Laser Beam Steering and Tracking using a Liquid Crystal Spatial Light Modulator * Emil Hällstig, & Johan Stigwall, Mikael Lindgren and Lars Sjöqvist Department of Laser Systems, Swedish Defence Research Agency (FOI), PO Box 1165, SE-581 11 Linköping, Sweden ABSTRACT A linear one-dimensional, 1x4096 pixel, zero-twist nematic liquid crystal spatial light modulator (SLM) was evaluated for laser beam steering and tracking applications. The commercially obtained SLM is designed to operate at, λ = 850 nm, allowing more than 2π phase modulation. Due to voltage leakage the phase modulation experienced by the wave front differed from the ideal calculated phase patterns. This cross talk between pixels reduces the diffraction efficiency. Different methods developed to compensate for this effect are presented. The usable steering range of the SLM was extended to ± 2 degrees using improved phase patterns. A simple model was developed to simulate the optical effects of the voltage leakage. Preliminary tracking experiments were carried out in a laboratory set-up using a moving corner cube retro reflector. The beam steering SLM was implemented in a transceiver for free-space optical communication. Initial results using the transceiver up to 180 m range are presented. Keywords: Laser beam steering, SLM, tracking, Fourier optics 1 INTRODUCTION Optical beam steering is commonly accomplished via mechanical systems like mirrors on gimbals. Such systems tend to be large, heavy and complex, so a non-mechanical all-electronic beam steering component would often be preferred. One suggested technique to achieve this is by means of optical phased arrays (OPAs), where a complex phase modulation is applied onto an outgoing wavefront [1]. A saw-tooth shaped phase pattern is readily designed to produce the same effect as a prism i.e., causing a deflection of the beam. By applying more complex patterns the beam can be shaped or split into multiple beams [2]. The ongoing development of phase modulating spatial light modulators (SLMs) increases the interest in this area. Today there exist several types of phase modulating SLMs, such as liquid crystal (LC), multiple quantum wells (MQW) and micro-electromechanical systems (MEMS). By utilizing VLSI technology developed by the electronic circuitry industry it is possible to construct liquid crystal on silicon (LCoS) SLMs [3]. These components have several properties that are required for laser beam steering e.g. a small pixel pitch and high optical efficiency. For applications where high optical transmission is of importance nematic LC is commonly used in configurations permitting pure phase modulation. From an application point of view non-mechanical beam steering and beam shaping are desired features in e.g. freespace optical communication, laser pointing, laser-based imaging and illumination system. Implementation on airborne platforms is of particular interest due to the requirements of low weight and volume and low power consumption. This is particular important for lightweight airborne platforms such as e.g. unmanned aerial vehicles. The OPA technology may offer enhanced flexibility in future laser pointing and tracking system. By combining beam shaping and tracking new capabilities can be obtained, for example, by altering the divergence of the beam. Another challenging feature may be obtained by splitting the beam into sub-beams in order to track several targets simultaneously. For a free-space optical communication system the OPA can be used for beam steering and tracking. Although, present LC SLM components do not fulfill system requirements with respect to achievable frame rates and optical efficiency, studies are required to improve the performance and provide information how to optimize next generation devices. Ultimately the OPA device can integrate both beam pointing and adaptive beam-shaping functions. * Corresponding author. Email: emil@foi.se; phone +46-13 37 8000; fax +46-13 37 8066; Dept. of Laser Systems, Swedish Defence Research Agency, P.O. Box 1165, SE 581 11, Linköping, Sweden. & Currently with: Photonics Laboratory, Chalmers University of Technology, Göteborg, Sweden.
