Contrast factor of a stack of F-P etalons and blocking filter
Daystar filter modelling and additional results
Air-spaced F-P etalon theoritical performances and comparison with mica-spaced etalons
Tilted air-spaced etalons in telecentric beam or in a f/115 convergent beam
Analysis of the PST modification (air-spaced F-P etalon) and comparison between collimated and telecentric mounts
Contrast factor of the F-P etalon and blocking filter assembly
Contrast factor of the F-P etalon : test of various stacking schemes
Fabry-Perot math and bibliography
The following figure compares the intensity of the solar spectrum and the transmission profile of a 0.6 A FWHM F-P etalon :
The width of the Ha absorption line is about 1 A at 4000 normalized intensity, 0.8 A at 3000 intensity and 0.55 A at 2000 intensity.
The role of the Ha filter is to block the unwanted light of the photosphere, in other words the light outside this absorption line (strickly speaking there is still some amount of photosphere light even in the Ha line ...).
We already know that some amount of light is transmitted by the F-P etalon outside its own FWHM. A more interesting question is how much light is transmitted by the filter outside the Ha line ? The ideal filter combination would block everything out of the Ha line.
Based on the solar spectra detailed profile (BASS2000) and on the transmission profile of the filter combination, we can calculated :
- The amount of light transmitted by the filter combination inside the Ha line. This is the "on-band light".
- The amount of light transmitted by the filter combination outside the Ha line. This is the unwanted "off-band light".
The above figure illustrates the case which a 1 A window, meaning that the 1 A window centered on Ha is declared "on-band", while the outside of this band is declared "off-band".
However, the results presented hereafter are made with a 0.8 A window (this does not change very significantly the ranking between filters, but makes easier the discrimitation between double-stack combinations).
Let's call "selectivity" of the filter the following ratio:
selectivity = on-band light / (total light transmitted by the filter)
This ratio is a very good indicator of the blocking capacity of the filter, and its ability to cut the unwanted photospheric light outside the Ha line.
- Selectivity is equal to 100% when the filter transmits the light from inside the Ha line, but no light outside Ha (square transmission profile centered on Ha).
- If slectivity is equal to 50%, it means that the light coming from inside the Ha line accounts for half of the total amount of light transmitted by the filter.
Modelling of the blocking filter (BF):
In order to calculate the selectivity of a filter stack, we need to take into account the Blocking Filter (BF). Indeed, a F-P etalon is not used alone but associated with a blocking filter whose role is to cut the unwanted interference orders of the F-P etalon.
Three different blocking filters are considered:
a) Andover 10 A 2-cavity filter (ref 656FS02). This is the filter used by DayStar. The profile used is the one of the "unblocked" version (data from Andover provided at 0.2 A resolution (txt file). The CWL is 6563 A (+2 A/-0) and peak transmission of 72%. By comparison, the "blocked" version has a peak transmission of 45% (Andover data).b) SolarSpectrum uses a 3-cavity 10 A filter. Its profile is approximated by the profile of Alluxa 656.3-1_OD4_7018 at 0.4 A resolution.
c) Coronado BF
Ha selectivity of various filter stacks in collimated beam
The following table presents the Ha selectivity of various filter combinations, based on the previous data.
Unless otherwise mentionned, etalons are mica-spaced.
Comments
- With a single stack 0.7 A mica-spaced etalon, only 30% of the light transmited by the filter (etalon+BF) comes from the chromosphere.
- The selectivity of a single-stack 0.55 A air-spaced etalons is about the same as a double-stack 1.3 A+ 1.3 A air-spaced etalons combination.
Ha selectivity of various filter stacks in telecentric beam
In the following simulations, it is considered that all etalons are finely tuned on Ha whatever the f-ratio (heat control for mica-spaced etalons, mechanical compression or pressure tuner for air-spaced etalons).
Ha selectivity of various filter combinations in a f/28 telecentric beam - Comparison of mica-spaced and air-spaced etalons
Some imaging tests
c) Visual tests with a small 55 mm diameter fluorite refractor and Baader TZ4 :
0.6A etalon (rear position) : filaments are faint, strong double limb effect.
0.6A etalon (rear postion) + 0.9 A etalon (rear position) : filaments are darker, faint double link effect.
0.7A etalon (front position) + 0.6A etalon (rear position) : filament are dark, no double limb effect.
=> the photosphere and the double limb effect are is no longer visible with the 0.7 A + 0.6 A stack
1) The FWHM is not the relevant indicator to assess the Ha selectivity of etalons (single or double stack).
2) The width at 10% or 1% peak transmission is a more relevant indicator of the selectvity of a combination (i.e. of the ratio between the light transmitted by the filter from the chromosphere to the total transmitted light). It is a good indicator for comparing and ranking single stack and multiple stack combinations.
3) A double stack 0.7A combination is more selective than a single stack 0.3A filter (75% selectivity versus 57%).
4) A double stack 0.6A and 1.5A combination gives about the same selectivity as a 0.3 A single stack etalon. This is confirmed by actual tests.