State of the art astrophysics demands extremely stable wavelength measurements, e.g. few cm/s scale Doppler radial velocimetry for Earth-like planet detection or multi-year cosmic redshift drift measurements. We present new techniques for 500 − 1000× improvement in stability using an interferometer in series with a spectrograph to form an Externally Dispersed Interferometer (EDI). When the received spectrum suffers a wavelength jitter, the phase of the moir´e pattern from the interferometer delay shifts in opposite directions for two signal paths, nonfringing and fringing; with appropriate weightings (“crossfading”) the net phase reaction cancels, stabilizing the spectrum. We present an improvement to our previous technique of multiple delays, using a single delay to crossfade, and demonstrate stabilization of ≳ 500× on existing Hale Telescope data. Single-delay EDIs are easier to construct and operate than those with multiple delays, and the EDI ensures that exactly the same pixels are used for the science and calibration signals, and in constant proportion under intensity fluctuations, greatly easing positional requirements.
We built an externally dispersed interferometer (EDI) testbed for exploring methods of improving high resolution spectrograph performance. We tested the EDI on the Keck Planet Finder (KPF) spectrograph May 11, 2022 measuring a Fabry-Perot (FP) etalon back lit by white light. This is also the first time an EDI has been used to measure a periodic source. The data shows that the EDI is useful for diagnosing the point spread function (PSF) width and shape, in particular the asymmetry of the PSF. This EDI ability comes because EDI can simultaneously measure both the conventional nonfringing spectrum, and the fringing derived spectrum. A conventional spectrograph resolution is limited by slit blur– the EDI resolution is not. A heterodyning effect shifts the fringing sensitivity peak to arbitrarily higher frequency, set by the interferometer delay value, and thus its resolution can exceed the spectrograph used alone. By comparing the Fourier transforms of the two measured signals, we can compare the phase shift changes, which gives information about the small asymmetry of the spectrograph blur, independent of the much larger asymmetry of the FP source spectrum. We show that comparing the phases of the nonfringing and fringing components versus harmonic number in the Fourier Transform is a useful method for measuring the asymmetry in the PSF. We report the first measurements of an EDI measuring a periodic source, which is a Fabry-Perot (FP) interferometer back illuminated by white light. The periodic character of the FP source created spikes in the Fourier transform, which was very convenient for analysis.
We demonstrate a key step along a technical route to achieving cm/s scale accuracy for astronomical spectrographs over long (multi-year) time scales, which is critical for the Doppler characterization of Earth sized exoplanets, and measurement of small cosmic redshift drift over many years. This same technique also enables searching exoplanet atmospheres for biosignificant molecules in direct planet imaging using, otherwise, insufficiently low resolution and drift prone dispersive (grating or prism) spectrographs. Using a method called crossfading for externally dispersed interferometers (EDIs) to get highly robust spectra, we recently demonstrated a factor of 1000 × reduction in the net shift of an EDI measured ThAr line to a deliberate simulated wavelength translation of the detector. This 1000 × gain in disperser stability can be combined with conventional stability gains afforded by fiber scramblers, vacuum tanks, and thermal control, to provide an additional 1 to 3 orders of magnitude reduction in the net point spread function shift drift. Crossfading combines high- and low-delay fringing signals that react oppositely in phase to cancel their net reaction to a detector wavelength drift. This can be implemented by an interferometer addition to a facility spectrograph.
We demonstrate a key step along a technical route to achieving cm/s scale accuracy for astronomical spectrographs over long (multi-year) time scales, which is critical for the Doppler characterization of earth sized exoplanets, and measurement of small cosmic redshift drift over many years. This same technique is also en- abling for searching exoplanet atmospheres for biosignficant molecules in direct planet imaging using otherwise insufficiently low resolution and drift prone dispersive (grating or prism) spectrographs. Using a new method called crossfading" for externally dispersed interferometers (EDI) to get highly robust spectra, we recently demonstrated a factor of 1000x reduction in the net shift of an EDI measured ThAr line to a deliberate simulated wavelength translation of the detector. This 1000x gain in disperser stability can be combined with conventional stability gains afforded by fiber scramblers, vacuum tanks, and thermal control, to provide an additional 1 to 3 orders of magnitude reduction in the net PSF shift drift. Crossfading combines high and low delay fringing signals that react oppositely in phase to cancel their net reaction to a detector wavelength drift. This can be implemented by an interferometer addition to a facility spectrograph.