In this study a commercial one-dimensional (1x4096) LC SLM was characterized and evaluated for beam steering purposes. The relation between applied command voltage and resulting phase delay was measured and used to correct the applied patterns in order to get a linear phase delay in the range [0 2π]. It has previously been reported that the steering efficiency of this device is reduced due to cross talk between individual pixels [4]. Due to the large ratio between liquid crystal thickness and pixel width (7:1) the ideal calculated phase patterns cannot be perfectly realized by the device. Losses in high frequency components in the phase patterns limit the diffraction efficiency and thereby the effective steering range of the system. In this study an approach to model this effect is presented and techniques to compensate the applied patterns are discussed. The intention is to implement the LC SLM as a non-mechanical beam steerer in a free-space optical communication link. The limited range of deflection angles of this component makes it well suited for small angle correction and optimization of the transmitted signal. An initial coarse aligning would be necessary but small movements could be compensated for with the SLM. A prototype of a novel transmitter / receiver for free-space optical communication utilizing non-mechanical beam steering was constructed and some preliminary measurements of beam steering at ranges up to 180 m are presented in this paper. 2 THEORY Deflection of a laser beam using an SLM is accomplished by applying a linear phase delay to the device. To limit the thickness of the LC layer, in order reduce the response time, the device is commonly designed for a phase range of [0, 2π]. By using blazed gratings with modulo 2π phase reset the steering range is not limited by the small phase range. The deflection angle α m of the m:th order is given by the grating equation as sin m mλ α = Λ, (1) where λ is the wavelength, is the pixel pitch and Λ is the period of the grating in number of pixels. The theoretical first order diffraction efficiency, η 1, versus deflection for a device limited only by the quantization into pixels is given by [5, 6] η æ 1 ö èλ ø 2 1 = sinc ç. (2) From these two equations it can be concluded that e.g. a three pixels blazed grating with 1.8 µm pixel pitch and λ=850 nm will give a theoretical first order efficiency of 68% and a deflection angle of 9 degrees. PHASE CHARACTERIZATION If the SLM only modulates the vertically polarized component, the horizontal component can be used as an interferometric reference [7]. This method is insensitive to external disturbances such as vibrations and air turbulence since light from the reference and the signal propagates through the same path. By using linearly polarized light rotated an angle 45 o with respect to the optical axis of the LC only one component will be delayed. Inserting an analyzer at -45 o followed by a photo detector the interference between the two polarization states can be measured. If the LC molecules are oriented so that the two states are phase shifted a multiple N times 2π the analyzer produces destructive interference and the photo detector shows a low signal. When the voltage over the LC is increased the phase shift is also altered and the signal from the photo detector increases. At the state corresponding to (N+0.5)2π the two polarization components will give constructive interference. As a complement to this measurement the set-up can be altered so that the polarizers are parallel and at 45 o. This procedure gives the inverse of the former measurement with maximum at N2π and minimum at (N+0.5)2π, respectively. Measurements of the spatial distribution of the phase delay and the corresponding RMS deviation were previously reported in [8]. In the present study care has been taken to decide what command voltage that corresponds to zero phase shift. This is especially important comparing the phase delay on different regions of the SLM and calculating the RMS deviation for different command voltages. It can be tempting to define the phase delay to zero when no voltage is
applied. Here the command voltage giving zero phase delay is defined as the voltage giving minimum intensity with the polarizers in the perpendicular configuration. FRINGING FIELDS AND THEIR COMPENSATION When the pixel spacing becomes smaller than the thickness of the LC layer the electro-optical behavior of the LC will be complicated [9]. A voltage leakage between adjacent pixels "smears out" the desired phase pattern due to unwanted rotation of the LC molecules at the boundaries. These so called fringing fields reduce the negative influence of the pixel structure but limit the diffraction efficiency of high spatial frequency components from the applied phase patterns. In beam steering applications the effects of the voltage step where the phase ramp is reset will be broadened causing a decrease in diffraction efficiency. As the number of such reset regions increase with steering angle the efficiency decreases. Figure 1 Schematic of the studied SLM. It is important to model the effects of the fringing fields in order to predict the performance and construct different compensation schemes to increase the beam steering efficiency. To simulate the effect of voltage leakage it has been assumed that the effect on the phase distribution approximately corresponds to a convolution by a Gaussian kernel. The resulting phase delay ϕ could then be described by ϕ ( x) θ( x) G( x) = (3) where θ is the ideal phase and G is a Gaussian kernel with 1/e width χ defined by 2 x 2 e χ G( x) =. (4) By comparing far field simulations utilizing this model with measured results the agreement for different widths can be investigated. If the maximum phase retardation of the device is more than 2π the voltage associated with high frequency components can be amplified in order to compensate for the fringing fields. The limited voltage range causes the system to be non-linear but there still exists several methods to achieve an amplified pattern. A simple method is to add a fixed compensation at each reset region. Consider a compensation kernel defined by ( ) = sgn ( ) x w I x x e I x I( x) = I0 ( x) max ( ) I ( x) ( ), (5)
