A separate Cookbook describes the necessary sequence of commands (reduce_switch, flatfield, extinction, change_quality, remsky, rebin). We do not suggest any change to this seqeunce. What has changed since the Cookbook was written are the method of analysing skydips and other opacity data for the extinction values, and the subsequent analysis of the rebin-ned image for parameters such as the peak value, the integrated flux (as measured, for instance, in a large software aperture) and the profile shape.
This document analyses jiggle maps of bright, point-like sources of known brightness (calibrators), in order to extract the basic characteristics of the acquired images : their shape and intensity. Observationally, one would observe calibrators in the same way as targets in order to extend and scale these characteristics to the target sources.
Jiggle maps of flux calibrators (planets and secondary calibrators ) taken between 05 December 1999 and 29 February 2000 form the basis of this analysis. Reductions were performed only on those maps (numbering almost 50), with n_integrations=3 or more, taken immediately before or after a skydip, or taken sometime between two skydips which are themselves taken less than one hour apart. This ensures that the values of tau used in extinction are sufficiently accurate to limit errors on the derived FCFs to 10% or less.
The skydips were analysed as described elsewhere , and a standard pattern of reduction was followed as described above . Calibrators are normally sufficiently bright that no particular effort was made to remove from the reductions (using change_quality) any bolometers that performed noisily on any individual night. While such a process, using the noise files as a guide, might not be beyond the scope of an automated reduction package, its omission here is mitigated to some extent by the knowledge that the central bolometers have in the past been relatively quiet, and that sky measures from noisy bolometers are essentially ignored by use of median filtering during remsky. Any remaining problems due to omission of this step may occur in data of low S/N, such as at 450microns in poor transmissions.
The practice described in the Cookbook has then been to extract the peak flux level in the rebinned images (in volts), and we repeat this procedure here using the kappa routine stats. In the case of data with weak source signal (eg, 450micron data taken in conditions of poor transmission), when noise in the data outshines the source signal and 'fools' stats into locating a noise peak, the gaia package was used to identify the location of the peak signal and to measure its strength.
The measured peak fluxes are then compared with the source brightnesses (from FLUXES) to derive the FCFs.
The FCFs determined from the above sample of jiggle maps using the 450w and 850w filters are summarized below :
| 850w | 219 + 21 | UT or airmass or tau . |
| 450w | 308 + 109 | chop - because of efficiency of observing cycle, UT - because of temperature effects upon dish shape, airmass - because of dish shape changes, and tau - for reasons not yet fully understood. |
Note also :
-
The two most extreme values shown in the 450micron plots were
discarded before the tabulated means and s.d.'s were calculated.
-
The tabulated results appear independent of the source being
used :
Half the sample was maps of crl618, and the mean and s.d. for the 25 measures at 850microns are 214+15, and for the 22 measures at 450microns are 273+57.
The above procedure relies on the signal voltage at the peak of the image for the purposes of determining source brightness and/or the appropriate FCF, and ignores the wealth of data contained in the whole image. We ought to be able to use this data to better constrain the performance of SCUBA in this mode.
The set of 850um calibration images described above were also analyzed using the psf routine within the kappa package for image profile parameters. psf fits a two-dimensional gaussian to the image, by fitting a function of the form
D = A exp(-0.5 * (r/sigma) ** gamma ).
where
- A is the peak signal
- r is the radial distance
- sigma is the mean profile width
- gamma is the 'radial fall-off' parameter, usually of value ~2.
Although these (49) data have been selected carefully already, it seems feasible to screen them further before deriving descriptive mean parameter values. For instance, the ratio
R =
peak value from
psf fitting
peak value from
stats
= 1.026+0.007
but some of these values may be derived from 'poor' fits. A plot of this ratio against the derived image orientation, for instance (see plot below left)
show a distinct clustering of data with orientations of zero (i.e. in the azimuthal chop direction, as one might expect). The plot above right, shows the derived axis ratio plotted against orientation, and again there is a clear subset of the data clustering around orientations of zero and axis ratios of between 1.0 and 1.2. We expect that good focussing and tracking should produce reasonably symmetric images and feel justified in eliminating particularly elliptical images from this analysis. It is possible, of course that some of our calibrators are intrinsically asymmetric (eg IRAS16293-2422) and that repeated observations in the same part of the sky has produced the clustering of elongated images with similar non-zero (70o) orientations. However, their elimination from this analysis for characteristic descriptors of SCUBA images is still justified.
