Tip-Tilt Wavefront Corrector for Large-Sized CCD Cameras

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1 ISSN , Astronomy Letters, 6, Vol. 3, No. 9, pp c Pleiades Publishing, Inc., 6. Original Russian Text c V.G. Kornilov, S.A. Potanin, A.S. Shugarov, 6, published in Pis ma v Astronomicheskiĭ Zhurnal, 6, Vol. 3, No. 9, pp Tip-Tilt Wavefront Corrector for Large-Sized CCD Cameras V.G.Kornilov, S.A.Potanin *, and A. S. Shugarov Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, Russia Received January 1, 6 Abstract A tip-tilt wavefront (image displacement) corrector has been designed and fabricated to increase the efficiency of direct imaging with large-sized CCD cameras. A plane-parallel glass plate tilting in two mutually perpendicular directions at an angle large enough to compensate for an image displacement of ±16 on a telescope with F mformsthebasisofthedevice.thedeviceallowsupto corrections per second to be made when a 1 m reference star is used. We investigate the effects of aberrations introduced by the plate on the image quality. We present the results of test observations with the corrector performed on the 1.5-m ZTE telescope at the Crimean Station of the Sternberg Astronomical Institute and the 1.5-m AZT- telescope at the Maidanak Observatory, where test images with 1-h exposures that completely realized atmospheric seeing were obtained. PACS numbers : n DOI: 1.113/S X Key words: active and adaptive optics, telescope efficiency, tip-tilt wavefront corrector. INTRODUCTION The efficiency of astronomical observations, be it direct imaging (CCD photometry) or investigation of one selected object (aperture photometry or spectroscopy), directly depends on how great the final image of a pointlike object is. The size of a longexposure image is determined by the combined effect of the size of the instantaneous optical image and the (random or systematic) displacement of its center. The first factor is determined by both the optical quality of the feeding telescope and the power of optical turbulence in the atmosphere. The second factor is also determined by the properties of both the telescope and the atmosphere. Clearly, the effect of atmospheric turbulence is hardest to eliminate this is the task of adaptive optics systems (see, e.g., the classic book by Roddier 1999). Therefore, the importance of the second factor can be determined by comparing it with the atmospheric seeing. Thus, for example, if the image is.5 (FWHM), then its displacements as a whole by.5 will deteriorate noticeably the situation. The trouble is that such displacements often increase with exposure time. Recall the factors that lead to displacements of the images as a whole: turbulence on scales of several meters, random refraction related to readjustment of temperature gradients, nonideality of mirror relieving systems, flexures of a telescope s axes and tube, wind * potanin@sai.msu.ru vibrations of a telescope, and a telescope s driving errors. These factors to be corrected by means of active optics systems were analyzed in detail by Avicola et al. (1998). The frequency of these phenomena is generally below 1 Hz (Glindemann 1997). Low-frequency trends are removed by automatic guiding systems. In a narrow sense, an automatic guide means a device that corrects a telescope s position by an image displacement signal; the correction frequencies are generally much lower than 1 Hz. A device that displaces an image using an additional optical element is usually called a corrector. In active optics systems used on large telescopes, the high-frequency wavefront tilt component is compensated for by secondary mirror tilts (Avicola et al. 1998; Itoh et al. 1998). Several - to -m telescopes without active optics were specially equipped with similar correction systems (Close and McCarthy 199; Glindemann et al. 1997; Probst et al. 1998; Jim et al. ). Such (basically) tip-tilt wavefront correctors are important components of adaptive optics systems that allow the necessary dynamic range of phase corrections on deformable mirrors to be reduced significantly (Guisard et al. ; Le Louarn and Hubin ). The tip-tilt wavefront correction is of particular interest for telescopes with good optics operating at good seeing. In this respect, the AZT- telescope (the optical quality is better than.3)atmount 61

