Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.apo.nmsu.edu/users/morgan/APO/SH_measurements/altitude.sweeps/aug.14-15.00/report.html
Дата изменения: Sat Mar 29 06:12:10 2003
Дата индексирования: Sun Apr 10 10:31:05 2016
Кодировка:
Поисковые слова: m 43
Analysis of the August, 2000 Shack-Hartmann Data

Analysis of the Shack-Hartmann Data Taken on August 14 and 15, 2000: Confirmation of the Tilt Coefficients and an Investigation of the Thermal Response of the Telescope Support Structure

Two nights of Shack-Hartmann data were acquired on the nights of August 14 and 15, 2000. On both of these nights complete altitude sweeps were done, taking Shack-Hartmann data at intervals of 10 degrees in altitude. There were no tilt coefficients installed in the telescope software at the time that these data were taken. Both Russet and Cameron should be congratulated on the acquisition of a very useful and important set of data. If only one of these nights of data had been acquired most of our current understanding of these data would have been impossible to obtain.

We use these data to derive independent estimates of the tilt coefficients that are used to eliminate coma due to sag of the telescope truss as it moves in altitude. These results compare favorably with those found on April 14 of this year.

The measurements of the telescope astigmatism reported here indicate that the changes which we implemented during the July 2000 shutdown have been quite successful in reducing the amount of astigmatism on the 3.5m telescope. Throughout these tests the maximum astigmatism seen was 0.25" and 0.18" is a more typical value. There does appear to be a systematic shift of the magnitude and orientation of this astigmatism as a function of telescope altitude. At high altitudes the astigmatism is usually below 0.15". I attribute this behavior to slight pinching of the primary mirror as it rests on the transverse support system. We have effectively eliminated astigmatism as the major limitation to image quality on the 3.5m telescope.

I have also used these data to investigate the behavior of defocus as a function of telescope altitude. The defocus data from August 14 were seen to be consistent with that found on April 14, but the data from August 15 were not. It is highly likely that thermal changes in the telescope on August 15 were responsible for the differences seen. The nature of these data have led to an investigation of the motions of both the truss and the secondary cage which one might expect based on purely theoretical grounds assuming the changing gravity loading with telescope altitude and thermally induced motions. This investigation has lead to the conclusion that the thermal changes in the primary to secondary distance are driven by thermal changes in the secondary support rods as well as by thermal changes in the truss. This is one reason why the thermal model that we are currently using to describe changes in the telescope is inadequate. I show at the end of this report the beginnings of an improved thermal model. However, putting together a good thermal model of the telescope is likely to be a difficult task. A partial solution to this problem, which we might want to consider, is to replace the steel rods on the secondary with a low thermal expansion material such as graphite.

A second conclusion from this investigation is that thermal changes in the telescope support structure are unlikely to be the cause of the changing secondary tilts of the telescope, which continue to be observed over time. This conclusion depends on the assumption that the secondary cage itself is solid and it not warping in its shape. I estimate here that warpage on the order of 2 mm is required to explain the types of shifts which we have seen in the alignment of the telescope mirrors. Motions this large in the secondary cage seem unlikely, but this should be investigated. At the end of this report I suggest a series of measurements that might help resolve this issue.

Finally, there are two other things of minor interest that these data shed some light on. First are indications that the secondary focus motions have slop on the order of 20 µm. This is of minor interest only in that this is simply confirmation of something we were already fairly certain of. Second, the data from 15 August show that there is some transient source of "noise" in the measurement of the telescope aberrations. This may be either the signature of small primary mirror oscillations which were seen on the night that these data were acquired or it might be the signature of rapid cooling of the telescope at the beginning of the night. Weather conditions indicate that it is unlikely that this "noise" was the result of telescope windshake. The noise appears almost exclusively in the x-tilt measurements of the telescope coma. This is quite unusual and is currently unexplained.

