Page 1 Pointing - 025 JAMES CLERK MAXWELL TELESCOPE Joint Astronomy Centre 665 Komohana Street Hilo, Hawaii 96720, U.S.A. JCMT Note MTUN025.00 ________ _ ___ Pointing - 025 Version 0, Sidney Kenderdine 1988-04-15 Version 1, Maren Hauschildt 1988-05-05: format of model 1 file changed Processed by MT_DOCUMENT: 7 June 1988 CONTENTS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . 2 1.1 Terminology. . . . . . . . . . . . . . . . . . . . 2 2 FUNDAMENTALS . . . . . . . . . . . . . . . . . . . . 2 2.1 Model 0 . . . . . . . . . . . . . . . . . . . . . 2 2.2 Theta(1) And Theta(2) . . . . . . . . . . . . . . 3 3 MODEL 1 . . . . . . . . . . . . . . . . . . . . . . 3 4 POINTING CORRECTION ROUTINES . . . . . . . . . . . . 5 4.1 Conclusions From Pointing Computations . . . . . . 6 5 SIGNS . . . . . . . . . . . . . . . . . . . . . . . 6 5.1 User-defined Offsets . . . . . . . . . . . . . . . 7 Pointing - 025 Page 2 JCMT Note MTUN025.00 7 June 1988 Pointing - 025 1 INTRODUCTION This note describes the new corrections introduced in 025, together with a number of routines which have been developed to test the effect of the new corrections. 025 includes (a) a new model (called model 1) of the telescope behaviour, based on the observed distortions of the structure as it drives in azimuth on an uneven track, and (b) the receiver and site dependent pointing corrections as described in mtun021. 1.1 Terminology. ___ In 025, AZ coordinates refer to az/el wrt the azimuth vertical. EN coordinates are encoder values. In what follows true_AZ is sometimes used, ___ meaning az/el wrt the geographical vertical. 2 FUNDAMENTALS 2.1 Model 0 The simplest form of the geometry of the telescope is specified by five angles: theta(1) and theta(2) to specify the non-verticality of the azimuth drive, theta(3) to specify the non-orthogonality of the azimuth and elevation drives, and theta(4) and theta(5) to specify the departure of the telescope beam _____ _ from a nominal structure axis at right angles to the elevation drive. Model 0 assumes that this description is adequate. It assumes perfect rotations about the drive axes and in its basic form that the five angles are constants. It can be extended, as described in mtin062, to allow theta(4) and theta(5) to be azimuth, elevation, and instrument dependent, in this way catering for flexure, non-axial mounting of receivers etc. Beam swings due to secondary mirror motions are also handled in this way. The effects on the pointing of theta(1) to theta(5) misalignments are listed in mtun005 (with one error in its original version, now corrected). Alternatively they can be investigated empirically by running the telescope task in simulate mode and noting the difference between EN and AZ coordinates (though not for theta(1) and theta(2), see below), or by the stand-alone programs - 2 - Pointing - 025 Page 3 JCMT Note MTUN025.00 7 June 1988 described in Section 4. 2.2 Theta(1) And Theta(2) Strictly speaking, the non-verticality of the azimuth drive as handled by the telescope task corresponds to the following sequence of operations: a) Rotate about the Earth's rotation axis by theta(2), i.e. treat theta(2) as a clock error b) Rotate about the east-west horizontal by theta(1), i.e. treat theta(1) as a latitude error c) Allow for refraction AZ coordinates correspond to the position after these three operations have been performed. The differences between AZ and EN values are therefore independent of theta(1) and theta(2). The refraction correction is based on elevation with respect to the azimuth-drive vertical. The current versions of the various pointing subroutines and stand-alone programs do not here follow the telescope task exactly. Instead they a) Assume that refraction is already allowed for b) Adopt a first order correction for theta(1) and theta(2) Since theta(1) and theta(2) are at most about 20 arcsec, second order effects should be negligible (see pointing computations, below). Comment: This area is slightly ragged in that neither the telescope task nor the pointing correction routines correspond to the real behaviour. I cannot believe that the differences matter, to present accuracy. 