The first performs the refinement based on the mosaics, and then propagates this backwards to the BCD. To do this, the frames must be first registered to each other and then mosaiced. 2MASS stars are extracted and then the mosaic pointing is refined. This has several undesirable features. First, this introduces the possibility of positional distortion due to propagated drifts. Since the initial positional accuracy is already as good as 1.5", the latter refinement may actually be systematicaly worse than doing nothing at all. Second, the back-propogation to the BCD is likely to be complicated due to the need to translate the positional and rotational changes in the mosaic backwards through the projection to the msaiced reference frame.

The second refines the positions on a DCE by DCE basis. This is the preferable approach. This will ensure positional accuracy prior to mosaicing, and should obviate the need for any further positional tweaking for the mosaicing step. Furthermore, by making the individual BCD positions more accurate, it will make the BCD more flexible for later custom processing by the users.

The following steps can be used to do the refinement.

1. This only works for full array data. Sub-array should not be position refined.
2. First, define an ensemble of BCDs that are taken simultaneously, and hence at the same telescope pointing. These can be easily identified as all BCDs with the same AORID and EXPID. When IRAC is commanded to take data, it takes data with all 4 arrays at the same time. Thus, for any given EXPID, there will be 1 frame from chanel 1, 1 from channel 2, 1 from channel 3, and between 1 and 4 from channel 4.
3. Run the source extractor on channels 1 and 2 and extract the star fluxes (in Jy) and locations (in RA and DEC). Note that this must be in flux units and in RA and DEC, and hence must be done on the BCD. The former allows flux matching, the latter means that the frame table (which defines the relationship between the four IRAC channels) is taken into account.
4. Retrieve from the 2MASS database all 2MASS stars that lie within channel 1 and 2 fields. The easiest way is to use a radius of 3.6' centered at the field centers. I do not know what the rate-limiting step is here. It could be done with two calls to the 2MASS database, one per channel, or one call centered between the channels, with a radius of 10'.
5. Match the 2MASS sources vs. the detected sources. A match will be made if two conditions are met:

   • They lie within 5" of each other. The match should be made in RA and DEC.

   • Their fluxes match to within a factor of 5. The expected flux for a source in each channel shall be determined from the 2MASS K-band magnitude of the star.

     Flux(channel 1) = 250 * 10^(Kmag/-2.5) Jy
     Flux(channel 2) = 160 * 10^(Kmag/-2.5) Jy

     For the record, the above uses the flux zeropoints of Tokunaga and assumes that the stars are colorless, which at these wavelengths is nearly true for most stellar classes.

6. If no matching stars are found in any frames, then no refinement is made. The existing CRVALi values are copied to the keywords RFCRVALi. RFCRVALi are keywords I have made up to hold the refined centerpoints.
7. If one matching star is found (over both frames), the offset in RA and DEC is computed, and this is propagated to all of the frames in the ensemble by adding the RA and DEC offsets to the values of CRVALi.
8. If two or more matching stars are found, then both the linear offsets in RA and DEC and an offset in twist angle should be computed and the results propagated to all the frames. Note that the twist will have to be encoded into an equivanlent to the CDi_j matrix. Do not try to fit the pixel size in the CD matrix, this is too many parameters and will be better known from other measurements. Note that by fitting to all the stars in all the frames at the same time, we are implicitly using the frame table and the fact that the positions of the arrays relative to each other are known and fixed.

Finally, we will want some diagnostic output. A HISTORY comment should appear in the header, with the size of the offsets, the number of stars used, and the scatter in the offsets for each star before refinement. A warning should appear in the header if the derived offsets exceed 15". An output table file should be made to be supplied with the BCD. This should include one line per 2MASS star, with the 2MASS positions, the pre-refinement positions, and the 2MASS and IRAC fluxes.