We will use a hydrogen alpha filter as an example to look in greater depth at how stacking multiple filters helps to narrow the bandwidth, but this can also be applied to the Calcium K line filters. The first important issue when stacking multiple filters together is that we not only lower the bandwidth but we also lower the transmission (brightness). For example, if our single stacked filter has a Tmax of 60%, double stacking will have a Tmax of 0.6 x 0.6 = 0.36, or 36%, just over half the image brightness of a single stack, and requiring about double the exposure time when imaging. This is also why triple or quad stacking starts to get ridiculous as there is less and less improvement in continuum suppression, but very significant transmission decreases. In figure 6 the curves shown are normalized for comparative purposes, in reality the transmission peak from multiple stacking is lower than single stacking.
Figure 6 Results of double and quad stacking on the transmission curve. This emphasises the fact that the reduction in bandpass has less actual effect compared to the reduction of the transmission "wings" (shape at the base) and the suppression of continuum light. All transmission curves are normalised for comparative purposes.
The second important issue is the shape of the transmission curve of light which the filter allows through. The top of figure 7 shows a detailed representation of the Hydrogen alpha absorption line with bandpass labelled and centred on the CWL (central wavelength).
However, this is not to be confused with what a manufacturer will state their filter to be in width. If we look at the bottom part of figure 7 we see the important phase ‘FWHM’ which stands for ‘full width at half maximum’. This is the bandwidth a manufacturer will state. This does not take into account how wide (see arrows) the base of the transmission curve may be. Take particular note that while the FWHM does not decrease too much with double stacking, it is the overall shape of the transmission curve which changes with the base becoming much narrower. It is this suppression of the tails which generate the most improvement in removing continuum light (photospheric leakage). Therefore quoting a FWHM bandpass figure can be fairly inadequate to describing the visual views we have and the quality of the details seen or imaged in the real world through these filters.
Figure 7 Top: detailed representation of the H alpha absorption line with bandpass labelled and centred on the CWL. Bottom: the transmission curves of a 0.7 and 0.5A filter and how it is placed within the absorption line.
So how does this equate to what we see in the real world? Here are two great examples taken by Bob Yoesle in both Calcium II K and Hydrogen alpha (Figure 8).
Figure 8 The effects of single and double stacking filters and the view of the solar surface.
In Calcium II K at 2.2A the surface is fairly uniform and flat but with the characteristic plage and supergranulation structure present. At 1.6A the surface becomes more textured and the delicate spicules of the chromosphere become visible (edge of the Sun’s disc). This faint chromospheric feature is hidden when too much bright continuum leakage is present. In Hydrogen alpha at 0.7A all of the features of the chromosphere are present including spots, filaments and prominences. If we take particular care to study the very edge of the solar disc we see what looks like a double limb effect. This is the result of continuum leakage, with light from the photosphere coming through from below giving the effect of a hard outline (photosphere) and a soft general chromosphere layer above. When we study this edge at 0.5A (double stacking) we see that this hard line has disappeared and a continuous ‘surface’ of the chromosphere is seen from disc centre to edge, and the spicules are continuous to the edge. This is a result of suppression of the continuum leakage. Another myth often quoted is that a narrower bandpass is better for disc detail but decreases prominence visibility. This is untrue. The prominences are just as visible in the 0.7A as the 0.5A photograph. The only reason this myth is told is due to the fact as mentioned previously, the narrower bandpasses (especially from double stacking) having less transmission and a subjectively perceived decrease in prominence visibility due to decreased image brightness.
However, viewing in the wings of Hydrogen alpha can also be a benefit. As described in Part 1 when viewing in the blue or red wing of the Hydrogen alpha line we are able to view material which is Doppler shifted away or towards us and also closer in towards the photosphere. In the blue wing we are able to see material moving towards us and in the red wing moving away from us which can greatly enhance the viewing of structure within prominences or filaments. Taken together with a centre line view, we can build up a picture showing dramatic changes in shape and detail. In the same way if we look at the disc surface, particularly in the region surrounding the sunspot area we are able to observe many bright points. If over a period of some minutes these bright points appear or disappear these are Ellerman bombs. These features can only be observed easily in the wings.
In conclusion, bandwidth is much harder to quantify than first thought. Using just a single FWHM figure can be misleading, and the customer should take careful note of the ‘overall’ shape of the transmission curve of the filter to be purchased. Why would one spend a lot of money for a 0.3 A filter which will essentially perform no better visually than 0.7A because the base of the curve is very broad, but then be overcome by the view from a 0.5A double stack filter because the base of the transmission curve is very narrow. Hopefully you may now be able to understand why this could be.
More information here http://www.astrosurf.com/viladrich/astro/instrument/solar/FP-Coro.htm
Special thanks to Bob Yoesle in helping me with this article.