Daystar Ha filter theoritical performances
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
This part has the ambition to go deeper in the analysis of the theoritical performances of Daystar Ha filter using the full formulae of the F-P given in Fabry-Perot math and bibliography, data available in Daystar whitebook, and measurements made at Meudon solar tower as a consistency check (ref W9).
Two very important information given in the Daystar white book allowed to set up a good modelling of the filter performances :
- the distance between successive transmission peaks (FSR = 26.3566 A, found after some tweaking to set the peak at 6563.8 A))
- the finesse (2, 17 and 90).
From these data is straightword to built up a model that matches perfectly the transmission curves given for various finesses in the Daystar white book :
Here is the relation between the finesse and the FWHM :
FWHM of the narrow band blocking filter :
In order to select the peak of tranmission at 6563.85 A, a blocking filter blocks the undesired orders. Daystar white book says that the FWHM of this filter is 10 A (about half the Free Spectral Range).They don't say if this FWHM is the same for all their filters.
The FWHM of the blocking filter was estimated to 4.5 A for the Daystar 0.3 A at Meudon solar tower (ref W9).
Once this model is set up ... we can play with it ...
The profile of the transmission curve of a one cavity F-P is a Lorentz curve which means that the foot of this curve is rather large. In other terms the bandwidth measured at half maximum (FWHM) is only part of the story of the ability of the filter to select the chromosphere light (H alpha) and cut the photosphere light (every wavelenghts outside Ha). Obviously, the contrast between the chromosphere and the photosphere increases as the FWHM descreases, still ... there is a lot of "out band pass" light, ie. light from the photosphere that is transmitted by the F-P filter, because of this large foot.
The bandwidth at 10% transmission is three times wider than at 50% transmission. This is the classical value for one cavity F-P filter.
If we remember that the photophere is much brighter than the chromosphere, we can understand that the bandwidth at 10% transmission will play an important role in the contrast of the Ha images.
Comparison with actual measurements :
The modeled profile is in perfect agreement with the measurements made at Meudon solar tower for a 0.3 A H alpha Daystar (see ref W9).
Double stack transmission :
One way to have a steeper profile is to double stack F-P filters. This is commonly done with front lens F-P filters such as Coronado filters. Here is the result of stacking two 0.6 A Ha Daystar filters.
The FWHM is now 0.38 A (instead of 0.6 A), and the transmission profile is steeper with a bandwidth at 10% equal to 2.28 FWHM (instead of 3 FWHM).
In orther words, a two-stack 0.6 A filter has a profile steeper that the 0.38 A filter, even if the FWHM is the same.
Note : professional in large solar observatories stack two or even three large size air-spaced F-P ....
An other way to cut down these transmission wings, could be to stack a 1.5 A FWHM filter on top of a Daystar filter (tests are ongoing ...).
If we remember that the photophere is much brighter than the chromosphere, we can understand that the bandwidth at 10% (or even 5%) transmission will play an important role in the contrast of the Ha images.
One way to have a steeper profile is to double stack F-P filters.
The following table gives the bandpass in function of the transmission level. These are the values for any perfect F-P etalon, air-spaced or not (Lorenztian transmission curve):
(simple stack F-P)
(double stack F-P of same FWHM)
50% FWHM FWHM b = 0.6436 * FWHM 10% 3.00 * FWHM 2.28 FWHM b = 1.47 * FWHM 5% 1% 9.95 * FWHM 3.00 * FWHM
D) CWL and FWHM in function of the angle of incident light in a collimated beam :
We have already seen this on the basis of formulae (1) and (2). It is fun to have a look at it throught the calculation of the transmission curves :
The shift of the center wavelength (CWL) is the same as given by formula (1) ... which is not surprising ...
More interesting, it can be noticed that the shape of the transmission (and the FWHM) does not change with the tilt. This is because the incoming beam of light is collimated (no convergence nor field angle).
In a non collimated beam (ie. if the incoming beam was a cone of light), such as with a Barlow lens or a telecentric system, the tilt of the axis of the incoming cone of light would broaden the FWHM.
Comparison with actual measurements :
The theory fits correctly with the measurements made at Meudon solar tower for a 0.35 A H alpha Daystar (see ref W9):