Expected Performance From WIYN Tip-Tilt Imaging
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1 Expected Performance From WIYN Tip-Tilt Imaging C. F. Claver 3 September 1997 Overview Image motion studies done at WIYN show that a significant improvement to delivered image quality can be obtained from fast tip-tilt corrections. Over the past two years we have obtained time series image centroid data at rates as high as 2Hz. These data show that typical RMS image motion at WIYN is.1-.2 arcseconds. Furthermore, we discovered that the telescope has strong coherent oscillations in the range of 23-28Hz with a maximum peak amplitude of roughly.1 arcseconds. We have isolated the source of these oscillations to the secondary mirror support, though the cause is still unknown. In other tests we have seen that the correlation of image motion with field angle remains high out to a radius of 3-4 arcminutes. Image Motion from Fast Track Fast Track is a high speed CCD based centroiding camera system. This system uses a small µm pixel frame transfer CCD manufactured by Photometrics Inc. to compute centroids at rates >2Hz. The CCD is thermoelectrically cooled and is capable of.1s exposure times. At WYIN the Fast Track camera head is placed on the imaging port using the standard CCD mount on the FSA, where the plate scale is.276 /pixel. The centroid data are captured and saved using a dedicated PC computer as a text file containing X-Y pairs. Because we are specifically interested in the frequency content of these data we required an accurate measurement of the sampling rate. Fortunately the Fast Track hardware provides an electronic synchronizing pulse which we measure with a high precision frequency counter to better than 1 part in 1,,. From this information we add a relative time stamp to the centroid data. Figure 1 shows a typical time series obtained with the Fast Track system. The raw data are transformed to the telescope elevation and azimuth axes by rotating the x-y coordinates. The angle of rotation is determined by the difference between instrument rotator and telescope elevation angles. The frequency content of the transformed data is estimated using a discrete Fourier transform (DFT). The Fourier transforms show two aspects of frequency content found in the data: coherent frequency power transform to narrow peaks, while random power is indicated by an exponential form decaying towards higher frequency in the Fourier domain. We observe both frequency characteristic in all the Frast Track data and are shown in the power spectrum of Figure 2. It is our interpretation that the coherent frequencies are generated by vibrations or other periodic phenomena from the telescope itself. The random frequency is generated principally from atmospheric sources; either from atmospheric seeing or from wind induced telescope bounce.
2 Elevation (arcseconds) Time (seconds) Azimuth (arcseconds) Time (seconds) Figure 1: Fast Track elevation and azimuth time series data obtained in May Power (arcsec 2 Hz -1 ) Exponential form of random power Coherent power Frequency (Hz) Figure 2: Typical Fourier power spectrum from WIYN Fast Track data. In all cases the Fourier power spectrum of Fast Track data below 15Hz is dominated by random type frequency power. The power spectrum below 1Hz follows Kolomogorov theory for atmospheric turbulence induced image motion reasonably well. Kolomogorov theory predicts the power spectrum to fall off as f 2/ 3 for low frequencies and as f 11/3 for high frequencies. The example spectrum in Figure 2 has a frequency exponent of -.55 for frequencies lower than 1Hz. However for frequencies above 1Hz the Fast Track data do not fall off as quickly as is predected by Kolomogorov turbulence theory. The measured exponent for the example in Figure two above 1hz, excluding the regions dominated by coherent power, is This would suggest that significant additional
3 random power is originating from non-atmospheric seeing sources (e.g. telescope wind shake). High Frequency Oscillation The power spectrum in Figure 2 has several regions showing significant coherent power, the most notable being the peaks grouped near 25Hz. The dispersion about the slower, larger amplitude variations seen in the time series data (Figure 1) are responsible for this power. Figure 3a display the same time series data for the elevation axis as Figure 1 after filtered only to contain power between 2-25Hz. The complex structure of frequencies is evident by the many beats seen in the high frequency time series. Figure 3b shows a single beat that has been isolated in detail as well as showing the dominant oscillations are well sampled. Close examination of the power spectrum between 2-25Hz shows there are at least 8 peaks that contain significant power (see Figure 4). Further more, the broad peak near 22.8Hz is unresolved and may contain as many as five separate frequencies..1 Elevation (arcsec) Time (sec).1 Elevation (arcsec) Time (sec) Figure 3a,b: The same elevation time series data as Figure 1 after being filter to contain only the frequencies between 2-25Hz. Note the strong beat pattern indicating a complex frequency structure. We have examined the high frequency component in many Fast Track data sets that have been taken at different elevations and instrument rotator angles. After rotating the x-y
