This paper presents a review of several applications of electrically addressed programmable spatial light modulators (PSLM’s), with emphasis on systems that use the twisted nematic liquid crystal television (LCTV). The complex operating characteristics of these devices are discussed, some methods used to measure their amplitude and phase response functions are described, and several examples of PSLM-based systems are presented. The systems are grouped into two basic categories: (1) optical correlation systems that use the PSLM’s as input and "matched filter" transducers and (2) wavefront manipulating systems that use the PSLM’s to implement other types of programmable pupil functions (other than "matched filters") in order to change the shape and/or direction of propagation of optical wave fields. Systems described include Fourier plane correlator-based target cuing and object recognition systems, joint transform correlator-based tracking and flow imaging systems, systems that scan, align, collimate, or focus a light beam, Fresnel lens systems, aberration generators, wavefront sensors, wavefront correcting systems, and a closed loop adaptive optics system.

1. Introduction

Programmable spatial light modulators (PSLM’s) are two-dimensional electrically addressable devices that function as reusable transparencies on which spatially varying amplitude or phase patterns can be written electronically, often with an output signal from a computer. In practice, there is cross coupling between the amplitude and phase modulation of such devices so that the modulation is really complex, although it is possible to operate them in a phase-mostly or amplitude-mostly mode [1].

PSLM’s come in many varieties such as magneto-optic devices (MOD’s) [2], deformable mirror devices (DMD’s) [3], and liquid crystal displays (LCD’s). Some PSLM’s such as the MOD can only be operated as binary or ternary (two-state or three-state) devices [4], while others such as the LCD can be continuously modulated to produce a large number of gray levels or phase levels. Since the LCD can operate in a binary, ternary, or continuous mode, this paper discusses the use of the LCD in all of these operating modes. There are many types of LCD [5], but only one is discussed in this paper, the nematic LCD, and all of the examples presented make use of a twisted nematic LCD that is driven directly with a standard NTSC video signal and hence is called the twisted nematic liquid crystal television (LCTV). The LCTV runs at the standard TV rate of thirty frames per second; the frame rate is limited by the properties of the nematic liquid crystal material. Another type of LCD, the ferroelectric LCD, can operate at frame rates exceeding ten kilohertz [6], fast enough to allow real-time implementation of any of the applications considered herein.

Section 2 presents the properties of a twisted nematic LCTV and methods used to measure those properties. Sections 3 and 4 contain descriptions of two types of PSLM applications: those based on optical correlation (Section 3) and those based on wavefront manipulation (Section 4). Section 5 presents a final summary.

2. The Twisted Nematic LCTV

 Basic Physical Properties of the Nematic Liquid Crystal

Nematic liquid crystals are dielectric anisotropic liquids which exhibit a low temperature phase with elongated molecules aligned in one direction with position disorder. This orientation order gives nematic liquid crystals the optical properties of a uniaxial crystal. Light propagating through such a liquid with its polarization parallel to the molecular direction encounters an extraordinary refractive index, but if its polarization is perpendicular to the molecular direction, it encounters a different refractive index called the ordinary index. The direction of the molecules is called the director of the liquid crystals and is the direction of the optical axis. The direction of the director is arbitrary in space. In practice it is imposed by forces such as the guiding effect of the walls of the container. The positive and negative direction of the director are indistinguishable.

Due to their unusual optical properties, nematic liquid crystals can be used to make variable, controllable refractive index devices. Such a device is made by filling the gap between two parallel glass plates with the liquid crystal material. The two glass plates are coated on the inside with transparent electrodes so that the device can be driven electrically. The inner surfaces of the liquid crystal cell are rubbed with a certain orientation so that the molecules align themselves with the surface microgrooves and parallel to each other. When an electric field of sufficient strength is applied to the electrodes of the liquid crystal device, the molecules away from the surfaces tend to realign in the direction of the applied field. If the applied field is in a normal direction to the surfaces of the device, the molecules away from the surfaces tend to tilt away from the initial orientation. This tilt angle of the molecules depends on the strength of the applied field and the distance of the molecules from the surface. Since the angle is tilted away from the surface it is called the tilt angle as illustrated in Fig. 1. When no field is applied, the equilibrium organization of the molecules is parallel to the surfaces of the cell, shown in Fig. 1(a). When an electric field above a certain strength (critical field) is applied, the molecules start to tilt away from the surface as shown in Fig. 1(b). When the applied field becomes strong enough (usually several times stronger than the critical field) all molecules tilt to 90°, that is, normal to the surfaces of the LCTV, except those next to the surfaces, as shown in Fig. 1(c) [7,8].

