On January 24, 1998 a Shack-Hartmann Sensor, made by Spot s.r.l., was tested at the 3.5-m telescope at the Apache Point Observatory. The sensor used was a prototype Puntino sensor. The purpose of the tests were to evaluate the performance and utility of this sensor for use on the 3.5-m. For this purpose, an initial evaluation of the alignment and optical quality of the 3.5-m telescope was done using this sensor. We present the results of these measurements here along with recommendations on the purchase of this sensor. These tests were conducted by Rajiv Bhatia, of Spot s.r.l. in Milan, Italy (note that these folks have a "front" company called TCE in Phoenix, Arizona. The contact at that company is Gerald Jones) and myself. APO personel present during these tests included Mark Klaene, Karen Gloria, and Jon Holtzmann from NMSU.
Preliminary results for only two frames, one taken at a zenith angle of approximately 33° and a second taken at a zenith angle of approximately 24°, are presented here. These frames were acquired in only a few minutes of actual telescope time. Each frame is taken from a single exposure of less than 1 minute duration on a moderately bright star. These tests were done during twilight and the early part of the evening. A very limited amount of telescope time was taken to complete this initial evaluation. In addition, the results presented here were available within a few minutes of taking the observations owing to the speed of the software analysis. Keep in mind that the intent here was not to do an exhaustive analysis of the telescope, but merely to evaluate the ease and utility of the sensor and its associated software for doing this task on a regular basis in the future.
A summary of our conclusions on the optical quality of the telescope is given in the following list. The telescope, as it is, is capable of giving images of 0.6" FWHM. This figure can be further improved by taking care of the following points as found from the SH tests:
Figure 1 shows an image of the sub-aperture spots measured taken at a zenith angle of 33°. Note that the spots are not clean stellar images, but show considerable change in shape across the telescope aperture. This is indicative of small scale roughness (roughness with spatial scales on the order of the sub-aperture sizes) in the figure of one or more of the mirrors. These measurements are not sufficient to distinguishing which mirrors are the cause of the optical distortions measured. However, by making similar measurements with the secondary rotated, such a determination could be made. Also note that we did not take the time to determine things like the absolute orientation of the mirrors in these images. But, this can be done and, once done, the software is capable of keeping track of this orientation.
The position of the secondary support cables is obvious in Figure 1. Compared to similar measurements on other telescopes, spot images on the 3.5-m show a pronounced signature of the secondary support structure. The presence of micro-roughness on one or both of the mirrors is possibly responsible for this effect. Micro-roughness will produce extended wings to the sub-aperture images which in sum create a background which accentuates the obscuration caused by the secondary structure. The issue of micro-roughness will come up again when we discuss the encircled energy plots below.
Zonal structure in the position of the spots can be seen in Figure 1. This is most obvious in a spreading between the 3rd and 4th spots from the right hand side of the mirror's outer diameter. This structure can be seen to extend at least ±45° from the horizontal.
Figure 2 shows the GUI window of the automatic analysis of the Spot-Optical software of the data from Figure 1. This analysis took less than 1 minute on the PC which we supplied for these tests. Note that on the bottom left of the GUI is a Diagnostic section which supplies the user with suggestions on actions that can be taken to improve the imaging performance of the optics. In the center of the window is a section which lists the aberrations present in the optics. The magnitudes of the aberrations are given in terms of their associated Zernike coefficients (wavefront errors in namometers, both X and Y components are given when appropriate) as well as in terms of their contributions to image blur in units of arcseconds. The defocus term implies that the Shack-Hartmann sensor was not at the best focal surface that the telescope has to offer. This was a probably a result of errors in the design of the mount which was constructed to hold the Shack-Hartmann sensor. The diagnostic section concludes that this could easily be corrected by moving the secondary away from the primary by 0.081 mm. For the magnification of the telescope, this is accomplished by moving the instrument back by 2.75 mm. Likewise, the tilt terms can often be corrected by simple adjustments in either the instrument mount or tilts of the secondary. The diagnostics section is quite clear on how far and in which direction such adjustments need to be made.
These measurements confirm that the current collimation procedure of the telescope is fairly good. Without any other measurements, with our current procedure we are able to place the optical centers of the secondary and primary within 0.12 mm of each other. Clearly, one of the great advantages of having the Shack-Hartmann sensor is that it enables us to quickly verify and improve this alignment. This is our first actual measurement of the optical center of the primary mirror.
The plotting package which comes bundled into the software is quite useful for visualization of the mirror distortions. Figures 3 and 4 show respectively a surface and contour plot of the 3.5-m mirror surface after the subtraction of the 2 Zernike terms defocus and tilt. The presence of astigmatism in the 3.5-m mirrors is clearly seen in the upturn of this surface in the X direction and also in the downturn of this surface in the Y direction.
