APO 3.5-m Altitude Sweep Measurements: 14 June 2000

This is a report on the results of the Shack-Hartmann (SH) data that were acquired on 14 June 2000. Russet's efforts in acquiring these data are much appreciated! At that time, an altitude sweep was taken under fairly good conditions. The tilt coefficients which were measured on 14 April 2000 had been installed in the telescope. SH measurements were made over a total altitude range of 53 degrees. SH frames were taken at approximately 10 degree intervals between the range of 87 degrees altitude to 34 degrees. Either 4 or 5 frames were taken at each altitude interval. The altitude sweep started with the telescope near the zenith and worked monotonically to lower altitudes. These data were acquired just before the shutdown in which we removed the air skirt on the primary mirror.

After the altitude sweep was completed a test of the effects of turning off the telex fans were then made. The telescope was returned to high altitudes and several SH frames were taken with the telescope exhaust fans on. The fans were then turned off and another set of SH frames was taken. The telescope was then moved to an intermediate altitude (68 degrees) and another "fans off" set of SH frames were taken. These tests were concluded by moving the telescope to a low altitudes (37 and 34 degrees) where "fans on" and "fans off" data were once again acquired.

Figure 1 shows the major telescope aberrations measured during the altitude sweep. The results of the initial altitude sweep were quite encouraging in one respect. With the altitude coefficients determined on April 14, 2000 installed we see no significant variation of coma as a function of altitude. All of the coma measurements lie within 0.1" of each other and have a standard deviation of only 0.04". This is excellent in that it implies that our tilt corrections are sufficiently accurate to not be a limitation in the telescope performance. Likewise, there is very little evidence of a systematic variation in the magnitude of either the astigmatism or the spherical aberration as a function of telescope altitude. I have also looked for and found no systematic variation of the angle of astigmatism as a function of telescope elevation angle. This lack of correlation between the orientation of astigmatism and telescope altitude is shown in Figure 2.

While there is no dependence of coma on telescope altitude, it can be seen from Figure 1 that the average value of the coma is 0.55", which is large. Coma this large is generated by tilts on the order of 45" or translations of M1 with respect to M2 of about 280 µm. The tilts of the mirrors can come motions of M1, M2, or a combination of both. Assume first that only M2 is moving. A 1 µm movement of a single M2 actuator is equivalent to a tilt of 0.61". A 45" tilt therefore requires a single M2 actuator motion of about 73 µm. This implies that while the tilt coefficients are accurate, the absolute positioning of the mirrors is not being maintained.

The motions required to create coma this large from only tilting M1 are even greater than those required for tilts of M2. A 1 µm movement of a single M1 hardpoint is equivalent to an M1 tilt of 0.13". A single M1 hardpoint must therefore move by 346 µm to create 0.55" worth of coma.

Figure 3 shows the results of the "fans on-fans off" tests. The temporal sequence of these points is important because the coma measured during some of these tests was significantly different than that seen during the altitude sweep shown in Figure 1. After the data from Figure 1 were taken, the telescope was returned to a very high altitude (approximately 87 degrees) and the filled data points in Figure 3 were acquired. The telescope exhaust fans were then turned off and the open points at 87 degrees altitude were taken. There appears to have been a shift in the telescope coma between the first and second measurements taken at 87 degrees. The first point, taken with the fans on showed telescope coma of 0.43", but the coma right after the fans were turned off was measured to be 0.53". At the same time, there is no indication of any variations in either the telescope astigmatism or in the spherical aberration.

This 0.1" change in coma is larger than anything seen in Figure 1 and its tempting to ascribe it to the state of the telescope exhaust fans, but you must remember that the first point shown in Figure 3 also represents a change in coma compared with the earlier measurements seen in Figure 1. Since the fans were on for these earlier measurements, one can conclude that the changes seen have nothing to do with the state of the fans. This conclusion is supported by the third point measured which was with the fans off at an altitude of 68 degrees. The state of the fans were not changed between this measurement and the last measurement at 87 degrees and yet these two points show the largest differential. The fans-on/fans-off test done at lower altitudes neither support nor contradict this hypothesis. The difference between the two measurements near 35 degrees is no larger than than the scatter seen earlier in Figure 1, but it does change in the same sense as the earlier test.