Some historical background on this data set

The data from the nights of 14 and 15 of August 2000 are some of the very first data acquired after the July 2000 shutdown. Two significant changes were made to the telescope at this time. First, the air skirt, which once sat underneath the primary mirror, was removed. Second, the plenums, which fit on top of the telescope exhaust tubes that extend inside the primary mirror hex cells, were removed. These changes were made in an effort to minimize the stresses that are placed on the primary mirror. Earlier Shack-Hartmann measurements indicated that there was a significant amount of astigmatism in the optics that caused approximately 0.3" blurs in the telescope stellar profiles. Raising the mirror by adjusting the location of the primary mirror hard points reduced this astigmatism to about 0.2" at the price of moving the mirror out of the center of the axial piston's range of motion. The air skirt was designed to force the airflow of the telescope exhaust fans to enter through the center hole in the primary. This was done in an effort to create a laminar flow over the surface of the primary. This laminar flow was desired to inhibit the formation of surface convection on the primary, which is thought by some to be a significant source of "mirror seeing".

The plenums, which were once installed on top of the telescope vent tubes, were meant to keep the flow of the exhaust air over the backside of the mirror front faceplate. It was thought that by keeping the airflow close to the front surface of the glass, you could more rapidly bring the mirror into thermal equilibrium with the ambient air. The force that the bellows on top of the vent tubes applied to the plenums when keeping them up against the front faceplate of the mirror was measured to be a fraction of a pound. In isolation this is an insignificant force on the mirror, but in aggregate we were worried that these forces could become a significant factor in distortion of the mirror. These considerations have motivated us to remove the plenums. Needless to say, we were also influenced to do so by the fact that their removal greatly simplifies the installation of the primary mirror!

A proper investigation of the effects of removing the skirt and plenums should include studies of the effects that these changes have had on the telescope optics, a study of the effects that these changes have had on the thermal cooling of the primary mirror, and a study of the effects that these changes have had on the typical seeing experienced by the telescope. I report here only on the first of these three investigations. I am also currently working on a study of the effects that these changes have had on the thermal cooling of the primary mirror. I hope to finish that report within a few weeks time. Unfortunately, we will most likely never know with much certainty the effects these changes have made on the telescope seeing because it will be very difficult to separate out the effects of telescope seeing from the changes in the telescope optical quality.

Telescope tilt coefficients: Coma

Figures 1a and 1b show the measurements of the secondary tilts required to correct for flexures of the telescope truss and the transverse flexures of the secondary mirror mount as the telescope moves in altitude. A comparison of these data with those obtained on 14 April 2000 shows very good agreement in the tilts required to correct for transverse flexure of the truss and secondary supports. All of these tilt values are therefore confirmed by the altitude sweep measurements made on 14 June which were done to check the tilt which were implemented after the April measurements. The work done during the shutdown in July has not significantly altered the tilt coefficients.

Sometime during the third week in August, the tilt coefficients seen in Figure 1a were applied to the telescope software. On August 1, right after the July shutdown, the TCC tilt coefficients were set to SecXTiltCoef 70.0 0.0 0.0. These were the tilts that applied when the data reported here were acquired. Sometime around August 20, when time was available to redo the telescope pointing model, the tilt coefficients were set to SecXTiltCoef 14.0 21.0 75.0. As shown in the report on the April 14th data set, these coefficients were derived by adding the fit values shown in Figure 1a to the coefficients that were active at the time the data were taken.

Two other things are worth noting in regards to the telescope tilt coefficients. Note that in Figures 1a and 1b there is an offset to the curves. The optimal x-tilt at 60љ in Figure 1a is very close to 0". But in Figure 1b, the optimal x-tilt is approximately -12". This offset is not well explained by the increased noise seen in the August 15th data. It appears to be a real variation of the zero point in the optimal tilt curves. This is one indication that the mirrors are moving with respect to each other on a nightly basis. We will revisit this notion when we discuss the defocus errors. A tilt of 12" is equivalent to a differential motion of 92 µm in one of the secondary actuators with respect to the other two! The differences seen in the zero points of the optimal tilt curves in Figures 1a and 1b represent substantial changes in the mirror tilts.

Second, it is curious that the tilt curves show zero point changes only in the x-axis. The zero points of the y-tilt curves were quite reproducible. It would seem likely that these changes are somehow related to the "noise" that was seen only in the x-tilt data on August 15. This might imply that we have a significant problem with the secondary actuator A. However, the Heidenhein encoder data on the secondary mirror is very clear on one point: we see more slop and vibration in actuators B and C than we do in actuator A. The noise and zero point drift in the x-axis would then seem to indicate that we have either coordinated noise in secondary actuators B and C (unlikely!) or motions of the primary mirror in sector A. Primary mirror oscillations were reported during the observation of August 15 and this may offer the best explanation of the "noise" seen in the August 15th data. A correlation between the PMSS oscillations and the noise seen in these data might be worth looking into.

