[Last Change: 05 Apr 2011 (rev 3)]
The HRMA focal length is defined (and used in the data system) as a conversion factor between the linear distances in the detector plane and angular distances in the sky. It has been determined by combining the linear sizes of the detector pixels measured prior to launch with the observed distances, in detector pixels, between X-ray sources in a star cluster (NGC 2516; see this memo for its optical astrometry). Prior to October 2001 (prior to CALDB v2.9), Chandra event files used the convention where one pixel of the sky coordinates (
The last line gives the on-axis value derived from SAOSAC simulations using the HRMA model based on pre-launch calibration, see Ping Zhao's memo (8/08/00). From that study, the focal length at off-axis angles corresponding to ACIS chips other than S3 is expected to be slightly smaller than the on-axis value. This difference (less than 0.5 mm) is much smaller than measurement errors and can be ignored.
A weighted mean of all values in Table 1 is
HRMA focal length
Maxim Markevitch , 1 Dec 01The HRMA focal length is defined (and used in the data system) as a conversion factor between the linear distances in the detector plane and angular distances in the sky. It has been determined by combining the linear sizes of the detector pixels measured prior to launch with the observed distances, in detector pixels, between X-ray sources in a star cluster (NGC 2516; see this memo for its optical astrometry). Prior to October 2001 (prior to CALDB v2.9), Chandra event files used the convention where one pixel of the sky coordinates (
X,Y in the event files) was equal in size to one physical pixel of the corresponding detector. The plate scale, or the angular size of the sky pixel (and therefore of the detector pixel under this convention) was derived using the NGC 2516 observations in all detectors near the optical axis, where the PSF is sufficiently narrow to allow adequate measurements (see this memo).
The ACIS physical pixel size at the focal plane temperature of -120C is 23.987±0.001 micron (68%) and the coefficient of linear expansion at t=-120C is d(ln(L))/dt = 1.9e-6 per degree C (Mark Bautz 9/20/00). Most of the ACIS data used for plate scale measurements were taken at t=-100C for which the above values give a pixel size of 23.988 micron. The difference between -100C and -120C, as well as the error of the physical size, are much smaller than our in-orbit measurement errors. (Note that prior to CALDB 2.9, the value was incorrectly assumed to be 24.000 micron.) The HRC pixel size is 6.42938±0.00006 micron (Steve Murray). Again, its uncertainty is much smaller than our measurement errors.
The followng table summarizes the angular pixel sizes for individual detectors derived from the NGC 2516 observations, and gives the corresponding focal lengths, F:
| Detector | pixel size | focal length | ||
|---|---|---|---|---|
| arcsec (68% error) | micron | mm | 68% | |
| ACIS S3 | 0.49109 (-0.00006 +0.0001) |
23.988 |
10075.3 |
2.1 |
| ACIS S2 | 0.49152 (-0.0002 +0.0001) |
23.988 |
10066.5 |
4.1 |
| ACIS I0 | 0.49137 (-0.0002 +0.0003) |
23.988 |
10069.6 |
4.1 |
| ACIS I1 | 0.49110 (-0.0002 +0.0002) |
23.988 |
10075.1 |
4.1 |
| ACIS I2 | 0.49132 (-0.0001 +0.0001) |
23.988 |
10070.6 |
2.1 |
| ACIS I3 | 0.49170 (-0.0003 +0.0001) |
23.988 |
10062.8 |
6.1 |
| HRC-I | 0.13174 (-0.00004 +0.00002) |
6.42938 |
10066.5 |
3.1 |
| HRC-S | 0.13176 (-0.00007 +0.00011) |
6.42938 |
10064.9 |
5.4 |
| SAOSAC simulations | 10069.8 |
1.1 |
||
F=10070.3±0.6 mm (a formal 68% uncertainty of the average, assuming all errors are statistical). If one excludes the simulation result (whose formal error may be an underestimate), the average is F=10070.9±1.2 mm, in agreement with the simulation result. There appears to be a marginally significant difference between the ACIS-S3 and HRC derived values, possibly indicating an unknown systematic uncertainty. Based on these data, the focal length is postulated to be
F = 10070 ±3 mm
whose 90% confidence interval includes a best-guess systematic uncertainty and approximately spans from the HRC to the ACIS values. The quoted uncertainty corresponds to 0.15" on the size of an ACIS chip. This value of the focal length has been included in CALDB 2.9 and applied for data processing since Oct. 2001. It should be compared to the previous value of 10061.62 mm.
Note also that the sky pixel convention has changed as of CALDB 2.9 -- the sky pixel is no longer tied to the physical detector pixel but rather postulated to be exactly 0.492" for ACIS and 0.1318" for HRC, keeping the old (pre-CALDB 2.9) values. One pixel of the DETX,DETY coords is also equal to the sky pixel, not the detector physical pixel. 