4 coordinates to elevation-azimuth we find that the position angle of the high frequency oscillations is constant relative to the telescope structure. The position angle is roughly 45 degrees from the elevation-azimuth axes. The discovery of these oscillations has led to significant effort to determine their location in the telescope structure and their cause. Ed Bell along with many others used an accelerometer to probe the telescope structure searching for the oscillations. The conclusion that was made from this survey is that the primary location is at the secondary mirror cell. In addition, Dan Blanco used finite element analysis to show that the natural modes of the secondary support structure are consistent with the high frequency oscillations seen in the Fast Track data. The position angle of the oscillations is also consistent with the 3-point mounting system used to hold the secondary cell to the upper support structure. Power (arcsec 2 Hz -1 ) Frequency (Hz) Figure 4: The power spectrum region from 22to 26Hz from Figure 2. The complex frequency structure seen in Figure 4 and in the filtered time series data is almost certainly caused by coupling of the secondary mirror cell motion to the various components of the telescope s top end. Regrettably, we have not yet been able to determine the source or driving mechanism for these oscillations. Interestingly, during Ed Bell s accelerometer tests we removed power from the entire telescope, from the cone room to everything in dome and on the telescope. Yet, the accelerometer still showed strong movement on the secondary cell at similar frequencies. We can speculate from these data that the diving mechanism is a combination of the extreme stiffness of the secondary support structure and random mechanical noise associated with any real structure. However, until further tests are done no definite conclusions can be made. Tip-Tilt Correction Modeling There are several was we can estimate the image improvement that can be gained from removing fast image motion with tip-tilt correction. One method is the integrated power spectrum versus frequency as shown in Figure 5. This way of estimating improvement is limited by the fact that noise in the Fourier power spectrum is always positive. This will cause a systematically increasing over estimate of the correction with increasing frequency. This effect can clearly be seen in Figure 5. However, the plots in Figure 5 are relatively accurate for lower frequency estimates and for estimating the net effect of the
5 clump of high frequency power between 22-28Hz. We will see in a later section real data taken at WIYN confirm these estimates at low correction frequencies. We will also show that the correction frequency is not the frequency bandwidth of the tip-tilt correction system. Estimated FWHM Improvement (arcseconds) i 35deg. Elevation r g i r g 76deg. Elevation Correction Frequency (Hz) Figure 5: Estimated image improvements from integrated power spectra in three colors, Gunn g, r and I, at near Zenith (76 degrees elevation) and at 35 degrees elevation. The Fast Track CCD system also allow the user to obtain snap shot images. During several Fast Track observing runs at WIYN we obtain a sequence of the images in order to estimate the improvements that can be made from tip-tilt correction. In Figure 6 we show a pair of coadded images from Fast Track with their respective profiles shown underneath. The image on the right are the raw unregistered images, while the left image is after registering the individual Fast Track snap shots. The measured FWHM of the unregistered image is.59 arcseconds. After registration the measured FWHM is.46 arcseconds, a net improvement of.13 arcseconds. There is also a substantial improvement in the peak intensity of approximately 4%.
6 Figure 6: Unregistered (right) and registered (left) Fast Track snapshot images and their corresponding profiles. SBIG Tip-Tilt Results Santa Barbara Instrument Group (SBIG) has been developing a tip-tilt correction module for use by the amateur astronomical community. This module uses their ST7 or ST8 CCD camera head which houses two CCD imagers; a large one for high quality imaging and a smaller one for guiding. The SBIG tip-tilt modul uses the smaller CCD to derive a tip-tilt correction signal that is applied to small right-angle mirror via voice coil actuators. The correction band width of this instrument is limited to approximately 3Hz primarily by the small CCD readout time. However, this is still sufficient for exploring the type of gains possible from tip-tilt correction at WIYN. Through George Jacoby, an agreement with SBIG was made for us to obtain a prototype device for testing at WIYN. Initial testing at WIYN showed encouraging results as seen in Figure 7. The measured FWHM of the star without the SBIG tip-tilt module active (right) is.75 arcseconds. With the tip-tilt correction active there is an improvement of.16 arcseconds to.59 arcseconds FWHM. Figure 7: A star in the field of the globular cluster M3 shown with (left) and without (right) tip-titl correction from the SBIG module.
