Why accurate true-colour images do not exist
The total throughput of the atmosphere, the telescope and the camera determines how a set of coadded images in red, green and blue (RGB) filters have to be weighted in order to produce an appealing colour image. In this respect, one often encounters the term true-colour image. This states that e.g. objects that are emitting dominantly in the blue parts of the spectrum then also appear blue in the image, and so on.
Images that show the colours of astrophysical objects as the human eye would see them, provided it was sensitive enough, are very difficult to create. This is because the spectrum emitted by nebula, stars and galaxies is a superposition of continuum radiation, emission and absorption lines. The RGB filters average all this over their bandpass, to which we then assign simple colours red, green and blue.
If an emission line lies once at the blue end of the green filter, and another emission line of same strength in a different object at the red end of the green bandpass, then both objects would appear with the same green colour in the image. To the eye they would likely appear different, even though the human eye has a similar "RGB" filtering. The same holds for the continuum of the spectrum, which is rarely flat as a function of wavelength. Thus RGB filters will never reflect the real colours accurately, in particular not for objects dominated by emission lines such as nebula. So-called true colour images are therefore always only an approximation to reality.
Filter manufacturers sometimes claim that their RGB sets have particularly chosen transmission curves and thus allow for a more natural colour representation than other filters. Looking at the extremely different quantum efficiencies of the cameras on the market, and in the light of what has been said above, such statements can be disregarded. As long as a blue filter covers the blue part of the spectrum etc, good-looking colour representations will always be possible. It is in my opinion much more important that the filters have good anti-reflection coatings and that their transmission curves maximise the throughput over the bandpass and thus make best use of the exposure time invested.
Personally, I am satisfied if in the final colour image blue things appear blue, green things appear green etc., and if the overall impression is "pleasing".
Colour weighting factors
In order to obtain such a pleasing image, weighting factors have to be applied to the coadded colour images. These depend on how the stacks were obtained, that is: are they straight sums or averages, and how long were the individual exposure times of the images? Since these factors vary depending on target, sky brightness, focal ratio etc, I divide the coadded images by the total exposure time in that filter. That is, my stacked images are normalised to 1 second, which makes comparison easier.
Before these colour channel images are combined into an RGB, they need to be weighted so that a pleasant image emerges. These weighting factors depend on:
The first three items do not depend on time and can be regarded as constant over time. Atmospheric extinction (transparency) is variable and has a significant impact even in very clear nights when targets are rising or setting. Depending on zenith distance, the light has to pass through a thicker atmospheric layer (see also the discussion about airmass), which can affect the weighting factors by 10% or more. If exposures are taken in different nights, the balance will in general be even more off.
It should be said here that under dark skies it is basically impossible or at least very difficult for the human eye (or the brain) to detect a slow and global change in atmospheric transmission by a factor of 1.1 or 1.2. Very thin cirrus, higher humidity or dust is just not visually discernible at night time. If one actually notices a change in extinction, the effect is usually much larger due to the logarithmic sensitivity of the eye.
Therefore, standard weighting factors can and will change from night to night on a significant level.
Correcting the weighting factors for galactic extinction
The last item, galactic extinction (by interstellar dust), can lead to significant reddening. Objects affected by this have their intrinsic colours highly distorted. It is up to the photographer to decide if the object should be shown as is, i.e. reddened, or if an attept is made to show its intrinsic colours.
The galaxy IC 342 is such an example, where galactic extinction attenuates blue light by factors of 1.7 and 2.3 with respect to green and red. These extinction factors can be obtained from NED and used to correct the weighting factors. For IC 342 NED reports E(B - V) = A(B) - A(V) = 0.558 and E(B - R) = A(B) - A(R) = 0.916. Taking the magnitude base, 2.51189, to the power of E(B - V) and E(B - R) then yields the previously mentioned correction factors.
In the following I describe two methods that can be used to determine the colour weighting factors.
G2 calibration
The sun has a spectral type of G2 and can be used as a "white" reference, which is about a natural consequence of the evolution of the human eye. One can take exposures in RGB filters of such a star with identical exposure times. The factors needed to rescale the images such that this star has the same brightness in all three filters are then the corresponding colour weighting factors. The factors obtained have to be corrected for atmospheric extinction, as blue light gets more strongly absorbed with increasing airmass. However, what is not taken into account with such external calibrators are the individual and varying conditions of each night.
To avoid this problem, one could identify a G2 star in the stacked images of the target, and then determine the weighting factor directly from the data. In this manner, all ill effects are taken into account automatically (inherent colour calibration). However, the following has to be kept in mind:
B-V calibration
As one cannot expect to have a classified G2 star in the field of view (future surveys will change that, though), one can relax the constraint and select stars which have similar colours like G2 stars. Astronomers measure colours as magnitude differences, such as B-V and V-R, where B,V and R correspond to magnitudes in blue, green and red filters.
G2 stars have on average B-V = 0.65 and V-R = 0.5. If one knows the magnitudes of stars visible in one's image in these filters, then one can select a sample of stars with similar colours than G2 stars, and use these as a white reference. Fortunately, magnitudes are reasonably well known down to magnitudes 18 or so all across the sky (e.g. through the NOMAD1 catalogue), and hence some reference stars can almost always be found. Ideally, one would allow for some tolerance, e.g. 0.6 < B-V < 0.7 and 0.3 < V-R < 0.7.
What is left to be done is to determine the average brightnesses of the corresponding counterparts in the red, green and blue stacked image, which directly yields the proper colour rescaling factors (giving these stars the same brightness in the three filters). THELI does the entire B-V calibration automatically with just one mouse click. If you are not using THELI and want to follow a more manual approach, then you can find the details on Bernhard Hubl's webpage. The average weighting factors I find for my ST10XME with this method are about:
| Filter |
weighting factor
|
| R |
1.05 - 1.25
|
| G |
1.00
|
| B |
1.8 - 2.0
|
And what if no stars similar to the G2 type are found? In that case one could still find a good white point by making all stars on average white. This leads to good results as well, but the blue channel is on average about 10% less enhanced than with the B-V calibration. The reason for this is that the average stellar population is somewhat reddish (for example, 80% of all main sequence stars in the solar neighbourhood are red dwarfs). It is worth mentioning here that this method has one advantage over the B-V calibration: it automatically corrects to some degree for the average galactic extinction along the line of sight.
Concluding
Professional astronomers usually don't care very much about true colour pictures. What they need is an accurate photometric calibration of their data. And often they are happy if their photometric calibration is accurate to within 5%. To achieve this goal, they observe standard star fields (stars with accurately known magnitudes and colours) several times a night. Compare this to amateur astronomy, where colour weighting factors are often not even determined by the observer but just copied from the web (some professional astronomers do this for their photometric zeropoints too, if they forgot to take standards). The uncertainties in most of these colour weighting factors (some of them given with two digits precision) are much higher than they appear. For example, the intrinsic errors of the B-V calibration factors are usually one the order of 10% for the blue channel, and a bit less for the red image.
Having said all this, I should offer some comfort: Most standard colour weighting factors will lead to pleasing colour pictures. However, one should not cherish the illusion of having created a highly accurate and precise colour picture with weighting factors that have been determined only once or even by somebody else. Most likely, it will not be accurate nor precise, but you'll still have a good looking picture.