Below we will look in detail at this change in coma between the first two measurements at 87 degrees altitude. For now, we note only two things. First, the results of the fans-on/fans-off tests were slightly ambiguous. If the telescope coma depends on the state of the telescope fans, the changes seen from this are no greater than the changes seen from other, unknown causes. There is no strong evidence to support the idea that the state of the exhaust fans affect the telescope aberrations.

Second, there appears to have been a change in the telescope astigmatism between the time that the data of Figures 1 and 3 were acquired. In Figure 1 the astigmatism varied between 0.2 and 0.3". In Figure 3 it was significantly lower, between 0.1 and 0.2". The reason for this change is currently unknown.

It is reasonable to question whether the coma changes seen are real or simply some manifestation of noise. If the coma changes seen here are real, then the accumulation of several small changes like those seen during this night could explain the large variations seen in the average values of the telescope coma measured on different nights. There is no doubt that the large coma changes (on the order of 0.5") measured on different nights are real. This is easily confirmed by tilting the secondary mirror and finding that the coma does indeed decrease in the ways predicted by the software. We are therefore quite confident that our systematic and noise errors lie well below 0.5". The difficult question is how much below 0.5" can we trust the Shack-Hartmann analysis?

The SH analysis computes an "internal" noise estimate which is based only on the inherent noise in the centroids of the SH spots. Inputs to this estimate include the brightness of the stellar signal and the CCD gain and read noise. The internal noise estimates for the single frame data are on the order of 0.02". Figure 4 shows the frame-by-frame analysis of the Shack-Hartmann data taken at the beginning of the fans-on/fans-off measurements. The fans-off data in Figure 4 which start around 6:05 UT show that at times, this is exactly the scatter that you measure for multiple frames of SH data. However, the earlier fans-on data show scatter on the order of 0.05". This is more typical of SH data that we have acquired to date. Figure 5 is another example of this. It shows the frame-by-frame analysis of the SH data taken with the telescope altitude near 35º. These measurements have a scatter which is on the order of 0.05". Based on the internal errors, variations as large as 0.1" should be rare. We see from Figures 4 and 5 that this is not the case. The scatter which is seen is approximately twice what one would expect from the internal errors. Clearly some other source of "noise" is affecting the SH results. This "noise" might be a real manifestation of small mirror motions driven by telescope accelerations or wind vibrations. For now, based on typical scatter in the measurements when conditions are as quiescient as possible, we assume that differences larger than 0.05" are significant. Based on the internal errors, this is a conservative estimate.

In Figures 3 through 5, the largest changes seen in the coma were differences of about 0.1" . Figure 4 shows the details of one of these 0.1" changes in coma. In this case, Figure 4 shows that the changes had taken place and then returned to its original state before the telescope exhaust fans were turned off. This supports the conclusion that the state of the telescope fans did not affect the telescope aberrations.

Coma differences of 0.1" imply either a 66 µm shift of M1 or a 9 µm tilt of a single M1 hardpoint. The PMSS data stream was running at the time of these measurements. The LVDT data show no motions in A,B,C or T sectors greater than 0.4 µm. The load cell data agree with the LVDT data. They show less than 0.003 µm shift in the mirror between these two times. The PMSS data therefore show that M1 did NOT move during these measurements. Note that this conclusion is independent of the assumption that the M1 hardpoints are stable because this stability is indicated by both the LVDTs and the load cells. Any such motion would therefore have to come from motions in M2. The air and mirror temperatures were stable and equal during the entire time of the measurements in Figures 1 and 3.