3 MODEL 1 _____ ____ Observations and inclinometer measurements show inter alia azimuth errors varying with azimuth at low elevation, arising from irregularities in the azimuth drive track. In no way are these effects compatible with 'pure' _____ _ geometry (model 0). Model 1 has been devised as a first stage in accommodating them. It allows three additional parameters, each varying arbitrarily with azimuth. The parameters are - 3 - Pointing - 025 Page 4 JCMT Note MTUN025.00 7 June 1988 a) F1(A). Change in azimuth encoder value. b) F2(A). Variation of theta(3) with azimuth; the essential part of this variation can be measured directly by inclinometer. c) F3(A). Change in elevation encoder value. The 025 telescope task, and all the stand-alone pointing routines, have this model available as an alternative to model 0. The three functions are supplied by look-up tables; linear interpolation is used between tabular values, although the actual behaviour is more likely to be a series of steps. The data for the model are held on a file of logical name 'model1'. The format of the file is typically as follows: pointing_model_1 30 0 1 5 12 30 3 -4 15 60 6 -9 17 etc whose lines are successively a) The header 'pointing_model_1', to identify the type of file b) The increment in azimuth in degrees between successive entries c) N lines of four values, giving azimuth, F1, F2 and F3 in arcsec for azimuth values of, in the above instance, 0, 30, 60 etc. N must be large enough to cover 450 degrees of azimuth (16 in the example given). N has an upper limit of 500, which could be increased if need be. The azimuth value is not used at the moment but primarily there for keeping track of which line corresponds to which azimuth. After the first line, blank lines, or lines beginning with asterisk (for comment), are ignored. If model 1 is in operation, the telescope task finds F1 to F3 for the current azimuth at each second. Standard model 0 geometry then applies, except that in converting from AZ to EN a) the encoder azimuth is decreased by F1 b) the value of theta(3) is taken as that from the telescope file plus F2 c) the del0 value is increased by F3, or equivalently the encoder elevation is decreased by F3. Note: Inclinometer measurements provide directly the inclination of the elevation drive as a function of azimuth. To first order the inclination is given by inclination = theta(3) + F2(A) + theta(2)*cos(lat)*cos(A) - 4 - Pointing - 025 Page 5 JCMT Note MTUN025.00 7 June 1988 - theta(1)*sin(A) It may be sensible to filter the measured inclination plot to remove the constant and cos(A), sin(A) components; what remains will then be orthogonal to other variations. Similarly it may be sensible to remove the first harmonic from F3(A). F1(A) must include the first harmonic, since pure geometry would imply F1 = constant. 4 POINTING CORRECTION ROUTINES Here I describe a set of programs and subroutines for handling pointing corrections. The routines are in a new a new subdirectory, of logical name mt_pointdir. They make extensive use of the subroutines in the telescope task library in mt_teldir; much of the calculation is then necessarily parallel to that done by the telescope task. It is intended to put all the subroutines into the mt_teldir library in due course. The most important subroutines are call point_ats2es(AZ,EL,THETA,MODEL,EAZ,EEL,OUT,STATUS) call point_es2ats(EAZ,EEL,THETA,MODEL,AZ,EL,OUT,STATUS) Point_ats2es converts true azimuth AZ and elevation EL to encoder azimuth EAZ and elevation EEL for given THETA(1) to (5) and MODEL (0 or 1); point_es2ats does the inverse. OUT is for holding an output message, STATUS is a return status (adam__ok is normal). All angles are real*8 in radians. Note that the 'input' azimuth and elevation are with respect to the geographical vertical; the conversions will only correspond to the telescope task's conversions between AZ and EN if theta(1) and theta(2) are both zero. The above two routines are used as the basis for a set of stand-alone programs. 1) Point_p1. This simply performs true azimuth/elevation to encoder values from arguments entered in convenient units from a terminal; it provides EN minus true_AZ values, with d(az) both on the sky and at the encoders. Type 'run point_p1' and the rest should be self-explanatory. 2) Point_p2 does the reverse operation. 