Twisted Nematic Liquid Crystals

The most common type of electrically addressable liquid crystal device is the liquid crystal television (LCTV) in which one of the two conducting transparent electrodes is coated in the form of a pixel array so that each of the pixels can be electrically driven individually. The twisted nematic LCTV is a LCTV in which the two rubbed orientations of the two inner surfaces are at different angles. The angular separation (twist angle) causes the orientations of the liquid crystal molecules to change continuously between the two plates. If a light beam propagates through such a device, the polarization of the beam will follow the direction of the director so that the device acts as a polarization rotator (see Fig. 2) [5]. Because the effective polarization rotation angle varies with the driving electric field, amplitude control of the light beam can be obtained by inserting the twisted nematic LCTV between two polarizers. In Fig. 2, the twisted angle of the LCTV is 90°, and the polarizer and analyzer are oriented perpendicular to each other. If no electrical field is applied to the LCTV, the maximum output light beam

is obtained. If an electric field is applied to the LCTV, the molecules tilt and the effective rotation angle varies so that the amplitude of the output light varies as well. If the applied field is strong enough, the molecules will all tilt to 90° (aligned with the electric field), and the input light will not rotate so that there is no output light because the polarization of the analyzer is perpendicular to the input light. Thus the amplitude of the output light beam can be controlled by the driving voltage. Note that the polarization rotation and the resulting amplitude modulation occur for incoming light polarized either parallel (as shown in Fig. 2) or orthogonal to the director of the liquid crystal.

Implementation of Phase-mostly and Amplitude-mostly Modes

For the twisted nematic LCTV illustrated in Fig. 2, when the incoming electric field is parallel to the director, the change of tilt with voltage also changes the refractive index from extraordinary to ordinary as the tilt varies from 0° to 90° , just as it did in the untwisted case shown in Fig. 1; therefore, the phase of the propagating wave is modulated significantly [9]. If the incoming electric field is orthogonal to the director, on the other hand, the propagating wave sees a refractive index that corresponds closely to the ordinary index for all values of tilt so that very little phase modulation results. This property allows the device to be operated in phase-mostly or amplitude-mostly mode by simply orienting the polarization of the incoming electric field parallel or orthogonal to the director, respectively. Thus, phase modulation can be obtained with very little cross-coupled amplitude variation if the incoming electric field is parallel to the director and the modulating drive voltage is small. Of course, the purest phase modulation is achieved by using an untwisted nematic liquid crystal device. Amplitude modulation with very little cross-coupled phase variation can be obtained by making the incoming electric field orthogonal to the director and by applying a slightly larger modulating drive voltage as is done when these devices are used for display applications. The appropriate choice of drive voltage is described in the next section.

Measurement Techniques

The Epson LCTV used in all examples presented in this paper is a twisted nematic LCTV taken from the Epson Crystal Image video projector. The Epson LCTV is made by filling a thin flat space between two conducting transparent electrodes with a nematic liquid crystal with positive dielectric anisotropy. The two electrodes are deposited on parallel glass plates, one of which forms a 320´220 pixel array. The pixel size is 55´60 mm with the pitch (center-to-center pixel spacing) size of 80´90 mm. The total aperture size of the LCTV is about 25´ 20 mm square.

Phase retardation measurements of the Epson LCTV's can be accomplished using interferometric methods. One such method uses a Young’s double slit interferogram [10]. The diagram of the experimental setup is illustrated in Fig. 3. The spatial filter acts as a point source to generate a spherical light wave that is collimated by the lens to produce a plane wave at the polarizer which is aligned parallel to the input director of the LCTV. After the polarizer, a polarized coherent plane wave is incident on the double slit attached to the LCTV. The double slit is made by cutting two slits in an opaque film. The two slits are approximately 0.3 mm wide and 10 mm long, with center to center separation of 0.8 mm. A CCD camera is used to record the interferograms.

In the experiment, if the LCTV is driven at one slit with gray-level zero and at the other slit with various gray-levels which change the refractive index of the LCTV, the optical path from the second slit to the CCD camera will be changed as the driving gray-level changes. This causes the optical path difference from the two slits to the CCD camera to change so that the detected interference fringes shift. There are two methods to measure the phase property from the shifting fringes. The most common method measures the fringe shift to obtain the phase retardation as a function of the driving voltage (in terms of gray-level). Alternatively, the change in irradiance at a fixed position as a function of the driving voltage can be measured using a detector placed at the interference plane, and this information can be used to obtain the phase retardation property of the LCTV [10].