The software enables the user to look at higher order effects by allowing the selective subtraction of lower order terms from the surface distortions. Figures 5 and 6 show surface and contour plots of the 3.5-m mirror after the subtraction of the 7 Zernike terms defocus, tilt, coma, sperical aberration, astigmatism, triangular coma, and quadratic astigmatism. These high order distortions are typically caused by problems with the mounting of the optics. The distortions seen in Figures 5 and 6 are significant, on the order of 100 nm (approximately 1/5 of a wave for visible light). It is possible that the distortions that are seen in Figures 5 and 6 are being caused by the mounting of the secondary mirror, but there is no correspondence between the distortions seen in the contour plots and the positions of the mirror supports. For example, Figure 6b shows the positions of the 3.5-m secondary supports scaled to the size of the surface distortion plots. This figure has been rotated to position the support positions over the largest distortions seen in the residual plots shown in Figures 5 and 6. The secondary mirror has 11 points of contact with the mount. There is a shaft in a central hole in the mirror which supports the mirror weight at its center of gravity, 3 points of contact on each of the 3 wiffles, and a single transverse support represented by the bar at the edge of the mirror. There is no clear correct orientation for how the supports fit on this plot. There is even less reason to suspect that these distortions line up with the primary mirror support. The primary mirror support system has essentially three concentric rings of pads supporting the mirror encompassing a total of approximately 64 points of contact. In this case, the separation of the points of contact are of much higher frequency than any of the distortions seen in the optical analysis.
Figure 7 shows the spot diagram for the telescope as derived from the Shack-Hartmann analysis. Figure 8 shows the equivalent encircled energy plot from the same analysis. The three plots that are shown in Figure 8 are the radially averaged encircled energy, the y-marginal encircled energy, and the x-marginal encircled energy. From this it can be seen that the optics are currently capable of placing 50% of the energy within a 0.6" diameter. Also visible is a wing on the encircled energy plot which extends all the way out to a diameter of 2". This rather long tail of the profile is due to the presence of zones and micro-ripple on the surface of one of the mirrors.
Figure 9 shows an image of the sub-aperture spots measured taken at a zenith angle of 24°. The rotation of the secondary spiders compared with those seen in Figure 1 is due to the rotation of the instrument rotator, which was left on during these measurements. The actual rotation of the image, compared with Figure 1 is 101.6 degrees. The rotation between Figures 1 and 9 is clock-wise. However, we will see shortly when comparing the contour plots, that it appears that the rotation between the equivalent contour plots is counter clock-wise. This apparent discrepency is due to differences in the display conventions between the countour plots and the images. The images are displayed with their origins in the upper-left corner. The contour plots have their origins in the lower-left corners.
Figure 10 shows the GUI window of the automatic analysis of the Spot-Optical software of the data from Figure 9. The most significant change in the mirror distortions between these data and the those taken at a zenith angle of 33° is the increase in coma from 0.09" to 0.23". This is indicative of a decentering as the secondary truss structure sags. This amount of change for a difference in altitude angle of only 11° is disturbing if it is correct. The telescope was initially collimated at an altitude of approximately 30°. This result clearly needs verification for it could represent a significant altitude axis variation if it is true.
As the telescope was moved to the smaller zenith angle, the defocus term decreased by 0.027 mm, implying that the secondary moved away from the primary by this amount as the telescope moved toward the zenith. This is not a large effect, this motion represents a barely noticable focus shift for a science instrument, but it is not in the direction that one might expect. At low zenith angles the force from the secondary weight is directed toward the primary. At high zenith angles this same force is directed along the secondary spider support cables. This shift of the secondary mass force vector would cause one to expect that the secondary-primary distance would decrease as the telescope was moved toward zenith, just the opposite of what is implied by the change in defocus. It seems unlikely that this effect can be explained by motions of the primary mirror. This amount of motion is 5-10 times the error in the primary support hardpoints. Again, if this measurement is accurate, it suggests unexpected mirror motions which should be investigated. No other significant changes were observed in the other aberrations.
Figures 11 and 12 show respectively a surface and contour plot of the 3.5-m mirror surface at a zenith angle of 24° after the subtraction of the 2 Zernike terms defocus and tilt. The effects of the increased coma from the sag of the telescope truss are easily seen in the left-to-right slope of the surface distortions. To compare Figures 11 and 12 with the similar figures taken from the data from 33° (ie. Figures 3 and 4), you must take into account the 101.6° rotation of the images due to the motion of the instrument rotator. For example, to compare the surface distortions seen in Figure 12 with those in Figure 4, you must rotate Figure 12 clock-wise by 101.6°. The large depression on the right hand side of Figure 12 corresponds with the depression seen at the bottom of Figure 4. From such a comparison it can be seen that there are many similarities between the two data sets. The gross features of the surface distortions are reproduced in both data sets.
