EDI Terminology

Angle-independent interferometer-- see Superimposing Interferometer

Astrometry -- The measurement of the angular positions of stars. This is an alternative method of detecting an exoplanet using the star's wobble. Instead of measuring the velocity of wobble one measures the position of the wobble.

CCD -- a sensitive 2 dimensional multichannel detector of (usually) visible light in wide use today, similar to those found in digital cameras

Delay -- The optical path length difference between the two arms of an interferometer

Detector noise -- Noise whose absolute amount is independent of the input signal flux, and can be thought of as an additive random signal coming from the detectors. Contrast with photon noise.

Dispersion -- Here it means the spreading of light into a spectrum using a prism or diffraction grating. Not to be confused with the usage in fiberoptics where it means the spreading of light in the time domain because of differing speeds for different wavelengths.

Dispersive Spectroscopy -- A prism or a grating disperses input light into a spectrum which is recorded by a multichannel detector, such as a CCD.

Etalon -- A parallel plate of glass used to delay light. In the EDI the etalon has anti-reflective coatings to prevent reflection from the surfaces. The term etalon used here is distinguished from another optical spectroscopic instrument called the Fabry-Perot etalon where the surfaces are deliberately coated with reflectors so that the light bounces back and forth many times.

Externally Dispersive Interferometry -- the series combination of an unequal-arm interferometer and a dispersive spectrograph that is outside the interferometer cavity.

Fixed Delay Interferometer & Exoplanet Tracker -- terms for an externally dispersed interferometer used by Jian Ge's group, now at Univ. of Florida.

Fabry-Perot etalon or interferometer -- An interferometer where the light bounces back and forth many times between two mirrors. For every input pulse and infinite series of output pulses is formed of gradually diminishing amplitude. This is distinct from the Michelson style interferometer where for every input pulse only two outputs are formed. The FP interferometer is useful for spectroscopy because its transmission spectrum is an extremely narrow peak.

Field-widened interferometer-- see Superimposing Interferometer

Fixed pattern noise -- Unwanted signal component that is usually constant or very slowly changing with time, but might vary spatially and so could potentially be confused with true fringes. Examples of fixed pattern noise are the pixel to pixel gain variations or cosmetic defects in CCD detectors, or parasitic interference caused by unwanted reflections from various air/glass surfaces.

Fringe -- a sinusoidal variation of intensity versus either wavelength or spatial position or both

Fringing Spectrometer, Fringing Spectroscopy -- an early name for the EDI technique

Fourier Transform -- a mathematical algorithm widely used in science and engineering that converts a signal which is intensity vs time into a spectrum which is amplitude vs frequency, and the latter is actually a complex spectrum where for each frequency both the phase & amplitude is specified. There is an associated inverse Fourier transform that converts the complex spectrum back into a time dependent signal.

Fourier Transform Spectroscopy (FTS) -- A purely interferometric method of measuring a spectrum. An interferometer's delay is scanned over a range while the output intensity is recorded. The intensity vs delay data is Fourier transformed to produce an intensity vs wavenumber spectrum. (Wavenumber is 1/wavelength). The EDI differs from FTS by the inclusion of dispersion, but also because the EDI delay is either fixed at a single value, or changed in a few big increments, not scanned over a multitude of infitesimally small increments.

Heterodyning -- the process of shifting the frequency f1 of a signal by multiplying it by a sinusoidal function of frequency f2. This generates two components, one are called beats (or moire patterns) and have a frequency (f1-f2). The other is an upshifted component (usually not used) having frequency (f1+f2).

Interferometer -- a device that splits the signal into two (or more) paths, delays these signal relative to the original signal, and then recombines all the signals. The net interferometer output will be very sensitive to signal wavelength when the delay is long, because depending on whether there is an even or odd number of half-wavelengths fitting inside the delay, the output will suffer destructive or constructive interference and hence vary from zero to unity. Hence a 2 cm delay interferometer has 40,000 wavelengths of green (500 nm) light fitting into the delay, so if the wavelength changes by 1 part in 80,000 the output makes a dramatic change from a bright fringe to a dark fringe.

