An Investigation of the 3.5-m Telescope Jumps

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Introduction

J1: The basic image description and what it tells us

Table 1: Image Parameters for J1

Image motion directions: calculation of the parallactic angle

Which actuator motions could be responsible for the observed image jumps?

February 7 Data

Can pistoning of the secondary actuators be a trigger for the observed image jumps?

Table 2. Image sequence vs piston value for the macro command: "m2test 0 X 5"

Conclusions

Appendix A: TCC log during J1 exposure

Appendix B: M2test Source

Introduction

On Feb 8, 2000 the APO 3.5-m telescope exhibited jump which was recorded in the image labeled abell0787_g.0107.fits. This image was a 300 second exposure of an Abell field through the g filter. For convenience, in this paper I will designate this image as "J1" The normal NA2 guider was not operational on this date. During this exposure a PC based telemetry system was running which recorded the movements of the primary mirror to an accuracy of approximately 2 microns in the A, B, C, and T axes of the primary mirror support system. No such telemetry of the secondary or tertiary mirrors was available.

After the analysis of J1 had been completed, I enquired if there were any images taken by people here in the department which showed similar jumps or smearing. This produced the following series of 4 images taken on Feb 7, 2000:

sn1999gp.0001.fits, sn1999gp.0002.fits, sn1999gp.0004.fits, and sn1999gp.0007.fits. Again, for convenience I designate these images J2 through J5 These data are of particular interest owing to the fact that they were all taken at a considerably different parallactic angle than J1 and all within 20 minutes of each other.

I report here on the analysis of these data and what it tells us about the causes of the image motion jumps. I also report here on the results of Feb. 17, 2000 piston tests of the secondary which were designed to investigate one possible cause of the jumps.

J1: The basic image description and what it tells us

Figure 1 shows the central section of the image in question, J1. The location of the telescope and the basic image parameters are given in Table 1. The numbers for azimuth (AZ), altitude (ALT) and rotator angle (ROT) show both the starting and ending values during the exposure. Note that the clock on the telemetry PC was set to MST rather than UT and was within 5 seconds of being exactly 1 minute slow. This clock correspondence has been verified by identification of motions of the LVDTs during slews of the telescope. It has been confirmed by looking at finding charts of the field that in this image North is to the top and East is to the left.

During the exposure of J1 the wind conditions were mild and the truss temperature was stable. The TCC log in Appendix A shows a truss temperature of 2.85 C and an air temperature of 3.8 C measured during this exposure. The wind direction was directly into the telescope enclosure slit, but its velocity was only 4.1 mph. Two minutes before the exposure the truss and air temperatures were measured to be 2.81 and 3.6 C. The wind velocity and direction were 4.7 mph and unchanged. Three minutes after the exposure the truss and air temperatures were 2.94 and 4.1C, respectively. The wind velocity had climbed slightly to 5.7 mph and was in the same direction.

Similar wind velocities and temperature prevailed during the J2 through J5 exposures. At that time the truss temperatures were between 4 and 4.2 C. The wind velocities were directed 180 degrees from the enclosure slit and were between 1 and 3.8 mph.

A quick look at Figure 1 will show that all of the stars have a secondary image to the right of the primary stellar profile. The secondary images of the two brightest stars in the middle of the image are present, but obscured by the wings of the primary images. The bore sight of the telescope is very near the two bright stars in the center of this image section. It can easily be seen that the secondary stellar images do not form a radial pattern about the telescope bore sight. Instead, there is a uniform shift to the right across the entire image. This eliminates the rotator as the cause of this image jump.

