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We describe a compact adaptive optical system using a spatial light modulator (SLM) as a single element to both measure and compensate optical aberrations. We used a low-cost, off-the-shelf twisted nematic liquid-crystal display (TNLCD) optimally configured to achieve maximum phase modulation with near constant transmittance. The TNLCD acts both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensation element. This adaptive setup is easy to implement and offers great versatility.
©2007 Optical Society of America
1. Introduction
Adaptive systems have been successfully demonstrated in the last decades as efficient tools for compensating time-varying aberrations of optical fields [1]. A conventional adaptive optical setup is composed of two basic subsystems, one of which measures the aberration and sends the appropriate control signals to the other one, which compensates it. The measurement subsystem consists on some kind of wavefront sensor, being the Hartmann-Shack the most widely used nowadays [2]. The compensation unit consists basically of a reconfigurable optical element, like a deformable mirror [3] or a liquid crystal spatial light modulator [4].
Liquid crystal spatial light modulators (SLM) offer some interesting features, which make them an interesting option for several applications. Although few years ago the trend was to use specialized devices, which were designed and manufactured for adaptive optics applications [5, 6], there is presently a growing interest in using off-the-shelf, low cost SLM based on twisted nematic liquid crystal displays (TNLCD) like those commonly found in video projectors. The main disadvantages of these TNLCDs are their relatively small phase modulation depth and the need of using relatively narrowband polarized light, which are counterbalanced by their high spatial resolution, easy addressability, direct compatibility with usual hardware and software, low cost and wide availability. Besides, their performance is steadily improving, driven by the research oriented to the optoelectronics consumer market.
These TNLCDs have been used, in combination with polarizers and retarder waveplates, to build SLMs able to generate diffractive microlens arrays to implement Hartmann-Shack wavefront sensors [7,8] as well as to produce or compensate different kinds of optical aberrations [7,9,10]. In this work we combine these two possibilities to build a compact and versatile adaptive optics module using a single SLM acting both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensating element.
2. Basic layout of the adaptive setup
Figure 1 shows the basic block diagram of the adaptive system developed in this work. The core of the system is a SLM located in the main path of the aberrated beam. During the measurement step an array of diffractive microlenses is encoded in the TNLCD, and an image of its focal spots is taken at the CCD with the aid of a beam splitter (BS). The focal spots are detected and labeled using appropriate image processing routines running in a conventional computer (PC), their centroids are calculated and their displacements with respect to a set of … reference positions are measured. The beam aberration is determined from these raw data using a suitable (e.g. least-squares) estimator [11]. This aberration, with opposite sign, is subsequently encoded into the TNLCD replacing the microlens array, starting in this way the compensation step. In case of time-varying aberrations, this loop is repeated as many times as necessary. RO1 and RO2 are two (optional) relay optics modules, useful to project onto the TNLCD the input pupil of the system, and to project the TNLCD onto the exit pupil; besides, they allow for matching the respective pupil sizes, making an optimum use of the available spatial resolution of the TNLCD. During the measurement step the exit beam at B is distorted due to its interaction with the microlens array and this implementation of the adaptive unit provides no useful beam to the optical systems located behind it. However, the measurement time can be kept within very small values using an efficient design of the image acquisition and processing routines. In fact, the microlens array should be displayed only during image acquisition by the CCD. During the image processing time, the TNLCD can be displaying the previous correction phase. In this way, the blind time can be reduced to the integration time of the CCD (in our case only 30ms). Once the aberration of the incoming beam is compensated, no further measurement has to be made until the quality of the output beam is degraded above a user-defined threshold.
3. Experimental results
In our experiments we used a TNLCD Sony Model LCX016AL, with an effective area of 26.6 × 21 mm2 and composed of 832 × 624 pixels (of effective size 26.7 × 21.3 μm2 each) arranged in a square array with center-to-center spacing of 32 μm. Optimum phase modulation was achieved with the help of two linear polarizers (P1, P2) and quarter-wave retarder plates (WP1, WP2) whose detailed configurations are described elsewhere [10, 12–13] (see Fig.2). The TNLCD phase modulation response with a small residual intensity variation was achieved by using the calibration of a TNLCD based on the so-called equivalent retarder-rotator approach [12]. The interpretation of a LC cell action as two successive rotations on the Poincaré sphere allowed to find a configuration for achieving phase-only modulation with a TNLCD based on the generation of equi-azimuth polarization states [13].