The physics of molecular vibration causes absorption spectra of atmospheric molecules to be a group of approximately periodic fine lines. This is fortuitous for detecting exoplanet biosignificant molecules, since it approximately matches the periodic sinusoidal transmission of an interferometer. The series addition of a 0.6 cm interferometer with a dispersive spectrograph creates moire patterns. These enhance detection by several orders of magnitude for initially low resolution spectrographs. We simulate the Gemini Planet Imager integral field spectrograph observing a telluric spectrum of native resolutions 40 and 70 for 1.65 and 2 micron bands– too low to resolve the fine lines. The interferometer addition increases the detectability of the molecular signal, relative to photon noise, to a level similar to a R=4400 (at 1.65 micron) or R=3900 (at 2 micron) spectrograph.
High-resolution broadband spectroscopy at near-infrared (NIR) wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar, with the TEDI interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec NIR echelle spectrograph. These are the first multidelay EDI demonstrations on starlight. We demonstrated very high (10×) resolution boost and dramatic (20× or more) robustness to point spread function wavelength drifts in the native spectrograph. Data analysis, results, and instrument noise are described in a companion paper (part 1). This part 2 describes theoretical photon limited and readout noise limited behaviors, using simulated spectra and instrument model with noise added at the detector. We show that a single interferometer delay can be used to reduce the high frequency noise at the original resolution (1× boost case), and that except for delays much smaller than the native response peak half width, the fringing and nonfringing noises act uncorrelated and add in quadrature. This is due to the frequency shifting of the noise due to the heterodyning effect. We find a sum rule for the noise variance for multiple delays. The multiple delay EDI using a Gaussian distribution of exposure times has noise-to-signal ratio for photon-limited noise similar to a classical spectrograph with reduced slitwidth and reduced flux, proportional to the square root of resolution boost achieved, but without the focal spot limitation and pixel spacing Nyquist limitations. At low boost (∼1×) EDI has ∼1.4× smaller noise than conventional, and at >10× boost, EDI has ∼1.4× larger noise than conventional. Readout noise is minimized by the use of three or four steps instead of 10 of TEDI. Net noise grows as step phases change from symmetrical arrangement with wavenumber across the band. For three (or four) steps, we calculate a multiplicative bandwidth of 1.8:1 (2.3:1), sufficient to handle the visible band (400 to 700 nm, 1.8:1) and most of TripleSpec (2.6:1).
We describe demonstrations of remarkable robustness to instrumental noises by using a multiple delay externally dispersed interferometer (EDI) on stellar observations at the Hale telescope. Previous observatory EDI demonstrations used a single delay. The EDI (also called “TEDI”) boosted the 2,700 resolution of the native TripleSpec NIR spectrograph (950-2450 nm) by as much as 10x to 27,000, using 7 overlapping delays up to 3 cm. We observed superb rejection of fixed pattern noises due to bad pixels, since the fringing signal responds only to changes in multiple exposures synchronous to the applied delay dithering. Remarkably, we observed a ~20x reduction of reaction in the output spectrum to PSF shifts of the native spectrograph along the dispersion direction, using our standard processing. This allowed high resolution observations under conditions of severe and irregular PSF drift otherwise not possible without the interferometer. Furthermore, we recently discovered an improved method of weighting and mixing data between pairs of delays that can theoretically further reduce the net reaction to PSF drift to zero. We demonstrate a 350x reduction in reaction to a native PSF shift using a simple simulation. This technique could similarly reduce radial velocity noise for future EDI’s that use two delays overlapped in delay space (or a single delay overlapping the native peak). Finally, we show an extremely high dynamic range EDI measurement of our ThAr lamp compared to a literature ThAr spectrum, observing weak features (~0.001x height of nearest strong line) that occur between the major lines. Because of individuality of each reference lamp, accurate knowledge of its spectrum between the (unfortunately) sparse major lines is important for precision radial velocimetry.