where x is the position relative to the step in pixels, w is the 1/e width and I 0 is the amplitude of the kernel. An example of a command voltage pattern compensated by the edge filter is shown in Figure 2a. The edge filter described above adds a compensation kernel at the edges. The reason for using this particular kernel shape was however, not well motivated. A more self-consistent method is to compare the desired phase pattern with the simulated one and iteratively modify the applied voltage. For each pixel, the voltage is increased if the phase is too low and decreased if the phase is too high. If v n is the applied voltage at iteration step n, δ is the desired phase pattern and ϕ is the simulated phase pattern, a simple algorithm would be: ( ) v v p δ ϕ = +, n+ 1 n (6) where p is a proportionality factor. The procedure described above (eq. 6) was used in the simulations of the phase pattern ϕ. In Figure 2b 75 pixels of a pattern compensated by such an iterative filter is shown. a) b) Figure 2 75 pixels of patterns compensated by the edge filter (a - solid) and the iterative filter after 20 iterations with p=11 (b - solid) compared to patterns only compensated by the look-up-table to give 2π linear phase modulation (dashed). TRACKING Tracking using a LC SLM can be realized by using two basic configurations. In both configurations a direction sensitive detector such as a CCD or quad cell can be used to generate the feedback signal but a single detector measuring the intensity can also be used if the beam is micro-scanned. In the first configuration the optical axis of the receiver channel is bore sighted with the outgoing beam, i.e. the light propagates twice via the SLM. The tracking algorithm is constructed to maintain the target in the center of the field of view. A position sensitive detector can detect the movement of the target and the corresponding adjustment of the phase pattern can be applied. A second tracking configuration was realized by using a static field of view of the receiver channel. By careful selection of lenses and detector the field of view can be made to overlap the efficient beam steering range. The position of the target then directly corresponds to a deflection angle and a unique phase pattern. In this case the light only propagates one time through the SLM (as in Figure 4a).
3 EXPERIMENTAL The spatial light modulator (SLM) used in this study was a reflective one-dimensional nematic LC SLM fabricated on a silicon back plane (BNS Inc., USA). The device consists of 4096 electrode strips that are 1 µm wide and approximately 6 mm long. The electrode spacing is 0.8 µm. For measurements of the phase response and steering efficiency a set-up was constructed by lenses, two polarizers, a non-polarizing beam splitter, an aperture and a fiber coupled diode laser. As detector a high dynamic mega pixel CCD from PULNIX was used. A schematic of the experimental setup is presented in Figure 3. Figure 3 Schematic of the setup for measurements of the phase response and diffraction efficiency. FP: fiber port, SLM:spatial light modulator, BE: beam expander, L: lens, CCD: camera, P: polarizer, D: iris To test beam steering, scanning and tracking at longer ranges the components were also mounted on a breadboard together with a Galilean telescope. The telescope gives approximately 5 times expansion of the beam. The beam splitter and the camera were mounted after the SLM so that the camera has a static field of view in which it detects any reflections, see Figure 4. a) b) Figure 4 a) Schematic layout of the beam steering setup. FP: fiber port, SLM:spatial light modulator, BE: beam expander, L: lens, CCD: camera, P: polarizer, D: iris, M:mirror. b) Photograph of the breadboard setup.
4 RESULTS AND DISCUSSION The spatial distribution of the phase response can be measured by analyzing each pixel in the CCD camera separately. If some care is taken to define how different pixels are related the uniformity can be analyzed. In this study the minimum intensity is used as reference. The measured distributions for some command voltages are presented in Figure 5a. In Figure 5b the average phase delay calculated for each command voltage is presented. Each pixel on the SLM can potentially be individually calibrated but in this study only the averaged phase response has been used to correct each pattern. If the lower or higher regions of the voltage range should be used a correction of the nonlinear phase response is necessary. Note that the phase delay decreases with increased voltage as the molecules rotate within the SLM so that the light experiences a lower refractive index at higher voltages. a) b) Figure 5 a) Measured phase distribution across the SLM as a function of position and voltage command. b) Spatially averaged phase response. As expected the uniformity of the phase delay is better for large voltages when the molecular orientation is driven by the applied electrical field and not relies on the internal structures of the SLM in its relaxed state (V=0). This also gives higher RMS deviation in the phase delay for lower voltages, see Figure 6. Note that only the relative phase shift between the polarization components has been measured and this does not give any information of the flatness of the wavefront after reflection at the SLM. To get the static phase distortion related to i.e. the flatness of the dielectric mirror further measurements have to be made.
