Tilt and Sag Coefficients for the 3.5-m Secondary Mirror: 14 April, 2000

On April 14, 2000 UT a series of Shack-Hartmann measurements were made at varying altitudes. Sixty second exposures of SAO stars between 7 and 8 magnitude were used for most of these measurements. Owing to the brightness of the twilight sky, the last couple of measurements were taken with 5th magnitude stars and used exposure times of only 10 seconds. Five Shack-Hartmann exposures were taken at each telescope altitude. These measurements were averaged to produce the results shown in this report. The tilts and sags shown are those given by the normal Shack-Hartmann analysis. All of these measurements were made with the collimation routine ON. The telescope focus was set before the first series of measurements and kept fixed throughout the rest of the exposures.

These measurements were taken immediately after the new Heidenhain encoders were placed on the secondary. These new encoders are positioned radially inward from the secondary actuators by approximately 1.75". The intent is to eventually use these encoders to make automatic corrections to the mirror position. However, as an initial precaution, during these measurements the control loop that accomplishes these feedback corrections was left off (MAXCORR was set to 0 for all three actuators). Without this feedback, off-telescope tests showed positioning errors on the order of 10 arcseconds in the secondary mirror position. Errors of this magnitude are clearly evident in the data presented here. Turning MAXCORR on may have a considerable beneficial effect for future measurements of this nature.

For future efforts along these same lines, it is important to note the correspondence between the tilt conventions used by the Shack-Hartmann software and those used by the TCC. The critical comparisons are given by the examples in Table 1. The correspondence between the defocus diagnostics given by the Shack-Hartmann software and that used by the TCC is trivial given the fact that positive TCC focus motions move the secondary towards the primary.

Table 1: Comparison of Shack-Harmann Diagnostic Tilts with TCC Motions

Shack-Hartmann Diagnostic Tilt	Corresponding TCC Tilt Required to Correct Collimation
Tilt M2 Bk by X"	change x-tilt by +X"
Tilt M2 Ft by X"	change x-tilt by -X"
Tilt M2 N1 by Y"	change y-tilt by +Y"
Tilt M2 N2 by Y"	change y-tilt by -Y"

As the telescope moves down in elevation, the secondary mirror moves in two directions. It moves away from the primary owing to the decreased axial force on the secondary spider rods. This motion results in a change of the telescope focus position as a function of elevation angle. The secondary also translates toward the front of the telescope owing to the flexure of the main truss and to flexures in the flex pivots which support the secondary mirror on the actuators. Earlier studies have indicated that the total amount of translation is about evenly split between the give in these two support elements. This translation results primarily in an increase in coma in the telescope optics.

Figure 1 shows the tilts required to correct for the translation of the secondary towards the front of the telescope as it moves from the horizon (at an elevation angle of 0 degrees) towards the zenith (90 degrees). There is no evidence for any variation of the y-tilts with telescope elevation angle. This is what we hoped to see! The scatter in the y-tilts has a standard deviation of 4.1 arcseconds. These errors are quite consistent with the mirror position errors seen when the Heidenhain encoders are not used for position feedback of the actuators. Its quite possible that the scatter in the points seen here are dominated by position errors of the actuators themselves.

The x-tilts in Figure 1 clearly show a variation with elevation angle. This variation is fit by the solid line shown in the figure. The functional form of the fit is given in the lower ledgend and was chosen to match that available in the TCC. The coefficients m1 through m3 need to be added to those that are currently in the TCC to correct for the secondary translation with respect to the primary.

Figure 2 shows the defocus as a function of telescope elevation angle as measured by the Shack-Hartmann analysis. We were not manually changing the focus during these measurements, but the collimation subroutine was active for this entire set of measurements. The collimation subroutine should have made the focus independent of telescope elevation angle, but Figure 2 clearly shows a residual variation. This implies that the coefficients used to correct for the telescope sag can be substantially improved.

Table 2 gives the TCC coefficients which are currently active, and the values that Figures 1 and 2 imply are needed to correct for both translation and sag of the secondary mirror. The current tilt and piston coefficients used by the TCC may be found in the TINST directory in the file DEFAULT.DAT. To obtain the new tilt and piston coefficients, the tilt coefficients from Figure 1 were coadded to the original tilt coefficients. Likewise, the coefficients from Figure 2 were coadded to the original pistion coefficients.

Table 2. Suggested Changes to the TCC Tilt and Sag Coefficients

Coefficient Name	Original Coefficients	New Values
SecPistCoef (constant term)	300 (µm)	280
(sin(altitude) term)	-410 (µm)	-400
(cos(altitude) term)	0 (µm)	-28
SecXTiltCoef (constant term)	-34 (arcseconds)	-107
(sin(alt) term)	0 (arcseconds)	24
(cos(alt) term)	0 (arcseconds)	71
SecYTiltCoef (constant term)	25 (arcseconds)	20
(sin(alt) term)	0 (arcseconds)	0
(cos(alt) term)	0 (arcseconds)	0

These new coefficients should be implemented on the telescope as soon as possible. The updates for the "piston" coefficients (I refer to this as "sag" in this report!) can be implemented immediately. However, the tilt coefficients required to correct for telescope coma might have to wait until a new pointing model can be acquired. The new tilt coefficients should be first entered into DEFAULT.DAT and then a new pointing model should be obtained. If this is not done, then pointing errors as large as 13 arcseconds will be superimposed on the current model. If the site staff thinks that additional pointing errors this large can be tolerated, then they can immediately implement all of these corrections.