We demonstrate speckle photography using an optically addressed multiple quantum well spatial light modulator. An optical Fourier transform is used to allow real-time displacement measurements.
© 1998 Optical Society of America
Speckle photography is a well known and widely used non-destructive evaluation tool.  Because it is a remote, non contact, whole field technique it has found particular use in metrology. Applications of speckle photography include surface deformation analysis, under mechanical or thermal loading conditions, and determination of in-plane translation and rotation. [2–5] Speckle photography has also been used for three dimensional particle velocimetry measurements.
Laser speckle photography uses coherent light to illuminate the surface of interest. A lens collects the reflected light which is then recorded by a suitable medium, e.g. photographic film or a CCD array. Because the surface is rough, the reflected light will necessarily contain speckle. The size of the speckle is determined by the F number of the imaging system. An applied strain, or in-plane displacement of the surface, causes a shift in the speckle pattern which is proportional to the direction of the local deformation. The whole surface displacement field is determined from a Fourier analysis of a double exposure speckle image.
Early implementation of speckle photography used photographic film to record the double-exposure of the surface speckle. Point wise determination of the displacement field was made by scanning a laser beam through the negative of the double speckle pattern. The direction and magnitude of the local displacement is determined from the orientation and spacing of the Young’s fringes that result from the optical Fourier transform. A substantial increase in speed has been realized by replacing the photographic film with a CCD camera. However, this approach requires a digital Fourier transform, making real time analysis difficult.
To circumvent this problem, optically addressed spatial light modulators can be used to record the speckle pattern. The pattern can then be read out with a coherent beam and optically Fourier transformed. Peterson, et. al. demonstrated speckle photography using the bulk photorefractive material BSO.  While this approach may be faster than digital processing it still requires relatively high laser powers and is limited to speeds of less than 1 KHz due to the insensitivity of these materials to light. Kobayashi et. al. used speckle photography for particle velocimetry using two optically addressed ferroelectric liquid crystal (FLC) modulators and a position sensitive photodetector.  This approach allowed them to measure particle velocities of up to 500 mm/sec. Cunningham et. al. used FLC SLMs to measure particle displacement .
In this paper we discuss the use of an optically addressed multiple quantum well spatial light modulator for speckle photography. Compared to other optically addressed SLM materials, multiple quantum wells offer several advantages. They are about ten thousand times more sensitive to light than bulk photorefractives. Unlike FLC material they exhibit a gray scale response and have a maximum speed of about 1 MHz rather than about 10 KHz.
The multiple quantum well optically addressed spatial light modulator (MQW OASLM) used in the experiment was a reflective p-i-n device described in detail elsewhere.  MQW OASLM’s are essentially artificial photorefractive materials. [10–13] A voltage is applied across the device which changes its absorption through the quantum confined Stark effect. Upon exposure to a write beam this voltage is locally screened by photocarriers. The screening pattern is maintained by trapping layers at both ends of the structure.
MQW OASLM’s integrate the light that falls upon them. As the absorbed fluence increases, the transmission of the device changes. When the absorbed fluence reaches the material’s saturation value, the change in transmission is maximized. The MQW OASLM used in our experiments exhibited a saturation fluence of 0.2 μJ/cm2.
The resolution of these materials is limited by charge diffusion and is typically about 10 μm. The device size used in the current experiments is 8 × 8 mm, resulting in about 800 × 800 resolution elements.
Due to Fabry-Perot interference effects, the contrast ratio (defined as the ratio of the maximum to minimum reflection coefficients of the OASLM) is a function of incident angle and wavelength. In our experiment the maximum contrast ratio was about 10:1. This figure does not directly translate into dynamic range however. The transmission of the OASLM is a continuous function of the writing fluence; hence the dynamic range will depend upon internal noise, surface scatter and non-uniformities in the optical response.
Fig. 1 shows the experimental set-up. Two laser diodes were used, one for writing the pattern on the MQW OASLM and the other for reading it out. The write-beam diode laser operated at a wavelength of 847 nm and illuminated a transmissive diffuser. The diffuser was imaged on to the surface of the MQW OASLM with a magnification of 35. The resulting image displayed a speckle pattern with a mean speckle size in the OASLM plane of 160 μm. The read-beam diode laser operated at a wavelength of 853 nm and illuminated the surface of the MQW OASLM. The MQW OASLM was imaged onto a Kodak 4.2 megapixel camera which has a 9 μm pixel size. In addition, reflected light from the OASLM was optically Fourier transformed using a 25 cm focal length lens and a 300 × 380 μm obscuring filter to block the DC component of the Fourier transform. The FT plane was then imaged at a magnification factor of 0.57, onto a Cohu 8420 camera which was connected to a frame grabber. The resolution of the camera/frame grabber combination was 13.6 μm.
The diffuser was attached to a variable amplitude and frequency shaker driven by a sine wave generator operating at 500 Hz. Faster speeds were not possible due to limitations of the shaker. The MQW OASLM was driven, synchronously with the shaker, in reverse bias by a 500 Hz square wave with an amplitude of 14 volts. The two write-beam pulses each had a duration of 100 μsec and the total intensity of the two write pulses was 95 μW/cm2. They were set in time at the extrema points of the shaker displacement when the quantum well bias voltage was on. The write pulses were used to record the initial and final displaced speckle patterns. A read pulse followed immediately after the second write pulse. The fluence of the read pulse was kept well below (<20%) that of the write pulses to avoid erasing the pattern written on the SLM.
The fringe patterns, in the Fourier transform plane, were also recorded as a function of shaker voltage on a SVHS recorder and are shown in the animation of Fig. 2. The dark rectangle in the center of the fringe pattern is an image of the obscuring filter. As the shaker amplitude is increased the spacing between the fringes decreases.
The actual displacement, X, of the diffuser is related to the measured fringe spacing by 
where λR is the wavelength of the read beam, f is the focal length of the transforming lens, MW is the magnification of the write beam illuminated speckle producing surface onto the SLM, MR is the magnification of the read beam between the FT plane and the camera, and S is the measured fringe spacing. Fig. 3 shows a plot of the diffuser displacement calculated from the measured fringe spacing vs. the directly measured displacement. The shaker displacement with voltage was measured directly by imaging a wire, attached to the shaker. Using this calibration, the actual displacement for a particular shaker amplitude was determined. Uncertainty in the read and write beam optics was the principle source of uncertainty. However, within the uncertainty (approximately 10%) it is clear that the two independent measurements of displacement agree very well over the 3–40 μm range indicated.
Speckle photography with optically addressed multiple quantum well SLMs can offer many advantages over conventional techniques. The speed of the approach is determined by the time scale of the displacement and the amount of available light. Moderate power diode lasers should be sufficient to drive the MQW OASLM to rates of tens of KHz. At higher speeds, in fact the MQW OASLM may have additional advantages. These devices exhibit a pattern persistence time of about 5 msec. Thus, for a periodic displacement, the device will integrate over many cycles, further reducing the amount of light necessary. When such persistence is not desirable an optical or electrical erasure pulse can be used. The technique was accurate to about 5%. Sources of inaccuracy included determination of the fringe spacing and small uncertainties in the magnification of the imaging system. Due to resolution limitations of the MQW OASLM some magnification of the speckle is necessary to measure displacements less than about 15 μm. Application of MQW OASLM’s to other forms of non destructive evaluation of materials such as speckle interferometry and double exposure holography also look attractive.
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