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From: "William Podgorski" <wap@cface4.harvard.edu>
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Date: Fri, 29 Sep 1995 11:07:36 -0400
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Subject: Co-ordinates
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On Sep 28,  9:34am, Richard J. Edgar wrote:
> Subject: reminder
>
> Bill,
>
>      This is a reminder that, at our Tuesday meeting, you signed up
> to provide conversions between whatever coordinates are used in the
> specification of mirror properties (scattering tables, in my case),
> and telescope coordinates.  Since our software has the ability to
> model misplaced mirrors, I suppose what I actually want is the
> coordinates, in the Kodak mirror system, of the fiducial point whose
> location is specified in our OSAC (actually trace-shell) inputs, for
> each of the 8 mirrors.
>
> 					thanks,
> 					Dick Edgar
>
>
> =============================================================================
> Richard J. Edgar edgar@head-cfa.harvard.edu | "It all depends, of course,
> Harvard-Smithsonian Center for Astrophysics | upon whether or not it depends
> 60 Garden St., MS 81, Cambridge, MA 02138   | or not, of course, if you take
> phone: (617)495-7249; fax: (617)495-7356    | my meaning."  --John Woolley
>-- End of excerpt from Richard J. Edgar


Dick,

In response to your E-Mail.

There are several HDOS co-ordinate systems which are relevant to both the
scattering and the surface maps. They are defined in the TRW mirror
spec, EQ7-002(Rev E). The Telescope Ensemble(TE)co-ordinate system
has its origin at the ideal focus and its Z azis positive from the
ideal focal plane towards the HRMA, along the optical axis. The ideal
optical surface geometry is specified in EQ7-002 with respect to the
TE system.

The HDOS optical metrology data is specified in separate Mirror Element(ME)
co-cordinate systems, one per optic. These ME co-ordinate systems are
aligned with their Z axes along the TE Z axis, but with their zero
point(in Z) offset such that Z=0 in the ME system is co-incident with
the beginning of the UNCUT optic(each uncut optic was 39" or 990.6mm long).
Their X axes are aligned with the optic primary zero azimuth reference
fiducial.

The transformations between the TE system and the ME systems are:

     Z_ME = Z_TE -  9103.6mm  (for all H's)

     and

     Z_ME = Z_TE - 10022.6mm  (for all P's)

The OSAC derived SAO raytrace uses a body centered co-ordinate system
for each optic. Unfortunately, the sense of our SAOSAC Z axis is opposite
that of the HDOS ME systems.

Anyway, the following series of operations is required to go from the
HDOS ME CS to our SAOSAC CS:

     1. Translate the origin of the ME CS to the center of the as-cut
        optic, distance is: (Z_ec + L/2) where Z_ec is the narrow end
        end cut value and L is optic length.

     2. Rotate by 180 deg about the(translated) X axis(which
        reverses the sense of the Z axis). This leaves the new
        X axis aligned with the ME X axis but reverses the sense of
        the Y axis. Angles in new system are measured in opposite
        direction(clocking) in new system.

     3. Rotate about the Z axis to move the X axis from the ME X
        to the desired SAOSAC X, by an angle TH_C, or optic clocking
        angle. We have a choice of sign conventions here, and we have
        chosen to to define TH_C as the POSITIVE angular rotation
        about the SAOSAC +Z axis which is required to align the SAOSAC
        X axis with the ME fiducial(X_ME axis).

