Abstract

The accurate spectral characterization of high-resolution spectrometers is required for correctly computing, interpreting, and comparing radiance and reflectance spectra acquired at different times or by different instruments. In this paper, we describe an algorithm for the spectral characterization of field spectrometer data using sharp atmospheric or solar absorption features present in the measured data. The algorithm retrieves systematic shifts in channel position and actual full width at half-maximum (FWHM) of the instrument by comparing data acquired during standard field spectroscopy measurement operations with a reference irradiance spectrum modeled with the MODTRAN4 radiative transfer code. Measurements from four different field spectrometers with spectral resolutions ranging from 0.05 to 3.5nm are processed and the results validated against laboratory calibration. An accurate retrieval of channel position and FWHM has been achieved, with an average error smaller than the instrument spectral sampling interval.

© 2010 Optical Society of America

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2009

A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: a personal view,” Remote Sens. Environ. , 1, S5–S16 (2009).
[CrossRef]

M. E. Schaepman, S. L. Ustin, A. J. Plaza, T. H. Painter, J. Verrelst, and S. L. Liang, “Earth system science related imaging spectroscopy—an assessment,” Remote Sens. Environ. 113, S123–S137 (2009).
[CrossRef]

L. Guanter, K. Segl, B. Sang, L. Alonso, H. Kaufmann, and J. Moreno, “Scene-based spectral calibration assessment of high spectral resolution imaging spectrometers,” Opt. Express 17, 11594–11606 (2009).
[CrossRef] [PubMed]

S. L. Ustin, A. A. Gitelson, S. Jacquemoud, M. Schaepman, G. P. Asner, J. A. Gamon, and P. Zarco-Tejada, “Retrieval of foliar information about plant pigment systems from high resolution spectroscopy,” Remote Sens. Environ. 113, S67–S77 (2009).
[CrossRef]

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

E. J. Milton, M. E. Schaepman, K. Anderson, M. Kneubuhler, and N. Fox, “Progress in field spectroscopy,” Remote Sens. Environ. 113, S92–S109 (2009).
[CrossRef]

2008

R. A. Neville, L. X. Sun, and K. Staenz, “Spectral calibration of imaging spectrometers by atmospheric absorption feature matching,” Can. J. Remote Sens. 34, S29–S42 (2008).
[CrossRef]

J. Brazile, R. A. Neville, K. Staenz, D. Schlapfer, L. X. Sun, and K. I. Itten, “Toward scene-based retrieval of spectral response functions for hyperspectral imagers using Fraunhofer features,” Can. J. Remote Sens. 34, S43–S58 (2008).
[CrossRef]

D. Baldocchi, “Breathing of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurement systems,” Aust. J. Bot. 56, 1–26 (2008).
[CrossRef]

2007

T. Hilker, N. C. Coops, Z. Nesic, M. A. Wulder, and A. T. Black, “Instrumentation and approach for unattended year round tower based measurements of spectral reflectance,” Comput. Electron. Agric. 56, 72–84 (2007).
[CrossRef]

L. Guanter, V. Estelles, and J. Moreno, “Spectral calibration and atmospheric correction of ultra-fine spectral and spatial resolution remote sensing data. Application to CASI-1500 data,” Remote Sens. Environ. 109, 54–65 (2007).
[CrossRef]

2006

L. Guanter, R. Richter, and J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features,” Appl. Opt. 45, 2360–2370 (2006).
[CrossRef] [PubMed]

K. L. Castro-Esau, G. A. Sanchez-Azofeifa, and B. Rivard, “Comparison of spectral indices obtained using multiple spectroradiometers,” Remote Sens. Environ. 103, 276–288(2006).
[CrossRef]

J. A. Gamon, A. F. Rahman, J. L. Dungan, M. Schildhauer, and K. F. Huemmrich, “Spectral Network (SpecNet)—What is it and why do we need it?,” Remote Sens. Environ. 103, 227–235 (2006).
[CrossRef]

2004

B. C. Gao, M. J. Montes, and C. O. Davis, “Refinement of wavelength calibrations of hyperspectral imaging data using a spectrum-matching technique,” Remote Sens. Environ. 90, 424–433 (2004).
[CrossRef]