It was originally thought that the increased noise in the August 15 x-tilt data could be attributed to the presence of wind on the telescope. However, the TCC weather logs do not support this. During the acquisition of the August 14 data, the wind speed was between 6 and 8 m/s (13-17 mph) and it had a direction of 20љ (where 0љ is due South and 90љ is East). At this time the telescope was pointed between 170 and 190љ, at least 150љ away from the wind direction. During the acquisition of the August 15 data, similar conditions prevailed. The wind speed was between 7 and 8 m/s (15-18 mph) at a direction of 40љ. The telescope was pointed between 150 and 250љ.

The main environmental difference between the two data sets was the time of night at which they were acquired. The August 14 data set was acquired near the end of the night after the telescope had reached equilibrium with the ambient temperatures. But the August 15 data were acquired right after the telescope was opened for observations. By way of illustration of this point I offer the following observations. At the time of the August 14 data acquisition the truss was cooling at a rate of only -0.19 C/hr. But during the August 15 data acquisition the truss was cooling at a rate of -1.26 C/hr. Its possible that the noise in the August 15 data could have been generated by cooling of the mirrors, but it seems unlikely that such a mechanism would be so clearly confined to the x-tilt motions.

Astigmatism and Spherical Aberration as a Function of Telescope Altitude

Figures 2a and 2b show the telescope spherical aberration as a function of telescope altitude for the nights of August 14 and 15. To compare these results with the coma shown indirectly in Figure 1, its useful to know that a mirror tilt of 25" is equivalent to coma of about 0.30" in the image plane. Figure 2 shows that at the time of the August 14 measurements spherical aberration was negligible compared to coma. But at the time of the August 15 measurements the telescope image quality was dominated by spherical aberration. In a separate (as yet unwritten!) report, using data from several other nights I will show that this variation of spherical aberration is the result of the time of night at which these two measurements were made. The August 14 data were taken at the very end of the night after the telescope had cooled to equilibrium with the ambient atmosphere. The August 15 data were taken near the beginning of the night, right after the dome had been opened. As reported in Figure 2, the telescope and mirror cooling rates during the acquisition of the August 14 and 15 data sets differed by about a factor of 6.

Figures 3a through 3d show the telescope astigmatism as a function of telescope altitude for the nights of August 14 and 15. Both nights show identical behavior of the magnitude and orientation of the astigmatism. As the telescope moves toward the horizon, the astigmatism increases from about 0.12" to 0.22" and the orientation rotates about 25љ in a counter-clockwise fashion. These data represent a significant step forward in the reduction of the telescope astigmatism. Even at altitudes as low as 30љ astigmatism remains a minor contributor to the image blur. Its possible that the current increases in astigmatism as a function of telescope altitude is the result of uneven support of the primary mirror by the transverse posts. But, at this level it's not something we need to worry about.

Defocus as a Function of Telescope Altitude

Figures 4a and 4b show the telescope defocus as a function of time and telescope altitude on the night of August 14. The first graph illustrates the effects of manually changing the telescope focus on the data. Figure 4b shows that on this night, the telescope focus had only a very minor dependence (10 µm) with telescope altitude. Focus changes this small are quite acceptable and will not seriously degrade the image quality of the telescope.

Similar measurements of the defocus as a function of altitude were made on April 14. At that time, the telescope focus was measured to change by approximately 50 µm over a 60љ range in telescope altitude. Shortly after those measurements, corrections were made to the TCC piston coefficients. The smaller variation measured here should be an indication of the improvements that those changes in the piston coefficients have made. However, the measurements which were then made on August 15 show that there are significant complications to this picture and we are not doing as well as these data seem to indicate. I will show below that the differences between these data and that measured on August 15 are probably the result of thermal variations in the telescope.

Figure 5 shows the telescope defocus as a function of telescope altitude as measured on the night of August 15. Unfortunately, several manual focus changes were applied to the telescope during the acquisition of these data and it is not possible to simply throw out a few points as I did in the analysis of the August 14 data set. This complication certainly adds significant uncertainties to this data set. However, it should be immediately obvious from comparing Figures 4 and 5 that the variation of telescope defocus with altitude was measured to be nearly 7 times greater than that seen on August 14! If the magnitude of the defocus variation with telescope altitude had been similar to what was measured earlier, the increased noise from the manual focus shifts would have been sufficient to completely mask the variation. However, the effect is clearly real and points to significant complications in the interpretation of the defocus data.