Fig. 2. Experimental setup for achieving phase-only modulation of a TNLCD. P: polarizer; QWP: a quarter-wave plate. In the above diagram, the x-axis coincides with the input molecular director of the liquid crystal cell. P1 and P2 are, respectively, the orientation of the polarizer and the analyzer. L1 and L2 are the angles of the slow axis of the quarter-wave plates with respect to x-axis.
As light source we use a green LED (Luxeon Star LXHL-MM1D™) with an emission spectrum centered in 530 nm with 35 nm bandwidth. Since the maximum depth modulation obtained with this device at 530 nm is slightly higher than 3π/2 rad, we used a four-level phase encoding scheme to display the wrapped phases corresponding to the microlens array and to the aberration compensating element. Full details of this procedure, as well as an analysis of its performance and limits can be found in Ref [10].
A demonstrative implementation of this setup is depicted in Fig. 3. Apart from the SLM (composed of P1-WP1-TNLCD-WP2-P2), three “4-f” optical systems are used, the first one (L1-L2,f'=160 mm) to project the input pupil on the TNLCD, the second one (L3-L4,f'=50 mm), in combination with a spatial filter (SF), used to remove the replicas of the wavefront produced by the diffraction grid formed by the square array of pixels of the TNLCD and a third one (L5-L6,f'=50 mm) to relay the image focal plane (IP') of L4 to the exit pupil. The first relay may be removed when the incoming aberrations are small enough as not to vary significantly by propagation across the space between the input pupil and the SLM [14]. On the other hand, the last relay can be eliminated by shortening the system and allowing the spatial filtering module L3-SF-L4 to form its image IP' directly on the exit pupil. A lens L7 is used to image the focal plane of the microlens array encoded in the TNLCD onto a CCD camera in order to measure the aberrations in a classical Hartmann-Shack configuration.
An additional optical path (not shown in Fig. 3) was used in our experiments in order to image onto separate areas of the CCD chip not only the focal plane of the microlens array, but also the image of the source (LED emitting area) given by the aberrated/compensated system, in order to get a simultaneous view of the system operation. The input aberrated beams, A, were produced with the help of photoresist phase plates encoding aberrations of shape and magnitude typical of human eyes [15, 16] and/or introducing increasing amounts of defocus.
Fig. 4. Grayscale representation of the four-level TNLCD patterns: (left) for generating a 9 × 9 diffractive microlens array; (right) for compensating the aberration produced by an artificial eye.
Typical four-level patterns sent to the TNLCD in the measurement and compensating steps are shown in Fig 4. Fig. 4 (left) corresponds to the pattern for generating a 9 × 9 diffractive microlens array with subpupil size 560 μm and focal length 4.2 cm (@ 530 nm) used in our experiments. Fig. 4 (right) corresponds to the pattern for compensating the aberration generated by an artificial eye with a phase plate representative of an eye aberration of average magnitude including high order Zernike terms up to 7th radial order (35 non trivial Zernike aberrations), with relatively strong astigmatic components and with partially corrected defocus.
Figure 5 shows the CCD images obtained at three consecutive slots of time in a typical demonstration run: Fig.5 (left), taken during the measurement step, shows at the left side the microlens array foci, and at the lower right the image of the LED source given by the system, strongly distorted due to the pass of the aberrated beam trough the microlens array; Fig.5 (center) shows an enlarged view of the original aberrated LED image, with the TNLCD in off-state. Finally, Fig. 5 (right) shows the corrected image, after the TNLCD was fed with the aberration (with opposite sign) computed after measurement. The collapsing of the aberrated PSF after compensation can be easily noticed. A low speed video of several aberration-compensation loops can be seen online clicking on Fig. 5 (left). To help visualize the compensation the loop was programmed to follow the steps displayed in the static images of this Figure, in such a way that the system first measures the aberration (LED image strongly distorted by the microlens array), then shows for a few seconds the aberrated LED image with the TNLCD in off state and finally the compensating phase is sent to the TNLCD (the PSF collapses and the LED image gets smaller).
