Interesting graphical demonstrations

Table of Contents

1. Moire & Resolution Boosting

2a. Moire & Doppler shift (no blurring)

2b. Moire & Doppler shift (with blurring)

3. Robustness to spectrograph distortions

1. Moire & Resolution Boosting
Resolution is classically defined as the ability to distinguish a doublet from a single line.

Wow factor: the moire pattern distinguishes the doublet from the singlet. Therefore the effective resolution has been increased!

Advantages: you can now increase the resolution of your spectrograph, even though you have a lousy grating or wide slits, or blurry lenses.

How'd they do that?: the mathematical process that creates moire patterns is called heterodyning. The math used to reverse the heterodyning is described in Refs. 5, 7, 8.

<-- Without interferometer (conventional spectroscopy)

Can't easily distinguish which "line" is actually a doublet

 

<--With interferometer (EDI)

The doublet on the right is distinguished (by presence of moire fringe)

Quantitative information obtained: From the phase and amplitude of moire fringe we can determine the depth of the valley in the doublet and its detailed position

2a. Moire & the Doppler shift (no blurring)
The created moire fringes shift in phase proportional to the slight Doppler wavelength shift of input spectrum (vertical lines). The entire pattern moves monolithically in a different dimension than the wavelength (horizontal) axis.

Advantages: The moire can be easily detected in spite of spectrograph blurring (see 2b), and is robust against instrument distortions.

Details: Stellar input spectrum is simulated by group of narrow vertical lines. Interferometer creates a periodic grid vs wavelength, which can be slanted so that phase varies vertically.

Unblurred (to let you see what's going on)



<---- Slanted interferometer fringe comb

Interferometer phase varies spatially across slit length

<--- Unslanted (uniphase) fringe comb

Interferometer phase uniform across slit length



<--- Unslanted (uniphase) with a small slit, as in an echelle spectrograph

2b. Moire & the Doppler shift (with blurring)

Wow factor: You can still see the moire shift even though the spectrograph has completely blurred the spectrum.

Advantages: Can use less expensive, smaller, more light efficient spectrographs. Slit can be opened wider to allow more starlight in (when the star is blurry due to atmospheric fluctuations). Diffraction gratings can be optimize for efficiency instead of resolution. Lenses can be removed (that were required to make a tight focus).

Blurred, to simulate an inexpensive or compact low res spectrograph.
Moire pattern is still quite visible even though individual lines in input spectrum are unresolved



<---- Slanted interferometer fringe comb

Interferometer phase varies spatially across slit length

<--- Unslanted (uniphase) fringe comb

Interferometer phase uniform across slit length



<--- Unslanted (uniphase) with a small slit, as in an echelle spectrograph

3. Robustness to spectrograph distortions

Wow factor: The moire pattern is the same (phase vs wavelength) even under severe wavelength distortions. This is because interferometer grid and the input spectrum are both distorted the same amount. (That is, it's a differential type of measurement.)

Advantages: Can use more efficient and less costly spectrographs. These were not feasible before, because they suffered too many distortions. Do not need to put spectrograph in expensive vacuum tanks or have expensive thermal controls.

Note: For the EDI Doppler velocity is not measured along the wavelength axis, but measured instead in phase-space which is much easier to measure accurately

Conventional Spectrograph
Suppose we are measuring the set of absorption lines below, but the spectrograph has severe distortions (curved lines). Then this could lead to a Doppler velocity error, since a shift along the wavelength axis is directly linked to Doppler velocity for the conventional method.

EDI Spectrograph
For the EDI the Doppler velocity is NOT measured ALONG the wavelength axis, so wavelength distortions have dramatically smaller effect. The Moire patterns for the distorted and undistorted spectrographs are nearly the same, because they are determined from phase (transverse) vs wavelength.

This holds true even when we don't use the slit length (vertical axis) to distribute the interferometer phases as shown above. In an echelle spectrograph we would not splay the fringe phase along the slit. Instead the Moire pattern phase can be determined from the 3 or 4 phase stepped exposures which are taken vs time. Splaying the phase vertically is useful for discussion purposes, and is mathematically equivalent to descrete phase stepping.

Note, we also simultaneously use a spectral reference such as an iodine cell. Thus we do not rely on stability of the interferometer during the phase stepped exposures, since changes in interferometer delay rotates both stellar and iodine Moire patterns the same amount of phase. During analysis, the difference between stellar and iodine Moire phases is used.

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David Erskine
derskine@spectralfringe.org

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