EDI Home

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.

Notable results include:
[1] demonstrated ~1 m/s Doppler precision;
[2] the 12 m/s pull of the moon on the Earth measured in sunlight;
[3] first stellar fringes Dec 1999 at Lick Obs. 1 meter;
[4] Exoplanets have been detected using EDI.


			June 2006

Externally Dispersed Interferometry
Lawrence Livermore Nat. Lab. & Space Sciences Lab. UC Berkeley

Principal investigators
David Erskine & Jerry Edelstein

	EDI is a new technique for the Doppler planet search and high resolution spectroscopy

	A method for boosting the stability & performance of grating and prism spectrographs, by inserting a small interferometer, like a "filter" in series with the beam, and processing the data to extract so-formed moire patterns

	Inexpensive & compact spectrographs can now perform: • Precision stellar Doppler radial velocimetry (planet detection!) • High resolution spectroscopy over a wide simultaneous bandwidth at good photon signal to noise ratio (paper) EDI can be used to upgrade your existing spectrograph, boosting its spectral resolution by factors of several (2x - 6x demonstrated) • A third application is the simultaneous measurement of angular differences between multiple stars using a long baseline interferometer, robust to drifts in the optical pathelengths... called spectral astrometry. • A fourth application is the metrology of any phenomenon which induces a change in an interferometer delay, such as accelerometry, thermometry etc. without the problem of fringe skip ambiguity inherent in laser based systems.

	Externally Dispersed Interferometry (EDI) was invented by David Erskine at LLNL in 1997. See Early History.

How it measures Doppler shifts

Shifts are 500x smaller than feature linewidths!
When the exoplanet pulls the star it creates a Doppler shift in the spectrum vs wavelength. This shift is difficult to measure with a grating spectrograph because it is a small shift easily confused with irregularities in the spectrograph dispersion. The typical linewidth of a stellar absorption line is equivalent to 6000 m/s, so that a Jupiter-class exoplanet Doppler shift of 12 m/s is 500 times smaller than the width of the line! This is a very difficult measurement for a conventional spectrograph, and can be easily overwhelmed by uncontrolled distortions in the instrument response.

The interferometer is the "vernier", the grating the "coarse" readout
The EDI technique uses an interferometer for the fine wavelength discrimination and a grating spectrograph for the coarse discrimination. It is like the vernier and coarse readouts on a precision instrument. The interferometer has a much simpler instrument response, robust to many distortions that plague the grating.


The EDI Method An unequal-path Interferometer is added to a dispersive spectrograph • 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

	Solar spectrum without fringes (upper) and with fringes (lower).

		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. The advantage of this is that the interferometer is independent of the thermomechanical instrument distortions that cause large velocity errors in the grating spectrograph.

Mathematically simple instrument response
The interferometer can provide superior fine wavelength discrimination because it has a mathematically simple and accurate response, a sinusoid with only three degrees of freedom: phase, amplitude, and intensity offset. In contrast the instrument response of a grating has hundreds of degrees of freedom: one for each groove of the grating, which can vary with temperatue and time and create significant velocity errors.

Interferometer has sinusoidal transmission
The interferometer "sorts" light into two outputs depending on very slight wavelength differences. The interferometer has two unequal arms so there is a relative delay between the two paths of light. If a whole number of wavelengths fits in the delay, then there is constructive interference and the light passes out the main output perfectly. If there is an odd number of half wavelengths, then there is destructive interference and the light passes totally out the complementary output and zero out the main output. (Every photon that enters the interferometer leaves the interferometer to be detected, except for minor mirror reflectivity losses. The only issue is *which* output the photon leaves by.) Thus for each output, the transmission function is sinusoidal versus wavelength (actually, vs wavenumber which is 1/wavelength).

Beats or moire patterns formed
When this transmission pattern is dispersed by the spectrograph it creates a periodic grid. This grid multiplies the input stellar spectrum. A consequence is that beats are formed between features and the grid, for the features that have similar size as the grid. These beats are also called moire patterns.

The Doppler effect causes phase shifts
In the EDI the wavelength shift creates a phase shift in the moire pattern. Often the interferometer phase is arranged to vary vertically so that a moire phase shift is a vertical shift. The phase shift is multiplied by 15,000 m/s per fringe proportionality (for a 1 cm delay in green light) to find the Doppler velocity.

This phase shift can be more easily measured than the horizontal shift because the moire patterns are broader than the narrow features that created them, and less susceptible to instrument distortions.


				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. Note that you can easily see the moire pattern move up and down even though you cannot resolve the individual vertical lines.

	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.

Moire patterns formed by heterodyning
The moire patterns represent originally high spatial frequency information (that is, narrow features in the spectrum) beaten down to low spatial frequencies (broad moire patterns). These broad moire patterns are more easily measured by small inexpensive and light efficient spectrographs. This is called a heterodyning process, and it shifts the spatial frequency of the input to a lower value by a known amount, set by the interferometer delay.

Heterodyning is reversed during data analysis
This optical heterodyning process is reversed numerically during data analysis to recover high spatial frequencies that would ordinarily not be resolved by the spectrograph.

Ordinary spectrum also recovered
The ordinary spectrum is also recovered from the data simply by adding all the phase channels vertically so that the moire patterns cancel. Hence the original spectrograph capabilities are retained. The moire signal is thus new information above and beyond the original spectrum. A composite spectrum is then formed from the ordinary + moire components. This composite spectrum has higher effective resolution than the native spectrograph, by factors of several. This is a method of defeating limits imposed by slit blurring, spectrograph optical aberrations, and the CCD Nyquist criterion.

	More explanation on how EDI boosts spectral resolution is at this page.

Site Index

Cover art Home Contact info Team Literature Errata Motivation How it Works (Doppler) How it Works (Res Boost) What is Heterodyning? Graphical Demos Photon noise simulation Experimental Demos
	Early History of EDI History ii Apparatus Schemes Apparatus Photos EDI vs FTS Spectral Astrometry News: EDI to go to Palomar (TEDI) First light at Palomar 6x res boost! Planets detected! Acknowledgements	Erskine's background Erskine's public. list

	www.SpectralFringe.org site maintained by David Erskine erskine1@llnl.gov