This gives a good estimate of the absolute distance between the HRMA focus to the CAP Datum A, and a good estimate of the uncertainty, which is about one millimeter.
SAOSAC Raytrace Calculation
Meantime, SAOSAC raytrace (with focus turned on, hence the scattering is turned off) gives the distance between the HRMA focus to the CAP Datum A to be 10079.772 mm, which differs only 0.17 mm from the average of the above measurements and well within the measurement errors. This is very important since the SAOSAC is build around the HRMA model based on the HDOS metrology, Kodak assembly and the XRCF X-ray test data; and it is completely independent of the above absolute measurements of the HRMA focus to Datum A distance. This indicates that the current HRMA model in SAOSAC is a faithful representation of the real HRMA regarding the focal length.Therefore the HRMA On-orbit Focal Length can be calculated with good faith using the SAOSAC. Figure 1 illustrates the method of this calculation. Rays from onaxis source come in parallel to the HRMA optical axis and are focused at the onaxis focal point F. The Focal Plane is a flat plane intersect with the optical axis at F. (Detector HRC-I is placed in this plane.) Rays from a offaxis source come in with a small angle theta from the optical axis and are focused on a curved surface between the Focal Plane and the HRMA. The HRMA Focal Length is the distance between points O and F on the optical axis. However, the position of O is unknown. In SAOSAC, the Z-axis is the optical axis and the CAP Datum A is at Z = 0.
For onaxis and offaxis sources, SAOSAC calculates coordinates of the best focal positions as (xo,yo,zo) and (x,y,z) (see Figure 1).
Let r' = sqrt[(x-xo)^2 + (y-yo)^2] FL = r'/tan(theta) + zo - zThis way the FL can be calculated using SAOSAC, for different energies and offaxis angles.
Results
Figures 2-7 show the results of these calculations for 6 energies ( 0.277, 1.497, 4.511, 6.404, 8.639, and 9.700 keV), 8 offaxis angles (1, 2, 3, 5, 7, 10, 15, 20 arcmin) and 4 azimuthal angles (0, 90, 180, 270 degree). Figure 8 is a colored summary plot of the results. The dotted line in the figure is the designed HRMA Focal Length and Plate Scale.It is seen that the HRMA FL is a function of energy and offaxis angle. And it is also slightly asymmetric azimuthally.
Table 1 shows the HRMA On-orbit Focal Length averaged for each energy within certain radii of offaxis angles.
For a near axis (theta =< 3 arcmin) soft source (E < 2 keV), the HRMA Focal Length = 10069.760 +/- 0.454 mm. Considering the systematic error of 1mm from the direct on-ground measurements. We have:
Table 1. Average HRMA On-orbit Focal Length (mm) Energy Offaxis angle within radius of (arcmin) (keV) 3 5 10 15 20 --------------------------------------------------------------- 0.2770 10069.782 10069.571 10069.164 10068.902 10068.563 0.463 0.571 0.787 0.988 1.303 1.4967 10069.737 10069.524 10069.116 10068.852 10068.509 0.463 0.573 0.790 0.994 1.313 4.5108 10068.465 10068.228 10067.723 10067.336 10066.773 0.470 0.621 0.957 1.334 1.982 6.4038 10065.213 10064.884 10064.154 10063.685 10063.064 0.688 0.965 1.506 1.874 2.460 8.6389 10063.697 10063.280 10062.373 10061.872 10061.308 0.938 1.318 2.162 2.472 2.837 9.7000 10063.219 10062.760 10061.841 10061.253 10060.722 3.145 3.419 3.600 3.722 3.820 --------------------------------------------------------------- Mean 10066.685 10066.374 10065.728 10065.316 10064.823 Error 3.079 3.254 3.601 3.813 4.063 ---------------------------------------------------------------
HRMA On-orbit Focal Length = 10069.8 +/- 1.1 mm HRMA Near Axis Plate Scale = 48.8196 +/- 0.0053 micron/arcsec
Back to: Telescope Scientist Home Page