"Sweet spot", "banding" and air-spaced Ha tilted etalon

(Copyright  Christian Viladrich)



This page presents:
1) How the sweet spot evolves into a sweet ring when an air-spaced etalon is to be tilted to tune its bandpass on Ha.
2) Hhe difference in size of the sweet spots between an air-spaced etalon placed in front position and in internal position (and collimated beam) halfway between the obective of the refractor and its focus.
3) Case of the Heliostars 76 and 100.



1 -Sweet spot and sweet ring

Case 1 : sweet spot for an air-spaced etalon having its CWL on Halpha at normal incidence

Application of (1) gives :

        -0.25 = -i_max 2, thus i_max = 0.5°

The diameter of the sweet spot is equal to twice de diameter of the solar disk (central cercle on the following figure) :











2- Sweet spot for an etalon placed in internal position
When an air-spaced etalon is place in a internal position in collimated beam, we have:
   
        delta CWL = -i^2  × F^2/f^2

with:
f = focal length of the collimator,
F = focal lenght of the telescope.

                   
                          For an air-spaced etalon placed in front position                                                                               For an air-spaced etalon placed halfway in the refractor OTA               
                       

Click on the images to scroll and display the numerical value of delta CWL for any points in the field.

Color scale:
- red : delta CWL = 0 A,
- bleu : delta CWL = 0.5 A or larger.


3 - Case of the Heliostar 76 and 100

The following figure presents the variation of the center wavelength (CWL) accross the field of view when the etalon is tuned at +0.15 A from Ha (i.e. on the red side of Ha) at the center of the field:




Calculations are donne for the Heliostars 76 and 100, and also for an hypothetical 150 mm f/8 refractor using either the etalons of the Heliostar 76 (40 mm etalon) or the Heliostar 100 (60 mm etalon), with associated collimating optics.


Since the measured FWHM of the Heliostar etalons is typically around 0.3 A, we can define the sweet spot as the region of the field of view where the CWL is within ±0.15 A of Ha. Indeed, it is most probable that no significant difference  will be observed in solar features when the CWL shifts by only ±0.15 A around  Ha.
The following table presents the value of the sweet sport diameter based on this definition. It is to be compared with the value of the solar diameter (around 30 arcmin):

 

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