Brian Backer, Zoran Ninkov, and William
Rochester Institute of Technology
Chester F. Carlson Center for Imaging Science
54 Lomb Memorial Drive, Rochester, New York
Internet Address: firstname.lastname@example.org
Turbulence is known to be the factor limiting
resolution in long exposure images taken through the earth's
atmosphere. Such degraded images can be described by the classical
Seidel aberrations. The purpose of adaptive optics in imaging is to
remove these aberrations to the maximum extent possible with
corrective optics and a reference object. Full compensation systems
are highly successful at this but are costly and complex. Significant
improvement in image quality can be obtained by removing only the
lowest order aberration of random tilts. These partial adaptive
systems have been used to produce high quality images in the visible
and infrared. For most systems, determining the orientation of the
incoming wavefront has required two separate imagers; one for
determining wavefront perturbations and another for field
integration. This has resulted in a need to split the incoming light
with beamsplitters or choppers. A new method of tracking tilts with
only one focal plane array has been devised. Experiments with a
Charge Injection Device (CID) and tip-tilt mirrors show a system
capable of first order motion correction. Limitations of the overall
system as well as results and analysis from experiments will be
Keywords: adaptive optics, charge injection device
(CID), actuators, control systems.
As astronomers strive to detect fainter sources, larger telescope apertures with diffraction limited performance have been constructed. The high resolution images that should result from the smaller airy diffraction spot are not realized because of the effects of optical turbulence. This is the result of local variations in temperature that create eddies of air varying in density. These density cells create pockets of differing refractive index n that act like lenses. All the small wavefront disturbances created integrate as they pass through the air column in the field of view (FOV). Since some parts of the image have used different optical paths while propagating to the detector plane, the final image has phase variations.1
By making all of the optical paths the same length, the distorted image can be compensated to a nearly diffraction limited image. The most common method for removing the phase variations uses a multiple actuator deformable mirror2 as the corrective element. Because the atmosphere is not static, these corrections must be repeated many times per second over the entire integration period. This rapid atmospheric motion requires constant detection of the wavefront variations for image compensation.
All adaptive optic (AO) systems use light sharing methods to sense wavefront variation and create a correction signal. A common way that this is achieved is through "field sharing"; beamsplitters split the field of view (FOV) into two spectrally identical images of differing intensities.3 Some percentage of the field light is used to obtain the correction signal and the rest accumulates on a focal plane array, usually a CCD. A second method proposes "time sharing".4 Pulsed atmospheric backscatter excited by a laser is deflected by the silver wedged chopper to the correction sensor for some fraction of time, t (dependent on the wedge size) while the rest of the chopper period (t-t) is integrated on the focal plane array. A third technique is "wavelength sharing". The input image is separated into different wavelength bandpasses using dichroic mirrors.5 Wavelengths at 0.65 ±0.05 mm are used for tip-tilt sensing, 0.72 ±0.1 mm wavelengths are diverted to the wavefront sensor, and 0.88 ±0.05 mm wavelengths are used for image capture. Each of these three methods has advantages suited for their particular applications. The major disadvantage for each is the loss of flux from the light sharing in their respective systems. Each technique reduces the image intensity at the integration detector and lead to longer integration times to get the same exposure.
2. PROJECT DESCRIPTION
A new technique for image compensation that uses a
CID instead of a CCD is described here. In this "image sharing"
configuration, the image shifts on the array are detected in a small
subarray that is randomly accessed on the CID, and sent to a three
actuator lead zirconate titanite (PZT) steering mirror. The main
advantage of this configuration is that 100% of the incoming light
goes directly to the CID which performs both the integration and
tip-tilt tracking functions of this correction system.
2.1 Charge Injection Devices
Considerable progress effort has gone into improving the performance of CID arrays that use preamp per row architectures. The advantages of CIDs over CCDs have been well described and include the ability to randomly access any pixel on the array. 6-9
In a CCD array, the charge must be transferred sequentially through adjacent pixels in the same column to a single readout row. From here the charge is transferred at high speed through the row to a readout amplifier. Pixels that are in the readout path of this charge must be readout as well and the signals in these pixels are destroyed in the process. Therefore there is no way to preserve the charge in a CCD pixel during readout. In addition, "bad" or poorly working pixels will adversely affect the transfer path and lead to bad rows and bad array segments. In a CID there is no transport of charge outside of a single pixel. This allows readout of a the pixel without a transfer process and inhibits bad pixels from affecting other pixels nearby.
