# SCUBA-2 Calibration

## FCFs

The FCF (Flux Conversion Factor), is the value needed to convert data from pW to Jy. The FCF is calculated by observing one of our ‘calibrators’, which are bright point-sources having well-known flux densities. Our primary calibrators are Mars and Uranus; see also our list of secondary calibrators (most commonly used are CRL2688, CRL618, and Arp220).

There are two types of FCF value, and the one you will want to apply to your own data depends on what you intend to do with the data i.e. investigate surface-brightness, or aperture photometry as opposed to measuring absolute peak flux densities.

• The peak (or beam) FCF:
Units: Jy/pW/beam
This FCF is the number by which to multiply your map if you wish to measure absolute peak fluxes of discrete sources.
• The aperture (or arcsecond) FCF:
Units: Jy/pW/arcsec2
This FCF is the factor by which to multiply your map if you wish to use the calibrated map to do aperture photometry.

Studying this calibrator data over several years has shown that the mean/median values are consistent over time with the exception of periods of time affected by hardware changes to the instrument. Therefore, we recommend using the standard FCF values listed below to calibrate your data.

## Standard FCF and Opacity (Tau) values

The values quoted below are derived from reductions of daisy maps of our calibrators using the MAKEMAP routine from SMURF, reduced with the ‘bright_compact’ dimmconfig file onto output maps with pixel size = 1 arcsec.

Note that the FCF’s below have been derived for a pixel size of 1 arcsec at both 450 and 850 micron. The FCF depends on the used pixel size (see Dempsey et al. 2013, and further down this page). These standard values are applicable to pixel sizes between 1-4 arcseconds. Outside this range, to calibrate science data, one should always re-reduce calibrator observations with the same pixel size as the science data (see below for more information on investigating FCFs on your own).

450μm FCF 850μm FCF
Beam 491 +/- 88 Jy pW−1 537 +/- 43 Jy pW−1
Arcsec 4.71 +/- 0.9 Jy pW−1 arcsec−2 2.34 +/- 0.1 Jy pW−1 arcsec−2

——- Note: Updating FCFs Fall 2019 ——-

Due to a new study on the FCFs throughout SCUBA-2’s history, the standard values listed above are subject to change in Fall, 2019. The new FCFs will be given in (Precipitable Water Vapour x Airmass) bins and details on how the FCF changes 2-3 hours after sunset and sunrise will be given. Preliminary results show:

– A 3% decrease in the 850 micron Peak FCF for data obtained after November 1st, 2016.

– A 7% decrease in the 850 micron Aperture FCF for data obtained after November 1st, 2016.

– A 9-12% increase in the 450 micron Peak FCF for data obtained before May 1st, 2018.

– A 4% decrease in the 450 micron Aperture FCF for data obtained before May 1st, 2018.

– A 15-20% decrease in the 450 micron Aperture FCF for data obtained after May 1st, 2018.

——–

The extinction correction at 450 or 850 microns can be found using the following formulae:

$Ext_{450}=\exp(-26\cdot\text{AM}\cdot[\tau_{225}-0.01196])$

$Ext_{850}=\exp(-4.6\cdot\text{AM}\cdot[\tau_{225}-0.00435])$

Here AM is the airmass and $\tau_{225}$ is the tau at 225 GHz (See: Dempsey et al. 2013, http://adsabs.harvard.edu/abs/2013MNRAS.430.2534D).

Note: Archival SCUBA-2 data should always be reduced with the latest STARLINK release.

## SCUBA-2 Calibration Database

The SCUBA-2 calibration database is a web-accessible database of SCUBA-2 calibrations that exists to allow JCMT users to easily determine the calibrations taken on nights where their projects were observed. Searches can be done either by date (single dates or ranges) or by project, which will automatically return calibrations from all dates where the selected project was observed. The database and web interface are currently in a functional if not especially user-friendly state, but several improvements and additional features are planned for the future.