2 6 KORNILOV et al. ρ, μm θ, apple Fig. 1. Main aberrations (in μm) vs. tilt angle (in degrees) for a plane-parallel plate H =7 mm in thickness for the short AZT- focus. 1 Spherical aberration, coma, 3 astigmatism, transverse chromatism. The horizontal dashed lines mark the. 3 and. 5 images. Maidanak (the median seeing is.6 (Ehgamberdiev et al. )) is particularly revealing. In direct imaging, the maximum exposure is limited to 3 5 min (Vakulik et al. 1997; Koptelova et al. 5), mainly because of the telescope s mechanics. The problem of designing a compact and reliable tip-tilt wavefront corrector for this telescope has long been around, but its practical solution began years ago after we designed the necessary electronic and software components. The second reason that prompted this work was the need for a practical testing of the tip-tilt wavefront corrector in terms of works on adaptive astronomical systems. CHOOSING AN OPTICAL LAYOUT OF THE CORRECTOR The initial considerations in designing the tip-tilt wavefront corrector were the following: (1) the linear size of the nonvignetted field of view is no less than 5 6 cm; () the working correction range must provide exposures longer than 1 h; (3) the system in operation should not produce tilts of the focal plane that would lead to a noticeable image defocusing on the detector; () the aberrations produced by the corrector s optics must be significantly smaller than the telescope s 3 1 aberrations and definitely smaller than the best atmospheric seeing at the observing size; (5) the correction errors of the stellar image position must be at least an order of magnitude smaller than the best seeing; (6) the losses of light in the corrector must be minimized; and (7) the device must be compact and should not change fundamentally the back focal length of the telescope, i.e., the location of the receiving equipment. The latter condition needs additional explanations. We consider this device as a working prototype. Naturally, it was necessary to avoid significant costs associated with the fabrication of massive bearing structures. Besides, the device was initially planned to be tested on different telescopes. We analyzed the following optical layouts: (1) correction by one mirror tilting in two directions; () correction by two synchronously tilting mirrors; and (3) correction by a tilting plane-parallel plate. The first layout is simple, produces no additional aberrations, gives no glare, and can have a large working range. It is not surprising that almost all of the designed tip-tilt wavefront correction systems use this idea (see, e.g., Le Louarn and Hubin ; Wang et al. 3; Claver et al. 3). However, to ensure the absence of defocusing at the edge of the field of view, the tilting mirror must be installed far from the focal plane. For example, to ensure a working range of ± with defocusing less than the diffraction depth of field (.1 mm for 35 A) for a telescope with a focal length of F mandafocalratiooff/8, the mirror must be moved to 6 mm. The two-mirror layout can remove the tilt of the focal plane, but a complex mechanical design that would provide a synchronous mirror displacement is required to avoid its displacement. In any case, these mirror layouts require a nonstandard location of the receiving equipment and, in some cases, an additional optical system flipping the focal plane is needed. The layout with a plate proves to be simplest in implementation (Thomas et al. ; Afanasiev 1997; Afanasiev and Moiseev 5). Orthogonal plate tilts can be easily produced with a gimbal suspension. In this case, in contrast to the mirror layouts, the ray path is not violated and the length of the back focal length of the telescope remains almost unchanged. However, a tilted plane-parallel plate in a convergent beam introduces additional aberrations (Michel son 1976). In Fig. 1, the main aberrations calculated for a telescope with F 1 m andf/8 (AZT- at the short focus) and a plate H =7mm

3 TIP-TILT WAVEFRONT CORRECTOR 63 in thickness are plotted against the plate tilt angle using formulas from Turygin (1966). It should be noted that, in contrast to the telescope s aberrations that depend on the distance to the optical axis, the additional aberrations are identical over the field. It follows from the plots in Fig. 1 that (1) the spherical aberration may be ignored, () the transverse chromatism dominates over the coma in broadband observations, and (3) the astigmatism has the strongest effect at tilt angles 15. Also plotted in this figure are the horizontal straight lines for a telescope without any atmosphere (.3) and at best seeing (.5). We see that the effect of aberration on the image becomes decisive under such conditions at tilts larger than 1. At tilts larger than 15, the images of all stars will be elongated toward the tilt by more than twice. Note that the accuracy of positional measurements will depend strongly on the spectral type of a star. For F/16 (the long Cassegrain focus of АЗТ- and the ZTE telescope), the coma and astigmatism decrease by factors of and, respectively, while the transverse chromatism remains the same. Since the linear size (.5) of the image in the focal plane is almost twice as large, large plate tilts are admissible and the working range in angular measure is almost the same. Since all aberrations are directly proportional to the