Figure 1: Physical properties of a CID pixel. The side view (right) shows the slice taken vertically through Poly 1.
Each CID pixel consists of two MOS capacitors created by the intersection of two polysilicon runs over gate oxide as in figure 1. Since the polysilicon runs are orthogonal to each other, each run can be used to control the pixel from the perimeter of the array's sensitive region. Each part of the vertical run lying over the thin oxide is referred to as the "collection pad" and the horizontal run is the "sense pad". The 2.5mm metal strap added to the sense pad blocks some incoming photons, but it improves the RC time constant and reduces readout noise.
The CID readout scheme is shown in figure 2. Photogenerated charge is accumulated when photons create electron-hole pairs in the silicon. Holes that diffuse to the area under the mismatched negative voltages drift to the larger potential well created under the collection polysilicon and are stored there. Readout starts by allowing the sense pad to float and obtaining a "zero level" that is amplified and stored on a capacitor. A positive potential is applied to the collection pad and holes flow into the sense wells. A second "signal" voltage is sensed and amplified. The difference between these two signals is proportional to the number of collected photons.
Holes can be restored to the collection well by applying the negative voltages used during accumulation and collecting of holes continues. This procedure is called non destructive readout (NDRO) and can be repeated numerous times for noise reduction and adaptive exposure. Accumulated charge is removed by injection in destructive readout (DRO). This is accomplished by applying a positive voltage to both pads and destroying the potential wells. The holes are repelled away from the polysilicon runs as the depletion layer is collapsed.
Figure 2: Photon collection and the readout scheme of
a single CID pixel.
2.2 PZT actuators
A piezoelectric actuator is an electro-mechanical device that undergoes a dimensional change when an electric voltage is applied. Materials made of lead zirconate titanite have been developed for their piezoelectric properties and the acronym PZT has been adopted for nearly all actuator ceramics. PZT extension can be modeled by a linear relationship with voltage, however this linear equation does not accurately predict the physical properties of PZT ceramics. For example, PZT ceramic actuators are known to have high hysteresis properties that cause differences in displacement when approaching the same physical position from higher or lower voltages.10 In addition, PZT materials are temperature sensitive and the value of the expansion coefficient, a, is a function of the ambient temperature. PZT materials are generally found in two categories. Hard PZT materials have good linearity and low hysteresis but are limited in extension. Soft PZTs have larger displacements but exhibit more hysteresis and higher deviations from linearity.
In our two inch circular housing, three high voltage
actuators are spaced to form an equilateral triangle. Using three
actuators provides three degrees of freedom: x tilt, y tilt and
focus. The actuators were created by stacking many PZT disks and
connecting them in serial. All three actuators are matched for equal
expansion coefficients to provide similar displacement with
3. INSTRUMENTAL SETUP
The setup of the project can be seen in figure 3. On an optical table, a white light source back illuminates an aluminum pinhole field in the light housing. A 1m focal length lens images the pinholes onto the array with magnification of one. A 33MHz 486 based PC uses a National Instruments (NI) parallel I/O board to interface with the drive electronics (SiCam) supplied and modified by Charge Injection Device Technologies Inc. (CIDTEC) of Liverpool, NY. The CID-38 array has a 512 x 512 pixel format with 28mm pitch and is mounted in a dewar for low temperature operation.
Figure 3: Laboratory schematic of the active optics experiments.
Two PZT controlled mirrors from Burleigh Instruments
are used for image redirection. The deformation mirror is constructed
of soft PZT material (35 arcsec maximum tilt) and is used to create a
2D displacement of the object on the CID array. To counteract this
induced image motion, a correction mirror attempts to move the object
in the opposite direction such that the image remains stable. The
correction mirror is constructed from hard PZT materials (12 arcsec
maximum tilt) and is controlled by feedback through the PC and a NI
digital-to-analog board. This 12-bit board has six channels of
output, three of which are configured for unipolar output between 0V
and 10V. This limits the sensitivity of each D/A channel to 2.44mV.
