Comparison of air-spaced (PST modification) and mica-spaced F-P etalons


1) Center Wave Length (CWL) and bandpass (FWHM) as a function of f-ratio of the telescope and tilt of the F-P filter (in collimated beam, telecentric beam or non-optimized telecentric system)

2) CWL shift and FWHM broadening in non telecentric systems (refractors and Cassegrain telescopes) and useful formulae

3) Daystar filter modelling and additional results

4) Air-spaced F-P etalon theoritical performances and comparison with mica-spaced etalons

5) Analysis of the PST modification (air-spaced F-P etalon) and comparison between collimated and telecentric mounts

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


Comparison of PST etalon in a collimated beam (refered here as "PST modification") or a telecentric beam.

Summary of main theoritical differences between air-spaced and mica-spaced etalons

Transmission profile

Same Lorentzian profiles for mica-spaced and air-spaced etalons of same FWHM

Acceptance angle

Air-spaced etalons have much smaller acceptance angle (smaller sweet spot, and need for mucher larger f-ratio in telecentric lens system)

Diffusion of light

Filter stack based on mica-spaced etalon consists in up to twelve optical elements.

Filter stack based on air-spaced etalon are made up of two optical plates for the etalon, one blocking filter and one ITF filter = 4 elements.

Uniformity of CWL and FWHM

Mica-spaced F-P : dependant on uniformity of the mica (thickness, transparency) and uniformity of the coating.

Air-spaced F-P : dependant on the quality of the window plates of the etalon (flatness, roughness, ...) and uniformity of the coating.

Polarization of light

The index of mica depending on polarization. Accordingly, mica-spaced F-P are used with polarisizing filters, meaning lower light output compared to air-spaced or fused-silica spaced etalon.

Optical set-up  Air-spaced etalon are usually mounted in collimated beam :
- Accordingly, the FWHM at the center of the field is equal to the nominal FWHM. This is the main reason why air-spaced etalon are often reported as more selective.
- On the other hand, the FWHM increases with field angle, resulting in a sweet spot effect.

Mica-spaced etalon are usually mounted in a telecentric beam :
- Accordingly, the FWHM at the center of the field is larger than the nominal FWHM. This is the main reason why air-spaced etalon are often reported as more selective.
- On the other hand, the FWHM does not change with field angle (no sweet spot effect).
In a telecentric beam, the f-ratio should be large enough to avoid a too large broadening of the FWHM (> f/30 for mica-spaced etalons, > f/45 for air-spaced etalons)

Step-up n°1 : PST etalon with its front divergent lens


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


with :

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).

Set-up n°2 : PST etalon in a telecentric lens system

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-ratio.

The results are even worse if we suppose the PST F-P etalon is indeed 1 A FWHM. However, the PST etalons show a lot of variability. The author measured one PST etalon at 0.35 A FWHM


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