Table 1. Image Parameters for J1

Instrument	SPIcam
Telescope port used	NA2
UT Time at beginning of exposure	05:11:36.15 ( 22:10:36 in M1 telemetry file)
Sidereal Time of exposure	07:18:51.0
Exposure Duration	300 sec
CCD Binning	2 x 2 (Image scale = 0.28"/pixel)
RA	09:27:21.8
DEC	74:26:29.9
HA	-02:08:30.8
AZ	168.32 - 168.61љ
ALT	45.53 - 45.70љ
ROT	96.46 - 97.75љ

The relative intensity of the primary stellar images to the secondary stellar images is 0.30. This implies that the telescope was pointed to the secondary position for a substantial amount of time (approximately. 100 sec) during this exposure. Chris Stubbs has pointed out that the unequal intensity ratios between the primary and secondary stellar images and the fact that there were only two images strongly suggests that the telescope was not oscillating during this exposure, but rather it experienced a single jump in position. If the telescope was oscillating during the entire exposure, then the primary and secondary images would have nearly equal intensities. Since they do not, an oscillation would have had to start or stop mid-way though the exposure to explain the image. Given the low frequency of these image jumps, this is unlikely to occur during a 300 second exposure. In addition, if the telescope had been in oscillation and stopped or started during the exposure, its unlikely that its final at-rest position (or initial starting position) would exactly coincide with the extreme positions of the oscillation. Under these circumstances one would expect to see three images of each star. Only two images of each star are present and on this basis we can safely eliminate the possibility that the telescope was experiencing an oscillation at the time of this exposure.

There are intensity minima seen between the primary and secondary stellar images The presence of an intensity minima implies that the telescope did not make multiple moves during this exposure, but rather experienced a single jump in image position.

The separation between the primary and secondary images is 1.6 arcseconds (5.7 pixels). The orientation of the secondary image to the primary is approximately 5љ up (towards the North) from the image horizontal. The restrictions that this places on the primary and secondary mirror positions are given below.

The hard-points on the primary mirror are located on an equilateral triangle centered on the primary mirror. Each hard point is 1.054 m from the center of the mirror. The distance between each hardpans and the base line between the other two hard points is therefore 1.581 m. The telemetry LVDTs are located at approximately the same positions as the hard points. Therefore, 1 microns of motion on a single LVDT is equivalent to a mirror tilt of 1x10^-6 / 1.581 = 6.33 x 10^-7 radians = 0.13 arcseconds. Ray tracing shows that an M1 tilt of 1 arcsecond results in 1.2 arcseconds of motion in the focal plane. Therefore, 1 microns of motion of a single LVDT on the primary is equivalent to a motion of 0.156 arcseconds in the telescope focal plane. A 1.6 arcseconds image jump therefore requires 10.2 microns of LVDT motion. The digitization of the LVDTs gives 0.9 microns/ADU. So we would require 11.4 ADU motion on the LVDTs to account for a 1.6 arcsecond shift in the focal plane.

The calculations for the effects of secondary actuator motions on image jumps are similar to those shown for the primary. The secondary actuators are located 0.2238 m from the center of the secondary. This gives an actuator-to-base-line distance of 0.3357 m. A 1 microns motion of a single secondary actuator results in a mirror tilt of 0.614 arcseconds. Ray tracing shows that a 1 arcsecond tilt of the secondary results in a 0.33 arcsecond motion in the image plane. We therefore have 0.205 arcseconds of image plane motion for a 1 microns tilt of the secondary. To account for a 1.6 arcsecond focal plane shift we therefore require 4.9 microns of secondary actuator motion. Note that each full step of a secondary actuator stepper motor produces a linear motion of 0.053 microns. It therefore takes 92 full steps (4600 micro-steps) on the stepper motor to produce a focal plane shift of 1.6 arcseconds.