        Figure 4. Measured polarization rotation.                Figure 5. Measured phase retardation.

Figures 4 and 5 contain measured data from an Epson LCTV for an input beam polarized parallel to the director. Figure 4 shows the variation of the effective rotation angle of polarized light passing through the LCTV and Figure 5 shows the change in phase retardation, both as a function of applied voltage or gray level. The phase data of Figure 5 was obtained using the double slit fixed point irradiance method described above and in reference 10, and the rotation angle data was measured directly by rotating the output analyzer of Fig. 2 for each value of applied voltage until the output irradiance was maximized. In Fig. 4, note that when the applied electric field is above the optical threshold (gray level 140 for this device), the effective polarization rotation angle starts to vary significantly with the applied field. However, for gray levels lower than this threshold and larger than the Freedericksz transition threshold [11], the twisted nematic liquid-crystal molecules tend to tilt, giving rise to phase modulation, but the rotation angle stays nearly uniform. At gray-level zero, the bias voltage on the LCTV exceeds the Freedericksz threshold in our experiments so that the phase retardation begins with driving gray-level zero as shown in Figure 5. Using this data, we see that the range of gray levels (voltages) that should be used to obtain phase modulation without significant coupled amplitude variation must lie between levels 0 and 140 for this device. Soutar, et. al., present a much more comprehensive analysis of the complex modulation characteristics of a twisted nematic LCTV [11].

3. Optical Spatial Filtering Systems

 Figure 6 is a schematic of a computer-controlled optical Fourier plane spatial filtering system [12]. In the diagram, SF is a spatial filter used to clean up the laser beam, L1 and L2 are Fourier transform lenses, and P1 and P2 are polarizers. The input and filter transducers can be LCTV’s or other types of PSLM. The system is implemented using a coherent laser beam and Fourier transforming lenses to accomplish the filtering task. The input image is written to a LCTV which acts as a reusable input transparency in the system. The laser beam passes through the input LCTV and is transformed by L1. The filter LCTV is placed at the location of the Fourier transform so that the transformed beam passes through the filter, accomplishing the Fourier plane filtering operation (a point by point multiplication of the Fourier transform by the filter function) at the speed of light. Lens L2 transforms the product to produce the spatial domain convolution of the two functions at the final image plane where a CCD camera is placed to record the resultant pattern The distance z₃₄ between the transducers is set so that the zero order diffraction pattern from the input LCTV just fits within the aperture of the filter LCTV, making it possible to perform a variety of spatial filtering operations. LCTV’s have been used to produce several types of optical spatial filters including gray scale apodized amplitude filters [12], matched binary phase-only filters,

 continuous phase-only filters, and amplitude weighted binary phase-only filters [13]. Inputs are usually binary or continuous amplitude images, but they can also be phase objects.

 Amplitude Spatial Filtering Systems A coherent optical spatial filtering system can be used to locate small objects of interest such as defects in an image using spatial frequency filtering of the Fourier transform of the image. A bandpass filter can be designed to pass the spatial frequencies of objects of a given size and thus extract those objects from a random or structured background, replacing them with bright spots of light whose positions indicate the locations of the objects in the original image. The spatial frequency bandpass simply passes those frequencies which correspond to the expected range of sizes of the objects of interest and blocks all other frequencies. Since the filter is implemented on a PSLM, the filtering is accomplished in real time. Furthermore, objects of different sizes can be located by searching with a bank of different size-selective filters.

This system has been built and used successfully to locate small objects of interest in a large field-of-view gray-scale image using the size-selective spatial filters described above with Hanning apodization to reduce the ringing in the filtered output images [12]. Figure 7(a) is the image of a terrain board simulation of a runway containing several airplanes as seen from a high altitude airborne platform, and Figure 7(b) is the output pattern produced by the optical spatial filtering system. The locations of the three airplanes show up as bright spots in the ouput pattern. Notice that the filter rejects the small white spots on the runway.