7 In the most recent tests done 18 September 1997 an updated version of the SBIG tip-tilt module prototype was used at WIYN. The data obtained during this run were used to show that the effective correction rate is down by roughly a factor of 1 from the nominal sampling rate. This effect can be seen by comparing the power spectra of uncorrected and tip-tilt corrected centroid data (see Figure 8). The data shown in Figure 8 were taken at roughly 3Hz sampling. The effective correction rate is where the two power spectra merge or cross, hence no reduction in corrected power, near 3Hz. There are many factors that cause the effective correction frequency to be so much lower than the sampling bandwidth. These include: the fact the image motion is non-periodic, non-zero lag between the time the correction is measured and applied, and physical overshoot of the tip-tilt mirror. In the figure below the increased power at heigher frequencies, above 3-4Hz, is indicative of mirror overshoot..2 Power (arcsec 2 Hz -1 ) Frequency (Hz) Figure 8: Uncorrected (solid) and tip-tilt corrected (dashed) centroid power spectra from the SBIG tip-titl module. During the 18 September 1997 run a WIYN the typical measured improvement was roughly.8-.1 arcseconds FWHM under.6 arcsecond seeing conditions. The time series data used for Figure 8 showed the RMS radial cenroid displacement of.11 arcseconds, while the corrected data showed.4 arcseconds. The difference of.7 arcseconds RMS is consistent with the improvement seen wit the tip-tilt module. Tip-Tilt Coherence Angle In all the tests and measurements discuss thus far we have been limited to either on axis measurements or a fairly small field of view. In order to asses the angle dependence of tip-tilt corrections we examined star trail data like the ones shown below (Figure 9). The
8 data were taken at WIYN with the science imager during scheduled T&E time. The telescope was moved in non-sidereal mode such that each pixel in the trailing direction represents.2 seconds or 5Hz sampling. The technique we used follows Christian and Racine (1985, PASP, 97, 1215), with the difference being their photographic versus our digital data. For each star trail we extracted one dimensional centroids for each time element along with measured FWHM. In order to estimate the correlation of image motion each star trail was synchronized relative to the others using their relative positions measured on a separate short untrailed exposure. Figure 9: Star trail data used for estimating the correlation angle for image motions at WIYN. In each of three images 5 stars trails were extracted netting 1 possible separations. The correlation of the one dimensional centroids are plotted against separation in Figure 1 (filled circles). For each star the linear drift in position was subtracted from the 1-D centroid prior to computing the correlation. As expected the correlation for close separations is near unity. However, we did not expect to find the correlation remain high over the large separations observed. The consistently higher correlation at large separations at WIYN over CFHT combined with the shallow power spectrum slope at frequencies above 1Hz (see above) lend further credence to the existence of a significant non-atmospheric component to WIYN image motion. The solid line in Figure 1 represent the separation from the guide star where no improvement is realized. Above this line improvement is possible, while below this line the images are degraded. The estimated break even radius for WIYN is roughly 3 arcseconds, where the 5% radius is ~2 arcseconds, and the 9% radius is ~45 arcseconds. The break even point is determined where the degradation from the low atmosphere correlation is offset by the perfect correlation of the telescope.
9 1.9 Correlation of Image motion (C ) δ WIYN (This work) CFHT (Chrstian & Racine 1985) Separation (acrsec) Figure 1: The one dimensional correlation of image motion versus separation. The solid horizontal represents a correlation of.77, which is the point of zero improvement. The dotted line is a low order polynomial fit to the WIYN data. Summary We have show using a variety of methods that we can expect to routinely improve the imaging at WIYN by.1-.2 arcseconds with high speed tip-tilt correction. Most of the gain is achieved below a correction frequency of 2Hz, which implies a desired sampling bandwidth of ~2Hz. Even though it is assumed the high frequency coherent oscillation will be removed by some other means, a tip-tilt system with a 2Hz bandwidth would reduce its contribution by an estimated 4-5%. Furthermore, we have shown that we can expect significant image improvements over relatively wide field, which is contrary to usual thinking for tip-tilt on 4M telescope. This is due to the fact there appears to be significant random power from the telescope, which has an infinite coherence angle. However, in estimating what we expect to obtain with a tip-tilt system at WIYN it is irrelevant where the image motion comes from. Thus, over a 5 arcminute diameter field we can expect to see improvements no worse than 6% of the on axis (guide star) signal.
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