## Real-time FPGA data collection of pulsed-laser cavity ringdown signals |

Optics Express, Vol. 20, Issue 8, pp. 8804-8814 (2012)

http://dx.doi.org/10.1364/OE.20.008804

Acrobat PDF (1140 KB)

### Abstract

This paper presents results from a pulsed-laser cavity ring-down spectrometer with novel field programable gate array real-time data collection. We show both theoretically and experimentally that the data extraction can be achieved from a single cavity ringdown event, and that the absorbance can be determined without the need to fit the ringdown time explicitly. This methodology could potentially provide data acquisition rate up to 1MHz, with the accuracy and precision comparable to nonlinear least squares fitting algorithms.

© 2012 OSA

## 1. Introduction

1. K. W. Busch and M. A. Busch, *Cavity-Ringdown Spectroscopy: An Ultratrace-Absorption Measurement Technique* ACS Symp. Ser. 720, American Chemical Society, Washington, DC, 1999. [CrossRef]

2. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and application,” Int. Rev. in Phys. Chem. **19**(4), 565–607 (2000). [CrossRef]

*et. al.*[3

3. D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. **23**(8), 1238–1245 (1984). [CrossRef] [PubMed]

*et. al.*[5

5. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. **59**, 2544–2551 (1988). [CrossRef]

6. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. **71**(2), 347–353 (2000). [CrossRef]

9. P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” in *Next-Generation Spectroscopic Technologies IV*, M. A. Druy and R. A. Crocombe, Eds., Proc. SPIE 8032, 80320C (2011).

10. K. K. Lehmann and H. Huang, “Optimal signal processing in cavity ring-down spectroscopy,” *Frontiers of Molecular Spectroscopy*, J. Laane, ed. (Elsevier2009) pp. 623–658. [CrossRef]

6. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. **71**(2), 347–353 (2000). [CrossRef]

9. P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” in *Next-Generation Spectroscopic Technologies IV*, M. A. Druy and R. A. Crocombe, Eds., Proc. SPIE 8032, 80320C (2011).

*et. al.*[11

11. D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum. **80**, 044102 (2009). [CrossRef] [PubMed]

*et. al.*[12

12. T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “Frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express **19**, 8092–8101 (2011). [CrossRef] [PubMed]

*I*(

*t*), is a simple exponential decay which is usually digitized and then fit with a three parameter function, The signal offset,

*O*, and initial laser intensity

*I*

_{0}are required fit parameters, but the cavity decay lifetime,

*τ*, is the only fit parameter needed to measure absorbance,

*A*: Here,

*n*is the index of refraction within the optical cavity,

*l*is the optical path length in the cavity,

*c*is the speed of light, and

*τ*

_{0}is the empty cavity decay lifetime. Several digitally based methods have been reported which can extract

*τ*from a digitized decay signal having 1000 points in as little as 200

*μ*s. It is worth noting that if the offset is stable over the course of an experiment, it may be treated as a constant and excluded from the fitting regime. With simultaneous fitting and acquisition, such systems could achieve data acquisition rates of 5 kHz. In previous work, Spence

*et. al.*[6

6. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. **71**(2), 347–353 (2000). [CrossRef]

*τ*. The methodology then deployed on a combination digitizer/ FPGA evaluation board producing the first digitally based system capable of acquiring

*τ*from fast exponentially decaying signals in real time at rates exceeding 1 MHz.

## 2. Theory: frequency component analysis

*et. al.*[12

12. T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “Frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express **19**, 8092–8101 (2011). [CrossRef] [PubMed]

*et. al.*[13

13. M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO_{2},” Appl. Phys. B. **81**, 135–141 (2005). [CrossRef]

*et. al.*[8

8. M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. **79**, 023108 (2008). [CrossRef] [PubMed]

*w*, with a sampling frequency of 100 MHz. These two signals could correspond to an empty cavity response (blue) and a cavity with a strongly absorbing species present (red). The waveform in Fig. 1(b) is constructed from five ringdowns by concatenating successive decay events after transposing every other event in time, and Fig. 1(c) is the power spectrum of this waveform. This power spectrum show a comb of characteristic frequency components whose magnitude vary with

*τ*. With a strongly absorbing species present, the time-domain signal in altered in such a way that results in a comb of peaks in the frequency domain where the lowest frequency components have almost equal intensity. Without an absorber present, the intensity of the peaks in the frequency domain vary greatly, especially between the two lowest frequency components

*I*

_{1}and

*I*

_{2}. In principle, the intensity of any individual peak in the frequency domain could be used to determine

*τ*, however, these individual peak intensities also vary with the initial intensity of the laser pulse,

*I*

_{0}. As shown below, the ratio of two frequency components, like

*τ*which can be rapidly determined using basic digital processing techniques.

