Externally Dispersed Interferometry Research Articles

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).

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.

An Externally Dispersed Interferometer Prototype for Sensitive Radial Velocimetry: Theory and Demonstration on Sunlight

ABSTRACTA theory of operation of a wideband interferometric Doppler spectroscopy technique, called externally dispersed interferometry (EDI), is presented. The first EDI prototype was tested on sunlight and detected the 12 m s−1 amplitude lunar signature in Earth’s motion. The hybrid instrument is an undispersed Michelson interferometer having a fixed delay of about 1 cm, in series with an external spectrograph of about 20,000 resolution. The Michelson provides the Doppler shift discrimination, while the external spectrograph boosts net white‐light fringe visibility by reducing cross talk from adjacent continuum channels. A moiré effect between the sinusoidal interferometer transmission and the input spectrum heterodynes high spectral details to broad moiré patterns, which carry the Doppler information in its phase. These broad patterns survive the blurring of the spectrograph, which can have several times lower resolution than grating‐only spectrographs typically used now for the Doppler planet search. This enables the net instrument to be dramatically smaller in size (∼1 m) and cost. The EDI behavior is compared and contrasted to the conventional grating‐only technique.