## Daily Changes in FCF

The figures below show the FCFs at 850 and 450 micron as a function of Hawaii Standard Time (HST) for observations of Uranus and Mars made in grade 1 and 2 weather. The size of the symbol is proportional to the WVM tau at 225 GHz. The FCF is larger during the day because of larger seeing and thermal deformations of the dish.

## Pixel Size

The pixel size used in the reduction of a calibrator can have a significant effect on the FCF derived. The effect is different for both the beam and aperture FCFs, and also for different calibrators. Below are a series of graphs of the three most commonly-used SCUBA-2 calibrators: Uranus, CRL2688, and CRL618, which together make up over 70% of SCUBA-2 calibrations. A collection of ~20 observations of each calibrator were chosen where the weather was Grade 1 and transmission was 30% or higher at both wavelengths. These calibrations were reduced at pixel sizes ranging from 1 to 8 arcseconds, the FCFs measured, and the results plotted.

The solid blue line marks the standard FCF quoted in Dempsey et al. 2013, with the dotted blue lines marking ±5% variation at 850µm and ±10% at 450µm (beam FCFs typically scatter more than aperture FCFs, due to greater sensitivity to things like telescope focus and shape of the dish).  At larger pixel sizes (~5 arcseconds) the SCUBA2_CHECK_CAL recipe can no longer determine beam FCFs for CRL618 and CRL2688 at 450µm, and thus they do not appear on the graphs.

### Match-filtering

The SCUBA2_MATCHED_FILTER recipe can be applied to data to help locate sources the size of the beam while suppressing residual large-scale noise. Applying a matched-filter to calibrators causes a small change to beam FCFS, as seen in the graphs below which show the beam FCFs from a collection of calibrators (the same used for the plots above, using only the 1-arcsecond pixel results) plotted against themselves before and after having a matched-filter applied.

While the changes are small, if you are concerned your results will be affected, we recommend that you apply the same matched-filter you use on your data to the calibration observations obtained for your project  deriving FCFs from them to compare to the standard values. More information about deriving your own FCFs is given below.

## A Note About FCF Units

Multiplying the brightness values of a reduced image in units of picoWatts by the Peak FCF will result in a map calibrated in units of Jy/beam. If one instead multiplies the brightness values of a reduced image in units of picoWatts by the aperture FCF, the map will be calibrated in units of Jy/arcsec2. For a point source, the measured peak in a map with units of Jy/beam is equivalent to the integrated total flux of the same source in a map with units of Jy/arcsec2.

To determine the total flux of a point source, we integrate over a 60″ diameter aperture centered on the source calibrated in Jy/arcsec2, then multiply by the area of a pixel in arcsec2 to yield an answer in units of Jy. A background flux value can be subtracted for a more accurate result (see the image below and Dempsey et al. 2013. MNRAS 430:3524.)

An observation of Uranus with 60″ (blue), 90″, and 120″ diameter apertures overlaid. The 60″ aperture encompasses the large majority of the source flux (the excess emission outside this aperture is very faint relative to the peak brightness and can be considered negligible) while the area between the 90″ and 120″ apertures is used to calculate the background flux.

In order to measure the peak flux in a map calibrated in Jy/beam, careful attention must be paid to the fit parameters. Below are 3 histograms comparing the measured total integrated flux in a map calibrated in Jy/arcsec2 with the measured peak flux in the corresponding map calibrated in Jy/beam. The peak flux was measured using the KAPPA command BEAMFIT, fixing the 2D gaussian fit to be symmetric with the FWHM indicated in the title. Note how varying the width of the Gaussian can cause either an overestimate or an underestimate of the total source flux measured by the 60″ aperture

## Investigation FCFs for yourself

Previous advice was to calculate your own FCF values using a calibrator closest to your science data (in both time and space). It has been noted, however, that significant outliers can skew your data if you are using a limited number of data points. Therefore, the recommendation is to use the standard values unless you are using a large pixel size (>4 arcseconds) or you are concerned that your matched-filter observations have a flux calibration significantly different from the standard values that you’d like to perform your own analysis.