These secondary motions are significantly larger than those being commanded by the secondary collimation process. The TCC logs show that during this exposure, the collimation process commanded the secondary to piston five times. The collimation commands occurred 54, 118, 172, 234, and 296 seconds after the start of the exposure. The requested piston motions were -0.21, -0.27, +1.54, -0.21, and -0.21 microns, respectively. The largest piston request of +1.54 microns occurred right after a weather update of the telescope temperature. The other pistons were correcting for the small range of altitude variations during the exposure. The telescope secondary truss temperature coefficient is currently 43 microns/љC. The 1.54 microns shift was appropriate for the telescope conditions and corresponds to an increase in the secondary truss temperature of only 0.04љC combined with an altitude piston of -0.18 microns. I will return to the issue of whether or not the collimation process could be the trigger for the image motions that we are seeing later. For now I will merely state that this does not appear to be likely at this time.

Figure 2 shows the primary mirror LVDT telemetry for the transverse axis at the time of this exposure. Very similar traces were observed for axes A, B, and C as well as for the Pressure Error channels (VPE) of all four axes. These traces are not shown here for the sake of brevity. No motions of the LVDTs were seen during the J1 exposure. The noise is on the order of 3 ADUs, which corresponds to 2.7 microns. This is much smaller than the 11.4 ADUs required to explain the image motion. We therefore conclude that motions of the primary did not cause the image motion in J1

Figure 3 shows a longer time sequence of the T axis LVDT data. Despite our conclusion above, motions of the primary mirror are occurring. The motions shown in Figure 3 show the bi-stable nature of such primary mirror motions. The magnitude of this particular mirror shift was approximately 7 microns, but at other times shifts in the C axis as large as 40 microns have been observed. All of these primary mirror motions appear to be triggered by slews of the telescope. This is seen in Figure 3 where the arrows correspond to the start of all of the slews that occurred during this time frame. J1 was exposed during the stable portion of this graph near the 22:13:20 time marker.

Ray tracing shows that a transverse motion of 1 mm will produce a shift of 5.74 mm in the telescope focal plane. A focal plane scale of 5.85"/mm means that a 40 mm shift will produce a 1.35" jump in the focal plane. This illustrates that if shifts such as these were occuring during our exposures, they could easily explain the image jumps that we see. However, these motions appear to be triggered only during telescope slews.

Image motion directions: calculation of the parallactic angle

Finally, we now turn to the question of what the direction of the image motion tells us. I first review here how to calculate the altitude, a, azimuth, A, and parallactic angle, g, for an image given a, the RA; d, the DEC; ST, the sidereal time of the observation; and l, the latitude of the observatory. The parallactic angle is defined as the angle from North towards the zenith. This angle therefore tells you the direction of the altitude axis on the image if you first know where North is. North is well known in our image independent of the TCC owing to the use of finding charts. I use these "by hand" calculations to verify that the TCC's parameter SpiderInstAng is an accurate measure of where the azimuth axis lies on the image.

Figure 4 shows the spherical triangle of interest when trying to calculate a, A, and gamma. The directions labeled N, Z, and S point toward the celestial north pole, the observatory zenith, and the star of interest, respectively. The angle from the north pole to the zenith is given by 90 - lambda. Likewise, the angle from the star and the zenith is 90 - a and the angle from the north pole to the star is 90 - delta. All three of these angles form the sides of the spherical triangle and are labeled in the figure. The interior angle, labeled h in the figure, is just the hour angle of the star. Likewise, A and gamma form the remaining two interior angles of the figure. By the definition of hour angle we have

( 1)

where ST is just the sidereal time of the observations. Note that by this definition, h is negative as shown in Figure 4. From the spherical triangle in Figure 4, the law of cosines gives us the following equation for a:

which resolves to:

( 2)

Solving for a by taking the arcsine of the right hand side of equation (2) is unambiguous owing to the fact that a must always lie between 0 and 90љ. Applying the law of sines to the same spherical triangle gives us an expression for A in terms of a:

which can be rearranged to:

( 3)

In this case, taking the arcsine of the right hand side of equation (3) introduces an ambiguity. For any given value, the right hand side of equation (3) may equal either A or , where sgn(A) is simply +1 if A is positive and -1 if not. Which value to use comes from an examination of the relative sizes of the legs in the spherical triangle. In general we have:

( 4)

This last case is illustrated by the spherical triangle in Figure 5. We will now show how to calculate gamma.

