CWL and FWHM in non telecentric systems

 

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

 


A) Case 1 : refractors with Barlow lens

 

This section compares different non telecentric lens systems having the same F/30 resulting ratio :

- a 150 mm F/30 refractor,

- a 150 mm F/15 refractor with a long X2 Barlow lens of -127 mm focal length (equivalent to the old Astrophysics Barlow lens),

- a 150 mm F/15 refractor with a short X2 Barlow lens of -55 mm focal length,

- a 150 mm F/7.5 refractor with a short X4 Barlow lens of -127 mm focal length (equivalent to Baader FFC),

- a 150 mm F/7.5 refractor with a short X4 Barlow lens of - 55 mm focal length (equivalent to Baader FFC).

In order to calculate the CWL and the FWHM, we need to calculate the field angle resulting from the Barlow lens. :

 

The magnification factor of the field angle converges to F/f when the magnification factor of the Barlow M increases (ie. collimated beam such as in the PST modification).

1) Center Wavelength Shift :

We can see that :

- It is better to have a native F/30 focus rather than use a Barlow lens to reach the F/30. This is because the Barlow lens increases the field angle.

- For a given magnification factor of the Barlow lens, it is better to have a longer focal length Balow (lower field angle). This is because the focal plane is farther away from the Barlow lens, which reduces the field angle.

- The combination of a refractor of shorter focal ratio (F/7.5) and a Barlow lens with larger magnification factor (X4) gives better results than a longer focal ratio (F/15) and a Barlow lens of a smaller magnification factor (X2). This is because the distance between the Barlow lens and the focus is larger in the first case, resulting in a smaller field angle (for the same distance to the optical axis).

In any case, the "sweet spot" is very small compared to a telecentric system, except for the F/30 refractor and the F/7.5 refractor with a X4 Barlow..

 

2) FWHM broadening :

A 150 mm F/30 refractor could be of use for Ha observations with a mica-spaced F-P etalon. Still, the performances would be much lower than with a telecentric system.

A 150 mm F/7.5 refractor with a X4 Barlow would have a very small sweet spot.

 

3) Conclusion :

A telecentric is by far preferable in all cases.

 


B) Case 2 : Cassegrain telescopes

Thie secondary mirror plays the same role as the Barlow lens. The previous formula given the magnification factor of the field angle still holds (f beeing the absolute value of the secondary mirror focal length).

Let's take the example of a Dall-Kirkhan 250 mm F/3-F27 telescope having the following characteritics :

D = 250 mm

F = 750 mm (ie. F/D = 3 for primary mirror)

f = 243 mm

M = 9 (ie.resulting focal ratio = 9 x 3 = 27)

The FWHM broadening away the optical axis is due to the field angle and to the field angle magnification factor.

The FWHM on the optical axis is set by the F/27 ratio. It would be the same for a teelscentric system with the same resulting F/27 ratio. Going to F/30 improves things :.

 

 

 

 

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