These voltages are then amplified 100x by a three channel high
voltage amplifier needed to operate the PZTs in the required voltage
Figure 4: The CID active optics readout scheme. The tracking subarray determines image motion while the integration region continuously collects photons.
In order to obtain the tracking signal there must be
a dedicated detector capable of rapid readout as described above. A
CID can be can act both as this tracking detector and the integrating
detector due to the random access capability of the array. To obtain
the correction signal, a small subarray is defined in software
(figure 4) for destructive readout. A tracking object in the subarray
is used to determine the image motion at the focal plane. During this
time, the rest of the array integrates photons until the shutter is
closed. The "center" of the tracking object can be determined three
ways that include using the coordinates of the maximum pixel value,
using the center of mass of the entire subarray, or only using an
unweighted center of mass around the maximum pixel value of the
object. We chose the latter techniques for accuracy and speed.
The steps involved in an extended integration using the CID are described as follows. After the mirror has been calibrated and centered, the starting point coordinates of the tracking object (x_start and y_start) in the subarray are obtained. The subarray is injected to clear built up charge and a new set of image coordinates (x_shift and y_shift) are determined. A correction signal is determined through matrix multiplication and the correction voltages sent to the PZTs. The subarray is again cleared and another short integration is used to get the next set of coordinates. The feedback loop continues until the extended integration is complete and the shutter closed.
Calibration of the correction mirror is done through interactive testing. Each of the actuators are independent and thus calibration of each actuator can be done individually. After a short PZT warm-up period, all three actuators are moved to their middle points. A stabilized pinhole image is captured in the tracking subarray and an initial centroid is determined. One actuator is then maximized and the new shifted centroid coordinates are determined. The first PZT is returned to the center point and the procedure is repeated for another PZT. With all three PZTs finished, there are 4 different centriods. Three x shifts (Dx0, Dx1, Dx2) and three y shifts (Dy0, Dy1, Dy2) are created by subtracting the maximized PZT coordinates from the initial centroid coordinates. Using these six shift parameters and constraining the sum of the applied voltages to a constant focus (z=15) results in the matrix equations below.
The tip-tilt processor calculates the voltages that
need to be applied to the actuators thus moving the tracking object
back to the start point. The linear equations above result in the
calibrated x and y values for specific voltage inputs. We want to
invert this procedure to obtain the voltages for a known spatial
displacement. This is done by inverting the matrix in software and
storing the values. The new matrix equation then produces a voltage vector
output for any unknown positional vector input.
The accuracy of the centroiding and tip-tilt processor was determined by keeping the deformation mirror fixed; the resultant image then remained motionless on the array. Two hundred frames of a stabilized pinhole were taken with the feedback loop off (correction mirror fixed) and the centroid of the object was determined for each frame. Random deviations in centroiding result from a combination of error in the centroiding algorithm and pixel nonuniformities on the array. A plot of the results from this experiment is seen in figure 5 and the rms noise is found to be soff=0.11 pixels. Although the mean of the centroid position hovers around zero there are extended periods where the centroid position is consistently displaced from zero, specifically between frames 0 and 40. This infers that there was a slow source of object movement on the optical table.
Figure 5: Plot of 200 fixed object centroids with the
feedback loop off
This procedure was repeated with the feedback loop enabled and the results are shown in figure 6. The increase in the rms noise to son=0.15 pixels is expected since the mirror adds a physical pixel displacement in addition to the centroiding noise. Here the low frequency shifts are gone and the mirror has correctly compensated for any slow drifting of the image position at the expense of adding a small amount of noise.
Figure 6: Plot of 193 fixed object centroids with the
feedback loop on. Seven centroid events were real time rejected by
the software as being to close to the edge of the subarray
Figure 7: Plot of induced motion centroids with the feedback loop disengaged (srms=1.74 pixels).
To test the ability of the system to perform real time correction, a moving object was created with the deformation mirror. A 0.3V p-p sine wave was amplified 1000x and applied to one actuator of the deformation mirror. The period was approximately 90 seconds and this created a slow moving tracking object that the feedback system could compensate. This input distortion created a ~6 pixel peak-to-peak sine wave on the array. Two hundred frames of the uncorrected distortion were captured with the feedback loop off (correction mirror fixed) and the centroids plotted in figure 7. The rms signal was found to be 1.74 pixels.