Figure 6 RMS phase deviation from the average phase delay over the SLM for different command voltages. VALIDATION OF COMPENSATION METHODS The far field intensity distribution can be calculated from the Fourier transform of the complex field distribution at the SLM. By constructing a numerical model of the SLM where each pixel is sampled by several data points the effects of complex defects like fringing fields can be studied. In Figure 7 the measured diffraction efficiency versus deflection angle is compared to the simulated result with a 1/e width of the Gaussian kernel χ=3.5 pixels. It can be concluded that the convolution by a Gaussian kernel mimics the effects of the fringing fields rather accurately. In Figure 7b the theoretical diffraction efficiency given in Eq. 2 is also plotted. It can be concluded that the fringing field has a large impact on the resulting diffraction efficiency. a) b) Figure 7 a) Measurement of first (solid) and zero order (points) diffraction efficiency for different deflection angles theta. b) Simulation of the corresponding diffraction efficiencies as in a) utilizing the phase smoothing model with the 1/e width of the Gaussian kernel χ=3.5 pixels, together with a plot of the theoretical diffraction efficiency (dash-dotted).
The different compensation schemes presented and discussed in section 2 were experimentally tested by measuring the diffraction efficiency versus deflection angle for different cases, see Figure 8. For the iterative filter the 1/e width of the Gaussian kernel is χ = 3.5 pixels. Especially for large angles the first order diffraction efficiency is considerably improved. The leakage into the zero order intensity is strongly suppressed by both compensation methods. This can be of importance when the quality criteria sometimes are the ratio between the steered beam and the second strongest beam. Figure 8 - Measured diffraction efficiency of the first and zero orders without compensation (solid and points) plotted together with the corresponding compensated cases with edge filter (dashed and crosses) and with iterative filter (dotted and circles). TRACKING AND BEAM STEERING A simple tracking experiment was carried out on the optical table using the SLM described above. A small corner cube located on a translation stage was tracked in one dimension using a tracking loop. A CCD camera was mounted so that the SLM steered both the outgoing beam and the field of view of the camera. By using a pixelated device other detectors such as a quadrant detector or a single photo detector could be simulated. Tracking algorithms for these three detectors (CCD, quadrant and photo detector) were implemented using a Labview interface to acquire the images from the camera, calculate the phase patterns and control the SLM. As expected, tracking using the positional information from the CCD performs very well as tracking on the intensity only can handle slow movements relative to the frequency of the feedback loop. It was noted, however, that higher diffraction orders sometimes disturbed the tracking by introducing unwanted reflexes. Initial tests of beam steering at long range were performed using the breadboard set up in Figure 4. In these experiments a red diode laser was used (λ 630 nm) to make the alignment easier. The phase patterns applied to the SLM were scaled to give 2π phase modulation. A CCD camera with a TV-lens was used to capture the intensity distribution on a screen positioned at a distance of 180 m from the transceiver (Figure 9). Each image corresponds to a region of approximately 30x6 cm on the screen. It is suspected that the strong zero order is due to reflections in the SLM cover glass since the device is coated for 850 nm but 630 nm was used in this particular experiment. The image to the right in Figure 9 corresponds to a pattern on the SLM with a periodicity of 82 pixels. This grating should by Eq. 1 give a theoretical translation of 77 cm at 180 m. In Figure 9 the deflection of the beam can be estimated to approximately 15 cm. The reduced deflection is due to the beam expander mounted after the SLM which expands the beam at the expense of a
smaller field of view. Thus, the broadening of the beam from 0.5 cm to 2.5 cm results in decreased deflection angles by a factor 5. Taking this into account the SLM with compensation for the fringing fields would be able steer a 850 nm laser in a range of ±1.25 m at 180 m. Figure 9 Intensity pattern on a screen at 180 m for ten different patterns with 0 to 50 wedges on the SLM. The height of each image is approximately 30 cm. A simple test of the scanning properties of the system was also performed. A corner cube with a diameter of 2 cm was mounted in front of the screen. The retro reflector was translated to an off axis position so that the reciever channel did not detect any reflected light. The SLM was used to non-mechanically scan a ±0.15 m region and the reflection from the corner cube was imaged onto a CCD camera at each position. The beam steering positions were set using the relation between the period of the gratings and associated deflections as previously measured in the far field (Figure 9). The corresponding intensities were calculated by integrating each image. The plot of the relative intensity vs deflection for two different positions of the corner cube, are depicted in Figure 10. Conclusively, the system with SLM and CCD camera was shown to be capable of simple 1D scanning. Figure 10 Reflected intensity when scanning the laser over a small retro reflector positioned 5 cm to the left (solid) and 9 cm to the right of the optical axis. The splitting into two peaks might be due to the poor beam quality produced by the diode laser.