plate thickness, just as is the linear image displacement, the aberrations can be reduced only by a decrease in the working range. The required working range is individual for each telescope; therefore, this question was investigated in advance using data on the operation of the corrector for the Raduga spectrograph (Potanin 5) on the ZTE telescope and direct imaging on the AZT- telescope (Koptelova et al. 5). Of course, the geometry of the device imposes its constraints on the limiting plate tilt, which must correspond to the admissible tilt from the conditions for the aberrations being small. The plate thickness H =7mm, which provides a limiting working range of ±16 for F mand±8 for F 1 m, was chosen from these considerations. GEOMETRY OF THE DEVICE AND ITS IMPLEMENTATION The requirement that the corrector should not change fundamentally the back focal length of the telescope, i.e., the location of the receiving equipment, directly determines the location of the corrector on the telescope. The corrector must be installed on the same flange as the receiving equipment, but on the opposite side. In this case, for example, on the ZTE telescope, the corrector must fit into the central hole of the mirror. This determined the main dimensions of the device O Fig.. Simplified optical and kinematic layout of the tiptilt wavefront corrector. For explanations, see the text. As was said above, the active optical element is plane-parallel plate 1 held in a gimbal suspension (Fig. ). The point of intersection of the gimbal axes coincides with the geometrical center of the plate. The plate can rotate around the Y axis that rests on the movable ring of gimbal suspension. This ring is secured to the X axis that rests on the fixed base of the corrector. The plate diameter is 1 mm. Drive 3 of the X axis is a stepping motor operating in microstep mode (16 microsteps per rotation) connected to the block fixed to the X axis by a strong capron cable. In this case, the reduction coefficient is 7.6 :1, which provides a plate tilt step of 1.8 or an image displacement step of 5 μm at the adopted plate thickness of 7.6 mm. This displacement corresponds to.5 for the focal length of the ZTE telescope (1 5 mm) and.9 at the short focus of the AZT- telescope (11 55 mm). The motor of drive was mounted on the fixed base of the gimbal lest the moment of inertia of the movable parts be increased. Its rotation is transferred to the movable Y axis by an intermediate block coaxial with the X axis and two intermediate blocks. Otherwise, this drive is identical to that of the X axis. For such a kinematic layout, rotation around the X axis will produce an equal rotation around the Y axis (if motor 5 is fixed), while rotation of the motor around the G 6 5 X Y 3

4 6 KORNILOV et al. X Y Z CCD 1 RS Fig. 3. Functional diagram of the control electronics of the tip-tilt wavefront corrector. Y axis will produce only rotation around the Y axis. This is taken into account at the software level of the corrector s control system. Light for the tracking system is taken from an offaxis star by diagonal mirror 6, which is installed in such a way that the beams on astronomical receiver 8 were not vignetted. After its reflection fromthe diagonal mirror, the light falls on detector 7 of the corrector not directly, but through an auxiliary mirror inserted in order that the corrector s array be in the focal plane of the telescope whose position is determined by the science CCD array. To accurately align the focus, the detector of the corrector was mounted on a slider that allows focusing within 15 mm. The linear field of view of the detector is mm; this corresponds to at the short focus of AZT- and.8.8 on the ZTE telescope. On average, one star brighter than 17 m falls within such a field of view, which is clearly not enough for the corrector s operation. Therefore, the entire device can be rotated around the telescope s optical axis (the Z axis) through an angle of 7 by a third stepping motor. This allows the zone of choice of a reference star to be expanded by a factor of 1 (one star brighter than 15 m ). Laboratory studies of the corrector s frequency characteristics showed that the plate resonance oscillation period is 5 ms at a damping time of 1 ms. In principle, such values allow up to ten corrections per second to be made, but the correction efficiency decreases in this case. The measured limiting frequency of the completely worked-out input perturbation is 3 Hz (at a sinusoidal displacement amplitude of an artificial star 1 ). This value does not depend on the detector s sampling rate if the sampling rate exceeds 1 Hz. THE CONTROL SYSTEM (ELECTRONICS) OF THE CORRECTOR The corrector s control system is simple. The corrector s electronics was built as a distributed control and data acquisition system. Its functional diagram is shown in