The cause of the large difference between the defocus changes seen on August 14 and 15 is thought to be temperature variations in the secondary support rods. The first clue to this comes from looking at the data in Figure 5 as a function of both time and telescope altitude. This comparison is shown in Figure 6. The first part of this graph shows what looks like a clear sign of temporal variations in the defocus data. I will assume here that the most likely causes of a slow temporal variation like that seen in Figure 6 are thermal variations in the telescope structure. This idea is supported by the fact that the telescope structure was experiencing major cooling rates at the time the August 15 data were acquired, but not while the April 14 nor August 14 data were acquired. This is indicated by the truss temperatures and cooling rates that are shown in Figures 4 and 5.

Figure 7 clearly shows that the truss temperatures continue to monotonically cool throughout the entire time period covered by the data in Figure 6. From Figure 7 we can estimate that the cooling time for the truss was approximately 1.41 hour. You cannot explain the second half of Figure 6 by appealing to temperature changes in the telescope truss because the truss temperatures change too slowly and they were monotonic at the time of the defocus reversal seen near 3:30 UT. This is the first reason to suspect that something other than the truss is driving the defocus changes seen in Figure 6.

In the next section I will show that theoretically one expects to find that the secondary support rods are as important as the truss in determining the spacing between the primary and secondary mirrors as a function of ambient temperature. This leads us to focus attention on the thermal behavior of the secondary support rods.

Back in May of 1996, Karen (of Loomis fame! Yes, we still miss you, Karen!) was kind enough to measure the temperature of the secondary support rods as the telescope cooled. She measured the temperature and tension on 4 of 8 of the support rods. Her measurements started right after the enclosure was opened and lasted for about 3 hours. Figure 8a shows the temperature data which she recorded for one of the 4 rods measured. The data are fairly well described by an exponential fit. From this data we can estimate an upper limit of 1 hour for the thermal time constants of the rods. The plot of the air temperatures on this same graph shows that the rod time constant could easily be (and probably are) significantly shorter than 1 hour. Figure 8b shows temperature differentials between secondary support rods at the time of the data shown in Figure 7a. Accept for very early in the cooling curve, the rod temperatures are all the same. The differentials seen early in the evening are significant, but below I will focus mostly on the common-mode temperature changes in the secondary support rods.

Thermal Effects on the 3.5m Telescope

In the final section of this report I investigate the primary-secondary mirror spacing as a function of the telescope temperatures. This investigation is driven by an appreciation that focus errors of only 10 µm are sufficient to degrade our image quality by 0.19". The defocus measurements reported above show that we are not currently capable of maintaining telescope focus to this accuracy for large portions of each night. I will show here that thermal changes in the secondary support rods are as important as thermal changes in the truss in determining the mirror spacing. The rods are almost certainly responsible for the telescope's current sensitivity to rapid temperature changes during the night.

I believe that an improved thermal model of the telescope is required if we are to hope to make efficient use of the improved telescope optics. I show the beginnings of such a model at the end of this report. However, we do not currently have enough data to support the implementation of a new thermal model. Future Shack-Hartmann measurements will be key to improving the telescope thermal model.

The calculations done here offer another reason to change the current design of the secondary cage. Owing to subtle asymmetries in the current design, the secondary cage drifts axially with temperature changes. This drift can be removed either by redesigning the cage to make the support rods truly symmetric or by changing the materials used in the current support rods. The current rods are made of 303 (Se) stainless steel. Replacing these with graphite rods would offer about a factor of 2 improvement in the thermal stability of the telescope.

The Thermal Expansion of the Truss

I use here a very simple model for the thermal expansion of the telescope truss. I start by giving values or a range of values for the pertinent telescope variables. For the 3.5m telescope we have:

If we only need to worry about thermal expansions of the truss and the glass, then the change in the M1-M2 separation from the thermal expansion of the truss and the mirrors is given by:

The current (as of 9/19/00) temperature coefficient in the TCC software is +43 µm/C. The difference between the expansion predicted above for the truss and that in the TCC software appears to be significant.