High-resolution broadband spectroscopy at near-infrared wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar. Observations of stars were performed with the “TEDI” interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec near-infrared echelle spectrograph. These are the first multidelay EDI demonstrations on starlight, as earlier measurements used a single delay or laboratory sources. We demonstrate very high (10×) resolution boost, from original 2700 to 27,000 with current set of delays (up to 3 cm), well beyond the classical limits enforced by the slit width and detector pixel Nyquist limit. Significantly, the EDI used with multiple delays rather than a single delay as used previously yields an order of magnitude or more improvement in the stability against native spectrograph point spread function (PSF) drifts along the dispersion direction. We observe a dramatic (20×) reduction in sensitivity to PSF shift using our standard processing. A recently realized method of further reducing the PSF shift sensitivity to zero is described theoretically and demonstrated in a simple simulation which produces a 350× times reduction. We demonstrate superb rejection of fixed pattern noise due to bad detector pixels—EDI only responds to changes in pixel intensity synchronous to applied dithering. This part 1 describes data analysis, results, and instrument noise. A section on theoretical photon limited sensitivity is in a companion paper, part 2.
High resolution broad-band spectroscopy at near-infrared wavelengths has been performed using externally dis- persed interferometry (EDI) at the Hale telescope at Mt. Palomar. The EDI technique uses a field-widened Michelson interferometer in series with a dispersive spectrograph, and is able to recover a spectrum with a resolution 4 to 10 times higher than the existing grating spectrograph. This method increases the resolution well beyond the classical limits enforced by the slit width and the detector pixel Nyquist limit and, in principle, decreases the effect of pupil variation on the instrument line-shape function. The EDI technique permits arbi- trarily higher resolution measurements using the higher throughput, lower weight, size, and expense of a lower resolution spectrograph. Observations of many stars were performed with the TEDI interferometer mounted within the central hole of the 200 inch primary mirror. Light from the interferometer was then dispersed by the
TripleSpec near-infrared echelle spectrograph. Continuous spectra between 950 and 2450 nm with a resolution
as high as ~27,000 were recovered from data taken with TripleSpec at a native resolution of ∼2,700. Aspects
of data analysis for interferometric spectral reconstruction are described. This technique has applications in im- proving measurements of high-resolution stellar template spectra, critical for precision Doppler velocimetry using conventional spectroscopic methods. A new interferometer to be applied for this purpose at visible wavelengths is under construction.
Externally dispersed interferometry (EDI) uses a hybrid spectrometer that combines a Michelson interferometer in series
with a grating spectrometer. EDI provides a means of deriving spectral information at a resolution substantially higher
than that provided by the grating spectrograph alone. Near IR observations have been conducted using the Triplespec
spectrometer mounted on the 5m Hale telescope. Spectra have been reconstructed at a resolution of ~27000 where the
resolution of Triplespec is ~2700. Progress in the development of the EDI technique is reported herein emphasizing
studies related to the accuracy of the reconstructed spectra.
An optical technique called "interferometric spectral reconstruction" (ISR) is capable of increasing a spectrograph's
resolution and stability by large factors, well beyond its classical limits. We have demonstrated a 6-
to 11-fold increase in the Triplespec effective spectral resolution (R=2,700) to achieve R=16,000 at 4100 cm-1to 30,000 at 9600 cm-1 by applying special Fourier processing to a series of exposures with different delays
(optical path differences) taken with the TEDI interferometer and the near-infrared Triplespec spectrograph at
the Mt. Palomar Observatory 200 inch telescope. The TEDI is an externally dispersed interferometer (EDI) used
for Doppler radial velocity measurements on M-stars, and now also used for ISR. The resolution improvement
is observed in both stellar and telluric features simultaneously over the entire spectrograph bandwidth (0.9-2.45
μm). By expanding the delay series, we anticipate achieving resolutions of R=45,000 or more. Since the delay is
not continuously scanned, the technique is advantageous for measuring time-variable phenomena or in varying
conditions (e.g. planetary fly-bys). The photon limited signal to noise ratio can be 100 times better than a
classic Fourier Transform Spectrometer (FTS) due to the benefit of dispersion.
The TripleSpec - Exoplanet Discovery Instrument (TEDI) is a device to use interferometric spectroscopy for the radialvelocity
detection of extrasolar planets at infrared wavelengths (0.9 - 2.4 μm). The instrument is a hybrid of an
interferometer and a moderate resolution echelle spectrograph (TripleSpec, R=2,700,) at the Cassegrain focus of the
Palomar 200" telescope. We describe our experimental diagnostic program using laboratory sources and standard stars in
different optical configurations, along with performance analysis and results. We explain our instrumental upgrade
development to achieve a long-term performance that can utilize our demonstrated, < 10 m/s, short-term velocity
precision.