It is recommended that data is reduced using the latest version of the STARLINK software. Both science and calibrator data should be reduced at the same time using the same configuration file and same pixel size. The process outlined below will yield several FCF values in a log.calstats file created in the directory in which it is run. Peak FCF values are listed as “FCFbeam” while Aperture FCF values are listed as “FCFasec”.

A few quick notes: The FCF values calculated should fall within 15-20% and 5-10% of the standard values at 450 and 850 microns respectively. If the FCF values calculated differ wildly this is likely due to the configuration file. As a first step re-reduce your calibrator with the dimmconfig_bright_compact.lis file and re-run the PICARD command. If your FCF’s still come in outside this 10% and 5% range contact your Friend of Project (FOP). If displayed, the calibrator reduced with the science configuration file may look awful (i.e. show deep negative bowling), but due to the profile fitting picard SCUBA2_FCFNEFD will make a reasonable estimate of the FCF. Be aware that the FCF for daytime observations, or for observations made within 2-3 hours after sunset are higher than those for nighttime observations.

To demonstrate, we’ll run the routine on an already-reduced calibration observation named s20131227_00013_850_reduced.sdf., which happens to be an observation of Uranus. The command to do so is

> picard -log sf SCUBA2_CHECK_CAL s20131227_00013_850_reduced.sdf

This will then produce a lot of output, which we’ll go over in sections. The first section looks like this:

Setting up display infrastructure (display tools will not be started until necessary)...Done
Picard Says: Pre-starting mandatory monoliths...Done
Checking for next data file: /export/data/dberke/tmp/s20131227_00013_850_reduced.sdf
Storing: s20131227_00013_850_reduced
Picard Says: Creating temporary bad observation rules file
A new group 20131227#-1 has been created
Overriding PICARD instrument class to PICARD_SCUBA2_850
Sorting Groups
REDUCING: s20131227_00013_850_reduced
Using recipe SCUBA2_CHECK_CAL specified on command-line Processing data for URANUS
Calling _UNCALIBRATE_SCUBA2_DATA_: undo calibration of given dat
File s20131227_00013_850_reduced already contains uncalibrated data

This first section is picard setting up the file to work on and selecting the correct parameters to use.

Calling _CROP_SCUBA2_IMAGE_: trim image to specified map size
Trimming image to specified map size
Output image will have WIDTH=150 HEIGHT=150 arcsec

This section shows the recipe cropping the image to 150 arcseconds on a side, centered on the calibrator. The default behavior is to measure the flux within a circle with a radius of 30 arcseconds. The noise in the image is measured in an annulus outside the central circle with an inner and outer radius of 45 and 60 arcseconds, respectively. See the image below for a visual representation:

The inner dashed black circle is where the flux is measured, while the annulus defined by the two dashed white circles shows the area where the noise of the image is measured. The two profiles on the right show cuts across the full image, both horizontally (top) and vertically (bottom). The solid black ring in the middle of the image is a contour at 50% of the beam strength.

Calling _SCUBA2_FIND_BEAM_SIZE_: determine beam parameters
Deriving the beam in the AZEL coordinate system using BEAMFIT
Fitting beam to s20131227_00013_850_reduced_crop
Beam size: 14.39 x 13.52 arcsec^2 at a PA of 37.96 deg E of N (S/N = 180.4)
Error beam fraction = 0.598, 4.9% higher than expected (0.57) at 850 um

This section is where the recipe determines the beam size. The two numbers given after “Beam size” are FWHM slices taken through azimuth and elevation, which allows the calculation of the orientation (given by the Position Angle). The S/N ratio and fraction of the flux in the error beam are also shown here (see Dempsey et al. 2013 for a full treatment of the error beam).

Calling _CALC_SCUBA2_FCF_: calculate an FCF for uncalibrated SCUBA-2 data
Calculating FCF for s20131227_00013_850_reduced (URANUS)
Calculating FCFs for URANUS:
Finding map peak and total flux...
Fitted peak at 0:00:00.000, 0:00:00.00
Plotting image profile + 2-d fit for data map...
Finding peak in matched-filtered map...
Fitted peak at 0:00:00.017, 0:00:00.0
Plotting image profile + 2-d fit for matched-filtered map...