The law of sines again gives us an analogous expression for the parallactic angle:

which reduces to:

( 5)

Like the calculation of A, this equation also suffers from the ambiguity of taking the arcsine. But, the solution is similar to that for A. Using a similar inspection of the figure we find:

( 6)

Solving equations (1) through (6) gives us values for a, A, and g. We will now apply these calculations and compare them with values found in the TCC log for the image J1 We start by converting the input parameters to decimal degrees and then proceed to solve equations (1) through (6). We have:

Looking at the TCC log (see Appendix A for a copy of the log during this exposure), we have immediate confirmation of most of the calculations above. Minor differences arise from the fact that the TCC makes more elaborate corrections such as those for refraction which are not considered here.

In order to compare the azimuth and parallactic angle calculations with those given by the log we must first consider differences in the angle conventions used in the spherical trig. calculations compared to those employed by the TCC. This comparison is illustrated in Figure 6. This figure shows a view looking down onto the observatory. The trig. conventions have A starting at zero in the North, increasing towards the West. The TCC convention has A equal to zero in the South, increasing towards the East. (Its pathetic to note that NEITHER of these conventions conforms to the normal astronomical convention of having A equal to zero in the North, increasing towards the East!) Given the convention differences seen in Figure 6, the following equation will convert the spherical trig. calculations to the TCC azimuth convention:

( 7)

Using this we find:

This is in fair agreement with the value given in the TCC log.

We now consider the comparison between gamma and the TCC equivalent, SpiderInstAng. The convention for the spherical trig. calculations have gamma equal to 0 when the direction to the zenith and North coincide, gamma increases as the zenith direction moves towards the East. Unfortunately, the definition of SpiderInstAng is somewhat convoluted. This is in large part why I have spent the extra time in doing the "manual" calculations!

SpiderInstAng is defined as the angle from the instrument +x axis towards the direction of increasing azimuth (not altitude!). SpiderInstAng is defined so that it always forms a right handed coordinate system between the +x axis and the direction of increasing azimuth. Normally, one would expect to find the +x axis pointing to the right as you view an image. This is not the case with SPIcam. Its instrument block is defined so that +x points towards the East in J1 (you can tell this because there is a negative scale factor in the x axis!). The TCC convention on the direction of angles is to assume that the "z" axis always points out towards the sky. For a right hand coordinate system, the vector cross product of x and y should point in the direction of z. In this case, +x is towards the East and +z is with your thumb pointing into the image. Therefore, increasing angles go from the East towards North! If this doesn't confuse you, nothing will. Figure 7 shows the two different angle conventions as viewed in the image. Figure 7a shows the spherical trigonometry conventions and 7b shows the TCC conventions for the equivalent angle, SpiderInstAng. The "manual" spherical trig. calculations agree with the TCC calculations of SpiderInstAng as long as you can keep all of the angle conventions straight!

For those of you hoping that I show you an easy way to be sure that you have gotten the calculations correct, I apologize! Having accomplished the manual checks for a given setup (i.e. SPIcam with an object instrument angle of 0љ) it becomes fairly easy to use the TCC SpiderInstAng for these calculations. If you are ever unsure of a given setup, however, I would recommend following through with the sperical trig. calculations as a means of verifying your conditions.

Which actuator motions could be responsible for the observed image jumps?

What then does all of this mean for the image motions seen in J1 First and foremost, the image motion does NOT correspond to either the altitude nor the azimuth axes. Therefore, we can eliminate these axes as the cause of this image motion. When all of the shenanigans above are applied to the image, you discover that the altitude axis points 50.4љ below the horizontal axis in J1, i.e. the zenith is towards the South-West in the image. The azimuth axis points 39.6љ above the horizontal axis, i.e. toward the North-West. These directions are shown in Figure 7. The image motions in J1 are seen to be about 5љ towards the North-West, approximately 55љ from the altitude axis. The image motion direction is shown by the heavy dashed line.

