Abstract

We present the design methodology for a sensor that can nonintrusively monitor target gas concentration levels in a power plant exhaust flow. The measurement is based on radiative emission by rovibrational transitions that are well isolated from emission features of other constituents and requires both moderate spectral resolution (typically 1 nm or below) and relatively high optical throughput. A Fabry-Perot interferometer provides this capability, and its conceptual design is discussed at length. High-temperature radiative emission of nitric oxide in a background of water was used as a sample system for the design of a prototype Fabry-Perot interferometer. Predictions for the instrument are a minimum resolvable NO column density of 100 parts per million times meter based on a simple background subtraction scheme with a gas temperature of 800 K. Improved order sorting can dramatically lower this minimum. The prototype instrument was calibrated and tested with a laboratory simulator; results are presented and compared with predictions.

© 2002 Optical Society of America

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  1. J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
    [CrossRef]
  2. G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).
  3. J. Vaughan, The Fabry-Perot Interferometer (Institute of Physics, Philadelphia, Pa., 1989).
  4. J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus: A Practical Guide to Design and Construction, 2nd ed. (Addison-Wealey, Reading, Mass., 1989).
  5. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge U. Press, Cambridge, UK, 1980).
  6. W. H. Steel, Interferometry, Cambridge Monographs on Physics (Cambridge U. Press, Cambridge, UK, (1967).
  7. L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
    [CrossRef]
  8. V. N. Del Piano, A. F. Quesada, “Transmission characteristics of Fabry-Perot interferometers and a related electrooptic modulator,” Appl. Opt. 4, 1386–1390 (1965).
    [CrossRef]
  9. J. V. Ramsay, “Aberrations of Fabry-Perot interferometers when used as filters,” Appl. Opt. 8, 569–574 (1969).
    [CrossRef] [PubMed]
  10. G. J. Sloggett, “Fringe broadening in Fabry-Perot interferometers,” Appl. Opt. 23, 2427–2432 (1984).
    [CrossRef] [PubMed]
  11. J. Spelman, T. E. Parker, “Radiative emission measurement of NO in hot, particulate-laden power plant flows,” Combust. Sci. Technol. 172, 23–33 (2001).
    [CrossRef]

2001 (2)

J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
[CrossRef]

J. Spelman, T. E. Parker, “Radiative emission measurement of NO in hot, particulate-laden power plant flows,” Combust. Sci. Technol. 172, 23–33 (2001).
[CrossRef]

1998 (1)

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

1984 (1)

1969 (1)

1965 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge U. Press, Cambridge, UK, 1980).

Brown, L. R.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Camy-Peyret, C.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Chance, K. V.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Coplan, M. A.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus: A Practical Guide to Design and Construction, 2nd ed. (Addison-Wealey, Reading, Mass., 1989).

Dana, V.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Davis, C. C.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus: A Practical Guide to Design and Construction, 2nd ed. (Addison-Wealey, Reading, Mass., 1989).

Del Piano, V. N.

Edwards, D. P.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Flaud, J.-M.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Gamache, R. R.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Goldman, A.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Hernandez, G.

G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).

Jucks, K. W.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Mandin, J.-Y.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Massie, S. T.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

McCann, A.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Moore, J. H.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus: A Practical Guide to Design and Construction, 2nd ed. (Addison-Wealey, Reading, Mass., 1989).

Nemtchinov, V.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Parker, T. E.

J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
[CrossRef]

J. Spelman, T. E. Parker, “Radiative emission measurement of NO in hot, particulate-laden power plant flows,” Combust. Sci. Technol. 172, 23–33 (2001).
[CrossRef]

Perrin, A.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Quesada, A. F.

Ramsay, J. V.

Rinsland, C. P.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Rothman, L. S.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Schroeder, J.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Skrien, S.

J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
[CrossRef]

Sloggett, G. J.

Spelman, J.

J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
[CrossRef]

J. Spelman, T. E. Parker, “Radiative emission measurement of NO in hot, particulate-laden power plant flows,” Combust. Sci. Technol. 172, 23–33 (2001).
[CrossRef]

Steel, W. H.

W. H. Steel, Interferometry, Cambridge Monographs on Physics (Cambridge U. Press, Cambridge, UK, (1967).

Varanasi, P.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Vaughan, J.