Thus, data with derived orientations significantly different from zero and derived axis ratios outside the range (1.0,1.1) are eliminated (leaving 28 images in the sample).
One further datum was eliminated on the basis of a peculiar value of R. One final datum was eliminated for having an odd value of gamma. The plots below show the distribution of gamma in the original sample (left) and after the above eliminations (right).
Clearly we could have used the value of gamma (2.154+0.007) as a discriminator from the outset and achieved the same resulting subset.
The ratio R from this screened subset, of 26 images, is 1.003+0.002, so from a photometric perspective the derivation of the FCF using stats is valid to high precision, and psf could be used as an aid in quality control as described above.
The observed FWHM measures of the image are 'deconvolved' where necessary (such as with the planets Mars and Uranus) by the source diameter, W, into estimates of the HPBW, using the formulae
HPBWmaj2 = FWHMmaj2 - 0.5
* ln(2)*W2
HPBWmin2 = FWHMmin2 - 0.5
* ln(2)*W2
HPBW2 = HPBWmaj * HPBWmin .
The above 26 images then have
- a mean axis ratio of 1.057+0.004 (s.e.m.), and
- a mean HPBW of 15.39"+0.25" (s.d.).
- time (i.e. date) (at least in the 3-month period investigated),
- chop size,
- airmass ,
- tau , or
- time of day .
The above analyses all used a 3" pixel size for the rebin-ning of the data in the AZ coordinate system. This broadens the final image somewhat from its intrinsic size, but at a level, one might imagine, in proportion to the ratio (pixel_size/HPBW)2, or about 4%. The effect is more dramatic at 450um.
Most of our calibration sources have peculiarities of size or shape that compromise the above analysis to some extent. The derivation of the beam size is best achieved from bright sources which can be observed quickly so as to avoid image smearing due to tracking errors, and in this regard the deconvolved images of Mars and Uranus should offer the highest S/N. The other calibrators, such as CRL618, although more pointlike, are comparatively weak, and the HPBWs determined using them may have a S/N component to the associated errors.
Blazars offer an additional source of information in this regard. They are, at least, point sources, although most of them are weaker than the calibrators. However, the brighter ones (3c273 and 3c279, for instance) are often tracked for purposes related to the Pointing project, and the integration times on them can be sufficiently long to provide higher S/N. The tracking data are conventionally taken using the map16 method and each integration of the subsequent map analysed for the map centroid in order to monitor the tracking of the telescope. However, these data can also be re-aligned using the determined centroids and so reconstruct the image of the blazar. This reconstructed image is then suitable for the above beam profile analysis.
One such analysis was done recently and yielded a reconstructed image that met the criteria above on gamma etc., and had a HPBW of 14.9", essentially confirming the result in the section above, as well as the analysis of Uranus data from October 1996 by Sandell. This is larger than the intrinsic beam (~14" ?) of the telescope at this about this wavelength quoted in the User's Guide; perhaps due to the quantized nature of the SCUBA rebin process. Whatever the cause, the broadening seems to affect true point sources (blazars) in the same way as point-like planets and secondary calibrators.
-
psf analysis of SCUBA jiggle maps of point-like sources
should yield
- gamma in the range 2.05 to 2.25
- axis ratios of 1.057+0.004
- major axis orientations w.r.t. the chop direction in the range +40o.
- HPBWs of approximately 15.0".
- If the image meets these criteria, the peak
value in the image map may be derived using
stats or
psf - the agreement in such cases is better than
1%. In the case of calibrators, the Flux Conversion Factor
may then be derived by comparison of this value (in volts) with the
source brightness (in Janskys); the latter coming either from the
fluxes program or from the
Secondary Calibrators web page.
-
There is no contribution from blazar image reconstruction
equivalent to that available at
850um.