2003

R. O. Green, B. E. Pavri, and T. G. Chrien, “On-orbit radiometric and spectral calibration characteristics of EO-1 Hyperion derived with an underflight of AVIRIS and in situ measurements at Salar de Arizaro, Argentina,” IEEE Trans. Geosci. Remote Sens. 41, 1194–1203 (2003).
[CrossRef]

E. V. Thomas, “Non-parametric statistical methods for multivariate calibration model selection and comparison,” J. Chemom. 17, 653–659 (2003).
[CrossRef]

2000

1998

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

R. O. Green, “Spectral calibration requirement for Earth-looking imaging spectrometers in the solar-reflected spectrum,” Appl. Opt. 37, 683–690 (1998).
[CrossRef]

1996

1992

J. A. Gamon, J. Penuelas, and C. B. Field, “A narrow-waveband spectral index that tracks diurnal changes in photosynthetic efficiency,” Remote Sens. Environ. 41, 35–44 (1992).
[CrossRef]

1966

B. Edlen, “The refractive index of air,” Metrologia 2, 71–80(1966).
[CrossRef]

1945

F. Wilcoxon, “Individual comparisons by ranking methods,” Biometrics 1, 80–83 (1945).
[CrossRef]

Acharya, P. K.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Adler-Golden, S. M.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Alonso, L.

L. Guanter, K. Segl, B. Sang, L. Alonso, H. Kaufmann, and J. Moreno, “Scene-based spectral calibration assessment of high spectral resolution imaging spectrometers,” Opt. Express 17, 11594–11606 (2009).
[CrossRef] [PubMed]

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

Anderson, G. P.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Anderson, K.

E. J. Milton, M. E. Schaepman, K. Anderson, M. Kneubuhler, and N. Fox, “Progress in field spectroscopy,” Remote Sens. Environ. 113, S92–S109 (2009).
[CrossRef]

Asner, G. P.

S. L. Ustin, A. A. Gitelson, S. Jacquemoud, M. Schaepman, G. P. Asner, J. A. Gamon, and P. Zarco-Tejada, “Retrieval of foliar information about plant pigment systems from high resolution spectroscopy,” Remote Sens. Environ. 113, S67–S77 (2009).
[CrossRef]

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

Bacour, C.

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

Baldocchi, D.

D. Baldocchi, “Breathing of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurement systems,” Aust. J. Bot. 56, 1–26 (2008).
[CrossRef]

Baret, F.

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

Berk, A.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Bernstein, L. S.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Black, A. T.

T. Hilker, N. C. Coops, Z. Nesic, M. A. Wulder, and A. T. Black, “Instrumentation and approach for unattended year round tower based measurements of spectral reflectance,” Comput. Electron. Agric. 56, 72–84 (2007).
[CrossRef]

Brazile, J.

J. Brazile, R. A. Neville, K. Staenz, D. Schlapfer, L. X. Sun, and K. I. Itten, “Toward scene-based retrieval of spectral response functions for hyperspectral imagers using Fraunhofer features,” Can. J. Remote Sens. 34, S43–S58 (2008).
[CrossRef]

Bridges, J. M.

Castro-Esau, K. L.

K. L. Castro-Esau, G. A. Sanchez-Azofeifa, and B. Rivard, “Comparison of spectral indices obtained using multiple spectroradiometers,” Remote Sens. Environ. 103, 276–288(2006).
[CrossRef]

Chetwynd, J. H.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, and S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375(1998).
[CrossRef]

Chrien, T. G.

R. O. Green, B. E. Pavri, and T. G. Chrien, “On-orbit radiometric and spectral calibration characteristics of EO-1 Hyperion derived with an underflight of AVIRIS and in situ measurements at Salar de Arizaro, Argentina,” IEEE Trans. Geosci. Remote Sens. 41, 1194–1203 (2003).
[CrossRef]

Colombo, R.

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

Coops, N. C.

T. Hilker, N. C. Coops, Z. Nesic, M. A. Wulder, and A. T. Black, “Instrumentation and approach for unattended year round tower based measurements of spectral reflectance,” Comput. Electron. Agric. 56, 72–84 (2007).
[CrossRef]

Dangel, S.

Davis, C. O.

B. C. Gao, M. J. Montes, and C. O. Davis, “Refinement of wavelength calibrations of hyperspectral imaging data using a spectrum-matching technique,” Remote Sens. Environ. 90, 424–433 (2004).
[CrossRef]

Dungan, J. L.