Working in cylindrical co-ordinates, the relationships between the ME
CS and the SAOSAC CS are as follows:

                    Z_O = (Z_ec + L/2) - Z_ME

                    TH_O - 2*Pi - TH_ME + TH_C

                    R_O = R_ME

                    where:

                        Z_O, Z_ME    - SAOSAC and ME CS Z co-ordinates

                        TH_O, TH_ME  - SAOSAC and ME CS rotation angles
                                       measured from the X axes, positive
                                       respective Z axes

                        R_O, R_ME    - SAOSAC and ME CS radial co-ordinates

Now, the axial data(all in mm):

                                                      ME Data Range
   Optic      Z_ec           L        Z_ec + L/2    Z_ME(N)    Z_ME(W)
   -----      --------   ---------    ----------    -------   ----------
     P1        95.29X      842.215      516.397      95.29X    937.505
     P3        74.223      842.208      495.327      74.223    916.431
     P4        74.198      842.208      495.302      74.198    916.406
     P6        74.19X      842.209      495.294      74.19X    916.399
     H1        77.818      842.192      498.914      77.818    920.010
     H3        74.193      842.197      495.291      74.193    916.390
     H4        74.185      842.225      495.297      74.185    916.410
     H6        74.183      842.200      495.293      74.183    916.383


Optic Axial Positions(Revised)
------------------------------

The nominal HRMA design places the apertures of the optics 80.8mm apart.
This is for an optic with aperture length 838.2mm(33in exactly). So the
nominal optic spacing, accounting for the fact that the optics are 2mm
oversized on each end(length=842.2), is 76.8mm. The optic spacing
to the CAP mid-plane is therefore 38.4mm, nominal.

Tom Casey has computed, based on HDOS data, offsets of each optic
from the nominal axial spacing. These offsets were transmitted to
Lester over the phone and are as follows:

      P1/H1:    +11.30mm/+0.16mm
      P3/H3:     -0.23mm/-0.26mm
      P4/H4:     -3.54mm/-0.11mm
      P6/H6:     -8.57mm/-2.00mm

                 where a POSITIVE value indicates a shift TOWARDS
                 the FOCUS

Given the above numbers and sign convention, we can compute the spacing
between the ends of the optics and the CAP mid-plane. We can also
compute the spacing between the ends of the optics and the CAP datum
planes, based on the AS-MEASURED CAP thickness of 49.911mm(1.965").


                   P's to CAP                 H's to CAP
              Datum "A"   Midplane       Midplane    Datum "D"
              ---------   --------       --------    ---------
Shell 1          2.14mm    27.10mm        38.56mm      13.60mm
Shell 3         13.67mm    38.63mm        38.14mm      13.18mm
Shell 4         16.98mm    41.94mm        38.29mm      13.33mm
Shell 6         22.01mm    46.97mm        36.40mm      11.44mm

I have computed two sets of SAOSAC offsets, one from Datum "A", and one
from the center of the CAP. The SAOSAC Z0 values then become:


     Optic         Z0 - From Datum "A"    Z0 - From CAP Mid-plane
     -----         -------------------    -----------------------
       P1               -423.247                 -448.202
       P3               -434.774                 -459.729
       P4               -438.084                 -463.039
       P6               -443.114                 -468.069
       H1                484.607                  459.651
       H3                484.189                  459.233
       H4                484.353                  459.397
       H6                482.451                  457.495

Optic Clocking
--------------

Data received from Kodak(Norm Discher) show optic clockings relative to
the zero degree fiducial on the MMIS(looking down). The clockings are of
the primary optic fiducial. Relationship to the HRMA co-ordinates will
come a little later as Gary Matthews is looking this up.

                    Clocking on MMIS(Note 1)

      Shell       P Mirror(deg)     H Mirror(deg)     (H - P)
      -----       -------------     -------------     -------
      P1/H1           30.00             76.25          46.25
      P3/H3           40.50             42.00           1.50
      P4/H4           30.00             63.00          33.00
      P6/H6           34.00            316.50         282.50

Note 1: Clocking angle of optic primary fiducial with respect to
        MMIS zero degree fiducial





      P1/H1


Bill

PS: More to come

-- 
===============================================================================
William A. Podgorski                Harvard-Smithsonian Center for Astrophysics,
                                       Smithsonian Astrophysical Observatory
Email: wpodgorski@cfa.harvard.edu   60 Garden Street, MS 5
Phone: 617 495 7363                 Cambridge, MA  02138
FAX:   617 495 7098                 USA