Figure 8: Plot of induced motion centroids with the feedback loop active (srms=0.41). Note that the increase in image stability is 425% over the non-corrected image.
The procedure was repeated with correction by enabling the feedback loop. The system is then setup to perform real time image correction. The plot of these 200 samples is shown in figure 8. Here the rms signal has been reduced to 0.41 pixels, which represents a 425% improvement in image resolution over the uncorrected image.
Figure 9: XY scatter plot of the corrected and uncorrected centroid points with distortion.
Figure 9 shows an xy scatter plot of the resultant centroids from the corrected and uncorrected experiments with added distortion. Here the spread of the different experimental centroids is evident and the correction is seen to be substantial.
The main constraint on the ability of the current system to perform real time correction is the limited bandwidth. Presently the system operates a complete feedback loop in about three seconds. This time is adequate for long period distortions such as those in the experiment or slow random fluctuations but at higher frequencies the correction algorithm is too slow to keep up with the distortions. Current timing estimates per frame are integration time (0.1s), readout of a subarray (30ms per pixel), determining the centroid (0.25s), and driving the D/A board (minimal). The largest amount of time is used to globally inject the array (1.5s). Not shown in the figure are other delays created by the software such as 'if' statements other logical software decisions; these are crudely estimated at around one second.
Figure 10: Feedback diagram showing some of the
timing constraints on the system.
For simulation purposes, three images were created
showing the effects of first order motion on an image. The images in
figure 10 were created with the feedback mirror turned off such that
there was no attempt at real time correction. A 5Hz sine wave was
used to drive one channel of the distortion mirror and the
integration time was adjusted so that the number of periods imaged
was approximately the same as in figures 7 and 8. For image 11(a), no
sine wave was applied to the distortion mirror and the image is the
psf of the optical system. The integration time used was about 1
second giving about five full periods of distortion for (b) and (c).
The peak intensity of the motionless point (a) in figure 10 is about
~9000 counts vs. ~4500 counts in the uncompensated image (b) and
~8000 in the compensated image (c).
Figure 11: Simulated images created (a) motionless, (b) distorted with no compensation, and (c) distorted with compensated by the CID system. The distorting wave used was a 5Hz sine wave and the integration time is about 1 second. The amplitude for the corrected sine wave was determined from the previous experiments where the correction factor was 425%.
5. CONCLUSION AND FUTURE WORK
The current feedback configuration is capable of good image correction but is bandwidth limited. The bandwidth will be greatly increased with a different type of injection. Currently a global injection of all the pixels is being used. This is done by applying a positive potential for around 1.5sec to all pixels in parallel. Another method of clearing pixels called subarray injection can be used. This method uses a quick positive voltage pulse that is applied sequentially to all pixels in the tracking subarray to clear the stored holes. Unfortunately, this procedure does not sufficiently inject the pixel unless the array temperature is low. A dewar capable of cooling the array to liquid nitrogen temperatures (77K or -273C) houses a preamplifier and the array, however the preamp was being modified and cold operation was unavailable at the time of the experiments described here.
At present, the array is warm and dark current build up is large. The CID will be run cold so that the dark current build up in the accumulation region of the array is reduced. This dark current effect is minimal for short integrations times but during extended integrations, it overtakes signal collection in the integration region.
More centroiding possibilities must be explored further. Calculation times for the centroid are substantial when compared to motions caused by the atmosphere. One solution being examined includes using a dedicated DSP card to calculate the centroid and perform other array processing such as flat fields and bias subtraction.
For future use in astronomical applications, a portable tip-tilt correction system will be designed for mounting at the focus of a Cassegrain telescope. This system has been previously envisioned8 and is shown in figure 12. Not shown in the figure are reimaging optics that will reduce the FOV and increase the angular magnification. In addition, a test source for in situ calibration, and additional mounting hardware will also be installed to make on site calibration of the PZT mirror possible.
Figure 12: Portable Active Optics Configuration for
use on a Cassegrain telescope.
This research was supported through an NSF
Engineering Directorate IUCRC grant and a New York Sate CAT grant. We
would like to thank Bob Wentink, Joe Carbone and Steve VanGorden
(CIDTEC) for their assistance with the CID and SiCam electronics.
Thanks also to Roger Easton and Scott Libonate (RIT) for their help
with the system.
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