Discussions with Russet on the behavior of the telescope focus as the telescope cools down at the beginning of the night do not help explain this discrepancy. She reports that at the beginning of the night one must often set an instrument focus below what one expects it to be later in the evening. But, this behavior is not consistent from night to night. In other words, she reports an inconsistent positive piston is required as the telescope cools. As shown above, the truss coefficient is a positive quantity, which shows that the truss expands when it warms up. In the 3.5m software a positive piston command moves the secondary closer to the primary. Therefore, as the truss cools and contracts we expect to make negative piston moves. Positive piston moves as the telescope cools, like those reported by Russet imply that the real telescope temperature coefficient is even lower than the current setting of 43 µm. This is inconsistent with the range of CTEs found in carbon steels.

The Thermal Expansion of the Secondary Support Rods

I must begin this discussion with a simple description of the secondary cage geometry. This geometry drives the thermal behavior of the support rods. Figure 9 shows one quarter of the rod and cage geometry. The rods are 1/2" 303(Se) stainless steel. They are held in tension (approximately 5000 lbs.) by turnbuckles near the truss blocks, which are not shown in Figure 9. There are a total of 8 support rods, two on each corner of the square truss assembly.

As the telescope moves from the horizon to the zenith, the support rods sag under the weight of the secondary cage load. This is the normal cause of telescope defocus as a function of altitude. The TCC software compensates for this motion by pistoning the secondary out as a function of telescope altitude. The current piston coefficient for the secondary rod sag in the TCC software is 400 µm. One might question how accurately this is known and whether this sag has any temperature dependence. I will show below that the answer to these questions is "not very well" and "no". The differential motion of the secondary cage as the telescope moves in altitude is not temperature dependent. However, the point from which this differential motion starts is. This is a somewhat subtle distinction that primarily affects the form that one chooses for a thermal model of the telescope. Below and in Appendix B I refer to the "absolute" secondary position when talking about the thermal motions of the secondary cage in an attempt to make this distinction clear. I hope this term does not prove to be confusing.

For those interested in the details, I show my derivation of the secondary sag in Appendix A. The total sag that the secondary will experience as the telescope moves from the horizon to the zenith is given approximately by

where

 

I show in Appendix A that the approximation above is good to about 10%. I also show there that this result is independent of the rod temperatures even if the rods are at different temperatures. All that is required for this equation to hold is that the rod temperatures stay constant during the altitude change. For the 3.5-m telescope we have

Putting these values into the equation above gives = 271 µm. The current sag coefficient in the TCC software is 400 µm. This represents a difference of about 30% from what is calculated here. It is unlikely that this difference can be explained by variations in the expansion of the steel or in the assumed elastic modulus. These parameters are too well known. The most likely source of error in this calculation is in the assumed weight of the secondary cage. Errors in the TCC software coefficient can come from the fact that these parameters are determined from a multi-parameter fit to data. Even if you assume that the data that were used for these fits had no errors, you can still have errors in the fit coefficients based on the fact that many of the parameters that are being fit are not truly orthogonal. At the end of this report I will show that a thermal model that uses the lower sag coefficient calculated above can actually give a better fit to at least a limited data set. This does not prove that the calculations above are a better estimate than what is currently being used in the TCC code, but it does illustrate how multi-parameter fits have the potential for hiding many errors in the assumed coefficients.

While it is true that the differential motion of the secondary as the telescope changes altitude does not depend on temperature, the absolute position of the secondary does. This temperature dependence is entirely due to the asymmetries in the current design of the secondary cage. In Appendix B I show that to an accuracy of about 10%, the absolute position of the secondary depends on the temperature of the support rods as follows

where

For the 3.5-m telescope this translates to

A Provisional Thermal Model of the 3.5-m

I have shown here the unexpected result that the secondary cage axial position is just as sensitive to the temperature of the secondary rods as it is to the temperature of the main truss!

This is a very important for it suggests that the thermal model of the telescope that is currently in the TCC software is never going to do a good job of correcting for telescope thermal effects. The current thermal model simply pistons the secondary based on measurements of the main truss temperature. The analysis above shows that you must include measurements of the rod temperatures if you hope to keep the telescope in focus during thermal changes.

