July 2001 W. Traub STAR-TRACK PLAN 2001 -------------------- Introduction ------------ The past and current star-acquisition code is slow, and is not tailored for acquiring and maintaining 3 star images from 3 telescopes on a single CCD detector. In June 2001 we typically spent up to 60 minutes trying to acquire a single bright star in all 3 telescopes, which is obviously unacceptable for science observing. Here I suggest an alternative scheme, which should be implementable with hardware currently in place at IOTA, should be totally automatable, and should allow us to spend less that 1 minute total time from initial nominal positioning of the telescopes to final 3-star lockup, for a star of any V-magnitude between about -1 and +11 (the latter for very red stars). The current star-acquistion procedure uses the siderostat to execute a spiral search, after the star has been visually identified on the acquistion TV monitor, and after it has been hand-paddeled into a little box taped on the monitor face, and after the observer has set the appropriate threshhold (adu) from the CCD, above which the star signal must rise before the computer will recognise it as a positive detection. The search is slow for three reasons: slow motion of siderostat, constant motion of star image across detector, causing smearing and dilution of signal; and the need to hand-paddle the star, hand-adjust the star threshhold level based on observing the detector noise level, and hand-select the CCD frame rate based on the expected brightness of the star. Worse, since our new optical arrangement asks for all 3 star images to fall on a single CCD (to decrease the possibility of drifting, and save money on star-tracker hardware), the above steps cannot be run in parallel for all 3 telescopes, but must be run sequentially. All of these impediments can be overcome, as described next. Tip-tilt mirror --------------- The tip-tilt unit is a Physik Instrumente S-340 Tilting Mirror. The spec sheet says the tilting angle is +/- 1 mrad per axis, at 0 to 100 V drive signal. The resolution is 1 micro rad. The resonant frequency is 1400 Hz without a mirror, and measured to be about 600 Hz with a mirror RTV'd in place. The tilt angle converts to +/- 206 arcsec physical mirror tilt, which is +/- 412 arcsec ray displacement after reflection from the mirror. Our units are mounted behind the telescopes, where angles are magnified by a factor of 10, so the corresponding angle on the sky is +/- 41 arcsec, or an 82 arcsec diameter field of view on the sky. We command the unit with a 12-bit D/A converter which has a total range of 4096 steps. The nominal position is centered at (X=2048, Y=2048). Each step on the sky is 82 arcsec/4096 step = 0.020 arcsec/step. CCD detector ------------ The detector pixels are in a 32x32 array, and each close to 1.0 arcsec on a side, so the detector can in principle see a field of view 32x32 arcsec, on the sky. However the long paths and finite diameter of optics at IOTA generally limits our useful field of view to approximately 16x16 arcsec on the sky, and perhaps 20x20 at the most. The rest of the beam is vignetted. When all 32x32 pixels are displayed to the observer, the detector is said to be working in "fine-pixed mode". Siderostat ---------- The siderostat has a pointing error which is typically as large as 50 arcsec, and rarely better than 20 arcsec. We take 40 arcsec as typical. If the typical radial error is 40 arcsec then the "2-sigma" radius is 80 arcsec, and the "3-sigma" radius is 120 arcsec. The 3-sigma diameter is 240 arcsec. From above, the detector field of view is about 16 arcsec diameter. Therefore the area to be searched is about 240/16 = 15 exposure fields in diameter, or about 15^2 = 225 exposure fields total. Search pattern -------------- The range of the tip-tilt mirror is 82 arcsec diameter (actually square), so the number of CCD exposures per diameter is 82/16 = 5, and the number of exposures per square field is 5^2 = 25. To cover more search space on the sky, we need to move the telescope by 82 arcsec in X or Y or both, and repeat the tip-tilt search pattern. If we expect to have to search at 9 such telescope pointings, in a 3x3 pattern, we will cover a sky area of 3x82 = 246 arcsec on a side, which is slightly more than the 3-sigma diameter. The search pattern should be to look first at the nominal pointing direction, at say (X,Y) = (0,0) arcsec, then step to (16,0), then (16,16), (0,16), (-16,16), (-16,0), (-16,-16), (0,-16), and (16,-16), which completes the inner ring of a square-pattern search, and gets us out to a diameter of 3x16 = 48 arcsec The next ring is spaced 16 arcsec farther out, and covers a diameter of 5x16 = 80 arcsec, which is the limit of what we cn do with the tip-tilt mirror alone, for a fixed siderostat angle. Next we move the telescope in a similar pattern, from the (X,Y) = (0,0) arcsec position, to (80,0) arcsec, and repeat the tip-tilt pattern above. Next go to telescope position (80,80), and repeat the tip-tilt pattern. And so on, until the inner ring of telescope offsets is completed, covering the full 240 arcsec diameter field. The star should have been discovered with 99 percent probability by this time. If not, the code should begin to search the second ring of telescope offsets. The observer should have the