 

Correlator Systems

If a matched filter is placed on the filter transducer of Fig. 6, correlation patterns are produced on the CCD. Extensive work has been done with binary phase-only correlation systems [14, 15]. At NMSU, optical and digital processors have been successfully integrated, resulting in a high speed hybrid optical/digital object recognition system The prototype recognition system incorporates several unique features: a miniature coherent optical correlator architecture built using pixelated spatial light modulators; ternary phase-amplitude synthetic discriminant function composite matched filters written at up to 300 filters per second onto a magneto-optic PSLM filter transducer to achieve scale, rotation, and aspect invariant recognition; a LCTV for real-time (up to 30 frames per second) input of gray scale or binary images to the correlator; and a correlation plane filter which statistically analyzes the responses from the composite matched filters arranged in a N-dimensional decision tree to perform efficient and reliable object recognition [16].

Joint transform correlators have also been built and used to track speckle motion in ultrasound images of blood flow and tissue motion [17]. The speckle movement is related to the motion of the blood or tissue; therefore, the system is a true flow-imaging system that measures velocity vectors by correlating sequential images from an ultrasound system. LCTV’s are used at the input and Fourier planes as gray scale image and spatial filter transducers, respectively. Filtering at the Fourier plane dramatically increases the signal to noise ratio at the final correlation plane and improves the system's tracking accuracy.

4. Wavefront Manipulation Systems

Programmable Pupil Functions

Programmable lenses can be implemented by operating the LCTV in amplitude mode, binary phase mode, or continuous phase mode; however, experimental results show that the continuous phase mode provides the best results in terms of both the light efficiency and focus quality. The overall quality of the lens depends on the pixel size of the LCTV; hence, an LCTV with finer pixels can provide smaller focal length lenses with better quality. Virtually any phase function can be implemented on the LCTV such as lenses, lenslet arrays, or aberrated pupil functions, and it can be used to study and demonstrate diffraction theory and aberration theory or to test a diffractive optical element design prior to manufacturing it for a given application [18].

             

Wavefront Measurement and Correction Systems

Figure 10 is a schematic of an adaptive optical system that corrects optical wavefront distortions using a phase-modulated LCTV and a feedback loop, so that the original distorion is then represented by the array of pixel voltages needed to remove the distortion. This technology was developed as a coherent adaptive optics system for wavefront sensing and correction, but it has also been used to measure wavefronts produced by phase objects and optical components [20].

Figure 10. Closed loop adaptive optics system diagram. B1, B2, and B3 are three beam splitters; M1 and M2 are two mirrors; L1 and L2 are two lenses; P is a phase object; S is a spatial filter; CCD₁ and CCD₂ are CCD detectors used to detect the interference pattern and point image, respectively.

In the current system, the LCTV aperture is reduced to a 1 cm square containing the central 128x128 pixels. A phase object P inserted in front of the LCTV distorts the wavefront in the bottom path and produces the interference pattern shown in Fig. 11(a) as it interferes with the reference beam that passes through the top path of the interferometer. Using the irradiance data from this interference pattern, the computer calculates the necessary driving function and writes it on the LCTV. As the wavefront is corrected, the fringes are erased leaving a single bright fringe as shown in Fig. 11(b). The dark points and lines in Fig. 11(b) for the fringe pattern after correction are due to a slight horizontal spatial misregistration of the LCTV pixels and the computer generated pixels placed on the LCTV to correct the phase errors.. This error is very small and can be corrected using a LCTV with individually addressable pixels in both dimensions. Figure 11(c) and 11(d) show the point image or point spread function produced by focusing the measured wavefront on CCD₂ as shown in Fig. 10. Fig. 11(c) gives the dispersed pattern of the point spread function of the seriously distorted wavefront before correction, and Fig. 11(d) shows the improved point spread function after correction, confirming the effectiveness of the method.

 

 

Fig. 11. Wavefront correction of a phase object: (a) interference fringes of the phase object, (b) interference pattern after correction by driving the LCTV, (c) point spread function of the uncorrected wavefront of (a), and (d) point spread function of the corrected wavefront.

 5, Summary

Several applications of PSLM’s have been presented in order to demonstrate the versatility of this type of two dimensional modulator. The conclusion to be drawn is that PSLM’s, and in particular LCTV’s, are extremely useful devices that can be used as either amplitude or phase modulators for signal processing, wavefront sensing, wavefront correction, wavefront manipulation and many other applications in imaging and nonimaging optical systems. Perhaps of most interest and future benefit are those techniques that make use of the real-time programmability of the PSLM to produce dynamically adaptive optical systems.

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