The TripleSpec Exoplanet Discovery Instrument (TEDI) is optimized to detect extrasolar planets orbiting midto-
late M dwarfs using the Doppler technique at infrared wavelengths. TEDI is the combination of a Michelson
interferometer and a moderate-resolution near-infrared spectrograph, TripleSpec, mounted on the Cassegrain
focus of the Palomar 200-inch Hale Telescope. Here we present results from observations of a radial velocity
standard star and a laboratory source over the past year. Our results indicate that focus effects within the
interferometer, combined with non-common-path errors between the ThAr calibration source and starlight, limit
our performance to several 100 m/s. An upgraded version of TEDI, TEDI 2.0, will eliminate this behavior by
mixing ThAr with starlight in a scrambled fiber before a redesigned interferometer with minimal focal effects.
The TEDI (TripleSpec - Exoplanet Discovery Instrument) is the first instrument dedicated to the near infrared radial
velocity search for planetary companions to low-mass stars. The TEDI uses Externally Dispersed Interferometry (EDI), a
combination of interferometry and multichannel dispersive spectroscopy. We have joined a white-light interferometer
with the Cornell TripleSpec (0.9 - 2.4 μm) spectrograph at the Palomar Observatory 200" telescope and begun an
experimental program to establish both the experimental and analytical techniques required for precision IR velocimetry
and the Doppler-search for planets orbiting low mass stars and brown dwarfs.
The TEDI (TripleSpec Exoplanet Discovery Instrument) will be the first instrument fielded specifically for finding low-mass
stellar companions. The instrument is a near infra-red interferometric spectrometer used as a radial velocimeter.
TEDI joins Externally Dispersed Interferometery (EDI) with an efficient, medium-resolution, near IR (0.9 - 2.4 micron)
echelle spectrometer, TripleSpec, at the Palomar 200 telescope. We describe the instrument and its radial velocimetry
demonstration program to observe cool stars.
Externally Dispersed Interferometry (EDI) is the series combination of a fixed-delay field-widened Michelson interferometer with a dispersive spectrograph. This combination boosts the spectrograph performance for both Doppler velocimetry and high resolution spectroscopy. The interferometer creates a periodic comb that multiplies against the input spectrum to create moire fringes, which are recorded in combination with the regular spectrum. Both regular and high-frequency spectral components can be recovered from the data - the moire component carries additional information that increases the signal to noise for velocimetry and spectroscopy. Here we present simulations and theoretical studies of the photon limited Doppler velocity noise in an EDI. We used a model spectrum of a 1600K temperature star. For several rotational blurring velocities 0, 7.5, 15 and 25 km/s we calculated the dimensionless Doppler quality index (Q) versus wavenumber ν. This is the normalized RMS of the derivative of the spectrum and is proporotional to the photon-limited Doppler signal to noise ratio.
The TEDI (TripleSpec Externally Dispersed Interferometry) is an interferometric spectrometer that will be used to explore the population of planets around the lowest mass stars. The instrument, to be deployed on the Palomar 200 Cassegrain mount, includes a stabilized Michelson interferometer combined with a medium resolution, broad band (0.8 - 2.4 micron) spectrograph, TripleSpec. We describe the instrument design and its application to Doppler velocimetry and high-resolution spectroscopy.
We describe a plan to study the radial velocity of low mass stars and brown dwarfs using a combination of interferometry and multichannel dispersive spectroscopy, Externally Dispersed Interferometry (EDI). The EDI technology allows implementation of precision velocimetry and spectroscopy on existing moderate-resolution echelle or linear grating spectrograph over their full and simultaneous bandwidth. We intend to add EDI to the new Cornell TripleSpec infrared simultaneous JHK-band spectrograph at the Palomar Observatory 200" telescope for a science-demonstration program that will allow a unique Doppler-search for planets orbiting low mass faint M, L and T type stars. The throughput advantage of EDI with a moderate resolution spectrograph is critical to achieving the requisite sensitivity for the low luminosity late L and T dwarfs.