If only the A actuator moves on the secondary, the image motion should be in the direction of the zenith. If only the B or the C actuator moves, it will move the image in an axis 60љ from the zenith axis. This is illustrated in Figure 8a where the locations of each secondary actuator is shown with respect to the zenith and azimuth directions. The perspective shown in Figure 8a is that of a person looking down at the primary, through the secondary mirror. The dotted vectors shown in Figure 8a show the axis of image motion if only the B or C actuators move. These are what I call the "natural" axes of motion. In Figure 8b I show the orientation of the natural B and C axes as projected on the image plane. Again, the heavy dashed line shows the direction of image motion in J1. Clearly, motion of a single actuator can cause image motion along either the directions shown, or 180љ to the drawn directions. Illustrated in the figure are those directions that are closest to the observed image motion. The image motion observed is within 5љ of the natural motion of the C actuator. This is within the error of the measured image motion, which was estimated to be on the order of 5љ on the basis of the scatter of measurements taken from 3 stars in the image. This result is suggestive that the observed motions are being caused by slop in the secondary actuator linkage. However, below we will show that these results are not reproducible. The Feb. 7 data makes this alignment appear to be simply coincidental.

The tertiary's actuators are rotated 90љ from those of the secondary. Figure 9a shows the orientation of the tertiary actuators with respect to the secondary actuators. The secondary actuators are shown in dotted lines and the tertiary actuators are marked 3A, 3B, and 3C. The directions to the zenith and azimuth are also marked. Figure 9a has the viewpoint of one looking down towards the primary, through the secondary and tertiary mirrors. The NA2 port is toward the right of Figure 9a. Figure 9b shows the orientation of the natural axes of motion for the tertiary as projected on the image plane. You can see that none of the natural tertiary axes of motion lie close to the direction of image motion which is again marked by the heavy dashed line. Actuator 3C has the closest natural axis and is about 25љ away from the observed image motion. This is far larger than can be explained by measurement errors. We can therefore eliminate the tertiary as the source of the image jump in J1.

February 7 Data

I now turn to the analysis of the image jumps seen on Feb. 7. Unfortunately, the primary mirror telemetry was not on at the time these data were acquired. The magnitude of the jumps in J2 through J5 were 0.9, 1.0, 0.8, and 0.9 arcseconds, respectively. The direction of the jumps were all between 46 and 55љ with an uncertainty in any given measurement of about 10љ. The parallactic angle (using the spherical trig. convention of Figure 7) varied between +109.8љ at the start of these observations and +106.7љ at the end. Figure 10 shows the observed image motion along with the natural angles of the telescope at this time. As in previous figures, the heavy dashed line marks the angle of image motion in images J2 through J5. Axes marked 2B and 2C refer to the secondary actuator axes while 3B and 3C refer to the tertiary axes. In this figure, I plot the natural axes of the secondary and tertiary in the directions which are closest to the zenith direction. This illustrates the easiest way to remember how these axes are oriented. The tertiary axes are always 30љ to the zenith while the secondary axes are always 60љ to the zenith. When comparing these axes with the plotted image motion, you should flip them 180љ in the figure. What stands out in this figure is that the only axis that comes even close to aligning with the observed image motion is the tertiary B axis. As was seen in Figure 9, this axis could not explain the motions seen in the Feb. 8 image jump. The jumps are therefore not consistently explained by a motion of any single actuator. The alignment between a single axis and a given image motion is therefore probably coincidental.

Can pistoning of the secondary actuators be a trigger for the observed image jumps?

