffuser. The light is diffracted by passing it through a sinusoidal grating with a peak-to-peak phase delay of 4.8 radians, extinguishing the zeroth order without losing overall power. The trend of measurements compares well with our theoretical model. To further reduce speckle contrast with the sinusoidal grating, we plan to investigate incorporation of a transversal shift of the grating or a varying grating period.