*τ*as a function of the powers of the fundamental frequency

*I*

_{1}and the first harmonic

*I*

_{2}. In this derivation we will show that the relation between

*τ*and

*I*

_{1}and

*I*

_{2}obtained using

*m*sampling windows can be evaluated by computing the integral of the product of the exponential decay described in Eq. (1) and a cosine function having the frequency of interest: Solving the integrals in Eq. (3) and Eq. (4), the ratio,

*R*, of

*I*

_{1}/

*I*

_{2}, is given by: Here,

*τ*′ is the decay constant

*τ*normalized with respect to the sampling window time

*w*, that is

*τ*′ =

*τ/w.*

*I*

_{1}and

*I*

_{2}are independent of any systematic signal offset

*O*and that the ratio

*R*is independent of the initial signal intensity

*I*

_{0}or the number of windows,

*m*. Indeed,

*R*is only a function of

*τ*′ and may be used to unambiguously determine

*τ*.

*S*=

_{i}*S*(

*t*),

_{i}*t*= 0,...,

_{i}*t*=

_{k}*w*, and the appropriate cosine function which, if the sampling window

*w*remains constant, is of fixed frequency: While composite waveforms like that shown in Fig. 1(b) have been used to demonstrate this technique, Eq. (6) may be applied to individual decay events; there is no need to construct a composite waveform. It is also important to note that calculating

*R*in Eq. (6) from a digitized signal is particularly suited for rapid acquisition using digital computing technology as it requires simple accumulation of two products of three discrete signals, two of which only change if the sampling window varies.

*τ*′ from the

*R*using Eq. (5) is problematic because the relationship needs to be solved numerically for each value of

*τ*′. However, as shown in Fig. 1(d),

*τ*′ is a near linear function of the ratio at

*τ*′ values greater than about 0.1. At ratios less than 0.1,

*τ*′ is small compared to

*w*and the corresponding frequency-domain signal approaches a comb of evenly spaced peaks, with the two lowest frequency peaks having near equal magnitudes, as illustrated in the red spectrum in Fig. 1(c). As a result,

*R*approaches 1 and

*τ*′ ceases to be a stable function of

*R*. Experimentally, this restriction is easily overcome by shortening the data acquisition window

*w*when

*R*falls below some threshold value.

*τ*′ from experimentally determined

*R*values are explored here. In the first method, referred to here as “theoretical,” Eq. (5) is used to generate a precise lookup table of pairs (

*R*,

*τ*′) that is then used, with linear interpolation, to determine

*τ*′ for a particular observed

*R*. Alternatively, a lookup table was also constructed using Eq. (6) by computing (

*R*,

*τ*′) with a set of noiseless ring-down waveforms having the same sampling frequency as the pulsed laser CRDS system used here. This second approach is referred to as the “empirical” method and has the same inherent digitization error as the experimental system.

*w*, such that

*τ*′ =

*τ*. For selected values of

*τ*, noisy signals were simulated using the model

*S*(

*t*) =

_{i}*e*

^{−ti/τ}+

*ε*, were

_{i}*ε*is white noise (normally distributed with mean 0 and standard deviation

_{i}*σ*∈ [0, .5]). The resulting signal

*S*(

*t*) was used to compute

_{i}*R*using Eq. (6) and to obtain

*τ*approximations for the theoretical and the empirical methods.

*S*(

*t*) was also fitted to an exponential decay using LM non-linear fitting. We repeated this simulation at least 100,000 times and for each of the three methods computed the relative error of the mean estimated

_{i}*τ*: that is,

*τ*= 0.3. At lower noise levels, both the empirical and the LM methods outperform the theoretical method. The differences in the theoretical and empirical methods reflect the error associated with using sums of discrete data points to approximate the integrals in Eq. (3) and Eq. (4). Interestingly enough, when the standard deviation of the noise is close to 20% of the initial intensity,

*I*

_{0}, the theoretical method dips below both the empirical and the LM methods, and remains roughly below the other two methods from then on. This suggests that if the signal to be analyzed is very clean one should use the empirical method, as its implementation is much faster than the LM method. If the signal is somewhat noisy, with noise levels 20% of initial intensity or larger the theoretical methodology is to be preferred. Simulation results using

*τ*values between .1 and .6 show similar dips in relative error of the mean estimated

*τ*at noise levels between 20% and 30% for the theoretical method.

*τ*as a function of the amplitude of the normally distributed noise added to the synthetic decay transients. At all noise levels the traditional LM method provides slightly better precision, but again this must be weighed against the speed of data analysis which is two to three orders of magnitude faster using the frequency component analysis methodology presented here.