The thermal analysis presented here suggests that a better model for the TCC thermal behavior might be achieved by assuming the following functional form for the secondary piston as a function of temperature

In Figure 10 I show how such a model is consistent with the defocus data taken on August 15. In Figure 10, the functional form above was assumed for the secondary sag and the defocus data were used to fit for the thermal time constant of the rods. The rod thermal time constant so derived was about 22 minutes. Figure 8 showed that the rod thermal time constant must be significantly less than 1 hour. The defocus data and the theoretical thermal expansion coefficients are shown to be consistent with this expectation.

What is shown here is clearly not proof of the model above, but it is encouraging. In Figure 10 it can be seen that the residuals from the model fit are no larger than about 25 µm. The defocus data in Figure 6 represents the residuals of the current TCC thermal model from the optimal focus position. These data are therefore equivalent to the residuals between the model fit and the defocus data shown in Figure 10. A look at Figure 6 shows 60 µm deviations from the current TCC thermal model. The fit in Figure 10 therefore appears to represents a factor of two improvement over the current TCC thermal model.

Can Miscollimation Be Caused by Thermal Effects on the Secondary Cage?

I have focused above on understanding the sag of the secondary as a function of temperature and altitude. However, I have also considered the effects that thermal changes might have on the tilt of the secondary mirror. My conclusions here are that it is unlikely that thermal stresses are responsible for any significant tilts of the secondary. This conclusion is based on two facts. First, tilts require thermal differentials between either the secondary support rods or the main truss supports. When these have been measured, they have been small as expected. Figure 8b is a good example. Maximum differentials in the rods appear to be on the order of 0.5º C. Differential rod temperatures of 0.5º can cause motions on the order of 30 µm, but these differentials are very transient. I suspect that thermal differentials of the truss supports will also be small, but someone might want to investigate this.

Second, tilts of the secondary cage must be very large before they will show up as increased coma. The reason for this is not completely obvious. This follows from the fact that coma may be caused by both translation of the secondary mirror as well as by tilts of the mirror. There is a position, called the "neutral point" by opticians, about which the secondary mirror can rotate without causing significant coma owing to the fact that when the mirror is on this surface the coma induced by its translation cancels that induced by its tilt. The location of the neutral point for the 3.5-m is shown by the center mark in Figure 9. If the cage is rotated about its geometrical center by an angle a1, then the mirror is rotated in space by this same angle. However, with respect to its neutral point it also rotates about an angle a0, which is related to a1 by the equation

where r is the distance from the center of the cage to the vertex of the secondary mirror and is the distance from the center of the cage to the neutral point. When you measure the mirror tilts by measuring the coma with the Shack-Hartmann sensor you are actually measuring (a1 - a0). Almost all cage tilts caused by motions of the rods will have their center of rotation near the optical neutral point. For example, a tilt of 10 arcseconds about the center of the cage results in a differential angle (a1 - a0) ~ 1 arcsecond. 10 arcseconds of tilt corresponds to a differential temperature on the rods of approximately 1.5 ºC, and a linear change of the rods of about 50 µm. To effect a coma change corresponding to a 10 arcsecond tilt therefore corresponds to a cage tilt of about 100 arcseconds or a linear stretching of the rods of about 0.5 mm.

Over the course of several nights we are seeing collimation changes on the order of 50 arcseconds. This corresponds to approximately 500 arcseconds of secondary cage tilt. This requires motions of the rods on the order of 2.5 mm. One might speculate that such tilts might come from slippage in the joints in the secondary cage. This possibility probably deserves some investigation. Because of this, I have the following suggestion for measurements that we might want to make on the 3.5-m.

A Suggestion for Engineering Measurements of the Secondary Cage Position

I would like for us to measure the stability of the secondary cage as the telescope cools down. I suggest that one way to do this would be to fix a small flat mirror to the bottom of the secondary cage. I would then bounce a laser off of this mirror while the telescope is at a fixed position. By measuring the position of the reflected laser beam and knowing the geometry between the laser, the flat mirror, and the reflected beam we might be able to monitor changes in the tilt of the secondary cage. Some very rough calculations suggest that we might be able to measure tilts of a few arcseconds in this manner. Making measurements before and after opening the dome would be good and making measurements in the presence of a wind would be worth while. Having a digital camera set up to make measurements of the laser beam would be a good idea. There are cameras available here at UW that we could use for these measurements.