Comparison of air-spaced (PST modification) and mica-spaced F-P etalons
1) Center Wave Length (CWL) and bandpass (FWHM) as a function of the F/D ratio of the telescope and of the tilt of the F-P filter (collimated beam, telecentric beam, non-optimized telecentric system)
2) CWL shift and FWHM broadening in non telecentric lens systems
3) Daystar filter modelling and additional results
4) Air-spaced F-P etalon theoritical performances
5) Analysis of the PST modification (air-spaced F-P etalon) and comparison with mica-spaced F-P etalons
6) Contrast factor of the F-P etalon and blocking filter assembly
7) Contrast factor of the F-P etalon : test of various stacking schemes
8) Fabry-Perot math and bibliography
Now we have a theoritical understanding of both mica-spaced and air-spaced F-P etalons, we can try and compare their relative performances. This comparison is limited to the use of these etalons at the focus of a telescope. More precisely, we are interested in comparing Daystar filters and PST etalon (refered here as "PST modification"). So we want to compare :
- A Daystar filter with a telecentric lens system.
- A PST etalon with its divergent and convergent lenses at the F/10 focus of a telescope.This is for example the set-up of Jean-Pierre Brahic with his 230 mm F/9 solar refractor : http://jp-brahic.chez-alice.fr/lunette_230mm.htm
- A PST etalon with a telecentric lens system. This for example the set-up of Regis Benedictis with his 200 mm HAT.
Most of observers are reporting very good results with the PST modifications and lower contrast with the Daystar filters.
For visual observations, it is not clear whether these comparisons are made on the same instrument, at the same magnification, with the same seeing, and a proper optical and mechanical set-up. The use of a true telecentric lens system is required for a Daystar filter, and the squareness of the F-P etalon is to be checked by auto-collimation.
It is no more clearer whether the comparisons are made with the same level of luminosity at the eyepiece (a brighter view can reduce the contrast of the image).
It has even been reported that Daystar filters give poor results though cirrus cloud while PST modification still gave good contrast !
Imaging observations should be easier to analysed. Still a lot of questions are pending. For example, JP Brahic took this interesting video with his 230 F/9 refractor :
It compares the two following set-up :
- X4 Televue Powermate + Daystar PE 0.5 A + Celestron focal reducer X 0.6,
- Glasspath X1.25 + PST etalon with its divergent and convergent lenses + Coronado BF15 + X2 Barlow.
Unfortunatly, the X4 Powermate is not trully telecentric and the Celestron focal reducer X0.6 is of average optical quality for high resolution imaging. Furthermore, the X1.5 scale factor between the two set-up does not facilitate comparison.
|Uniformity of CWL and FWHM||
Summary of requirements for proper use :
|Telecentric lens system|
|Squareness of etalon to optical axis (can be checked easilly by auto-collimation)|
|F/30 or higher|
We assumed the following data for the PST :
- a 20 mm diameter air-spaced F-P etalon with FWHM = 1 A
- front divergent lens of -200 mm focal length (ie f/d = 10).
Requirements on the optical path :
xxxxxxxxxxxGraph to be placed here xxxxxxxxxxxxxxxxx
F : focal lens of the refractor
D : diameter of the refractor
(i) The focus of the refractor should be set at the rear focus of the Barlow lens. In other words, the PST Barlow + F-P assembly should be placed 200 mm before the focus of the refractor. This turns the incoming convergent beam formed by the objective of the refractor into a collimated beam (with field angle). This is true whatever the F/D ratio of the objective of the refractor.
(ii) The F-P etalon receiving a collimated beam with a field angle, there is a shift of the CWL, but no FWHM broadnening.
(iii) The field angle at the F-P etalon is equal to the incoming angle multiplied by F / f (see graph).
(iv) Because the divergent lens in front of the etalon has a f/d = 10 ratio, the objective of the refractor is vignated to F/10. In other words, a 100 mm F/8 objective would have an effective diameter of 80 mm. Accordingly, this set up is to be used with objectives having F/D > 10.
(v) On the other hand, for a given theoritical resolution of the refractor (ie. for a given diameter D), the sweet spot increases with smaller field angle, ie. lower F / f ratio, or shorter focal lens F, or smaller F/D.
(vi) From (iv) and (v), we can conclude that the optimal balance between the largest theoritical resolution and the largest sweet spot is reached when F/D = 10.
CWL shift in function of objective focal length :
The following figure shows the drop in the diameter of the sweet spot when the focal length of the refractor increases :
The "native PST" with its 400 mm focal length has a 0.25 A CWL shift for a 15 arcmin angle (radius of the sun). This is why it covers the full solar disk in Ha.
Sweet spot radius :
This figure is another way to present the previous results :
If is remember that the focal lenght F indicated in this figure is the native focal length of the refractor. The resulting focal length of the combined system can be increased by adding a Barlow lens after the F-P etalon.
The conclusion is that we should keep the native focal length of the refractor as short as possible in order to cover the largest possible sweet spot for a given diameter D. In other words, the optimal F/D ratio is 10.
How to increase the radius of the sweet spot ?
Given that the field angle increases with the factor F/f, one solution to have a larger sweet spot would be replace the -200 mm FL divergent lens of the PST etalon by a divergent lens of longer focal length (eg. -400 mm or longer).
Here we only keep the air-spaced etalon of the PST without its divergent and convergent lenses. The F-P is placed behind a telecentric lens system.
We have already seen this figure. It shows that air-spaced F-P etalons require much larger F/D ratio.
The results are even worse if we suppose the PST F-P etalon is 1 A FWHM.
So, it is difficult to understand how a 1 A air-spaced F-P etalon can give any good results in a F/28 telecentric beam. Maybe there is still something not considered properly in all this analysis ? Or could it be an indication of the PST etalon being actually a composit solid air-spaced etalon ? This would be surprising for a low cost F-P etalon.
A measurement of the CWL = f (tilt) for the PST could help solving this mystery...
The simulations are not very favourable to the air-spaced PST F-P etalon when we compare it to a mica-spaced etalon.
This does not fit completly with observations. More side by side comparisons are required ...