A responsitivity-based criterion for accurate calibration of FTIR spectra: theoretical development and bandwidth estimation

An analytical expression for the variance of the radiance measured by Fourier-transform infrared (FTIR) emission spectrometers exists only in the limit of low noise. Outside this limit, the variance needs to be calculated numerically. In addition, a criterion for low noise is needed to identify properly calibrated radiances and optimize the instrument bandwidth. In this work, the variance and the magnitude of a noisedependent spectral bias are calculated as a function of the system responsivity (r) and the noise level in its estimate (σr). The criterion σr /r <0.3, applied to downwelling and upwelling FTIR emission spectra, shows that the instrument bandwidth is specified properly for one instrument but needs to be restricted for another. ©2011 Optical Society of America OCIS codes: (120.0280) Remote sensing and sensors; (120.3180) Interferometry; (120.5630) Radiometry; (120.6200) Spectrometers and spectroscopic instrumentation; (280.4991) Passive remote sensing. References and links 1. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27(15), 3210–3218 (1988). 2. L. A. Sromovsky, “Radiometric errors in complex Fourier transform spectrometry,” Appl. Opt. 42(10), 1779– 1787 (2003). 3. R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004). 4. R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004). 5. D. L. Cohen, “Noise-equivalent change in radiance for sampling noise in a double-sided interferogram,” Appl. Opt. 42(13), 2289–2300 (2003). 6. P. M. Rowe, Department of Geography, University of Idaho, 875 Perimeter Drive, Moscow, Idaho 83844, S. P. Neshyba, C. J. Cox, and V. P. Walden are preparing a manuscript to be called, “A responsivity-based criterion for accurate calibration of FTIR emission spectra: identification of in-band low-responsivity wavenumbers.” 7. G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009). 8. A. Shimota, H. Kobayashi, and S. Kadokura, “Radiometric calibration for the airborne interferometric monitor for greenhouse gases simulator,” Appl. Opt. 38(3), 571–576 (1999). 9. V. P. Walden, R. L. Tanamachi, P. M. Rowe, H. E. Revercomb, D. C. Tobin, and S. A. Ackerman, “Improvements in the data quality of the Interferometric Monitor for greenhouse Gases,” Appl. Opt. 49(3), 520– 528 (2010). 10. P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008). 11. P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004). #137173 $15.00 USD Received 17 Nov 2010; revised 15 Feb 2011; accepted 18 Feb 2011; published 8 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5451 12. D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006). 13. M. Jackson, Mathematics Department, University of Puget Sound, 1500 N. Warner, Tacoma, WA 98416 (personal communication, 2010).