Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

After the invention of lasers, in the past 50 years progress made in laser-based display technology has been very promising, with commercial products awaiting release to the mass market. Compact laser systems, such as edge-emitting diodes, vertical-cavity surface-emitting lasers, and optically pumped semiconductor lasers, are suitable candidates for laser-based displays. Laser speckle is an important concern, as it degrades image quality. Typically, one or multiple speckle reduction techniques are employed in laser displays to reduce speckle contrast. Likewise, laser safety issues need to be carefully evaluated in designing laser displays under different usage scenarios. Laser beam shaping using refractive and diffractive components is an integral part of laser displays, and the requirements depend on the source specifications, modulation technique, and the scanning method being employed in the display. A variety of laser-based displays have been reported, and many products such as pico projectors and laser televisions are commercially available already.

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Laser-based displays: a review

The spatial coherence of laser sources has limited their application to parallel imaging and projection due to coherent artifacts, such as speckle. In contrast, traditional incoherent light sources, such as thermal sources or light emitting diodes (LEDs), provide relatively low power per independent spatial mode. Here, we present a chip-scale, electrically pumped semiconductor laser based on a novel design, demonstrating high power per mode with much lower spatial coherence than conventional laser sources. The laser resonator was fabricated with a chaotic, D-shaped cavity optimized to achieve highly multimode lasing. Lasing occurs simultaneously and independently in ∼1,000 modes, and hence the total emission exhibits very low spatial coherence. Speckle-free full-field imaging is demonstrated using the chaotic cavity laser as the illumination source. The power per mode of the sample illumination is several orders of magnitude higher than that of a LED or thermal light source. Such a compact, low-cost source, which combines the low spatial coherence of a LED with the high spectral radiance of a laser, could enable a wide range of high-speed, full-field imaging and projection applications.

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Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging

We utilize spatial and angular diversity to achieve speckle reduction in laser illumination. Both free-space and imaging geometry configurations are considered. A fast two-dimensional scanning micromirror is employed to steer the laser beam. A simple experimental setup is built to demonstrate the application of our technique in a two-dimensional laser picture projection. Experimental results show that the speckle contrast factor can be reduced down to 5% within the integration time of the detector.

Laser speckle reduction due to spatial and angular diversity introduced by fast scanning micromirror.

Lasers have enabled scientific and technological progress, owing to their high brightness and high coherence. However, the high spatial coherence of laser illumination is not always desirable, because it can cause adverse artefacts such as speckle noise. To reduce spatial coherence, new laser cavity geometries and alternative feedback mechanisms have been developed. By tailoring the spatial and spectral properties of cavity resonances, the number of lasing modes, the emission profiles and the coherence properties can be controlled. In this Technical Review, we present an overview of such unconventional, complex lasers, with a focus on their spatial coherence properties. Laser coherence control not only provides an efficient means for eliminating coherent artefacts but also enables new applications in imaging and wavefront shaping. High spatial coherence of laser illumination is not always desirable, because it can cause adverse artefacts such as speckle noise. This Technical Review describes unconventional lasers that have inherently low and/or tunable spatial coherence.

Complex lasers with controllable coherence

A Barker binary phase code of maximum length 13 has previously been used for speckle reduction in line-scan laser projectors, and a speckle contrast factor decrease down to 13% has been achieved. In this Letter, Barker-like binary phase codes of lengths longer than 13 are used at an intermediate image plane. It is shown by theoretical calculation that a much better speckle reduction with a speckle contrast factor up to 6% can be achieved by using longer binary phase codes other than the Barker code.

Speckle reduction in line-scan laser projectors using binary phase codes.

Speckle reduction by moving diffuser has been previously studied in display systems with coherent light sources, such as lasers. In this Letter, we propose a motionless diffractive optical element (DOE) for speckle reduction. The DOE was designed based on finite-element method simulations, fabricated using micromachining technology, and characterized for despeckle efficiency. Experiments using a DOE with two gratings have indicated that the speckle was suppressed to 50%, which shows fair agreement with theoretical analysis. With some modification of this DOE, the speckle noise can be reduced to 10% according to the theory.

Speckle reduction using a motionless diffractive optical element

Speckle suppression in projection displays with a laser light source can be achieved by imaging a changing diffuser with random phase cells onto the screen. Theoretical expressions for the speckle contrast in this method have been earlier obtained in the case when different realizations of the phase diffuser produced statistically independent patterns of the light field on the screen. In the present paper, these expressions are generalized in the case when different realizations of the phase diffuser produce partly correlated speckle patterns. The possible structure of a motionless changing diffuser is presented. It includes a dynamic diffractive optical element (DDOE) and a light homogenizer. The DDOE can be based on the electrically controlled spatial light modulator (SLM) with a deformable polymer layer. This type of SLM can handle high light power and, therefore, can be used in projection displays with powerful laser beams.

Speckle suppression in projection displays by using a motionless changing diffuser.

In this paper, a method is proposed to create a pair of one dimensional binary phase modulator matrices 1D-BPMs, which is mathematically equivalent to a single two-dimensional binary phase modulator matrix 2D-BPM based on Sylvester constructed Hadamard matrices. An advantage of 1D-BPM over 2D-BPM is that the number of drive electrodes can be reduced from N2 to 2N for a N×N Hadamard phase matrix, thus simplifying the drive interconnects and drive electronics. 1D-BPM can be based on electro-optical material and hence can be driven electrically, which is an advantage over the 2D-BPM which is usually etched on a glass substrate and actuated mechanically to implement the speckle reduction in laser projectors. We have discussed the algorithm for constructing the pair of dynamic 1D-BPMs to replace the 2D-BPM. Preliminary experiments are performed to demonstrate the validity of our concept.

Vladimir Kartashov

Papers

Laser speckle reduction due to spatial and angular diversity introduced by fast scanning micromirror.

Speckle reduction in line-scan laser projectors using binary phase codes.

Speckle reduction using a motionless diffractive optical element

Speckle suppression in projection displays by using a motionless changing diffuser.

Replacing Two-Dimensional Binary Phase Matrix by a Pair of One-Dimensional Dynamic Phase Matrices for Laser Speckle Reduction