opportunity to abort any search at any time, and either stay at the aborted position or return to the original starting position. To improve the signal-to-noise ratio, we often use on-chip binning to group together 4x4 fine pixels into one "coarse pixel". The display to the observer is then 8x8 coarse pixels. The reason this gives improved S/N is that the same star photons are detected in either case (over the total 4 arcsec square), however only one read noise is added to the photon noise in the coarse pixel mode, instead of 16 read noise values. The net gain is 16^1/2 = 4, or about 1.5 stellar magnitudes. We use coarse pixels for star-tracking, and probably they should be used for star acquisition too. Tip-tilt search time -------------------- The readout speed of the CCD is independent of the fine- or coarse-pixel mode, and is about 240 frames/sec, or about 4.2 msec/frame. The CCD readout electronics includes an A/D converter, which has a gain of a few electrons/adu. The read noise is a few adu per read. The total range of the digitizer is 4096 adu. If the star is very bright, we adjust the frame rate to be fast, up to 240 frames/sec, so that the star brightness does not exceed the 4096 limit; if the limit is exceeded, the output merely saturates at 4096, and in particular it does not roll over to zero, so the situation is not harmful, but saturation is to be avoided because it is basicly a non-linear response. This occurs for bright stars, about visual magnitude 0 or -1. From experience with the star-tracker, we have some guide as to the expected count rate in adu units. The data here are for fine-pixel mode, but roughly the same values should hold in the coarse-pixel mode. I have normalized the adu level per frame to a frame rate of 100 Hz, i.e., 0.010 sec per integration. I get about 100 adu at V=7, 250 adu at V=6, 500 adu at V=5, 1300 adu at V=4, and 3500 adu at V=3. From memory, a typical noise level is about 20 adu. If the star is very faint, so that its signal is barely above the read noise and photon noise, then we slow down the frame rate, to 10 or sometimes even 5 frames/sec, so each frame integrates for a relatively long time on the star. In the extreme case, we also have to drop the star detection threshhold to be less than 5 or so times the rms noise, in order to keep the star locked up, however it can then easily get lost if a noise spike occurs, and the situation is delicate. This limit occurs for stars of visual magnitude about 11 or 12 and for a red star, such that there are extra photons at the red end of the spectrum where the CCD is most sensitive. Let us assume that the typical star has V = 7 mag. Then in 0.01 sec it will produce about 100 adu in a pixel, where as in tracking the light actually falls on 4 pixels equally, so the total count is 400 adu. Let us assume that the 100 adu is our minimum rate (it could be 4 times larger). Let us also assume that the noise level is 20 adu (from above). Therefore a single exposure is a 5 sigma detection, since star/noise = 100/20 = 5. This is sufficient to be very confident that we really have a star in the field, and no further exposures are needed. At this rate we can cover all 225 exposures in 225x0.01sec = 2.25 sec, assuming zero time to move the tip-tilt mirror or the telescope between exposures. The time to move the tip-tilt mirror can be estimated from the lab data that we took in July 2000 for the S-340 and its drive electronics. Here we drove the mirror with a full-amplitude 100 volt peak-to-peak sine wave, at frequencies ranging from 0 to 400 Hz. We found that the amplitude fell off with frequency, approximately as a Lorentzian, centered at 0 and with a half-width (the 3db point) of 120 Hz. (The resonance occured at 800 Hz.) Thus if the mirror is commanded to move a distance of 82 arcsec from rest, and to come to rest at the end, in a time of 0.5x(1/120)sec = 4.2ms, which is exactly what one-half cycle of a 120 Hz cosine wave is doing, then it will in fact respond sluggishly and only move half the requested distance, which is 41 arcsec on the sky. Scaling to our situation, where each step of the mirror needs to be only 16 arcsec, we see that the mirror might be expected to move tht distance in (4.2ms)x(16/41) = 1.6ms. I think that this analysis is not the corect way to do the calculation, but it is good enough for an estimate of what will happen. The conclusion is that if we send a step command to the mirror to move the standard 16 arcsec width of the CCD detector field, that then the mirror will respond by doing what we ask in a time which is on the order of 2 ms, which is small compared to the nominal exposure time of 10 ms (i.e. 100 Hz). thus the mirror will go to the new field and settle in a time which is short compared to the integration time, and the star will thus not be appreciably smeared by this motion. We can thus step the mirror at the full 100 steps per sec and still expect that the exposure at each step will be almost as perfect as if the mirror had been sitting there all the time, with no smearing or streaking of the image. This is a big advantage. If we want to be very conservative, we can let the mirror sit at each new exposure position for several frames, say 5 frames, and still require only 5x2.25 = 12 sec total exposure time for a 3-sigma detection. Telescope