Contrast factor of the F-P etalon and blocking filter assembly

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

Back to the solar spectrum :

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 job 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 would block everything out of the Ha line.

From the solar spectra and transmission profile of the filter, we can calculated :

- The amount of light transmitted by the F-P etalon inside the Ha line. This is the "on-band light".

- The amount of light transmitted by the F-P etalon outside the Ha line. This is the unwanted "off-band light".

We will calculate these values assuming a 1 A width for the Ha line (ie. 4000 intensity level). This means that the 1 A band centered on Ha is declared "on-band", while the outside of this band is declared "off-band".

(The conclusions would be about the same if we considered a 0.8 A width for the Ha line).

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.

- If equal to 100%, it means that the filter transmits the light from inside the Ha line, but no light outside Ha (square transmission profile centered on Ha).

- If equal to 050%, it means that the light coming from inside the Ha line accounts for half of the total amount of light transmitted by the filter.

Assumption on the blocking filter (BF):

A F-P etalon is not used alone but associated with a blocking filter. The role of the BF is to cut the unwanted interference orders of the F-P etalon, and to a very small extend, to cut some part of the light in the tails of the Lorentzian profile of the F-P etalon.

As we don't know exactly what is the FWHM of the BF used by Daystar, Coronado or Lunt, we will assume two differents values : 6 A and 4.5 A FWHM. A single cavity profile is assumed.

Ha selectivity of various filter combinations

a) The following table gives the Ha selectivity of various filter combinations, assuming a 6 A FWHM blocking filter (single cavity) for the selection of the correct order :

 Combination Selectivity FWHM (Å) Width at 10% tranmission (Å) Width at 1% transmission (Å) 0,7 Å 42 % 0,7 2,1 7,0 0,6 Å 46% 0,6 1,8 6,0 0,5 Å 51% 0,5 1,5 5.0 0,4 Å 57% 0,4 1,2 4.0 0,3 Å 65% 0,3 0,9 3.0 0,6 Å + 1,5 Å 68% 0,53 1,3 2.8 0,6 Å + 0,9 Å 78% 0,46 1,07 2.2 0,7 Å + 0,7 Å 79% 0,45 1,03 2.1 0,3 Å + 1,5 Å 82% 0,6 Å + 0,6 Å 85% 0,39 0,88 1.8 0,3 Å + 0,9 Å 89% 0,7 Å + 0,7 Å + 0,7 Å 90% 0,35

- With a single stack 0.7A filter, only 42% of the transmited ligt comes from the chromosphere.

- While the FWHM of the 0.6 A + 1.5 A combination (FWHM = 0.53 A) is much larger than the FWHM of a single stack 0.3 A filter, its selectivity is about the same (68% versus 65%). In other words, the blocking of the unwanting photospheric light is about the same in both cases. It is also to be noticed that the width at 1% tranmission is about the same (2.8A versus 3.0 A).

- The selectivity of the 0.6A + 0.9A combination is greater than a 0.3A alone, which is consistent with imaging tests (see in next page).

- The classic 0.7A + 0.7A stack has twice the selectivity of the single stack 0.7A : about 80% of the light transmitted is from the chromosphere (versus 42% in the 0.7A single stack). This is the very reason of the improved contrast. The selectivity is even much better than the one of a single stack 0.3 A (79% versus 65%), in line with a much narrower width at 1% transmission (2.1 A versus 3.0A).

b) Imaging tests :

FP-contrast-2.htm

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

d) Some more calculations with a 4.5A (single cavity) FWHM blocking filter (instead of 6 A FWHM) :

Combination On-Band light / Total light
0.6 A
0.48

0.5 A

0.54
0.3 A
0.67
0.6 A + 1.5 A
0.69
0.6 A + 0.6 A
0.86

- The increase of the selectivity is very marginal when going from a 6 A to a 4.5A (single cavity) filters.

NB : mica-spaced etalons are assumed here. The impact of the FWHM of a BF in air-spaced etalon would be larger since the FSR (ie. the distance between two sucessive order) is about 10 A, compared to an FSR of about 26 A in Daystar mica-spaced etalons.

Another example : a double stacked 0.7 A Coronado

Here is another example with a double stack 0.7 air-spaced F-P etalon (eg Coronado) associated with a 6 A FWHM blocking filter.

NB : as for the transmission profile, it makes no difference if the F-P is air-spaced or not.

The selectivity of the double stacked 0.7A air-paced etalon (stacked with a 6A FWHM single cavity BF) is about 75%.

Conclusion on filter stacking :

1) The FWHM is not the relevant indicator to assess the Ha selectivity of etalons (single or double stack).

2) The width at 1% transmission is much more relevant of the selectvity of a combination ( ie. of the ratio between the light transmitted by the filter from the chromosphere to the total transmitted light). The width at 1% transmission is a good indicator for comparing and ranking single stack and double stack combinations.

3) A double stack 0.7A combination is more selective than a single stack 0.3A filter (79% selectivity versus 65%).

4) A double stack 0.6A and 1.5A combination gives about the same selectivity as a 0.3 single stack etalon. This is confirmed by actual tests.

5) The impact of the BF filter (6 A or 4.5A FWHM single cavity) is very marginal on mica-spaced etalons (because of larger FSR), compared to air-spaced etalons (smaller FSR).