Fig. 3. The main component of the control electronics is a guiding CCD camera that we designed on the basis of an Elektron ISD9AP CCD detector with μm pixels. The camera consists of two parts: a compact CCD detector head 6 mm in diameter and 6 mm in length and controller 1 placed at a distance of about 1.5 m from the corrector. All three drives are controlled by identical controllers of stepping motors 3 that provide a microstep mode of stepping motor operation (eight microsteps per step) and processing of the limit stops. The limit stops define theranges of platetilts aroundthex and Y axes and the rotation of the entire corrector around the Z axis. All controllers are connected to a control computer by a four-wire, galvanically isolated bidirectional serial communication line based on the RS 85 interface. Data are transferred at a rate of Mb/s, which allows readout from the CCD camera up to 5 samples/s. The communication line is connected to a parallel port of the control computer through a special converter. The controller of the CCD camera provides horizontal and vertical binning of an arbitrary number of pixels and reading of a rectangular window with arbitrary sizes. This allows us to minimize the amount of transferred data when the corrector operates in the tracking mode, while providing an optimal relationship between the contribution of readout noise and the accuracy of determining the image center for a reference star. The readout noise of the CCD camera is 19e for 16-bit signal digitization. The guiding window typically contains 5 1 pixels and it takes 5 ms to transmit the image of the guiding window at the chosen data transfer rate. Since it takes 5 1 ms for idle shifts in the case of an unfavorable window location (in the corner opposite to the output amplifier of the CCD detector), the data exchange rate is quite sufficient. Since a full-frame CCD array is used, an exposure time shorter than 5 ms gives rise to a noticeable blurring. Therefore, a readout rate of more than frames per second was not used. Note that the controller modules used in the corrector s control system were designed as part of a general approach to the astronomical experiment at the Sternberg Astronomical Institute and were adapted for the task in question on a microcode level. For example, such systems were used in the MASS

5 TIP-TILT WAVEFRONT CORRECTOR 65 instrument to measure the vertical profile of optical turbulence (Kornilov et al. 3), in the ZTE control system (Kornilov and Shatskii 5), and the like. Similarly, the driver for data transfer over the RS 85 line and most of the software modules were also used previously for control and data acquisition under the Linux operating system. THE MAIN ALGORITHM AND SOFTWARE The tracking system of the corrector is a digital discrete system. The system functions as a cyclic performance of the following operations: (1) obtaining another image of a reference star, () calculating the necessary correction, and (3) transmitting control commands to the plate tilt motors. Basically, its task is reduced to calculating the necessary number of steps (Δs X, Δs Y ) of the motors of the X and Y axes to correct the displacement of the image centroid for a reference star (Δh, Δv) in pixels relative to some initial position found on the detector. Although the exact relationship between the differential displacements (Δx, Δy) in the focal plane and the tilt angles (Δα X, Δα Y ) is not linear, the deviation from the linear law in the working zone does not exceed 1% and the following linear transformation is used in the algorithm: Δy = H n 1 n Δα X, Δx = H n 1 n Δα Y, (1) where H and n and the plate thickness and refractive index, respectively. The relationship between the displacements Δy and Δx and the displacements on the detector s array Δv and Δh depends on the diagonal mirror position and the detector s orientation, but it is also linear. The plate tilt angles (rotations of the gimbal suspension axes) depend linearly on the rotations of the motor axes Δs X and Δs Y. As a result, the resulting direct and inverse relationships in general form appear as (Δs X, Δs Y )=C (Δv, Δh), () (Δv, Δh) =C 1 (Δs X, Δs Y ). All of the quantities involved in the algorithm depend only on the parameters of the corrector itself, not the telescope. The matrix C can be calculated from its geometrical parameters, but determining the matrix C 1 from a calibration procedure with an artificial star is preferred. Specifying a sequence of displacements in motor steps (Δs X, Δs Y ) i and measuring the corresponding positions on the array of the corrector s detector (Δv, Δh) i, we can determine first C 1 and the inverse matrix C. As was mentioned above, the control program runs under Linux. In fact, a limited test version virtually without user interfaces was used in the 5 Y ( ) (b) X 6 6 