search time --------------------- Now we must add to this the time to step the telescope (siderostat). The distance per telescope move is 80 arcsec in either X or Y or both. The slew rate of the telesope is about 800 arcsec/sec, so the slew requires only about 80/800 = 0.1 sec, at full speed. However the update time on the telescope is currently 1 sec, which probably means that we will need at least 2 sec to start and stop the slew motion, plus 1 sec in between for the motion itself (at less than full speed of course), so the total time to reposition the telescope is probably about 3 sec per move. To cover the full 3-sigma search space we need to look at (240/80)^2 = 9 full tip-tilt fields, which requires 9 telescope moves, and therefore 9x3 = 27 sec of time. The total 3-sigma search time is therefore the integration plus telescope slew time, which is, at most, for a V=7 star, about 12 + 27 = 39 sec. For a fainter star, we should probably simply spend more time per exposure, by a factor of 2.5 per magnitude, so the integration times will expand to 30, 75, 188, and 470 for stars at V of 8, 9, 10, and 11 respectively. So the total 3-sigma time to integrate and slew comes to 57, 102, 215, and 500 sec for V of 8, 9, 10, and 11 respectively. If we can reduce the probable telescope pointing error from the 40 arcsec assumed above, to a target value of 20 arcsec, then the search times will drop by a factor of (20/40)^2 = 1/4, and the above values scale to give total 3-sigma search times of 10, 14, 25, 54, and 125 sec for V of 7, 8, 9, 10, and 11 respectively. This essentially fulfills the initial goal of finding a star within one minute, for nearly all stars of interest. Triple-search strategy ---------------------- The search outlined above is for a single telescope. Since we have 3 telescopes, we need to provide a plan and time estimate for the triple-search. To start, all 3 telescopes should start their searches simultaneously. They all share a single CCD detector, so when a star shows up, all searches should be stopped. Then we decide which telescope has found the star by closing shutter S0 (fix) and S1 (d1) and S2 (d2) in pairs, and if the star remains, then the non-closed beam is the one which has the star. We note the telescope which found the star, and its offset (the total of the tip-tilt plus siderostat offsets, in a coordinate frame of RA and DEC, which will take a little interesting math to figure out), and we send the telescope to that position and center the tip-tilt mirror to its nominal position, and we close off the corresponding shutter. Next we continue the search pattern for the remaining 2 telescopes, picking up where we left off, i.e., not starting a spiral anew but rather continuing the original one. When we get another star detection, we repeat the process for these 2 beams, lock up the next telescope on the star, just as before, and continue the search with the lone remaining telescope. The additional time incurred for the dance of the shutters is probably something like 3 sec per detection, or an additional 6 sec on top of the above times. Finally, after each telescope has found its star, we must check to see that the star has not drifted away. Typically the telescopes have a periodic gear error which makes them mis-point by about 10 arcsec for a 2 sec interval, about once every 20 sec or so (all from memory, and not very accurate). Thus the star may need to be searched for one final time, but now only over a field of diameter roughly 20 arcsec, which can easily be done by a new cycle of tip-tilt exposures, and should take less than 1 sec each, for an additional 3 sec for this final step. As each is re-found, its shutter should close, so as not to confuse the search for the remaining stars. After all three stars are re-found, their shutters should open one by one, and the star placed in the center of its proper quadrant on the CCD detector. Perhaps the safest method is to place T1 in Q1, T2 in Q2, and T3 in Q3, where Q1 is (say) upper left, Q2 upper right, and Q3 lower left. This leaves one free quadrant, Q4, which should probably be measured along with the others, for a continuing update on the background level and noise fluctuations. This should add about 3 sec for all 3 telescopes. Triple-search total time ------------------------ The total time for the search, for all 3 telescopes, including the final wrap-up phase, is found by adding the above values appropriately. The times (sec) as a function of V magnitude, for a 3-sigma search (i.e., out to 3 times the probable error of the telescope pointing), for each of the cases of a telescope rms pointing error of 20 and 40 arcsec, is tabulated here: Total 3-telescope search time (sec) Telescope rms V=7 V=8 V=9 V=10 V=11 40 arcsec 41 69 114 217 512 20 arcsec 22 26 39 66 137 The rationale for a 20 arcsec rms pointing error is clear: it allows us to complete the star search in less than 1 minute in almost all cases. Interface --------- A user-friendly interface needs to be designed to run the star-search routine. Ideally it will report the state of each search, the offset of each telescope and tip-tilt mirror (in delta RA and delta DEC, or roll, tilt, or something useful), the background noise level, the number of noise sigmas to make a detection threshhold, the threshhold