Stacking and colour images¶

This tutorial takes several short exposures of one field in each of the Johnson B, V and R filters and turns them into a deep frame per filter and a colour picture. Along the way you calibrate the deep frames photometrically, which also gives the colour image a correct white balance.

The steps are: calibrate the positions of every frame, stack each filter, measure the stacks, compose the colour image, and convert it to PNG.

You need Munipack (the munipack alias from Installation) and, for the last step, the small fitspng converter. If you have not used Munipack before, the Quick start explains the single-frame steps in more detail.

Get example data¶

To try the tutorial without your own data, simulate the frames. First download a catalogue of the field, the open cluster M67:

munipack cone --Johnson-patch -r 0.25 -o cone.fits -- 132.85 11.81

This needs a network connection. The default catalogue, UCAC4, carries B and V magnitudes and Sloan r and i; --Johnson-patch converts the latter to Johnson R and I, so cone.fits has Bmag, Vmag and Rmag columns.

Then render three 20-second exposures per filter, each pointed a few arcseconds away from the others, as when you dither the telescope:

seed=0
for f in B V R; do
  n=0
  for pos in "132.844 11.806" "132.850 11.810" "132.856 11.814"; do
    set -- $pos                       # $1 = RA, $2 = Dec
    n=$((n + 1)); seed=$((seed + 1))
    munipack artificial -c 'cone.fits[1][Bmag<50 && Rmag<50]' -f $f --col-mag ${f}mag \
      --rcen $1 --dcen $2 --width 800 --height 800 --scale 3600 \
      --exptime 20 --psf GAUSS --hwhm 1.5 --cosmics-freq 0.1 \
      --gain 2 --readnoise 5 --bias 100 -B 16 \
      --seed $seed --no-watermark --mask m67_${f}_$n.fits
  done
done

This writes nine frames, m67_B_1.fits … m67_R_3.fits, of 800 × 800 pixels of one arcsecond each (--scale is in pixels per degree). Each frame has its own noise (a different --seed) and a few cosmic rays, so the stacking has something to reject. The filter in brackets keeps only stars that have all three magnitudes; a star missing from one band would come out with a false colour.

With your own data, put your frames in place of these, one file per exposure with a FILTER keyword of B, V or R, and calibrate them first with phcorr (bias, dark and flat). Download the catalogue with cone around your own field.

1. Calibrate the positions¶

Stacking aligns the frames by their world coordinates (WCS), so every frame needs an accurate one. The simulated frames, like those from most telescopes, already carry a rough WCS; astrometry refines it. Find the stars, measure them, and match them to the catalogue:

munipack find -f 3.5 m67_?_?.fits
munipack aphot m67_?_?.fits
munipack astrometry -c cone.fits m67_?_?.fits

astrometry writes the fitted WCS into the header of each frame. Check the error of the fit for one of them:

munipack fits -K CRDER1,CRDER2 m67_V_1.fits

The values are in degrees; here they are around 0.1″, a tenth of a pixel, which is plenty for stacking.

Tip

If your frames have no WCS at all, tell astrometry where the telescope pointed and the plate scale, for example --rcen 132.85 --dcen 11.81 --scale 3600; see astrometry.

2. Stack each filter¶

kombine reprojects the frames of one filter onto a common grid and averages them. Give the same grid to every filter, so that the three stacks line up pixel for pixel, as colouring needs. Here it is centred on the cluster, as large as the frames, with north up (--angle 0) and not mirrored (--reflex no):

for f in B V R; do
  munipack kombine --rcen 132.85 --dcen 11.81 --width 800 --height 800 \
    --scale 3600 --angle 0 --reflex no -o m67_$f.fits m67_${f}_?.fits
done

You get m67_B.fits, m67_V.fits and m67_R.fits. The image is the sum of the exposures with the background removed, and the total exposure time is in EXPTIME. The STDERR and MAXDEV extensions hold the error of each pixel and its largest deviation:

munipack fits m67_V.fits
munipack fits -K FILTER,EXPTIME m67_V.fits

The default average is a mean clipped by the noise model of the frames, which rejects cosmic rays and hot pixels. --arith gives a plain mean that needs far less memory, for long series already free of cosmic rays. Here the output keeps the scale of the inputs; if you resample to larger pixels and want total star fluxes for photometry, add --flux-conserve.

3. Measure the stacks¶

The stacks are ordinary frames, so you can measure them like any other. kombine does not copy the GAIN and AREA keywords, so look them up in a single frame:

munipack fits -K GAIN,AREA m67_V_1.fits

The stack is a sum in ADU, so its gain is that of the single frames. Put it back, so that aphot gets the errors right:

munipack fits --update --key GAIN --val 2.0 --com "[e-/ADU] gain" m67_B.fits m67_V.fits m67_R.fits
munipack find -f 3.5 m67_B.fits m67_V.fits m67_R.fits
munipack aphot m67_B.fits m67_V.fits m67_R.fits

Then calibrate each band against its catalogue column:

for f in B V R; do
  munipack phcal -c cone.fits --photsys-ref Johnson --area 0.99 -f $f \
    --col-mag ${f}mag --col-magerr e_${f}mag --syserr auto m67_$f.fits
done
munipack fits -K CTPH,CTPHERR 'm67_V_cal.fits[PHOTOMETRY]'

The area of the telescope, 0.99 m² from the single frames, is given with --area. phcal may print a note about floating-point exceptions; it is harmless.

This writes m67_B_cal.fits, m67_V_cal.fits and m67_R_cal.fits, with the image in photons and a PHOTOMETRY table of calibrated magnitudes. The last command shows the calibration factor CTPH of the V stack and its error. The magnitudes agree with the catalogue to about a hundredth of a magnitude.

4. Compose the colour image¶

colouring transforms the bands into the CIE 1931 XYZ colour space. List them from short to long wavelength, B, V, R:

munipack colouring -o m67_colour.fits m67_B_cal.fits m67_V_cal.fits m67_R_cal.fits
munipack fits -K NAXIS3,CSPACE m67_colour.fits

m67_colour.fits is a cube with one plane per colour component; the CSPACE keyword names the colour space. Because the inputs are calibrated, the bands are already balanced and the colours are natural: the giants of M67 come out yellow-orange, the hot stars bluish.

Tip

You can also colour the uncalibrated stacks m67_B.fits … directly, but then balance them yourself, with --white-star x,y on a star of B − V near zero or with weights -w. Without either, colouring warns that the weights are undefined and the colours false.

5. View and convert¶

An ordinary FITS viewer shows the cube as three grey planes. To see the colours, convert it to PNG with fitspng (packaged as fitspng in Debian and Ubuntu; it is not in the Docker image, so run it on the host):

fitspng -o m67_colour.png m67_colour.fits

m67_colour.png is an sRGB image ready for any viewer or web page. fitspng --help lists options for the tone curve and saturation, useful when the faint parts of a nebula need lifting.

Next steps¶

kombine: output grids, mosaics, moving targets and resampling.
colouring: colour spaces, weights and white balance.
astrometry and phcal: matching and calibration options.
phcorr: bias, dark and flat corrections for real frames.
artificial and cone: simulated frames and catalogues.