3) Point_p3 computes for fixed true_AZ the first and second derivatives of the azimuth and encoder errors with respect to the five paramerers theta(1) to theta(5) d(encoder_az_or_el)/d(theta(i)) d2(encoder_az_or_el)/d(theta(i))d(theta(j)) The first derivatives may be compared with the table in mtun005. The second - 5 - Pointing - 025 Page 6 JCMT Note MTUN025.00 7 June 1988 derivatives show the extent to which the different corrections are orthogonal; some results are given in the next section. 4) Point_p5 computes the inclination of the elevation axis for model 1 and stated theta(1) to theta(5). 5) Point_lsq is a least-squares fitting of (x,y) data to a parabola, written for analysis of secondary mirror focussing data. It should be self_explanatory following 'r point_lsq'. 4.1 Conclusions From Pointing Computations 1) Program point_p3 when run for a variety of azimuths at elevation 80 degrees shows that second derivatives, when not zero, are typically of the order 30 milliarcsec (per arcsec)**2. Values of theta(i) can be up to 300 arcsec for theta(4) from secondary mirror chopping and perhaps up to 60 to 100 for theta(1) to (3). The departures from linearity are then about 1 arcsec. They are twice this at elevation 85 degrees. For most elevations pointing errors and corrections can in practice be handled additively. Theta(5) is orthogonal to all other effects and can always be handled additively. 2) The routine point_p5 can be used to demonstate the relation between inclination and other variables (Section 3). 5 SIGNS There is ample scope for confusion. With some trepidation, having handled virtually no real data, I give the following resume of what I believe the position to be. Mtin062 defines daz0 and del0 as follows: if the telescope is imagined swung without distortion so that the elevation drive is east-west and horizontal and the nominal telescope axis pointing to the north horizon, then the actual beam would be at (daz0,del0) in azimuth and elevation. If say both daz0 and del0 were positive, then the encoder values needed to bring a source into the beam would be less than the true az/el values. By convention, errors are quoted as Error = actual encoder position minus demanded encoder position They are the values that would be displayed if the tracker-ball had been used to point the beam to the source and would be negative in the present example. Hence - 6 - Pointing - 025 Page 7 JCMT Note MTUN025.00 7 June 1988 Observed error = EN - AZ = - (daz0,del0) Errors are fitted by 'fit7' of August 1986 and its successors. Each parameter, e.g. theta(3), has a contribution at any az and el weighted by factors given in mtun005; the signs of the factors are arbitrary from parameter to parameter but not from az to el for the same factor. When parameters are fed into the telescope task via telescope.dat, they have the same sign as in the output from the fitting program. Theta(3) and theta(4) are handled as described in mtin062. The effect of this is that when the corrections are introduced, Residual error + correction = EN - AZ = - (daz0,del0) ___ From the table of mtun005, theta(4) has a weight factor of -1 wrt ___ azimuth and zero wrt elevation. Therefore for a first-order azimuth correction put in by theta(4), residual error - theta(4) = EN - AZ = - daz0 i.e. theta(4) is daz0 and not minus it. Elevation encoder zero has a weight of +1; del0 is therefore equivalent to minus d(encoder zero). In 025 theta(5) is regarded as the del0 of the nominal telescope axis and is put into telescope.dat as an explicit parameter. It is suggested that future pointing analyses fit for theta(5) with a weighting of -1, so as to be parallel to theta(4) and daz0, rather than with +1 to give an explicit encoder zero change. A future stage of fitting will be to include the Cassegrain flexure and Nasmyth terms as described in mtin062. The expressions derived are (daz0,del0) contributions and are handled by the telescope task as such, i.e. as additions to theta(4) and theta(5). To determine the constants from fitting, it is therefore necessary for the weighting factors in the fit _____ program to be minus the expressions given in mtin062. 5.1 User-defined Offsets The 025 telescope task allows the user to introduce empirical corrections to the daz0 and del0 used by the telescope task. By convention these have the same sign as the observed errors they are trying to correct for. The effect of a positive user-defined offset is therefore to decrease the effective daz0 and del0. - 7 -