SCUBA2_CHECK_CAL uses different fits to determine the beam parameters and the FCFs. This section simply shows the process of finding the fit for the FCF.

Determining FCF of type ARCSEC:
Flux = 63.6506; Data = 26.911 pW arcsec**2
Storing new FCF for 850: 2.365 +/- 0.001 Jy/arcsec**2/pW (cf 2.34: 1.1% higher)

This section of the recipe shows the calculation of the aperture (or arcsec) FCF. The FCF is calculated like so:

$\text{FCF}_{\text{arcsec}}=\frac{S}{I_{0}A}=\frac{63.6506\,\text{Jy}}{26.911\,\text{pW}\,\text{arcsec}^2}=2.365\,\text{Jy}\,\text{pW}^{-1}\,\text{arcsec}^{-2}$

where S is the known flux in Janskys, I0 is the measured signal in pW, and A is the pixel area in arcsec2.

Determining FCF of type BEAM:
Flux = 62.1037; Data = 0.108763 pW
Storing new FCF for 850: 571.001 +/- 1.053 Jy/beam/pW (cf 537: 6.3% higher)
Determining FCF of type BEAMMATCH:
Flux = 62.1037; Data = 0.111419 pW
Storing new FCF for 850: 557.388 +/- 2.442 Jy/beam/pW (cf 537: 3.8% higher)

This section of the recipe shows the calculation of the beam (or peak) and beammatch FCFs. Both are calculated similarly; for brevity only the beam FCF calculation is shown.

$\text{FCF}_{\text{peak}}=\frac{62.1037\,\text{Jy}}{0.108763\,\text{pW}}=571.001\,\text{Jy}\,\text{pW}^{-1}$

The beammatch FCF is calculated using a forced fit to the data, which is why the “data” number it uses is slightly different to the one used for the beam FCF.

Using ARCSEC/BEAM FCF ratio to derive beam area:
derived = 241.44 arcsec^2/beam / FWHM = 14.60 arcsec
empirical = 229.75 arcsec^2/beam / FWHM = 14.24 arcsec
Derived beam area is 5.1 % higher

This section of the recipe shows the empirical and derived beam area and FWHM. The beam area is the ratio of the beam FCF to the aperture FCF:

$\text{area}=\frac{\text{FCF}_{\text{beam}}}{\text{FCF}_{\text{asec}}}=\frac{571.0001\,\text{Jy/beam/pW}}{2.365\,\text{Jy/asec}^2\text{/pW}}=241.44\,\text{asec}^2\text{/beam}$

while the FWHM is calculated from the beam area using the following equation:

$\text{FWHM}=\sqrt{\frac{\text{area}}{1.1333}}=\sqrt{\frac{241.44\,\text{asec}^2}{1.1333}}=14.60\,\text{asec}$

The empirical beam area and FWHM are calculated using the standard FCF numbers from Dempsey et al. 2013.

Calling _CALIBRATE_SCUBA2_DATA_: calibrate data using standard, given or derived FCF
Picard Says: Calibrating data in mJy/beam
Multiplying s20131227_00013_850_reduced_crop by 537000 mJy/beam/pW
Calling _CALC_NOISE_: calculate noise in image

Calling _SCUBA2_MATCHED_FILTER_: apply a matched-filter to reduced SCUBA-2 maps
Creating PSF image, normalizing, smoothing and subtracting from original: done
Applying matched filter to s20131227_00013_850_reduced_crop_cal,
smoothing and subtracting from original: done
Re-Calculating NEFDs for current Frame map...

Calling _WRITE_CHECKCAL_LOGFILE_: write flux/nefd/fcf info to log file
Writing results to log file, log.checkcal... done

Calling _WRITE_CALSTATS_LOGFILE_: write logfile with results from calibrator analysis
Recipe took 31.701 seconds to evaluate and execute.

Picard processing complete
Processed one recipe which completed successfully
Exiting...

Picard Says: Goodbye

The remainder of the recipe involves calibrating the image, applying a matched filter to smooth the resulting image, and writing out the results to various log files.