*w*, on precision. Figure 5 shows a plot of the relative standard deviation in t as a function of window size. For these simulations,

*τ*= 0.3,

*δτ*= 0.001, and

*w*is varied from 0.8 to 3.0. Gaussian distributed random noise was added to each trace with

*σ*= 0.2. For both methods an optimal data acquisition window of 1.5 or 5 times the decay constant is observed. Performance degrades at shorter times due to truncation of the decay waveform. At longer times, performance degrades due to additional introduced noise.

## 3. Experimental

*R*= 0.9995). The optical cavity was evacuated using an oil-free diaphragm pump and

*μ*L quantities of NO

_{2}(g) mixed with room air were injected into the cavity through a septum using a gas-tight syringe. Light exiting the cavity was detected using a photomultiplier tube (Hamamatsu H8443). The resulting signal was digitized either by a PC interfaced LeCroy digital oscilloscope (LT3720, 500 MHz) or by an FPGA digital signal processing development kit (Altera EP3C120), which consists of a high-speed mezzanine data conversion daughter card interfaced with a Cyclone III FPGA development board. This relatively inexpensive development kit achieved data sample rates of 100 MHz.

*R*by implementing Eq. (6). It is important to note that each stage of this circuit executes in a point-by-point fashion calculating

*R*in real time. The circuit is enabled by the falling edge of a ring-down event from the photodetector. When enabled, on each clock cycle (at a rate 100 MHz) the daughter board digitizes the signal from the photodetector and provides the signal to the FPGA board. Simultaneously, and also at 100 MHz, the board generates corresponding cosine function values and multiplies the digitized waveform by the result. The results of this multiplication are accumulated in a sum and the ratio of the sums is calculated and provided to Latch 1. While enabled, the output of Latch 1 follows the input showing the value of

*R*as the ringdown transient it obtained. Once data has been acquired, the sums accumulated, and

*R*calculated over the pre-determined sampling window,

*w*, the enable signal goes logic “low,” stops all calculations, resets the accumulators, disables Latch 1 freezing its output at the final value of

*R*, and activates Latch 2 providing the most recent value of

*R*to the digital-to-analog output. As a result, the output of Latch 2 changes at the pulse rate of the CRDS system potentially allowing a slower data acquisition system to monitor

*R*in real time. Indeed, the purpose of the second latch is to provide constant output while the circuit is disabled or acquiring and analyzing a new decay trace.

## 4. Results and discussion

*S*, is monitored at all times at a rate of 100 MHz and shows noise typical of a pulsed laser based CRDS system. Prior to triggering, the value of

*R*is latched at the result from the previous ring-down event. Upon detection of a laser pulse, the FPGA enables calculation of both cosine functions (

*C*

_{1}and

*C*

_{2}) and calculates

*R*as the exponential decay is acquired. The choice of

*C*

_{1}=cos(

*πt/w*) and

*C*

_{2}=cos(2

*πt/w*) correspond to the numerical approximation given in Eq. (6) and the conditions described by Fig. 1(b) and Fig. 1(c). After acquiring and analyzing data over the entire decay window (

*w*= 28

*μ*s or 2800 data points),

*R*is again latched at its final value until the next laser pulse is detected. One of the benefits of this type of analysis is immediately apparent; the high-frequency noise present on

*S*is effectively filtered out when the ratio of the two sums is calculated.

*S*tended to overshoot the decay baseline. Attempts to bypass the transformer led to excessively noisy waveforms. Despite the perturbation to the decay waveform, accurate absorbance values were obtained as empty cavity and sample decay traces were impacted equally.

*R*in real time, the only practical limitation to data acquisition speeds is the decay time of the cavity itself. Indeed, assuming a minimum of 100 points is needed to adequately characterize the noisy output of a CRDS system, the FCA/FPGA presented here could acquire and analyze decay transients at 1 MHz. Faster digitizer/FPGA systems could further increase the speed of data acquisition.

*R*is communicated by the FPGA as a DC signal through a digital-to-analog converter output. For slower pulsed systems, this method is problematic as it is sensitive to baseband noise in the analog transfer of data. In future systems, we will explore exporting

*R*as either a frequency- or amplitude-modulated signal which should greatly reduce susceptibility to added noise. Depending on the application, we can also leave

*R*digital.

