Imaging, Spectroscopic, High-Contrast, and Interferometric Instrumentation

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

[+] Author Affiliations
David J. Erskine

Lawrence Livermore National Laboratory, Mailstop L-487, 7000 East Avenue, Livermore, California 94550, United States

Jerry Edelstein, Edward Wishnow, Martin Sirk

University of California, Space Sciences Laboratory, 7 Gauss Way, Berkeley, California 94720, United States

Philip S. Muirhead

Boston University, Department of Astronomy, 725 Commonwealth Avenue, Boston, Massachusetts 02215, United States

Matthew W. Muterspaugh

Tennessee State University, Boswell Science Hall, Nashville, Tennessee 37209, United States

James P. Lloyd

Cornell University, Carl Sagan Institute, Astronomy Department, 60 Garden Street, MS-10, Ithaca, New York 14853, United States

J. Astron. Telesc. Instrum. Syst. 2(4), 045001 (Dec 02, 2016). doi:10.1117/1.JATIS.2.4.045001
History: Received February 13, 2016; Accepted November 2, 2016
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Abstract.  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).

© 2016 Society of Photo-Optical Instrumentation Engineers

Citation

David J. Erskine ; Jerry Edelstein ; Edward Wishnow ; Martin Sirk ; Philip S. Muirhead, et al.
"High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: part 2, photon noise theory", J. Astron. Telesc. Instrum. Syst. 2(4), 045001 (Dec 02, 2016). ; http://dx.doi.org/10.1117/1.JATIS.2.4.045001


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