value, the status of each telescope (searching, locked), and the peak adu value of each detected star. The same window could be used for the continuing star-tracking function. Added values then should be the centering rms error (could be pixel units or arcsec), as a measure of seeing. Of course it is crucial to have an IDL image of the CCD detector at all times. Dark frame ---------- Before any star acquisition starts, a frame rate should be selected, either by hand or somehow automated to the expected star signal, but always in the range of about 5 to 240 Hz. A dark field should be taken next, by averaging say 25 frames, and the noise statistics calculated as the rms fluctuation of each pixel about its mean value, and the mean subtracted from all subsequent frames, and the average rms value noted for later threshhold calculation (i.e., 5 times the rms, or whatever value is requested by the user, but a default of 5 seems reasonable). It is up to the observer to ask for the dark frame under apropriate circumstances, i.e., the telescopes pointing at blank sky, the CCD detector cooled for at least 20 minutes, the sky brightness the same as to be used for later observations, the room lights off, and the lights in the tank off. Telescope solution vector ------------------------- The key to decreasing the telescope rms pointing is to have a good telescope solution vector procedure, so that it can be quickly executed when a telescope is moved to a new position, or if the telescope mirrors have been adjusted. This is the topic of a separate memo. Frame-grabber board ------------------- A frame-grabber capability would speed up the initial approximate pointing process, which was in fact ignored in the above analysis. Thus, in order to achieve and possibly even beat the estimated search times, the initial ponting offset should be a small as possible, and this will be greatly improved if we can digitize the acquisition TV camera image, using a frame grabber board, and then have the telescope quickly move by the estimated offset between the observed star position with the TV camera, and the previously memorized "best" position on the frame, as determined from the position of the preceeding star after it had been centered using the above triple-search procedure. Telescope and exit beam and delay correspondences ------------------------------------------------- The telescopes are numbered 1 (north), 2 (south), and 3 (west). Each of telescope 1 and 2 output beams can be sent to either a fixed set of mirrors, or to the 1st delay line set of mirrors (SD1 plus LD1). Telescope 3's output beam always goes to the 2nd delay line (SD2 plus LD2). As these beams emerge into the lab, they are called, from left to right as you face them, "fix", "d1", and "d2", since these pipes are always connected to the fixed or 1st or 2nd delay lines. There is a shutter at the end of each pipe, and the shutters are likewise labeled as belonging to either fix or d1 or d2. telescope star=north star=south T1 d1 fix T2 fix d1 T3 d3 d3 The decision as to whether telescope 1 (T1) goes to fix or d1 depends upon where the target star lies. If the star is north from the zenith, then T1 goes to d1; if the star is south of the zenith, then T1 goes to fix. Likewise, if the star is north then T2 goes to fix, and if south then T2 goes to d1. Recall that T3 always goes to d2. Actually there is an overlap of a few degrees overhead where either set of paths is OK, but this is only a narrow strip on the sky. The actual act of steering the T1 and T2 beams to either fix or d1 is done by a pair of mirrors located in the corner of the array, where the mirrors sit on motorized stages, and these are triggered by flipping the appropriate switch on the box mounted on the wall near the VxWorks rack; the flip can probably be done by computer command as well, but I'm not sure about this. The reason for the beam-switching complication is that when we built the original 2-telescope IOTA we could only afford to build a single delay line, d1, but we did leave room for later adding d2, which we have now done in 2000-2001. Auto-yaw -------- The star-tracker CCD can easily be used to monitor the position of the mag-light behind each telescope before and after each LD line is moved. This measurement can then be easily used to command the yaw motor on each LD cart. The advantage is that we can now slew the LD in order to change the net delay when moving between target and calibrator star. This is very efficient because we can move the LD much faster (20 cm/sec) than the SD (1 cm/sec), and in addition, with 2 SD carriages on our rather short Anorad table top, we have less room to move these carriages about, and therefore we have much less freedom iin choosing a calibrator star, a process which is already difficult due to lack of SD moving room, and the slowness of the SD. Being able to move the LD iinstead would speed up this process by several minutes per target-calibrator pair, increasing our net efficiency. Conclusion ---------- The combination of (1) an automatic tip-tilt based routine, (2) a good telescope solution vector routine, (3) a frame-grabber board routine, and (4) an auto-yaw capability, will give IOTA a modern, fast, and scientifically productive set of tools which will cut down on our overhead time dramatically.