J. Vaughan, The Fabry-Perot Interferometer (Institute of Physics, Philadelphia, Pa., 1989).

Watson, R. B.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge U. Press, Cambridge, UK, 1980).

Yoshino, K.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Appl. Opt. (3)

Combust. Sci. Technol. (1)

J. Spelman, T. E. Parker, “Radiative emission measurement of NO in hot, particulate-laden power plant flows,” Combust. Sci. Technol. 172, 23–33 (2001).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Spelman, S. Skrien, T. E. Parker, “Power plant exhaust gas simulator for the development of optical diagnostics,” Rev. Sci. Instrum. 72, 3699–3705 (2001).
[CrossRef]

Other (5)

G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).

J. Vaughan, The Fabry-Perot Interferometer (Institute of Physics, Philadelphia, Pa., 1989).

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus: A Practical Guide to Design and Construction, 2nd ed. (Addison-Wealey, Reading, Mass., 1989).

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge U. Press, Cambridge, UK, 1980).

W. H. Steel, Interferometry, Cambridge Monographs on Physics (Cambridge U. Press, Cambridge, UK, (1967).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of a FPI with scanning abilities. The transmitted radiation is given by an Airy function, expressed in Eq. (2) and illustrated in Fig. 2.

Fig. 2
Fig. 2

Transmission [Airy function given in Eq. (2)] as a function of wavelength for two reflectivities assuming zero substrate absorption (log scale).

Fig. 3
Fig. 3

Single transmission maximum (instrument profile) of Eq. (7) for several collection angles assuming the entire area of the plates is used (60 mm). Increasing θmax increases the etendue but also broadens the instrumental profile. Note the shift of the central wavelength toward shorter wavelengths as the collection angle gets larger.

Fig. 4
Fig. 4

HITRAN7 simulated water absorption spectrum and spectrum resulting from convolution with the instrumental profile of FPI. Simulation was for 1% water in a 4.18-m path length at room temperature, i.e., ambient atmospheric conditions.

Fig. 5
Fig. 5

Comparison of synthetic water and nitric oxide spectra after convolution with the instrumental profile of a FPI for several spectral resolutions.

Fig. 6
Fig. 6

Instrumental profiles of FPI with plate misalignments ranging from 0 to 200 nm.

Fig. 7
Fig. 7

Misalignment effect on instrumental profiles for two collection angles assuming that the entire area of the plates is used (60 mm).

Fig. 8
Fig. 8

Polishing specification (λ/M) as a function of reflectivity. Higher reflectivities (or more stringent degradation requirements) dictate the need for improved polishing.

Fig. 9
Fig. 9

Experimental setup used to test the prototype FPI either with a blackbody source or an emission furnace.

Fig. 10
Fig. 10

Monochromator scan of the bandpass filter function. Multiple orders of the FPI are visible; the average free spectral range is 11.43 nm and compares well with the prediction of 12 nm.

Fig. 11
Fig. 11

Comparison of predicted and experimentally obtained spectra. The predicted resolution was 0.68 nm after surface defects and misalignment degradation were taken into account.

Fig. 12
Fig. 12

Comparison of predicted and experimental power from nitric oxide emission at 700°C. Note the similarity of slope indicating sensitivity as predicted.

Tables (1)

Tables Icon

Table 1 Specifications of a Prototype FPI Design

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

2nd cos θ=mλ,
τλθ=1-A1-R21-R21+R2-2R cos4πnd cos θ/λ,
Δλfsr=λ22nd.
FR=πR1-R,
ΔλI=ΔλfsrFR.
C=1+2FR/π2.
ψλ=Ap  τλdΩ=Ap0θmax τλθ2π sin θdθ,
P=τoptNλ,bbλ1λ2 ψλελdλ,
ελ=1-exp-Nσλl,
Fnet-2=i Fi-2.
ΔλsΔλI  2δΔλfsrλΔλI,
FS=M2,
PNO=2πτopt ApNλ,bbλ1λ20θmax τλθθdθελdλ.
PNO=εNOPbb=1-1-εsys1-εbkg Nλ,bbψmonoΔλ,
εsys=1-exp-NσlNO+Nσlbkg,
εNO=1-1-εsys1-εbkg.

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