We now consider the motions of M2 as measured by the secondary encoders. At the time of these measurements, the inner Heidenhain encoders were in use on the secondary. These are the spring-loaded encoders closest to the M2 actuators. These encoders have 2 µm periods, 4 pulses per period, and times-10 interpolators which give a resolution of 0.05 µm/encoder count. However, the Galil software gives the Heidenhain encoder outputs in µ-step units. These µ-step units are defined as the distance that an M2 actuator moves for a single µ-step of the stepper motors. For a lead-screw of 40 tpi, a 60:1 harmonic drive reducer, 200 steps/revolution steppers, and 50 µ-steps/step, we have 1.0583 x 10**-3 µm/µ-step. This means that each encoder count is 0.05 /1.0583x10**-3 = 47.24 µ-steps/encoder count. In other words, the Galil software multiplies the encoder counts by 47.24 to put it into µ-step units, and there are 0.0010583 µm/µ-step. Therefore a movement of 9 µm in a single M2 actuator, which causes a change of coma of 0.1", is equivalent to a change of 8500 µ-steps in the encoder outputs.

The Galil software always moves the actuators in units of 50 µ-steps (i.e. one full stepper motor step). If a motion of less than 25 µ-steps is requested, the command is ignored. Therefore, one always expects to see the secondary mirror move in increments of 50 * 1.0583x10**-3 = 0.0529 µm.

Figure 6 shows the positioning of the secondary encoders during the time period of the measurements in Figure 4. The first panel in Figure 6 shows the commanded positions of the secondary actuators. Most of the mirror commands are purely piston motions which do not change the tilt of the secondary. These are probably just the result of focus changes. There appears to be no correlation between these secondary positon changes and the changes in the coma as measured in Figure 4. For example, between the first two points in Figure 4 is seen a decrease in the coma of about 0.07" and yet these measurements were made before the first piston command at 5:53:24 UT (5.890 UT). Between the third and forth data points in Figure 4 a piston motion of about 6 µm was made in both directions (at 5:57:18 and at 5:58:12) and yet no change at all was seen in the measured coma.

These results lead either to the conclusion that the errors in the determination of the coma coefficient are larger than we estimate above and are on the order of 0.1". Or we are lead to believe that there are motions of the mirrors that are not being registered by the M1 and M2 encoders. Such motions would include the flexing of the secondary vanes or the secondary cage itself. (Note that motions of the primary hardpoints are ruled out on the basis of the M1 LVDT measurements).

Summary

We can conclude from these measurements that the altitude tilt coefficients are correct in form and magnitude, but we still have a significant problem with zero point drifts in the positions of M1 and M2. The tilts of the mirrors are more likely to be a problem rather than a translation of the mirrors simply because these are smaller motions.

There is no clear altitude dependence of the telescope astigmatism or spherical aberration in this data set. However, it does appear that one change in the telescope astigmatism was seen during the night. The cause of this change is not known.

There is no clear dependence of the telescope aberrations with the state of the telescope exhaust fans.

The M1 and M2 encoders have failed to pick up motions which can explain either the long term or the short term drifts in coma that are measured by the Shack-Hartmann analysis. There is no correlation between the measured mirror motions and the apparent nightly changes in telescope coma. This implies that either we are underestimating the errors in the Shack-Hartmann results or we have motions of the mirrors from effects which are not properly measured by the M1 and M2 encoders. Possible candidates for such effects would include flexures of the truss and secondary cage. Since there were only very small changes in the telescope temperature during these measurements, its unlikely that these postulated motions are temperature driven.

The long term drifts (i.e. night-to-night drifts in the mirror positions) might be explained by a translation of M1. No translations of M1 were seen during the course of these measurements, but it is possible that such shifts had taken place sometime between the time the telescope was last collimated (I believe this was back in April!) and these data which were taken on 14 June. Measurements taken after the July shutdown imply that this might be a possible explanation of the nightly drift. I will discuss those measurements in the next report.