Internally Dispersive Interferometry -- this term is not used as such, but would describe instruments such as the Spatially Heterodyning Spectrometer (SHS) (by Harlander et al. at U of Wisconsin) where the dispersive element (diffraction grating) is a part of or internal to the interferometer cavity. These can produce very high spectral resolution, but only over a small simultaneous bandwidth.

Moire -- the graphical analogy to beats created when two musical instruments play notes of slightly different pitch, say 500 Hz and 501 Hz, and a 1 Hz beat frequency is heard. Except that we are now talking about spatial frequency instead of frequency in the time domain, that is, the number of lines per distance across the page or whatever the horizontal variable is. The process of forming moire patterns or beats is called heterodyning in the electrical engineering sciences.

Phase-stepping -- Where the interferometer delay is incremented several times in small steps, smaller than the wavelength, so that true fringes can be distinguished from other "bad" signal components (called fixed pattern noise). Only the true fringes will vary sinusoidally in synchrony with the applied phase step. Examples of fixed pattern noise are the pixel to pixel gain variations or cosmetic defects in CCD detectors, or parasitic interference caused by unwanted reflections from various air/glass surfaces.

Photon or shot or Poisson noise -- Statistical fluctuations due to the fact that light arrives in discrete bundles. This creates noise that, as a percentage of the continuum, decreases with increasing flux by one over the square root of the flux. This is more important for optical wavelengths than infrared because in the short wavelengths the energy per photon is higher and so there are fewer photon per unit power of illumination. This is a reason why FTS instruments have not been as popular in the visible as in the infrared. The FTS has a very poor photon limited signal/noise ratio, but in the infrared where photons are plentiful, this noise is less important than other kinds of noise such as detector noise. Contrast with detector noise.

Radial velocity -- velocity measured along the line of sight, distinguished from velocity of a target perpendicular to the line of sight. Radial velocities are measured by the Doppler effect. Transverse velocities would be measured by noting how the angle of the object changes with time.

Simultaneous bandpass or bandwidth -- The wavelength range over which the instrument can measure the spectrum simultaneously, as oppose to, say, scanning a narrow bandpass instrument over a wider bandwidth over time. In the past, many spectrographs have achieved high resolution at the expense of a narrower bandpass. The EDI is notable in that it can increase spectral resolution while preserving the original bandwidth.

Spatial frequency -- the number of lines or features per unit distance. Analogous to the ordinary "frequency" but occurs in the spatial domain instead of temporal.

Spectral Interferometry -- The field of study where interference phenomena are used to measure the wavelength characteristics of light. Distinguished from other applications of interferometry such as to measure distances or angles of light beams.

Superimposing Interferometer -- Superimposing, wide-angle, WAMI, angle-independent, field-widened are synonyms here. In this kind of interferometer, the output rays from both arms are made to (by the use of an etalon [glass plate] or combination of lenses) superimpose so that both the delayed and undelayed images of the source are superimposed longitudinally, transversely and in magnification. This creates an interferometer that imprints the same delay on every ray, so that uncollimated beams from extended sources can be used and produce high visibilty fringes. This allows the use of blurry star images, light from wide diameter fibers, 1-d imaging along the spectrograph slit, and use of many optical fibers placed along the slit as used in the multi-object instrument of Jian Ge's group [Ref. G] . In contrast, for non-superimposing interferometers the light must typically be sent through a small pinhole before the interferometer so that the range of ray angles and/or positions are very limited. A "WAMI", which means wide-angle Michelson, is described by Hilliard & Shephard, J. Op. Soc. Am., 56, 362 (1966). We use that principle in the interferometer of Figure H10.

Wavenumber -- A measure of the frequency of light popular with spectroscopists equal to 1/wavelength, where wavelength is measured in centimeters. The wavenumber is proportional to the frequency of light, f = c/lambda, but is usually more convenient to use. For the case of interferometers, the wavenumber is a more useful unit than wavelength because the transmission function for an interferometer is perfectly sinusoidal when expressed versus the wavenumber. Also, if you express the dispersion axis of a spectrum in wavenumbers, then when you find the spatial frequency of some signal in spectrum, it has units of features per inverse cm, which is the same as units of cm, which is the same unit as the interferometer delay. Hence we can rapidly say that a 2 cm delay interferometer will produce a sinusoid with spacing of 0.5 wavenumber.

Wide-angle interferometer, WAMI-- see Superimposing Interferometer

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