J. A. Gamon, A. F. Rahman, J. L. Dungan, M. Schildhauer, and K. F. Huemmrich, “Spectral Network (SpecNet)—What is it and why do we need it?,” Remote Sens. Environ. 103, 227–235 (2006).
[CrossRef]

Edlen, B.

B. Edlen, “The refractive index of air,” Metrologia 2, 71–80(1966).
[CrossRef]

Estelles, V.

L. Guanter, V. Estelles, and J. Moreno, “Spectral calibration and atmospheric correction of ultra-fine spectral and spatial resolution remote sensing data. Application to CASI-1500 data,” Remote Sens. Environ. 109, 54–65 (2007).
[CrossRef]

Field, C. B.

J. A. Gamon, J. Penuelas, and C. B. Field, “A narrow-waveband spectral index that tracks diurnal changes in photosynthetic efficiency,” Remote Sens. Environ. 41, 35–44 (1992).
[CrossRef]

Fox, N.

E. J. Milton, M. E. Schaepman, K. Anderson, M. Kneubuhler, and N. Fox, “Progress in field spectroscopy,” Remote Sens. Environ. 113, S92–S109 (2009).
[CrossRef]

Francois, C.

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

Gamon, J. A.

S. L. Ustin, A. A. Gitelson, S. Jacquemoud, M. Schaepman, G. P. Asner, J. A. Gamon, and P. Zarco-Tejada, “Retrieval of foliar information about plant pigment systems from high resolution spectroscopy,” Remote Sens. Environ. 113, S67–S77 (2009).
[CrossRef]

J. A. Gamon, A. F. Rahman, J. L. Dungan, M. Schildhauer, and K. F. Huemmrich, “Spectral Network (SpecNet)—What is it and why do we need it?,” Remote Sens. Environ. 103, 227–235 (2006).
[CrossRef]

J. A. Gamon, J. Penuelas, and C. B. Field, “A narrow-waveband spectral index that tracks diurnal changes in photosynthetic efficiency,” Remote Sens. Environ. 41, 35–44 (1992).
[CrossRef]

Gao, B. C.

B. C. Gao, M. J. Montes, and C. O. Davis, “Refinement of wavelength calibrations of hyperspectral imaging data using a spectrum-matching technique,” Remote Sens. Environ. 90, 424–433 (2004).
[CrossRef]

Gitelson, A. A.

S. L. Ustin, A. A. Gitelson, S. Jacquemoud, M. Schaepman, G. P. Asner, J. A. Gamon, and P. Zarco-Tejada, “Retrieval of foliar information about plant pigment systems from high resolution spectroscopy,” Remote Sens. Environ. 113, S67–S77 (2009).
[CrossRef]

Goetz, A. F. H.

A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: a personal view,” Remote Sens. Environ. , 1, S5–S16 (2009).
[CrossRef]

Green, R. O.

R. O. Green, B. E. Pavri, and T. G. Chrien, “On-orbit radiometric and spectral calibration characteristics of EO-1 Hyperion derived with an underflight of AVIRIS and in situ measurements at Salar de Arizaro, Argentina,” IEEE Trans. Geosci. Remote Sens. 41, 1194–1203 (2003).
[CrossRef]

R. O. Green, “Spectral calibration requirement for Earth-looking imaging spectrometers in the solar-reflected spectrum,” Appl. Opt. 37, 683–690 (1998).
[CrossRef]

Guanter, L.

L. Guanter, K. Segl, B. Sang, L. Alonso, H. Kaufmann, and J. Moreno, “Scene-based spectral calibration assessment of high spectral resolution imaging spectrometers,” Opt. Express 17, 11594–11606 (2009).
[CrossRef] [PubMed]

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

L. Guanter, V. Estelles, and J. Moreno, “Spectral calibration and atmospheric correction of ultra-fine spectral and spatial resolution remote sensing data. Application to CASI-1500 data,” Remote Sens. Environ. 109, 54–65 (2007).
[CrossRef]

L. Guanter, R. Richter, and J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features,” Appl. Opt. 45, 2360–2370 (2006).
[CrossRef] [PubMed]

Hatchel, D.

D. Hatchel, ASD Technical Guide3rd ed. (Analytical Spectral Device, 1999).

Hilker, T.