Figures 13 and 14 show the surface and contour plots of the 3.5-m mirror surface at a zenith angle of 24° after subtraction of the 7 Zernike terms defocus, tilt, coma, spherical aberration, astigmatism, triangular coma, and quadratic astigmatism. Some of the major features in the earlier figures (ie. Figures 5 and 6) are reproduced here. Once again, there is little or no correspondence between these distortions and the positions of the secondary support structure. Figure 14b show the mirror supports superimposed on the surface distortion contours. The orientation for the mirror supports on this plot corresponds to the orientation shown in Figure 6b with the image rotation taken into account. And again, I emphasize that we do not know the proper orientation of the supports on these plots; the point to be made here is that there is no clear sign of the support structure in the contour plots.
Figures 15 and 16 show the spot diagram and encircled energy plots for the data taken at a zenith angle of 24°. The FWHM of the encircled energy plot is still found at about 0.6", but the extended wings increase slightly from what is measured at a zenith angle of 33°. Here the 95% encircled energy point occurs at a diameter of 1.37". At a zenith angle of 33°, the 95% encircled energy point was found at 1.33".
The software that comes with this device is excellent and easy to use. It goes a long ways towards helping the user interpret complex and difficult data. What is not evident in the preceeding comments is that there is an entire body of tutorial material which comes with the software which is of equal value in explaining what is going on with the data analysis. For instance, the software includes a large number of simulations of aberrations and there effects on the measurements. It also includes a large number of diagrams which explain the terms used in the analysis. The importance of such material on training people to use this equipment should go unnoticed. In my opinion, the software is the primary thing that is being purchased here.
The near real-time analysis which this package allows would enable rapid tuning of the telescope parameters. One example which this data set makes clear is that you could easily take measurements of the aberrations at several zenith angles and create a look-up table of the tilt corrections that the secondary must make to compensate. The telescope software already has in it the capability to make many of these adjustments. Some are unused because the coefficients used in the corrections are not trusted. Being able to rapidly measure the aberrations of the telescope under varying conditions will be a great help in all of these situations.
With this instrumentation we would no longer have to consider modifications to the tertiary mount which would enable the alignment of the primary and secondary's optical centers. This instrumentation allows us to measure the effective optical center of the primary (we already know that of the secondary). Its probably easier to use than any technique that would require us to move the tertiary. This alone probably justifys the cost of this device.
This instrumentation would enable us to immediately verify and test the effects of the new secondary. It might also be possible to use this device for analysis of dome or mirror seeing. We did not have time to test this possibility, but it is plausible that it can be done. On Spot Optical's home page, they show examples of efforts to use the device for this purpose.
I recommend that APO purchase one of these devices for the 3.5-m. The current estimate of the cost of the device and software is approximately $30,000. In my opinion, the cost is the only good argument against obtaining this device. One could argue that a similar capability can be obtained for much less by the purchase of the software package from LaPlacian Optics. This package costs only $2500 and enables you to determine the Zernike coefficients of your distortions. This software works with out of focus images and since we already have science instruments which can take this data, it requires no extra hardware. However, this software does nothing for you when it comes to interpreting these results. This is precisely where the Spot s.r.l. software shines. In addition, after having had a chance to work with the LaPlacian Optics software, Charles Corson reports that this software is not currently capable of making allowance for the cat-eye mask that is on our primary mirror. For these reasons, this option does not offer an equivalent capability.
The results of the initial measurements on the 3.5-m are both comforting and a little suprising. They are comforting in that this analysis indicates that our current method of telescope collimation is doing a fairly good job. This analyis is in good quantitative agreement with our past efforts to determine the optical quality of the telescope and our observational experience with the telescope under excellent seeing conditions. They are suprising in that from the two measurements that were made, the changes in the surface distortions are very hard to understand. The variations that we observed with only a small variation in telescope position are perhaps larger than we might have expected. Chris Stubbs has suggested the possibility that the analysis of the optical aberrations are in fact tainted by the fact that we allowed the rotator angle to vary between the two exposures. He argues that small scale structure in the mirrors (presumably the secondary) might cause anomalous variations in the computed aberrations. If we do purchase this device, it would be well worth our while to systematically study the optical variations of the telescope as a function of its orientation.