_{2}(g) in room air obtained at the maximum laser firing frequency of 20 Hz. FCA analysis was used to obtain this spectrum in real time, and the ringdown waveforms were also recorded and later analyzed using Levenberg-Marquardt nonlinear least squares fitting (we used the value for

*τ*obtained from the previous fit as our initial guess for the next fit). Both methods gave statistically equivalent results. A minimum detectable absorbance, calculated from Eq. (2) and Eq. (5), was determined to be 5.3×10

^{−6}cm

^{−1}, calculated with respect to the empty cavity ringdown time and standard deviation,

*τ*

_{0}= 16.5 ± 0.4

*μs*. The molar absorption coefficient for NO

_{2}at 539nm is 1.8 × 10

^{−19}M

^{−1}cm

^{−1}[14

14. A. C. Vandaele, C. Hermans, P. C. Simon, M. Van Roozendael, J. M Guilmot, M. Carleer, and R. Colin “Fourier transform measurement of NO_{2} absorption cross-sections in the visible range at room temperature,” J. Atm. Chem. **25**, 289–305 (1996). [CrossRef]

^{−9}or 10ppb.

_{2}(g) in room air. The NO

_{2}(g) concentration was much greater than the CRDS system and is presented to show that the two methods qualitatively agree, and reveal the same spectral features.

*χ*

^{2}given by least squares fitting regimes. We do, however, note that our fast analysis times allow us to analyze each transient in real time: this allows us to discard data points that appear to be well outside the mean.

## 5. Conclusions

_{2}(g) in room air using a pulsed-laser based CRDS system. This technology could greatly expand real time monitoring of gasses using this ultra-sensitive absorption technique.

## Acknowledgments

## References and links

1. | K. W. Busch and M. A. Busch, |

2. | G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and application,” Int. Rev. in Phys. Chem. |

3. | D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. |

4. | D. Z. Anderson, “Reflectometer based on optical cavity decay time,” US Patent Office US4571085 (1986). |

5. | A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. |

6. | T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. |

7. | N. J. van Leeuwen, J. C. Diettrich, and A. C. Wilson, “Periodically locked continuous-wave cavity ringdown spectroscopy,” Appl. Opt. |

8. | M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. |

9. | P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” in |

10. | K. K. Lehmann and H. Huang, “Optimal signal processing in cavity ring-down spectroscopy,” |

11. | D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum. |

12. | T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “Frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express |

13. | M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO |

14. | A. C. Vandaele, C. Hermans, P. C. Simon, M. Van Roozendael, J. M Guilmot, M. Carleer, and R. Colin “Fourier transform measurement of NO |

**OCIS Codes**

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

(300.1030) Spectroscopy : Absorption

(300.6360) Spectroscopy : Spectroscopy, laser

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: November 21, 2011

Revised Manuscript: March 3, 2012

Manuscript Accepted: March 19, 2012

Published: April 2, 2012

**Citation**

T. G. Spence, M. E. Calzada, H. M. Gardner, E. Leefe, H. B. Fontenot, L. Gilevicius, R. W. Hartsock, T. K. Boyson, and C. C. Harb, "Real-time FPGA data collection of pulsed-laser cavity ringdown signals," Opt. Express **20**, 8804-8814 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8804

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### References

- K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy: An Ultratrace-Absorption Measurement Technique ACS Symp. Ser. 720, American Chemical Society, Washington, DC, 1999. [CrossRef]
- G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and application,” Int. Rev. in Phys. Chem.19(4), 565–607 (2000). [CrossRef]
- D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt.23(8), 1238–1245 (1984). [CrossRef] [PubMed]
- D. Z. Anderson, “Reflectometer based on optical cavity decay time,” US Patent Office US4571085 (1986).
- A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum.59, 2544–2551 (1988). [CrossRef]
- T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum.71(2), 347–353 (2000). [CrossRef]
- N. J. van Leeuwen, J. C. Diettrich, and A. C. Wilson, “Periodically locked continuous-wave cavity ringdown spectroscopy,” Appl. Opt.42(18), 3670–3677 (2003). [CrossRef] [PubMed]
- M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum.79, 023108 (2008). [CrossRef] [PubMed]
- P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” in Next-Generation Spectroscopic Technologies IV, M. A. Druy and R. A. Crocombe, Eds., Proc. SPIE 8032, 80320C (2011).
- K. K. Lehmann and H. Huang, “Optimal signal processing in cavity ring-down spectroscopy,” Frontiers of Molecular Spectroscopy, J. Laane, ed. (Elsevier2009) pp. 623–658. [CrossRef]
- D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009). [CrossRef] [PubMed]
- T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “Frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express19, 8092–8101 (2011). [CrossRef] [PubMed]
- M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B.81, 135–141 (2005). [CrossRef]
- A. C. Vandaele, C. Hermans, P. C. Simon, M. Van Roozendael, J. M Guilmot, M. Carleer, and R. Colin “Fourier transform measurement of NO2 absorption cross-sections in the visible range at room temperature,” J. Atm. Chem.25, 289–305 (1996). [CrossRef]

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