**Summary**

Capella was observed in April 2002 and the data were processed with the standard pipelines to Level 1a. Spectra of the level 1a tg_lam values (in energy) were created with HAK s/w and bright lines fit. The centriods of bright HEG and MEG lines on the plus and minus sides of the ACIS-S array were used to estimate any changes required in the spacing of the ACIS-S CCDs, that is changes to the sizes of the "chip gaps".

The result for this one observation/measurement is that the chips should be shifted in TDETX direction by the following amounts in pixels:

S0 : 0.53 S1 : 0.31 S2 : 0.20 S3 : 0 (0 by definition) S4 : -0.03 S5 : -0.23

That these values are all less than or about 1/2 a pixel is confirmation of a stable (and well adjusted) chip geometry (the current chip gaps were determined back in the Fall of 1999 soon after launch!)

**Software**

The measured centroid values in energy were manually entered
in the file
**chip_gap_solve.2583.pro**.
This file also has the IDL calculations to solve for the chip gaps and
chip offsets from the given measured line locations.
The output of running the file (by doing IDL> @chip_gap_solve.2583.pro)
has been captured in the output file
**chip_gap_solve.2583.txt**.

**Method**

The assumption is that a line seen on one side of the ACIS-S array should be measured to have the same wavelength when seen on the other side, that is lambda(m=-1) = lambda(m=+1). Note that no assumption about the absolute line wavelength is made. Any difference between these wavelengths is assumed to be due to a calibration error in the size of the chip gaps. Another term is also included which allows that the zeroth-order for the HEG and MEG gratings (that is the corresponding HRMA shell pairs) can be offset from each other as well. (Early-on a large offset, 0.42 pixel, was seen but has been traced to a s/w error in HAK code. As listed in the output file above an offset of 0.15 is measured in the 2583 observation.)

For each given line some linear combination of these six parameters (5 gap width changes and 1 HEG-MEG zeroth-order offset value) describes the measured plus-minus difference. The linear combination depends on which gaps are between the minus-order location and the plus-order location, that is, which chips the orders fall on. The chips which different lines fall on are given in the table below (taken from the output file), e.g., the MEG plus/minus first orders of the 6.6[479]A Si resonance line lands on chips S2 and S3 and so the plus/minus difference will depend on the size of the S2-S3 chip gap and the HEG-MEG zeroth-order offset.

Plus - Minus Differences (pixels) Spec/Wav./chips Measured Fit Difference MEG/6.6 S2-S3 : -0.221173 -0.262278 0.041 MEG/8.4 S2-S3 : -0.303384 -0.262278 -0.041 MEG/9.2 S2-S4 : -0.268236 -0.227809 -0.040 MEG/12. S2-S4 : -0.202741 -0.227809 0.025 MEG/15. S1-S4 : -0.371021 -0.334123 -0.037 MEG/19. S1-S4 : -0.281866 -0.334123 0.052 HEG/6.6 S2-S4 : 0.0961790 0.0808198 0.015 HEG/8.4 S1-S4 : -0.102865 -0.0254945 -0.077 HEG/9.2 S1-S4 : 0.0365172 -0.0254945 0.062 HEG/12. S1-S5 : 0.170756 0.170756 -0.000 HEG/15. S0-S5 : -0.0522898 -0.0522899 0.000

For the 11 lines listed above, a matrix relates the measured values to the parameter values

[lambda(plus) - lambda(minus)] = [Matrix] * [Parameters: 5 gaps and HEG-MEG offset]where the rows of the matrix are the linear combinations appropriate to each measured line and the matrix is given by:

[0.0, 0.0, 1.0, 0.0, 0.0, -2.0*meg_delta_frac] [0.0, 0.0, 1.0, 0.0, 0.0, -2.0*meg_delta_frac] [0.0, 0.0, 1.0, -1., 0.0, -2.0*meg_delta_frac] [0.0, 0.0, 1.0, -1., 0.0, -2.0*meg_delta_frac] [0.0, 1.0, 1.0, -1., 0.0, -2.0*meg_delta_frac] [0.0, 1.0, 1.0, -1., 0.0, -2.0*meg_delta_frac] [0.0, 0.0, 1.0, -1., 0.0, +2.0*heg_delta_frac] [0.0, 1.0, 1.0, -1., 0.0, +2.0*heg_delta_frac] [0.0, 1.0, 1.0, -1., 0.0, +2.0*heg_delta_frac] [0.0, 1.0, 1.0, -1., -1., +2.0*heg_delta_frac] [1.0, 1.0, 1.0, -1., -1., +2.0*heg_delta_frac]

Singular value decomposition is used to find the best-fit values of the 6 parameters in this over-constrained system using IDL procedures "svdc" and "svsol".

**Uncertainties**

Note that errors are not included at this time. Single
measurements may have uncertainties around 0.2 pixel... A total of 11
measurement differences are used to determine 6 unknowns: the 5
gap changes and one HEG-MEG zeroth-order
offset value. The scatter around the
fit differences is in the table at the end of the output file, see the
last column of the table shown above.
These "Difference" column
values are all less than 0.1 pixel in size(!), suggesting
that this level of accuracy may be attainable... Uniform analysis
of all Capella data sets is recommended for a definitive result.

*Please send any comments to
Dan Dewey at dd@space.mit.edu.*