During the engineering run of Feb. 17 we ran pistoning tests of the secondary to ascertain if these motions were inducing unwanted motions of the secondary mirror. A special macro was written for SPIcam called m2test which allowed us to exercise the pistoning motion of the secondary while monitoring its effect on image motion. The macro is a modification of the normal dofocus macro. Its source is included in Appendix B. A total of about 30 minutes of on-sky time was taken, alternating between frames of data taken with m2test and normal dofocus frames. A total of 6 frames were analyzed; 3 m2test frames and 3 dofocus frames. An exposure of 10 seconds was used for each image on the frames. At the beginning of these exposures, the telescope was at an elevation angle of 67љ and ended at an elevation of about 64љ. The telescope azimuth started at 325љ (i.e. toward the South) and ended at about 310љ. The parallactic angle during this time was +31љ (using the spherical trig. convention! See Figure 7.), putting the direction of the zenith off to the North-East in these exposures. The natural axes for the B and C secondary actuators were therefore at -29љ and +91љ, respectively. The natural C axis was therefore almost exactly due East.

The m2test macro was designed to take an even number of images at varying secondary piston settings. Like dofocus, m2test stores all of its exposures on the same CCD frame by shifting the CCD charge between exposures. The direction of piston motion and the magnitude of this motion was changed between each image in the frame. The command input parameters are initial piston value, initial piston increment, and number of image pairs to take. Assuming that the command was invoked with an initial piston value of -50, an initial piston increment of X , and a total number of image pairs to take was 5, the piston sequence performed by the command would be as shown in Table 2.

All of the m2test frames analyzed were taken with X=15 microns. Alternating with these were frames taken with the command "dofocus -50 15 10". The differences between the m2test frames and the dofocus frames were that in the dofocus frames the secondary was pistoned in a uniform direction and magnitude while in the m2test frames the pistoning direction was reversed between exposures and the magnitude of each piston increased throughout the frame. The positions of the stellar centroids were determined in each sequence with the IRAF routine "imexam".

Table 2. Image sequence vs piston value for the macro command: "m2test 0 X 5"

Image Sequence Number	Piston Value
1	-50
2	+X
3	-2X
4	+3X
5	-4X
6	+5X
7	-6X
8	+7X
9	-8X
10	+9X

Figures 11 and 12 show a typical example of these data. The routine m2test was used to acquire the data shown. In these figures the image sequence corresponds to secondary piston settings of -50, -35, -65, -20, -80, -5, -95, +10, -110, and +25 microns, as you go from 0 to 9 in the figure. Because of the reversals of piston direction in the m2test data, the image sequence should be viewed primarily as a temporal index. The column or row position of each stellar image was measured and subtracted from the mean position for each star. The column measurements shown in Figure 11 are almost exactly in the direction of the natural C secondary axis. The row measurements shown in Figure 12 are 29љ away from the natural B secondary axis. Neither axis closer than 30љ to the azimuth or altitude axes. The three points at each piston index are from three different stars on the image. The centroid errors for each stellar position determination is proven to be on the order of 0.2 pixels (0.06") by comparing the results of the 3 stars on the same image. Almost all of the deviations seen are common-mode motions of the image, rather than scatter from centroid position errors. Similar measurements were made with a dofocus frame with similar results.

In all of the data acquired, the peak-to-peak image motions seen were about 2 pixels which corresponds to 0.56". This is about one third of the motion the was seen in J1 and about one half of the motion seen in J2 though J5. The peak-to-peak magnitude of the image motion was similar for both the m2test data and the dofocus data. Although the column data shown in Figure 11 looks fairly random, the row data in Figure 12 looks more like a slowly varying temporal sequence of motions. Figure 12 is more typical of the rest of the data in this respect. The data are not characteristic of random jumps to bi-stable positions. Reversal of the piston motion does not effect the overall characteristics of the image motions observed. Most of the motions seen here are small, on the order of 0.2 arcseconds or less, and temporally correlated.

