Publ. Natl. Astron. Obs. Japan Vol. 11. 1 – 11 (2008) Optical Seeing Measurements with an Optical Telescope on a Radio Antenna Nobuharu U kita, Bungo Ikenoue, and Masao Saito (Received 2007 October 31, Accepted 2008 January 30) Abstract Individual images of a video CCD camera with a 10-cm objective lens recorded for pointing performance tests of a prototype 12-m antenna for the ALMA project have been analyzed to evaluate both antenna tracking accuracy and optical seeing at the NRAO VLA site. Data of star image centroid motion have been compared with readouts of angle encoders and inclinomters on the azimuth axis in the yoke structure of the antenna. Under good tracking conditions, a power spectral density (PSD) of image motion during tracking over about 5 minutes had a Kolmogo rov power index of ?2/3. At frequencies > 4 Hz, the PSD showed a steeper decline due to a finite exposure time of the video camera (1/30 seconds) than ?2/3, which suggests a wind speed of about 3 m s?1 at the level where the main turbulence occurs. At lower frequencies, a flattening of the PSD was observed with a turnover frequency of about 0.05 Hz, which in turn suggests an “outer scale” of about 60 m, a length of large-scale disturbances in Kolmogorov’s model. The image centroid fluctuations observed during all-sky pointing tests showed a dependence on air mass A as A0.5 and were 0.5 to 0.9 arcseconds rms at the zenith. These measurements suggest that observations for 2–3 seconds can determine a star position with a typical error of 0.3 to 0.6 arcseconds. Keywords: optical seeing: radio telescope: pointing 1. Introduction diagnosis (e.g., Mangum, 2000; Ezawa et al., 2004; Ukita et al., 2004, hereafter Paper I; Mangum et al., 2006). Recent For ground-based astronomy, atmospheric seeing is of submillimeter telescopes have achieved high angular resolu- great concern, and numerous works both experimental and tions better than 10 arcseconds at their shortest operational theoretical have been extensively made (e.g., Hardy, 1998; wavelenghts; and hence they are required to have high point- Roddier, 1999; Avila, 2002). Traditionally single aperture ing accuracy better than one arcsecond. However, atmo- telescopes had been used to estimate seeing quality from star spheric turbulence causes temporal movements of star image trails recorded on photographs. But they had suffered from positions, an order of one arcsecond, which seems to make wind shakes and telescope tracking errors. In order to avoid it difficult to measure the antenna pointing/tracking errors these problems, a new technique was developed to measure with a 0.1 arcsecond accuracy. What they have done and the relative motion of the two images formed through two plan to do looks like the classical methods astronomers/engi- small pupils on a common telescope. This technique, differ- neers had tried a half century back. But time has passed; the ential image motion monitor (DIMM), is inherently insensi- understanding of the atmospheric seeing have made much tive to such errors. Recently DIMMs have been widely used progress and the advent of modern antenna drive technology for evaluation of optical seeing for observatory site testings makes it feasible for an antenna mount to track a star and (e.g., Sarazin and Roddier, 1990). to scan the sky with a sub-arcsecond accuracy. Therefore One of key parameters of optical turbulence is the outer an assessment of characteristics of optical seeing over a test scale of refraction index fluctuation obeying Kolmogorov's site is crucial for planning and execution of antenna pointing "two-thirds law" (e.g., Avila, 2002). The flattening of its performance evaluation. We have revisited the data of stel- spectrum below the outer scale is necessary to represent lar images obtained for pointing evaluation tests (Paper I) a finite energy input. While differential methods such as of a prototype 12-m antenna for the Atacama Compact Ar- DIMM are only sensitive to high frequency components, in- ray (ACA) of the Atacama Large Millimeter/submillimeter terferometric and absolute image motion measurements are Array (ALMA) project to address characteristics of optical sensitive to outer-scale effects (e.g., Martin, 1987; Tokovinin, seeing over the NRAO VLA site (34?.1 N, 107?.6 E) in New 2002). Mexico, the United States. Optical pointing telescopes (OPTs) have become stan- In Paper I, we have described the prototype 12-m ACA dard equipment on radio antennae for pointing and tracking antenna and its preliminary test results. Ikenoue et al. (2005, Nobuharu UKITA and other 2 hereafter Paper II) have reported on our OPT system and a design (Mangum, 2000; and Mangum et al., 2006), however detailed evaluation results. In this paper, we focus on charac- the image aquisition system (Paper II) was our own style. teristics of centroid motion of star images. Section 2 briefly Since eigenfrequencies of the antenna in azimuth and eleva- describes our antenna pointing system and OPT system. We tion are about 