Those data are taken primarily for pointing purposes, often in
(otherwise unusable) grade 3 weather conditions (taucso
> 0.1), and, critically, in a manner that does not allow full
sampling at 450um.
-
Analysis of the 450um jiggle maps of the calibrators will suffer the
same uncertainties over source size and deconvolution as at 850um,
but the proportional size of the source to the 450um beam, and
hence the statistical error induced by the correction, is greater.
- The sky conditions under which similar S/N can be achieved at 450um are rarer, so the available dataset will be smaller. Restricting tau850 to be < 0.4 and including observations with marginally abnormal axis ratios leaves 23 useful 450um data from the above dataset.
The 23 450um jiggle maps mentioned above were analysed in the same manner as their 850um counterparts. Apart from the 5 maps of Mars the images are noticeably noisier and a majority show increased noise in bolometer b11 in ring 2 which could conceivably distort the fitting process. However, this concern is dispelled by a comparison of the mean statistics of all 23 with the 5 maps of Mars (shown in the table below), and the analysis of Mars maps taken in December 2000 when the SW array was particularly quiet.
None of these statistics is quite as useful a discriminator as at 850um, but in general the 450um images are not significantly different from nominal 2-D gaussians.
The HPBW seems a strong function of airmass , with a formal relationship given by :
HPBW450um = 6.00"+0.44" + (1.60+0.34)*airmass
There appears a weak trend with chop size, but this is more a reflection of the fact that the smaller chop throws used in this sample were taken at lower airmass. The HPBW also possibly improves through the night (see the plot against UT ), although the relatively few morning-shift calibration maps show large scatter. It seems uncorrelated with time (within the 3 month period of the study), or tau.
The mean HPBW and axis ratio imply image dimensions of 7.6" x 8.9", which are confirmed by the dimensions derived from a map of Uranus taken in June 2000.
This section may be skipped for those less interested in the technical matters of optimizing profile fitting. The results do little to deter the would-be user from adopting most of the proffered rebin default parameter values.
Click here.
-
There are modest differences (7%) between the peak flux determined from a
map using
stats
and
psf.
As with the
850um work above,
profile fitting might be useful for diagnosing odd images, but it is
not essential for the purposes of peak flux calibration.
-
The default choices of profile kernel (linear), kernel scale and output
pixel size (3")
seem reasonably optimal at their current (June 2000) values.
-
The HPBW of the 450um beam in this period (early 2000) is a strong
function of
airmass. It might be as small
as 7.5" at the zenith but is typically 8.4" at airmass 1.5. The assumption
within the fluxes program of a HPBW of 8.0" seems perfectly
sensible, although we still need to determine the impact of
different values of HPBW upon the derived flux.
Analysis of standard jiggle maps of Mars taken during December 2000 shows
no appreciable change in the properties of the 850W and 450W beams in the
year since the above analysis. Click
on the link above to see this new analysis.
The above analyses have assumed throughout that the imaged sources have
been essentially point-like, and that their brightnesses may be
obtained from their peak signal strengths. In reality the best way to
obtain such measures is with
PHOTOMETRY rather than jiggle mapping,
but the answers, of course, should agree. Jiggle-mapping is the preferred
method for observing extended sources, such as galaxies and
nebulae, although it should also be restricted to the
observation of relatively small extended sources, say, those smaller
than 90" in extent, in order to ensure that chopping onto 'empty'
sky can still occur.
Sources more extended than this may
be mapped in jiggle-map mode by taking a mosaic of overlapping
fields provided sky levels can be determined in each field in each
overlap region so that a uniform sky background level can be obtained.
We recommend using the
remsky
parameter ADD = false always, and to measure the sky level on each frame
before adjusting and mosaicing.
Flux measurements are then really made with respect to the adopted 'sky' level.
It is important therefore to reduce the edge effects from each frame before
mosaicing - using the TRIM parameter of
rebin.
[ For targets that are large enough to require mosaicing, and certainly for those
that fill the 2 arcminute FOV of SCUBA, a better (and more efficient) observing
technique is
scan-mapping. ]
The observational procedures for calibration are unchanged : it is
necessary to observe a calibrator with the same configuration (chop)
as the target, but the data analysis may take one of several forms
depending upon the astronomy involved.