T. Hilker, N. C. Coops, Z. Nesic, M. A. Wulder, and A. T. Black, “Instrumentation and approach for unattended year round tower based measurements of spectral reflectance,” Comput. Electron. Agric. 56, 72–84 (2007).
[CrossRef]

Huemmrich, K. F.

J. A. Gamon, A. F. Rahman, J. L. Dungan, M. Schildhauer, and K. F. Huemmrich, “Spectral Network (SpecNet)—What is it and why do we need it?,” Remote Sens. Environ. 103, 227–235 (2006).
[CrossRef]

Itten, K. I.

J. Brazile, R. A. Neville, K. Staenz, D. Schlapfer, L. X. Sun, and K. I. Itten, “Toward scene-based retrieval of spectral response functions for hyperspectral imagers using Fraunhofer features,” Can. J. Remote Sens. 34, S43–S58 (2008).
[CrossRef]

Jacquemoud, S.

S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. Zarco-Tejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: a review of use for vegetation characterization,” Remote Sens. Environ. 113, S56–S66 (2009).
[CrossRef]

S. L. Ustin, A. A. Gitelson, S. Jacquemoud, M. Schaepman, G. P. Asner, J. A. Gamon, and P. Zarco-Tejada, “Retrieval of foliar information about plant pigment systems from high resolution spectroscopy,” Remote Sens. Environ. 113, S67–S77 (2009).
[CrossRef]

Kaufmann, H.

Kneubuhler, M.

E. J. Milton, M. E. Schaepman, K. Anderson, M. Kneubuhler, and N. Fox, “Progress in field spectroscopy,” Remote Sens. Environ. 113, S92–S109 (2009).
[CrossRef]

Liang, S. L.

M. E. Schaepman, S. L. Ustin, A. J. Plaza, T. H. Painter, J. Verrelst, and S. L. Liang, “Earth system science related imaging spectroscopy—an assessment,” Remote Sens. Environ. 113, S123–S137 (2009).
[CrossRef]

Markwardt, C. B.

C. B. Markwardt, “TMIN function minimization,” http://cow.physics.wisc.edu/~craigm/idl/idl.html (2008).

Meroni, M.

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

Milton, E. J.

E. J. Milton, M. E. Schaepman, K. Anderson, M. Kneubuhler, and N. Fox, “Progress in field spectroscopy,” Remote Sens. Environ. 113, S92–S109 (2009).
[CrossRef]

Montes, M. J.

B. C. Gao, M. J. Montes, and C. O. Davis, “Refinement of wavelength calibrations of hyperspectral imaging data using a spectrum-matching technique,” Remote Sens. Environ. 90, 424–433 (2004).
[CrossRef]

Moreno, J.

M. Meroni, M. Rossini, L. Guanter, L. Alonso, U. Rascher, R. Colombo, and J. Moreno, “Remote sensing of solar-induced chlorophyll fluorescence: review of methods and applications,” Remote Sens. Environ. 113, 2037–2051 (2009).
[CrossRef]

L. Guanter, K. Segl, B. Sang, L. Alonso, H. Kaufmann, and J. Moreno, “Scene-based spectral calibration assessment of high spectral resolution imaging spectrometers,” Opt. Express 17, 11594–11606 (2009).
[CrossRef] [PubMed]

L. Guanter, V. Estelles, and J. Moreno, “Spectral calibration and atmospheric correction of ultra-fine spectral and spatial resolution remote sensing data. Application to CASI-1500 data,” Remote Sens. Environ. 109, 54–65 (2007).
[CrossRef]

L. Guanter, R. Richter, and J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features,” Appl. Opt. 45, 2360–2370 (2006).
[CrossRef] [PubMed]

Nesic, Z.

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Figures (7)

Fig. 1
Fig. 1

Distribution of selected absorption features over the incident irradiance spectrum (black curve). Solid vertical lines refer to solar Fraunhofer lines, dashed vertical lines refer to molecular oxygen absorption features, and gray areas are the spectral regions affected by water vapor absorption.