6 Hz, it is useful to record each video frame show our analyses of both optical seeing at the VLA site and image at 30 Hz to detect tracking errors associated with tracking errors of the prototype antenna. Section 3 discusses these frequencies, if any. The video signal was digitized power spectral density (PSD) of star image motion. Detailed with a frame grabber of 8 bit (National Instruments, Model analyses have revealed a flattening of the PSD with a turn- NI1407), and recorded on a PC (DELL Optiplex GX260) in a over frequency of about 0.05 Hz, which seems to be related bitmap image format of 640 × 480 pixels. The data rate of 0.5 to the outer scale effect. Section 3 also discusses achievable Gbyte per minute is high, which is, however, a piece of cake measurement accuracies under actual seeing conditions. And for a storage device of modern computers. The plate scales we demonstrate that the OPT system on the radio antenna is were 1.16 arcsecond per image pixel in both horizontal and a powerful diagnosis tool to reveal tracking errors such as vertical. A typical star image size (FWHM) was about 2 to 4 stick-slip friction error, tiltmeter output oscillation, and ab- arcseconds. A red filter (R64) was used to make observations normal oscillation of the antenna control servo-loop. during daytime. An effective wavelength was estimated to be 740 nm from response curves of the CCD and the filter. 2. Equipments and Measurements The OPT was installed on the ACA 12-m antenna which was built at the NRAO VLA site at an elevation of 2120 m. 2.1 An Optical Pointing Telescope and an Antenna under Test The antenna site is located near the center of the Plains of San Agustin in New Mexico, a flat highland of a vast extent of about 30 km. The antenna has an alt-azimuth mount (figure The optical pointing telescope was a 10-cm diameter 1). The ALMA specification of "absolute" pointing accuracy refractor with a focal length of 920 mm and a 2X extender for the whole sky is 2.0 arcseconds rss. It also requires offset lens that gives a final focal length of 1840 mm on a peltier pointing accuracy of 0.6 arcseconds rss for 4 degrees for 15 cooled CCD camera (Cohu 4920). The telescope tube and a minutes. The maximum speeds are 6 and 3 degrees s?1 i n support tripod to the central hub of the antenna main reflec- azimuth and elevation, respectively. The maximum accel- tor structure were made of invar to minimize flexure due erations are 24 and 12 degrees s?2 in azimuth and elevation. to thermal deformation. The telescope was of the NRAO The antenna has angle encoders of a 360 deg/25 bit resolu- Figure 1: The ACA prototype 12-m antenna under test. A 10-cm optical pointing telescope (OPT) is located behind a hole indicated. The OPT tube and a support tripod as well as the reflector back-up structure are made of low thermal-expansion material. Optical Seeing Measurements with an Optical Telescope on a Radio Antenna 3 tion and 40 milli-arcseconds (mas) calibration accuracy of December 6 and 7, 2003. CCD images were continuously (Ukita et al., 2001). Two servo-inclinometers (Shinko Denki, recorded for about five minutes. The 30 frames per second Model LSO-C1) were used to detect tilt variation of the azi- (fps) has actually been reduced to 24 fps due to missing muth axis due to thermal deformation of the pedestal mount frames. Command positions and encoder readouts were structure and runout motion of an azimuth bearing, namely also recorded every 48 milli-second. During the runs, the erroneous motion related to imperfect raceway grooves of star were at elevation angles of 65 to 75 degrees. The wind a bearing. It incorporates a pendulum and an actuator coil speeds at 9 m from the ground were about 1 m s?1. Figure with a servo circuit of force-balance closed-loop configura- 2 is a sample of the data recorded from 8h21m to 8h26m of tion. Inclination is proportional to the amount of feed-back. December 7 (UT). The upper panel shows a time history of It has a response frequency of about 1 Hz. It is located on the the star positions in elevation; and the lower panel displays azimuth axis in the yoke structure to avoid the centrifugal elevation servo error which is differences between encoder force of the antenna azimuth rotation. readout and sum of command position and pointing model The OPT is rigidly fastened to the central hub of the correction. The standard deviations of the star positions were main reflector (figure 1). Vibration measurements with ac- 0.6 arcseconds in both azimuth and elevation. Those of the celerometers on both the OPT and the backup structure of servo errors range from 10 to 20 mas in azimuth and from 30 reflector have shown that they oscillate with the same ampli- to 70 mas in elevation. tude and phase in frequencies 4 Hz, the PSD showed a its own near 31 and 45 Hz with an amplitude of 23 mas rms. steep decline which had a power index of ?1.54 ± 0.07 (3?). Since these higher frequency components are smoothed out At lower frequencies, a flattening of