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Title: 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 amore » 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. As a result, 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).« less
Authors:
 [1] ;  [2] ;  [2] ;  [2] ;  [3] ;  [4] ;  [5]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
  3. Boston Univ., Boston, MA (United States)
  4. Tennessee State Univ., Nashville, TN (United States)
  5. Cornell Univ., Ithaca, NY (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-725507
Journal ID: ISSN 2329-4124
Grant/Contract Number:
AC52-07NA27344
Type:
Accepted Manuscript
Journal Name:
Journal of Astronomical Telescopes, Instruments, and Systems
Additional Journal Information:
Journal Volume: 2; Journal Issue: 4; Journal ID: ISSN 2329-4124
Publisher:
SPIE
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; interferometers; interferometry; photons; spectrographs; spectroscopy; numerical integration; sensors; point spread functions; equipment and services; dispersed interferometry; doppler radial velocimetry; high resolution spectroscopy
OSTI Identifier:
1346137

Erskine, David J., Edelstein, Jerry, Wishnow, Edward, Sirk, Martin, Muirhead, Philip S., Muterspaugh, Matthew W., and Lloyd, James P.. High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 2, photon noise theory. United States: N. p., Web. doi:10.1117/1.JATIS.2.4.045001.
Erskine, David J., Edelstein, Jerry, Wishnow, Edward, Sirk, Martin, Muirhead, Philip S., Muterspaugh, Matthew W., & Lloyd, James P.. High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 2, photon noise theory. United States. doi:10.1117/1.JATIS.2.4.045001.
Erskine, David J., Edelstein, Jerry, Wishnow, Edward, Sirk, Martin, Muirhead, Philip S., Muterspaugh, Matthew W., and Lloyd, James P.. 2016. "High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 2, photon noise theory". United States. doi:10.1117/1.JATIS.2.4.045001. https://www.osti.gov/servlets/purl/1346137.
@article{osti_1346137,
title = {High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 2, photon noise theory},
author = {Erskine, David J. and Edelstein, Jerry and Wishnow, Edward and Sirk, Martin and Muirhead, Philip S. and Muterspaugh, Matthew W. and Lloyd, James P.},
abstractNote = {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. As a result, 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).},
doi = {10.1117/1.JATIS.2.4.045001},
journal = {Journal of Astronomical Telescopes, Instruments, and Systems},
number = 4,
volume = 2,
place = {United States},
year = {2016},
month = {10}
}