Fig.. Comparison of the images obtained with the (a) switched-off and (b) switched-on correction system. The ZTE telescope is 1.5 m in diameter and the exposure time is 1 min. Arcseconds are along the X and Y axes. observations. However, the structure of the gtools program implies its interaction with other control programs. Thus, for example, based on the current plate tilt, commands for the telescope s drives can be generated to return the image to the center of the working zone, based on information on a sudden increase in the image size of a reference star, commands can be generated for the astronomical CCD camera on its temporary shutting to select the best images, the detector of the corrector can also serve as an exposure meter in flat-field imaging, etc. OBSERVATIONS In the summer of 5, we performed test observations with the ZTE telescope at the Crimean Station of the Sternberg Astronomical Institute. The astronomical receiver was a multicolor photometer with a VersArray-13 CCD camera with a linear 6 7-mm field. Since the corrector could not yet rotate around the Z axis in this period, there were certain difficulties in choosing reference stars when studying program objects. In order that a suitable star fall on the detector of the corrector, the program object generally had to be displaced from the field center. Nevertheless, we obtained a number of CCD images that led us to conclude that the corrector was operable. Recall that the ZTE telescope without any image stabilization system is totally unsuitable for direct imaging with exposures longer than 1 min (Potanin 5). The corrector made it possible to take exposures as long as min. Figure shows portions of the images of the same region with the switched-on and switched-off correction system at an exposure time of 1 min. The FWHMs of the stellar profile

6 66 KORNILOV et al. ( ) (b) I, ADU I, ADU Dec. R.A. Dec. R.A. Fig. 5. Comparison of the stellar profiles obtained with the (a) switched-off and (b) switched-on correction system on the AZT- telescope with an exposure time of 1 h. Dec. and R.A., in arcseconds, are along the axes. in the images with the switched-off and switchedon correction system are.5 and 1., respectively. Our observations showed that to reliably compensate for the wavefront errors at frequencies up to.5 Hz ( corrections per second), the reference star must be brighter than 15 m, which is 1 ṃ 5 worse than the estimated value. This is because the array of the photometer was located far from the estimated focal plane and the star could not be focused on the detector of the corrector. The image of the reference star was >5. This deteriorated appreciably the signal-tonoise ratio, although 8 8 binning was used. In September 5, the corrector was mounted at the short focus (F/8) of the 1.5-m AZT- telescope at the Maidanak Observatory. The astronomical receiver was a standard 8 (3 1 mm) CCD camera. Since the estimated offset of the focal plane on this telescope is fairly large (designed for the standard use of an offset adapter), the corrector was placed inside a specially fabricated drum installed in place of the offset adapter. By these observations, the corrector could rotate around the Z axis and a new control program was prepared. The focal planes of the detector of the corrector and the science CCD camera were closely matched. The images on the detector of the corrector were 1, which allowed stars to 18 m to be used as reference ones at about two corrections per second. Clearly, in this case, no problem with the choice of a reference star arose. The wavefront tilt errors could be compensated for using bright (1 1 m ) stars up to a frequency of 6 Hz ( corrections per second). To investigate the operation of the corrector, we chose four frames of the open cluster NGC 1193 obtained on 9 (the R and V bands) and 3 (the B and V bands) September, 5, the last image was obtained with the switched-off correction system, all with an exposure of 1 h. There are many bright stars (5 5 stars with S/N > ) in these images. For comparison, images of this cluster were obtained on each of these nights with exposure times of 1 and s in the V band. Figure 5 shows the image profiles for the same star (S/N ) constructed for the frame with the (a) switched-off and (b) switched-on correction system. In the case without correction, the image stretched almost by 1 at an angle of 3 to the direction of diurnal motion and, which is even worse, essentially broke up into three parts. Since the seeing on this night was 1., it can immediately be concluded that the limiting exposure time in such a situation is only 3 min. Assuming that this drift is typical of AZT- and knowing the working range of the corrector, we can estimate the limiting exposure time as 3 h. Indeed, the corrector s operation log shows that the drift ranged from 6 to 8 for the remaining hour exposure times. The mean value of a single correction