Fig. 5. CCD images obtained at three consecutive time intervals in a typical demonstration run. Video file (4 MB) [Media 1]
The video in Fig. 6 shows the real time performance of the present version of this system under strong and continuous defocus changes. The input wavefront started with +1.56 diopters of defocus and was reduced at a continuous rate of -0.13 D/s (diopters per second). The video displays the same three steps as the previous one (measurement using 61 unvignetted microlenses - aberrated image - compensated image), but now the incoming aberration is variable in time so that the computed phase sent to the SLM in the compensation step does not match exactly the actual aberration at that time. The CCD exposition time was set to 30 msec and the camera sent a video stream at 16 frames per second. Pixels were 2×2 binned resulting in an image size of 315×550 pixels.
Fig. 6. A real time video of the performance of the system when compensating continuously varying amounts of defocus. Video file (1.9 MB) [Media 2]
The timer indicates the elapsed time since the beginning of recording. Note in the video sequence that the compensation allows resolving the spatial structure of the LED emitting surface. The initially undistorted LED image is 7 pixels wide (FWHM) at the imaging camera (pixel size 6.4 μm). This FWHM quickly increases with defocus (e.g. it is 10 pixels for 0.1 D of defocus and 70 pìxels for 1.45 D of defocus). After compensation, the resulting measured width is 7 pixels again.
4 Additional remarks and conclusions
The proposed setup has some limitations common to most pixelated TNLCD-based SLM: (i) it requires the use of polarized light, so that for completely unpolarized input beams a 50% of the power is lost at the first polarizer P1; (ii) the light shall also be relatively narrowband, both for avoiding chromatic dispersion at the TNLCD cells and for allowing a proper functioning of the quarter-wave plates WP1, WP2, although, as it has been shown, it can cope well with a typical LED bandwidth and (iii) the spatial frequency content of the aberration to be efficiently compensated is limited by the Nyquist limit associated to the fundamental spatial frequency of the TNLCD pixel array (in order to allow a proper filtering of the unwanted diffraction orders, avoiding cross-talk). There are two additional power loss factors associated with some low-cost devices as that used in our experiments: the losses due to the relatively small fill factor of the TNLCD cells, and those due to the power going to diffraction orders other than that of interest, due to the use of a four-level phase encoding scheme. The spatial superposition of these diffraction orders with the compensated exit beam may be avoided by spatial filtering if a suitable carrier frequency is introduced on the SLM, at the expense of reducing the spatial bandwidth of the aberrations to be compensated for. The use of the four-level phase encoding is due to the 3π/2 phase modulation depth of our device and may be avoided if full 2π phase modulation cells are used.
Note that since the SLM measures the optical aberrations of the wavefront incident on it, the deleterious effects on the exit beam of the aberrations introduced by the SLM itself and all the optics located behind it must be carefully taken into account. In the experimental results shown in this paper these aberrations have not been compensated for. However this is not a fundamental limitation of this setup, since the static aberration introduced by all these elements may be measured once by conventional methods (e.g. interferometry or wavefront sensing), and the corresponding compensating phase may be encoded as a constant nulling term in the SLM to get rid of it (see e.g. Refs [7, 9, 10]).
No other fundamental factors limit the performance of this device, whose temporal bandwidth is determined in our case by our particular image acquisition and processing routines which can in principle be substantially improved. The main advantages of this setup are its great versatility, low cost, easy addressability and control and, last but not least, its seamless integration with the PC-based hardware and software commonly used in optoelectronics applications. Video projector TNLCDs are nothing else than computer screens in which different “images” are displayed to make the SLM act as a wavefront sampling device (a microlens array) or a wavefront corrector. No special drivers, external power supplies or specific programming are required.
Given the wavelength dependence and the power losses at the SLM, this adaptive setup is not, in its present form, particularly indicated for broad bandwidth or low irradiance applications such as incoherent imaging of faint astronomical sources through the turbulent atmosphere. Whether or not the light efficiency of this device is enough to apply it to near real time compensation of human eye aberrations is still to be determined. It is however quite well suited to be used as an active compensation unit in optical setups where the aberrations (even of highly complex shape and magnitude) are not very fast changing in time.
Acknowledgments
This work has been supported in part by the Spanish Ministerio de Educación y Ciencia, grants FIS2005-05020-C03-02, FIS2004-02404 and European Regional Development Fund, by the agreement between the Universitat Jaume I and the Fundació Caixa Castelló (Bancaixa), grant P1-1B2006-29 and by the Polish Ministerstwo Nauki i Informatyzacji under Contract Number 4 T07D 003 29 1691/T07/2005/29.
References and links
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