Externally Dispersed Interferometry
EDI is a novel technique for the Doppler planet search
A method for boosting the stability & performance of existing dispersive spectrographs, by adding a small interferometer prior to the slit, and processing the moire patterns
With the EDI, your inexpensive & compact spectrograph can now perform:
How it measures Doppler shifts
Shifts are 500x smaller than feature linewidths!
The EDI Method
• The interferometer causes a periodic fringe vs wavelength
• The fringe pattern beats with the spectrum
• Heterodyning creates a moire pattern
• High-resolution features are measurable through the moire
• Nyquist limit and slit blurring are defeated
• The fringe fiducial allows error removal
• Phase stepping nulls instrumental errors
Doppler wavelength shifts are measured through phase shifts of "fringes" which form moire patterns seen in the spectrum. (The interferometer can't be used effectively alone because otherwise the fringes of many different wavelengths having many different phases would fall on the same detector pixels and wash itself out.) The grating spectrograph separates the fringes so that the fringe visibility can be high. But otherwise the key role of measuring a Doppler shift is with the interferometer.
Mathematically simple instrument response
Beats or moire patterns formed
You can confirm this by looking at this animation from far away, or by looking at the lower animation which is blurred to simulate spectrograph blurring.
Bottom line: with the EDI method you do not need to resolve the individual absorption lines. You can obtain ~1 meter/sec Doppler velocities with a small low resolution spectrograph and inexpensive interferometer by measuring the moire patterns.
More explanation on how EDI works for Doppler velocimetry is at this page.
How EDI measures high resolution spectra
A second important application of EDI has been demonstrated by our group: boosting the spectral resolution of an existing spectrograph by factors of several.
Ordinary spectrum also recovered
Bottom line: we can boost the spectral resolution of any spectrograph by demonstrated factors of 2x to 6x and beyond by inserting a small interferometer near the slit and processing the moire fringes with our special algorithm.
More explanation on how EDI boosts spectral resolution is at this page.
Early History of EDI
www.SpectralFringe.org site maintained by
10x resolution boost demo'd on starlight at Mt. Palomar 200 inch Hale telescope
Externally Dispersed Interferometry (EDI) was invented by David Erskine at LLNL in 1997. See Early History.
Demonstration of interferometric resolution boosting to 10-fold, which is the highest demonstrated to date on starlight (June 2011). The resolution and lineshape accuracy of a conventional spectrograph can be increased by factors of several by combining it in series with a small interfemeter, taking data in multiple exposures, then recombining the exposures after special data processing. Normally, the limiting spectrograph resolution scales with spectrograph size, since it is usually limited by detector pixel size, or aberrations in spectrograph lens optics, rather than slit width. The instrument lineshape accuracy is also stabilized by the mathematically simpler behavior of an inteferometer. Hence, EDI is a method of achieving the high performance of a much large spectrograph at the low size and cost of a smaller spectrograph. The tradeoff is slightly lower photon signal to noise and more complicated data analysis. However, the improved instrument lineshape stability often makes the net performance a winner over the naked spectrograph, since many spectrographs are limited by their poor lineshape stability (affected by air convection, thermal drifts etc.) rather than photon noise performance.
Here is reconstructed spectrum of starlight (kappa CrB) to a resolution 10x higher than the native spectrograph used without the EDI interferometer. The spectrograph was the IR "Triplespec" spectrograph of bandwidth 4000 to 10,000 cm-1 and resolution ~2700 at 4000 cm-1, mounted on the Cassegrain output hole of the 200 inch telescope at Mt. Palomar Observatory. The green dashed curve is the Triplespec spectrum without benefit of the interferometer, at a resolution of 2700. It cannot resolve many of the narrow features caused by atmospheric absorption (telluric lines). The red curve is the spectrum reconstructed by combining 7 delays worth of fringing data and special Fourier processing, in a technique called ISR (interferometric spectral reconstruction) or resolution boosting. It has an effective resolution of 27,000 and agrees well with a model of telluric features calculated by Henry Roe and artificially blurred by us to that resolution. A ThAr spectral lamp provides calibration emission lines. This graph shows only a small (110 cm-1) section of the reconstructed bandwidth which extends 6000 cm-1 from ~4000 cm-1 to ~10000 cm-1. The ISR technique is described in these 3 papers: Ten-fold SPIE, Scot16Bppr2.pdf, BoostApJ1693b.pdf. See our latest page on Res boosting.
David J. Erskine
(Above) Simulation of a cross-fading EDI using real EDI data of a ThAr spectral calibration lamp measured while at Mt. Palomar Observatory in 2011, and software recently improved by the PI. Each interferometer delay measures a moire pattern which, after numerical processing, creates a wavelet in the ouput spectral space. The wavelet envelope is defined by the dispersive spectrograph, and its phase by the interferometer. (The horizontal axis is wavenumber which is reciprocal of wavelength in cm). The simulated insult drift ∆x in the dispersive spectrograph can be seen in the shift of the wavelet envelope (slanted dashed lines). The sum of the wavelets forms the output peak (red curve), which is narrower than the envelope (hence there is resolution boosting). By choosing weights of each wavelet strategically, we can make the location of the output peak (dotted line) virtually independent of the disperser insult drift ∆x along the horizontal axis. (Actually it's a 1000 times smaller, which is so small you cannot see it by eye here.) This is really cool!!
The same spectral freature produces moire patterns having opposite polarity slopes, from two interferometer delay combs (having slightly different periodicities). An unwanted sideways translation (disperser drift ∆x) would produce opposite polarity errors, which can cancel when we combine the signals.
<-----Our January 2022 iPoster using fun animations of Moire fringes in our Crossfading technique, prepared for the AAS 239th meeting.
-------- Latest two posters July 2022 --------
(left) Demos of single-delay Crossfading technique, and (right) preliminary EDI measurements diagnosing the Keck Planet Finder spectrograph's blur width and shape (in engineering tests at UC Berkeley Space Sciences Lab), prepared for the SPIE Astronomical Instruments meeting in Montreal 2022 July.
---- Other interesting recent graphics ----