Fig. 2
Fig. 2

Example of algorithm application to synthetic data at the H α Fraunhofer line. (a), (b), and (c) are obtained by resampling the MODTRAN4 spectrum to the initial nominal values of FWHM and SS, while (d), (e), and (f) refer to the final results of the optimization. Dotted curve in (a) and (d), original reference MODTRAN4 irradiance spectrum, E mod ( SSI = 0.01 nm , FWHM = 0.06 nm ) ; solid triangles in (a), E mod resampled to the nominal parameters of the measured spectrum ( SSI = 0.1 nm , FWHM = 0.2 nm , SS = 0 nm ); open triangles in (d), E mod resampled to retrieved parameters ( SSI = 0.1 nm , FWHM = 0.5 nm , SS = 0.3 nm ); solid circles, E meas ; open circles, E meas_sc . (b) and (e) Ratio between E meas_sc and E mod . (c) and (f) Scatter plot between E meas_sc and E mod .

Fig. 3
Fig. 3

Algorithm application to spectrometer 1 (OceanOptics HR4000 tuned 200 1100 nm ) at different spectral windows: (a), (b) and (c) solar Fraunhofer lines of window 3; (d), (e), and (f) solar Fraunhofer line of window 7; (g), (h), and (i) terrestrial atmosphere absorption feature of window 8; (l), (m), and (n) water vapor window 13. (a), (d), (g), and (l)  E meas_sc , E mod with nominal parameters, and E mod with retrieved parameters. (b), (e), (h), and (m) ρ computed as the ratio between E meas_sc and E mod with nominal and retrieved parameters. (c), (f), (i), and (n)  E meas_sc versus E mod with nominal and retrieved parameters. SS and FWHM are expressed in nanometers. The outputs of the C ratio and C r cost functions were similar, so that only those of C ratio are shown in plots (a), (d), (g), and (l).

Fig. 4
Fig. 4

Algorithm application to spectrometer 2 (OceanOptics HR4000 tuned 717 804 nm ). Same as Fig. 3, with the following windows: (a), (b), and (c) water vapor window 9, and (d), (e), and (f) terrestrial atmosphere absorption feature of window 10.

Fig. 5
Fig. 5

Algorithm application to spectrometer 3 (ASD HH Pro). Same as Fig. 3 with the following windows: (a), (b), and (c) solar Fraunhofer lines of window 3; (d), (e), and (f) solar Fraunhofer line of window 7; (g), (h), and (i) terrestrial atmosphere absorption feature of window 8; and (l), (m), and (n) terrestrial atmosphere absorption feature of window 10.

Fig. 6
Fig. 6

Algorithm application to spectrometer 4 (ASD FS FR Pro). Same as Fig. 5.

Fig. 7
Fig. 7

Regression analysis between retrieved and laboratory measured SS (top plots) and FWHM (bottom plots). (a) and (d) refer to spectrometer 1 (OceanOptics tuned 200 1100 nm ), (b) and (e) refer to spectrometer 3 (ASD HH Pro), (c) and (f) refer to spectrometer 4 (ASD FS FR Pro). Regression lines and their statistics are reported for the two cost functions used.

Tables (3)

Tables Icon

Table 1 Fraunhofer Lines (Origin in the Solar Atmosphere) and Atmospheric Absorption Features (Origin in the Earth’s Atmosphere) Exploited in this Study a

Tables Icon

Table 2 Characteristics of the Spectrometers Used (OceanOptics, USA, and Analytical Spectral Devices Inc., USA) a

Tables Icon

Table 3 Spectral Shift and FWHM Retrieved by the Algorithm Application with Cost Functions C r and C ratio and by Laboratory Calibration at the Various Spectral Windows a

Equations (4)

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ρ ( SS , FWHM , λ ) = E meas_sc ( λ ) E mod ( SS , FWHM , λ ) ,
C ratio ( SS , FWHM , N , λ 0 , λ 1 ) = λ o λ 1 ( ρ ( SS , FWHM , λ ) ρ smooth ( ρ , λ , N ) ρ smooth ( ρ , λ , N ) ) 2 ,
C r ( SS , FWHM , λ 0 , λ 1 ) = 1 r E meas_ E mod ( SS , FWHM , λ 0 , λ 1 ) ,
E mod ( λ , SS , FWHM d ) λ = λ hw λ = λ + hw E mod ( λ , SS , FWHM o ) K ( λ λ ) d λ , K ( λ λ ) = 2 2 ln 2 2 π FWHM d 2 FWHM o 2 exp ( 4 ( ln 2 ) λ 2 FWHM d 2 FWHM o 2 ) ,

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