the PSD was discern- by a finite frame exposure time of 1/30 seconds, the error ible, except for the lowest two data points (open circles in due to the OPT vibration is significantly reduced to 4 Hz. A straight line with + marks is a PSD of a secular tracking drift error of 0.35 arcseconds per 5 minutes. (b) an average PSD of the servo error. A sharp component in the servo error at 0.9 Hz was seen only in the error in elevation. secular drift of 0.35 arcseconds per 5 minutes (a straight line consisted of 1 to 3 sub-runs of 20 to 25 minutes in which with + marks). The PSD in the lower frequencies < 2 Hz is about 70 stars were measured. Each star, brighter than mv < fitted to a following empirical equation: 3.5 magnitudes, was observed for 1.8 to 3.6 seconds. F (v) = A (v2 + v02)?1/3, Figure 4 shows an example of measurement data towards Polaris on March 20, 2004. Figures 4a and 4b display where A is a constant and v 0 is a turnover frequency. We star trails for 2.7 seconds in azimuth and elevation, respec- have found that the turnover frequency to be 0.047 ± 0.012 (?) tively. Figures 4c and 4d are differences between angle en- Hz. The estimate of uncertainty has been made by using 100 coder readouts and commanded angles corrected for pointing PSD data sets which are generated by randomly adding the model. This quantity includes both servo errors and offset measurement errors mentioned above. values which the control circuit calculates based on data of The PSD of the servo error was much smaller than that the metrology system such as inclinometers. This quantity of the image motion except for a sharp component at 0.9 Hz. is a little bit confusing. But we did not have proper tapping It was seen only in the error in elevation. We have tried to points to monitor offset values in the control circuit. Figures identify the source of this error, but we have failed. 4g and 4h are outputs of inclinometer readout in cross-elevation axis and in elevation axis, respectively. Under a normal 2.3 All-Sky Pointing Measurements operation condition, the inclinometer output is expected to have a nearly constant value for a short period. The figure All-sky pointing measurements were made over nine 4g seems to display such a condition. Therefore we blames nights in 2004 March and one daytime in 2004 June. A to- the servo-loop for a "stop-and-go" behavior seen in figure tal of 14 runs of the measurements (Table 1) were obtained 4c. The sawtooth shape is typical for servo error due to non- along with logging data of command positions and readouts linear friction torque variation at low speed, referred to as of the angle encoders and the servo-inclinometers. Each run "stick-slip", in the azimuth bearing. Optical Seeing Measurements with an Optical Telescope on a Radio Antenna 5 Figure 4: A sample of all-sky pointing measurement data for Polaris on March 20, 2004. (a) Image centroid trail measured with the OPT, (c) servo error, (e) star position fluctuation after subtraction of the servo error in azimuth. (g) Inclinometer readout of cross elevation axis. (b), (d), (e), and (h) in elevation. strongly suggest that the antenna mount itself was stable but the inclinometer for elevation produced a factitious output oscillation excited by a large deceleration just before the antenna reaches to a target star. As a result, the antenna deviated from the target star. Since the inclinometers sit on the azimuth axis, they may not receive unwanted acceleration in azimuth rotation. But the fast motion in elevation pushes the yoke base, and the inclinometer for elevation may receive unwanted acceleratioin. The considerations suggest that differences between the time profiles of figure 4a and 4c and between those of figure 4b and 4d, shown in figure 4e and 4f, seem to be true components of image motion due to atmoFigure 5: Zenith angle dependence of standard deviations of image motion. An arrow indicates a measurement which has shown abnormal oscillation (see Appendix-B) spheric seeing. Figure 5 shows standard deviations of the image motion described in the previous paragraph against air mass. Figures for all 14 runs are shown in Appendix-A. A thin line in- On the other hand, the inclinometer output in elevation dicates a least square fit of them. At the zenith, the standard displayed a large unsteady variation (figure 4h). There is a deviations of image position was 0.51 arcseconds. A power close resemblance between a rectangular pattern of the off- index was 0.47, which is close to the expected value of 0.5. set time histroy (panel d) and an low-pass filter output time Table 1 lists these values thus obtained for the 14 mea- profile expected from the inclination readouts. Also there is surement runs. The fifth column gives the variances at the a close resemblance between the rectangular pattern (figure zenith, the sixth column the power indices, the seventh col- 4 d) and the observed star trail pattern (figure 4b). These umn root mean square of individual variances for each run,