7 TIP-TILT WAVEFRONT CORRECTOR 67 was 1.5 motor microsteps or.13 for three corrections per second. Analysis of the images with a working corrector showed that (1) the image sizes do not depend on position in the frame and range from.9 to 1.1 in different frames and () the stellar images are almost circular (the elongation ranges from. to.6). If the image elongation is assumed to be the result of chromatism introduced by the plate, then the upper limit for it is.3. This is clearly an overestimate, since the image elongation in the frames with exposure times of 1 and a is also.5, although the plate was not tilted. Thecorrector splateservesasasourceofadditional glare. The linear size of the main (rereflection from the plate surface) glare is 5 mm and. of the light from the glare-producing star goes into it. However, more intense glare emerges in the array filter gap in the astronomical CCD camera. During ourr-band observations, 1% ofthe lightwent into this glare! CONCLUSIONS Our studies of a working mock-up of the tiptilt wavefront corrector have shown that, although its design is simple, it is fairly efficient and allows the low-frequency wavefront distortions introduced by a telescope and, partly, by the atmosphere to be completely compensated for. Studying the flat-field problem remained beyond the scope of this paper, because a distinctive flat field to eliminate the spatial photometric nonuniformity is required for each position angle of the corrector and each tilt of its plate. However, since the plate is located far from the focal plane and since its diameter definitely ensures the absence of vignetting on the science CCD array, we do not expect a big problem here. The main factor that restricts the use of this wavefront tilt correction method is significant transverse chromatism. When a large working range is not needed or when large drifts can be compensated for by the telescope s motion, the plate thickness can be reduced considerably. In this case, its moment of inertia will decrease proportionally together with chromatism and the resonance frequency will increase. The resonance frequency can be increased by using stepping motors with a large stabilizing moment and by increasing the reduction coefficient by a factor of. The latter is also needed for more efficient use at the short focus of the AZT- telescope, since the correction step of.9 is too large at excellent seeing (.5). Published data on the operation of tip-tilt wavefront correctors show that the atmospheric seeing improves noticeably if the limiting frequency of the tracking system of the corrector reaches 5 7 Hz. Consequently, the resonance frequency and the detector sampling rate in the working model of the corrector should be increased by a factor of 3. Although our corrector is primarily designed to work with large-sized CCD cameras, it can also be used successfully with other astronomical instruments, such as a classical photometer, a classical infrared photometer, and a slit spectrograph. ACKNOWLEDGMENTS N. Shatskii and B. Safronov helped us enormously at the first stage of our work. V. Konichek, A. Sergeev, I. Sinel nikov, A. Zheleznyak, and A. Aliev helped us with the test observations. N. Slabkaya and A. Savvin also provided great help in fabricating the optical and mechanical components. We are sincerely grateful to them. REFERENCES 1. Adaptive Optics in Astronomy, Ed. by F. Roddier (Cambridge Univ. Press, Cambridge, 1999).. V. L. Afanas ev and A. V. Moiseev, Pis ma Astron. Zh. 31, 1 (5) [Astron. Lett. 31, 19 (5)]. 3. V. L. Afanas ev, TIP-TILT Hydrogenation System, hq/ lsfvo/ mouser/ manual/ node.html (1997).. K. Avicola, J. A. Watson, B. V. Beeman, et al., in Adaptive Optical System Technologies, Ed. by D. Bonaccini and R. K. Tyson, Proc. SPIE, 3353, 68 (1998). 5. Ch. F. Claver, Ch. Corson, R. R. Gomez, Jr., et al., in Large Ground-based Telescopes, Ed.byJ.Oschmann and L. Stepp, Proc. SPIE 837, 3), p L. M. Close and D. W. McCarthy, Jr., Publ. Astron. Soc. Pac. 16, 77 (199). 7. S. A. Ehgamberdiev, A. K. Baijumanov, S. P. Ilyasov, et al., Astron. Astrophys., Suppl. Ser. 15, 93 (). 8. A. Glindemann, Publ. Astron. Soc. Pac. 19, 68 (1997). 9. A. Glindemann, M. J. McCaughrean, S. Hippler, et al., Publ. Astron. Soc. Pac. 19, 688 (1997). 1. S. Guisard, L. Noethe, and J. Spyromilio, in Optical Design, Materials, Fabrication, and Maintenance, Ed. by Ph. Dierickx, Proc. SPIE 3, 15 (). 11. N. Itoh, Y. Horiuti, K. Asari, et al., Advanced Technology Optical/IR Telescopes, Ed.byL.M.Stepp, Proc. SPIE 335, 85 (1998). 1. K. Jim, A. Pickles, T. Hubert Yamada, et al., Publ. Astron. Soc. Pac. 11, 716 (). 13. E. Koptelova, E. Shimanovskaya, B. Artamonov, et al., Mon. Not. R. Astron. Soc. 356, 33 (5).

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