High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: part 2, photon noise theory

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)

Keck Planet Finder: Zerodur optical bench mechanical design

The Keck Planet Finder (KPF) is a fiber-fed, high-resolution, high-stability spectrometer in development for the W.M. Keck Observatory. To measure Doppler shifts to 0.5 m/s or better requires some of the optics be stable to 2 nm vertically and 2 nrad in pitch angle throughout a potentially one hour long observation. One traditional approach to this thermal stability problem is to build a metal bench and then control the spectrometer thermal environment to milli-Kelvin levels. An alternative approach used by KPF is to employ a Zerodur bench of extremely low coefficient of expansion (CTE), which relaxes the thermal stability required for the spectrometer assembly. Furthermore, Zerodur optics with integral mounts are used where possible, and are placed in contact with the bench through Zerodur shims. Springs are used to preload the optics and shims within pockets machined into the Zerodur bench. We will describe how this approach has been adapted for each optic (some of which are 450 mm high with a mass of 30 kg), and how the system meets our earthquake survival requirement of 0.92 g. This mounting scheme allows us to avoid using high-CTE metals or adhesives within the optic mounting system, and therefore fully exploit the high thermal stability of the Zerodur optical bench

KPF: Keck Planet Finder

KPF is a fiber-fed, high-resolution, high-stability spectrometer in development at the UC Berkeley Space Sciences Laboratory for the W.M. Keck Observatory. The instrument is designed to characterize exoplanets via Doppler spectroscopy with a single measurement precision of 0.5ms_(-1) or better, however its resolution and stability will enable a wide variety of astrophysical pursuits. KPF will have a 200mm collimated beam diameter and a resolving power of >80,000. The design includes a green channel (440nm to 590 nm) and red channel (590nm to 850 nm). A novel design aspect of KPF is the use of a Zerodur optical bench, and Zerodur optics with integral mounts, to provide stability against thermal expansion and contraction effects

High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 1, data analysis and results

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

Precise Stellar Radial Velocities of an M Dwarf with a Michelson Interferometer and a Medium-resolution Near-infrared Spectrograph

Precise near-infrared radial velocimetry enables efficient detection and transit verification of low-mass extrasolar planets orbiting M dwarf hosts, which are faint for visible-wavelength radial velocity surveys. The TripleSpec Exoplanet Discovery Instrument, or TEDI, is the combination of a variable-delay Michelson interferometer and a medium-resolution (R=2700) near-infrared spectrograph on the Palomar 200" Hale Telescope. We used TEDI to monitor GJ 699, a nearby mid-M dwarf, over 11 nights spread across 3 months. Analysis of 106 independent observations reveals a root-mean-square precision of less than 37 m/s for 5 minutes of integration time. This performance is within a factor of 2 of our expected photon-limited precision. We further decompose the residuals into a 33 m/s white noise component, and a 15 m/s systematic noise component, which we identify as likely due to contamination by telluric absorption lines. With further development this technique holds promise for broad implementation on medium-resolution near-infrared spectrographs to search for low-mass exoplanets orbiting M dwarfs, and to verify low-mass transit candidates.Comment: 55 pages and 13 figures in aastex format. Accepted by PAS

Keck Planet Finder: Zerodur optical bench mechanical design

The Keck Planet Finder (KPF) is a fiber-fed, high-resolution, high-stability spectrometer in development for the W.M. Keck Observatory. To measure Doppler shifts to 0.5 m/s or better requires some of the optics be stable to 2 nm vertically and 2 nrad in pitch angle throughout a potentially one hour long observation. One traditional approach to this thermal stability problem is to build a metal bench and then control the spectrometer thermal environment to milli-Kelvin levels. An alternative approach used by KPF is to employ a Zerodur bench of extremely low coefficient of expansion (CTE), which relaxes the thermal stability required for the spectrometer assembly. Furthermore, Zerodur optics with integral mounts are used where possible, and are placed in contact with the bench through Zerodur shims. Springs are used to preload the optics and shims within pockets machined into the Zerodur bench. We will describe how this approach has been adapted for each optic (some of which are 450 mm high with a mass of 30 kg), and how the system meets our earthquake survival requirement of 0.92 g. This mounting scheme allows us to avoid using high-CTE metals or adhesives within the optic mounting system, and therefore fully exploit the high thermal stability of the Zerodur optical bench

Mid-infrared interferometry with high spectral resolution

The Infrared Spatial Interferometer (ISI) is a three telescope interferometer system that operates near 11 microns wavelength using heterodyne detection with CO2 lasers as local oscillators. Stellar measurements have been made using consistent instrumentation for 20 years, allowing comparisons of stellar sizes of red giant and Mira stars over time intervals which are long in comparison to stellar luminosity periods. Recent visibility and closure phase measurements of the star Betelgeuse have been fitted to simple image models and these results have been added to the 17 year record of stellar observations. A new area of investigation of stellar properties at very high spectral resolution will begin in the 2010-2011 observing season. The design of a new digital spectrometer-correlator system is discussed. This system will obtain visibility measurements on-and-off individual spectral lines and the continuum, simultaneously

Observations of Late-Type Stars with the Infrared Spatial Interferometer

The Infrared Spatial Interferometer (ISI) has been conducting mid-IR measurements of red supergiant and AGB stars for about 20 years. This paper reviews the ISI system and results with an emphasis on measurements of changes in stellar sizes and shapes, and those of the surrounding dust shells, over time scales of weeks to decades. The long-term measurement record provides important new observables for stellar theory. A new spectrometer-correlator system is discussed where this system will measure visibilities on-and-off individual molecular spectral lines