Fabry-Perot etalon testing with an Ha lamp

(Copyright François Rouvière  - Christian Viladrich)

(1) Test in diffuse light: 

  1. Principle
  2. Theorical approach, calculation of FSR and FWHM, example of measurement procedure
  3. Test of a Coronado SM 40 mm etalon
  4. Test of a Coronado SM III 60 mm tilt and Rich View etalons

(2) Test in collimated beam: 

  1. Principle
  2. Examples

Test in diffused light : principle

Objectives of the test :
- get a qualitative estimation of the etalon uniformity accross its aperture (CWL),
- get a quantitative estimation of the FWHM and FSR of the etalon.

Optical setup (front left to right) :

- a Ha lamp is used as the light source ;

- a diffuser is placed 25 cm away from the lamp ;

- the etalon is placed next to the diffuser ;

- a camera focussed at the infinite takes an image of the interference pattern (not shown).

Principle of the test : 

The etalon is used as an Fabry-Perot interferometer. A system of circular fringes can be observed by looking directly into the etalon or with a camera focused at infinity. The wavelength is fixed (given by the Ha lamp, whose FWHM is negligeable). Thus, the transmission profile is a function of the angle i of incident light.When used as a Fabry-Perot filter instead, the trannsmission curve of the etalon  is as a function of the wavelength λ, the angle of incident light being fixed.

Qualitative interpretation of the fringe pattern: 

(a) Qualitative information on the CWL and uniformity

The test takes advantage of the following observations:

- if the CWL of the etalon at normal incidence is precisely set on the Ha line, the central fringe reduces into a central spot, 

-  if there is a small CWL offset, a small central dip appears in the central spot, 

- as the CWL offset increases, the central fringe evolved into a ring whose diameter increases with the CWL offset.

Central interference pattern observed through a thermo-regulated mica-spaced etalon at three different settinngs of wavelengths : Ha, Ha +0.5A, Ha + 1.0 A. At +0.5A, the top of the central peak flattens. At Ha + 1.0 A, it turns into a small ring.

When moving the eye (or the camera) laterally along a diameter of the aperture, the eye (or the camera) samples different areas of the etalon. The surface of the sampled area is determined by the size of the pupil (or the aperture stop of the camera). If the CWL is uniform across the surface of the etalon, the central fringe pattern (spot or ring) remains unchanged. Any change in the central fringe pattern indicates nonuniformity of the CWL along the diamater sampled..

This test of the uniformity of the CWL is qualitative but quite sensitive and relevant.

(2) Qualitative information on the FWHM

The width of the fringes is related to the finesse  of the etalon. The larger the finesse, the thinner the fringes :

Simulations made with webmatematica - https://wp.optics.arizona.edu/jcwyant/mathematica/webmathematica/

Quantitative interpretation of the fringe pattern :

François Rouvière (contributor to Solar Astronomy book) established the formulae for deriving the FSR and the FWHM of the etalon from the interference pattern. A big thanks for this ! The calculation is based on the measurement of the radius and FWHM of successive rings.

Each fringe (except the central peak)  has a Lorentzian profile, which have to be measured with great care and good S/N. FITyk software is used for least-square fitting a Lorentzian function to each fringe.

Etalons tested so far:

Etalon FSR FWHM Delta CWL
Coronado SM40. 12.1 A 0.74 A negligeable
Coronado SMIII 60 8.5 A < 0.55 A from 0.55 A (center) to 0.60 A (at 25 mm from etalon center)
Coronado SMIII 60 RichView. 8.9 A < 0.58 A from 1.20 A (center) to 1.25 A (at 20 mm from etalon center)

Important note: local or  integrated FWHM ?
The FWHM and CWL of a filter vary locallly depending on the area sampled on the etalon.
This test measures the FWHM and CWL integrated over the aperture stop of the lens of the camera.
- If the diameter of the aperture stop is equal to the diameter of the etalon, then the measured FWHM and CWL are average of the full aperture of the etalon.
- If the diameter of the aperture stop is small (for example 5 mm), then the measured FWHM and CWL are average of the diameter of the spot (5 mm) and changes from one spot to the other.

 For an etalon placed in front position:
- All parts of the etalon contribute equally to the quality (i.e. contrast) of the image. Accordingly, the relevant value to qualify the etalon performence is the FWHM (and CWL) integrated over the full aperture of the etalon, and not the local values of FWHM and CWL.
- However, the mapping of the local values of FWHM and CWL can still be used to calculate the average (or integrated) values over the full aperture of the etalon. The integration of the FWHM of the full aperture of the etalon  is correct only if it takes in consideration both the local values of FWHM and CWL. For example :
    - If we assume an etalon with local values of FWHM all equal to 0.3 A, but whose CWL changes dramatically of  +/1 A for one area sampled to the other.
    - Then an average FWHM of 0.3 A is derived if the calculation of average FWHM takes  into account only the statistics of the local values of FWHM, while the actual value integrated over the aperture of the etalon is much greater because of the strong variation of CWL over the aperture of the etalon.

  For an etalon placed in rear position:
- Let's assume an observation of the Sun with a 2 m focal length telescope. The diameter of the solar disk at the focal plane is about 2 cm.
- All  the area of the etalon within its central 2 cm diameter contribute equally to the contrast of the image.
- Accordingly, ther relevant value for the observation is the average (or integrated) values of  FWHM and CWL, and not the local values.

2 - Test in collimated beam

Objective of the test :
- The test is only qualitative (at this stage).
It investigates transmission variations across the etalon aperture. These variations result from local variation of peak transmission, CWL and to a lower extent FWHM across the surface of the etalon. Indeed, if the CWL is exactly on the Ha line, any FWHM nonuniformity has no impact on the resulting image.

- For mica-spaced etalons, the transmission variations can be due to improper mica cleavage, striae, inclusions or refractive index inhomogeneities. For air-spaced etalon, transmission variations can result from thickness variation in the air gap.

Optical setup (front left to right) : 

- a Ha lamp is used as the light source ;

- a 55 mm f/8 refractor is used as a collimator to illuminate the entire surface of the etalon.  A 5 mm aperture stop placed next to the lamp limits the angular aperture of the light source to 1:88 (= 5 mm/440 mm) or 0.65°. Accordingly, the most oblique beam (0.32°) introduces a CWL shift of 0.1 Å for air-spaced etalon and 0.04 Å for mica-spaced etalon, which is quite acceptable ;

- the etalon is placed in front of the refractor lens and square to its optical axis ;

- the image of the etalon is taken by a camera (not shown in the figure) placed about 50 cm in front of the etalon. The focus of the camera is set on the etalon surface. 

Note : As the light beam is collimated, the aperture of the camera determines the area of etalon sampled. For example, a 50 mm FL f/1/8 lens samples a 28 mm diameter area. This is usually large enough for mica-spaced etalons, but small compared to the free aperture of air-spaced etalons.

Examples :

The test is very sensitive to non uniformities. Here are two mica-spaced etalons which look terrible in these images, but still show excellent uniformity at the telescope.

Nikon Z6 camera - 50 mm f/1.8 Nikkor lens.

Here are three different areas (28 mm in diameter) sampled over a Coronado SM40 etalon.

Nikon Z6 camera - 50 mm f/1.8 Nikkor lens - 12-bit RAW file - 0.5s exposure - 200 ISO.

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