Ray-tracing Diagnostics

Problems with the SPARO tertiary template, or are they?.

This report details the current state of the investigations into the beam size discrepancy via the condensing mirror of the SPARO setup of the Viper telescope. The problem detailed in the initial report seem to be primarily a result of our reliance that the CR ray on the template was the center ray in a supplied ray trace file (1.3 m OA ray) and an important sign flip on one of the vectors. After a number of confusing results detailed elsewhere we now realize that the template CR is not the 1.3m OA ray, and that we should define our coordinates relative to something more definite (the chopper). This report mimics and extends the previous analysis using the 1.35 m OA ray that is the real center ray for the Viper system (and possibly the SPARO/Viper template). We show that the difference in the angle of incidence at the Condensing (marked as tertiary) mirror in the initial report disappears.

The following Beam4 ray trace file was used:

6 rays      sparo.ray
  Y0      X0     Z0   @wave
 0.000:1.300000:-1.0:       B
 0.000:1.000000:-1.0:       :
 0.000:1.600000:-1.0:       :
-0.350:1.300000:-1.0:       :
-0.350:1.300000:-1.0:       :
0.0000:1.350000:-1.0:       G
Additional columns were used to glean output data from the ray trace, however these four columns were the only input data.

The configureation file used in the raytracing of SPARO is the following:

    Z        X       Y      C         S     Mir/Len   T       P       R 
   1.5  :   0.0   : 0.0 :-.333333:.01020408: mirror: 0.0 :   0.0   : 0.0 :    :
  -0.5  :   0.0   : 0.0 : 1.1429 :.41699219: mirror: 0.0 :   0.0   : 0.0 :    :
-.00273 :-0.07317 : 0.0 :  0.0   :   0.0   : mirror: 0.0 :   0.0   : 0.0 :    :
-.589941:-1.148669: 0.0 :1.023577:-1.30073 : mirror: 0.0 :92.935396: 0.0 :    :
-.60982 :-0.76102 : 0.0 :  0.0   :   0.0   : detect: 0.0 :-36.51063: 0.0 :    :
        :         :     :        :         :       :     :         :     :    :
        :         :     :        :         :       :     :         :     :    ;
This is the same information used in the report from October, 2000.

The measurements involve tracing the central ray in both BEAM3 and then manually on the stainless steel template that was made in 1998 at CMU using this information. It is now known that the 'CR' marked on the template was drawn by Tom Renbarger of NU while at Pole, useing a mark on the secondary indicating the position of the central ray.

Based on the work of the past few months, two sets of measurements with the template are possible.

  1. Using a coordinate system to measure the points of impact with the various surfaces (secondary, chopper, etc.), and translating them into the system used in Beam4. This translation is indicated here. It is then possible to determine the distances between the points (the optical path length) and the angles between the incident and reflected rays, using the dot-product of the normalized vectors. The uncertainties in the position measurements are unknown, but are likely around a few millimeters.
  2. Physically measuring the OPL with a meterstick on the template. These measurements are accurate to with in several (less than 5) millimeters. The angles between incident rays are measured with a protractor, to an accuracy of ~1 degree (due to the overly wide ray markings).
Measurements in Beam4 are made using the InOut command in the ray table, using the P (OPL variable) and the vector variables (U,V,W) at each surface. To find the difference between the chopper and the condensing mirror (surfaces 3 and 4 in the optics table above) you simply use OPL=P4-P3. Similarly, the angle of incidence at the chopper is arccos( * ), where * is the scalar product of the two vectors.

For the determination of angles using the scalar product to find the cosine, it is highly important to make sure the vectors are tail to tail. Normally, this error is easy to catch. However in the October report, the angle at the condensing mirror was very close to 90 degrees, leading us to a false conclusion. Therefore, special care was taken in this analysis.

Angle of Incidence for the Central Ray (degrees)
Using method 1. above
Measured: BEAM3: Difference:
Secondary: 20.5697 20.5558 0.013873
Chopper: 32.8452 33.6104 -0.7652
Condensing: 47.673 47.317 0.356

Path difference between surfaces (cm)
Using method 1. above
Measured: BEAM3: Difference:
Prime Focus to Secondary: 58.92 cm 58.9162 cm 0.0038 cm
Secondary to Chopper: 63.5125 cm 63.626 cm -0.1135 cm
Chopper to Condensing: 56.379 cm 55.814 cm -0.565 cm
Angles of incidence (degrees)
Using method 2. above
Measured: BEAM3: Difference:
Secondary: 20.55 20.5558 -0.00585
Chopper: 32.55 33.6104 -1.0604
Condensing: 47.25 47.317 -0.067
Path difference between surfaces (cm)
Using method 2. above
Measured: BEAM3: Difference:
Prime Focus to Secondary: 58.65 cm 58.9162 cm -0.2662 cm
Secondary to Chopper: 63.45 63.626 cm -0.176 cm
Chopper to Condensing: 55.5 cm 55.814 cm -0.314 cm

Investigations of other files on disk reveal that this is, in fact the setup that bears the closest resembelence to the template. Secondly, we are doubly sure this is the correct optical setup for SPARO in that 0.7 meters of the primary are illuminated by a focused beam, just like the real telescope.

Thus, after comparing with the original report, the anaomolies at the condensing mirror are no longer present, regardless of how the points are measured. In terms of accuracy, the first method is probably more accurate, but by both measures, the parameters on the condensing mirror are well within the boundaries established by the other surfaces. Investigations are ongoing, however.

Last updated August 22, 2001 by C. Greer.