The cause of the small incremental changes seen in these data could be explained by slow changes of the secondary position or by tracking errors. The data shown in Figures 11 and 12 were taken over a period of about 100 seconds. The telescope moves over a very small range during this time period. Its seems unlikely that the pointing model has terms in it that can contribute to changes on a spatial scale this small. If these are tracking errors, they must be errors in the drive motions themselves which take place over a period of several tens of seconds. If the motions seen are the result of motions in the secondary mirror, they do not appear to be influenced by either the direction or magnitude of secondary pistoning. Finally, these slow motions are not characteristic of the motion that caused the image blur in J1 in either temporal behavior nor in magnitude. These could have caused some of the smaller motions observed in J2 through J5 which appear to be true smearing of the stellar images rather than discrete jumps like that seen in J1. However, the motions seen on Feb 8 (J2 through J5) we all uniform in direction. A uniform direction of motion would imply that the row and column motions seen here should be correlated. While there might appear to be such a correlation seen in the data of Figures 11 and 12, the larger set of data shows no such correlation. While we cannot rule out the possibility that these motions are intimately related to the image jumps observed in J1 through J5, it should be kept in mind that none of the data acquired so far appear to support this.

Conclusions

The basic conclusions of this report are as follows. We now know that the primary mirror does indeed move during slews. Bi-stable jumps in the primary mirror position have been seen in both the C and T axes. Motions as large as 40 microns have been observed in C. These motions are easily large enough to cause image motions of several arcseconds, however, the primary appears to move only at the beginning of a slew. As such, motions of the primary mirror appear to be resulting in changes in the collimation and an increase in the scatter of the pointing models, but are not the cause of image jumps during an exposure. The primary mirror telemetry showed that the image motion observed in J1 was NOT caused by unwanted motions of the primary mirror.

The TCC logs shows that no operator induced commands were responsible for the jumps in the images. Neither is there any evidence that the automatic commands sent by the collimation process are responsible for the problem.

The direction of the image motions showed that they were not caused by unwanted motions of the altitude and azimuth axes. Likewise, the images show that the rotator cannot be blamed for the image jumps. The directions and magnitudes of the four image motions observed on Feb. 7 are all similar. However, the directions of the image motions observed on Feb. 7 and 8 are not consistent with each other. Nor are they consistent with any natural motions that one would expect from the secondary and tertiary actuators.

Finally, tests of the effects of pistoning the secondary made on Feb. 17, 2000 show that mirror pistons do not appear to stimulate the image jumps. However, image motions measured during these tests indicate that there are small motions on the order of 0.1 arcseconds taking place nearly continuously which are clearly degrading the imaging performance of the telescope. These motions are fast enough that most of their effects will not effectively be suppressed by the guider. The image "jumps" that are being reported are possibly only the largest of these motions. However, most of the motions observed during these tests showed small correlated motions taking place over many tens of seconds rather than large, rapid jumps of 1 to 2 arcseconds and it should be kept in mind that none of the data clearly supports a connection between the slow motions observed and the observed image jumps. The time scale of even the slow motions makes it unlikely that the pointing model can be blamed for these errors. The slow motions are common mode motions all across the entire image and cannot therefore be attributed to seeing variations.

The combination of all of these tests is quite puzzling. The direction of the image jumps indicates that the altitude and azimuth axes are not to blame for these motions. And yet the small temporally correlated motions observed on Feb. 17th seem to point to tracking errors. Therefore, if they are tracking errors, then both axes must be in error at the same time. The lack of a correlation between the image motions observed and the natural directions of either the secondary or the tertiary actuators appears to indicate that these linkages are not responsible for the motions. Like the tracking, this is only true if one assumes that it is unlikely that more than one actuator moves at a time. Clearly if more than one actuator is moving at a time, any jumps can be explained by slop in the actuators. However, the image motions observed on Feb. 7th were quite uniform in direction. Its very unlikely that coordinated motions in more than one axis could have caused such a repetition of motion! Other possibilities for contributors to these motions include stress relief of the secondary cage or of the secondary vanes and flexures in the instruments themselves. I have not investigated any of these possibilities.