5 CONCLUSIONS The spatial phase properties of a 1D commercial LC SLM were measured and it was concluded that the RMS deviation of the phase delay decreased with increased voltage. The spatially averaged phase response was used to correct the patterns applied to the SLM in order to get a linear 2π phase modulation. The fringing field was assumed to give a phase smoothing corresponding to the convolution with a Gaussian kernel. Comparisons between simulated far field intensities utilizing this model and measured results were in good agreement. Two methods to compensate the effects of the fringing field were examined. 1) An edge filter that amplify the voltage at the reset regions of the phase ramp. 2) An iterative scheme utilizing the convolution with a Gaussian kernel. Both compensation methods showed an improved beam steering performance with an increased first order intensity and considerable suppression of the zero order. The combined improvement of having a stronger first order and reduction of leakage into the zero order increases the usable steering range by more than a factor of two. The system was mounted on a breadboard to demonstrate preliminary beam steering, scanning and tracking capabilities over 180 m range. 6 ACKNOWLEDGEMENT This work was supported by Advanced Instrumentation and Measurements (AIM) graduate school, Uppsala University and the Photonics in Defence Applications program run jointly by the Swedish Defence Research Agency (FOI) and the Defence Materiel Administration (FMV). 7 REFERENCES 1 P.F. McManamon, T.A. Dorschner, D.L. Corkum, L.J. Friedman, D.S. Hobbs, M. Holz, S. Liberman, H.Q. Nquyen, D.P. Resler, R.C. Sharp and E.A. Watson, Optical phased array technology, Proc. IEEE, vol. 84, pp. 268-298, 1996. 2 L. Ge, M. Duelli, R. Cohn, Enumeration of illumination and scanning modes from real-time spatial light modulators, Optics Express 7(12), 403-416 (2000) 3 K. A. Bauchert, S. A. Serati and A. Furman, Advances in liquid crystal spatial light modulators, Proc. SPIE, vol. 4734, pp. 35-43, 2002. 4 J. Stockley, D. Subacius and S. Serati, The influence of the interpixel region in liquid crystal diffrcation gratings, Proc. SPIE, vol. 3635, pp. 127-136, 1999. 5 K. L. Tan, S. T. Warr, I. G. Manolis, T. D. Wilkinson, M. M. Redmond, W. A. Crossland, R. J. Mears, B. Robertson, Dynamic holography for optical interconnections. II. Routing holograms with predictable location and intensity of each diffraction order, J. Opt. Soc. Am. A 18(1), 205-215 (2001) 6 E. Hällstig, L.Sjöqvist and M. Lindgren, Intensity variations using a quantized spatial light modulator for nonmechanical beam steering, Opt. Eng., vol. 42(3), pp. 613-619, (2003) 7 E. Hällstig, L. Sjöqvist and M. Lindgren, Characterization of a liquid crystal spatial light modulator for beam steering, Proc. SPIE, vol. 4632, pp. 187-196, (2002). 8 S. Harris, Characterization and application of a liquid crystal beam steering device, Proc. SPIE 4291-17, (2001) 9 M. Bouvier and T. Scharf, Analysis of nematic-liquid-crystal binary gratings with high spatial frequency, Opt. Eng., vol. 39, pp. 2129-2137, (2000).