We describe the use of Externally Dispersed Interferometry (EDI) for high-resolution absorption spectroscopy. By adding a small fixed-delay interferometer to a dispersive spectrograph, a precise fiducial grid in wavelength is created over the entire spectrograph bandwidth. The fiducial grid interacts with narrow spectral features in the input spectrum to create a moire pattern. EDI uses the moire pattern to obtain new information about the spectra that is otherwise unavailable, thereby improving spectrograph performance. We describe the theory and practice of EDI spectrometers and demonstrate improvements in the spectral resolution of conventional spectrographs by a factor of 2 to 6. The improvement of spectral resolution offered by EDI can readily benefit space instruments operating from the near IR to the far UV by reducing spectrograph size or increasing instantaneous bandwidth.
A theoretical technique is described for boosting the temporal resolving power by several times, of detectors such as streak cameras in experiments that measure light reflected from or transmitted through a target, including velocity interferometer (VISAR) measurements. This is a means of effectively increasing the number of resolvable time bins in a streak camera record past the limit imposed by input slit width and blur on the output phosphor screen.
The illumination intensity is modulated sinusoidally at a frequency similar to the limiting time response of the detector. A heterodyning effect beats the high frequency science signal down a lower frequency beat signal, which is recorded together with the conventional science signal. Using 3 separate illuminating channels having different phases, the beat term is separated algebraically from the conventional signal. By numerically reversing the heterodyning, and combining with the ordinary signal, the science signal can be reconstructed to better effective time resolution than the detector used alone. The effective time resolution can be approximately halved for a single modulation frequency, and further decreased inversely proportional to the number of independent modulation frequencies employed.
Externally dispersed interferometry (EDI) is a technique for enhancing the performance of spectrographs for wide bandwidth high resolution spectroscopy and Doppler radial velocimetry. By placing a small angle-independent interferometer near the slit of a spectrograph, periodic fiducials are embedded on the recorded spectrum. The multiplication of the stellar spectrum times the sinusoidal fiducial net creates a moire pattern, which manifests high detailed spectral information heterodyned down to detectably low spatial frequencies. The latter can more accurately survive the blurring, distortions and CCD Nyquist limitations of the spectrograph. Hence lower resolution spectrographs can be used to perform high resolution spectroscopy and radial velocimetry. Previous demonstrations of ~2.5x resolution boost used an interferometer having a single fixed delay. We report new data indicating ~6x Gaussian resolution boost (140,000 from a spectrograph with 25,000 native resolving power), taken by using multiple exposures at widely different interferometer delays.
The Spectral Astrometry Mission is a space-mission concept that uses
simultaneous, multiple-star differential astrometry to measure exo-solar planet masses. The goal of SAM is to measure the reflex motions of hundreds of nearby (~50 pc) F, G and K stars, relative to adjacent stars, with a resolution of 2.5 micro-arcsec. SAM is a new application of Spectral Interferometry (SI), also called Externally Dispersed Interferometry (EDI), that can simultaneously measure the angular difference between the target and multiple reference stars. SI has demonstrated the ability to measure a λ/20,000 white-light fringe shift with only lambda/3 baseline control. SAM's structural stability and compensation requirements are therefore dramatically reduced compared to existing long-arm balanced-arm interferometric astrometry methods. We describe the SAM's mission concept, long-baseline SI astrometry method, and technical challenges to achieving the mission.
We demonstrate solar spectra from a novel interferometric method for compact broadband high-resolution spectroscopy. The spectral interferometer (SI) is a hybrid instrument that uses a spectrometer to externally disperse the output of a fixed-delay interferometer. It also has been called an externally dispersed interferometer (EDI). The interferometer can be used with linear spectrometers for imaging spectroscopy or with echelle spectrometers for very broad-band coverage. EDI's heterodyning technique enhances the spectrometer's response to high spectral-density features, increasing the effective resolution by factors of several while retaining its bandwidth. The method is extremely robust to instrumental insults such as focal spot size or displacement. The EDI uses no moving parts, such as purely interferometric FTS spectrometers, and can cover a much wider simultaneous bandpass than other internally dispersed interferometers (e.g. HHS or SHS).
An imaging white light velocimeter consisting of two image superimposing Michelson interferometers in series with the target interposed is demonstrated. Interferometrically measured 2D velocity maps can be made of moving surfaces using unlimited bandwidth incoherent and extended area sources. Short pulse and broadband chirped pulse lasers can be used to provide temporal resolution not possible with monochromatic illumination. An approximately 20 m/s per fringe imaging velocimeter is demonstrated using an ordinary camera flash for illumination. Radial and transverse velocity components can be measured when the illuminating and viewing beams are non-parallel.
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