1 Introduction

Nitrogen dioxide (NO2) is one of the major air pollutants that are primarily produced in the atmosphere by combustion processes. At very high concentrations, NO2 is an oxidizing, toxic, and corrosive gas. Trace amounts of NO2 may irritate airways in the human respiratory system and may lead to the development of asthma and other respiratory infections [1]. Furthermore, NO2 is known to be responsible for photosmog and acid rain [2]. Accordingly, monitoring atmospheric NO2 gas has always been a subject of great interest. Therefore, and over the years, many techniques based on different physical and chemical principles have been developed including optical methods [3, 4]. Most of the optical methods use the strong and broadband absorption of NO2 molecule over the spectral range 250–650 nm [4,5,6,7,8,9,10,11,12,13,14,15,16,17]. This absorption broadband has a maximum absorption cross section of about 0.8 × 10−18 cm2/molecule at wavelengths around 448 nm. It also has many peak-like features spectral widths of about 1 nm and cross section variations up to 0.4 × 10−18 cm2/molecule [18].

One of the common and powerful optical methods is the Differential Optical Absorption Spectroscopy (DOAS), which has been employed to detect NO2 gas traces over very long open paths, for instance, a detection limit of 0.15 ppb was achieved over a 5-km light path length [4]. DOAS mainly employs a broadband light source, such as a xenon lamp, a telescope, and a spectrometer, making the setup relatively expensive and complex. The intensity of the light sources is one important factor that may limit the sensitivity of this technique [4]. Although lasers have much higher intensities and are much easier to collimate than lamps, their bandwidths are too narrow for DOAS applications. Another common and sensitive optical method for gas detection is the Tunable Diode Laser Absorption Spectroscopy (TDLAS) [19]. However, it is difficult to use on the NO2 absorption broadband, since most of single-mode external cavity tunable diode lasers have limited hop-free tuning ranges of tens of GHz (~ 0.01 nm). These tuning ranges are much narrower than the NO2 absorption peak-like structures. Another well-established sensitive optical method is the photoacoustic spectroscopy, which can achieve low detection limits, for example, a detection limit of 0.20 ppb can be attained for a 100-mm long NO2 gas cell [11]. However, the sensitivity of the photoacoustic spectroscopy method can be degraded from the absorption of the laser light reflected from the cell windows or scattered by aerosols in the cell [20]. The DIfferential Absorption Lidar (DIAL) is another optical method that can yield spatial NO2 distribution with an NO2 detection limit of about 1 ppb over few kilometers range. Nonetheless, high-power expensive lasers as well as complex emitting and receiving optics are usually required [14]. Another sensitive optical method is the Laser-Induced Fluorescence (LIF), which has been employed to detect traces of NO2 with low detection limit, for example, a 10-ppb detection limit was reported over a one-minute acquisition time [15]. But LIF generally requires very low sample pressure, powerful lasers, and delicate experimental calibration [plat]. Traces of NO2 gas were also detected using cavity enhanced absorption spectroscopy (CEAS) and cavity-ring down spectroscopy (CRDS). For example, a detection limit of 3 ppb at a pressure of 65 mbar was obtained using a cavity length of about 50 cm [5]. Even though CEAS and CRDS can achieve low detection limits, they are relatively complicated and require regular optical alignment. Many studies in literature using blue diode lasers to detect NO2 utilize one or two fixed wavelengths on the absorption band of NO2 [6,7,8,9,10,11]. This approach might not be enough to positively identify and accurately measure NO2 since possible interferences from different sources of absorption, such as from Rayleigh scattering, could shift the measured absorption signal, and hence might negatively affect the accuracy of the measurement.

In this work, we present a simple, low-cost, and sensitive optical method to measure traces of NO2 gas based on direct absorption spectroscopy. The method employs a multimode Fabry–Perot blue diode laser that is current-tuned around 450 nm over a peak-like structure of the NO2 absorption spectrum producing a unique signature of NO2 absorption. A simple laser diode is used instead of an intricate and expensive tunable single-longitudinal mode laser, which makes the method robust and economic. The rest of the paper is organized as follows. Section 2 presents a theoretical treatment on the extraction of the transmission curves for NO2 from the spectra of the multimode current-tuned diode laser. The next section details the experimental setup for measuring the laser emission spectra as well as the transmission curves. In Sect. 4, the results of both simulation and measurements are discussed. Finally, Sect. 5 concludes the paper.

2 Theory

A typical low power commercial Fabry–Perot blue diode laser has a single transverse mode and many longitudinal modes. At fixed injection current and fixed laser temperature, these longitudinal modes span a spectral region of a width of about 1 nm. The emission spectrum of a diode laser can be tuned either by changing the laser injection current or temperature. Since tuning with current is much faster that tuning with temperature, in this study, current is used to tune the laser.

When a multimode laser beam passes through a sample containing NO2, the transmission T of the laser beam varies with the laser injection current i. The shape of T(i) curve is also a function of the laser temperature, which can be selected to produce a favorable shape for the transmission curve. To monitor NO2 concentration, the variation in the T(i) curve should be as large as possible to maximize the signal-to-noise ratio. Also, it is desirable if the shape of T(i) curve has some structure, like a peak-like shape, for the NO2 absorption to have a distinctive signature. The T(i) can be obtained experimentally, by measuring the transmission through a known concentration of NO2, or it can be calculated from the NO2 absorption cross section if the spectra of the laser are known at different laser currents and temperatures.

In the following, the method of calculating the transmission curve T(i) from the molecular absorption cross section and the spectra of a multimode laser will be outlined. According to the Lambert–Beer’s law, when an incident monochromatic light beam of wavelength \(\lambda\) and intensity \(I_{0} \left( \lambda \right)\) passes through an absorbing gas sample of length l and number density C, the intensity of the transmitted light beam \(I_{T} \left( \lambda \right)\) is given by

$$I_{T} \left( \lambda \right) = I_{0} \left( \lambda \right)e^{ - Cl\sigma \left( \lambda \right)} ,$$
(1)

where \(\sigma \left( \lambda \right)\) is the molecular absorption cross section of the gas molecules as a function of wavelength. The transmission at \(T\left( \lambda \right)\) at wavelength \(\lambda\) is defined as the ratio of the intensity of the transmitted beam to the intensity of the incident beam

$$T\left( \lambda \right) = I_{T} \left( \lambda \right)/I_{0} \left( \lambda \right).$$
(2)

For a light source of a finite bandwidth with an intensity spectrum \(I\left( \lambda \right)\) extending from \(\lambda_{\min }\) to \(\lambda_{\max }\), the intensity of the source can be obtained by integrating over its intensity spectrum \(\int_{{\lambda_{\min } }}^{{\lambda_{\max } }} {I\left( \lambda \right){\text{d}}\lambda }\). Thus, for a multimode laser, the incident laser beam has an intensity of \(\int_{{\lambda_{\min } }}^{{\lambda_{\max } }} {I_{0} \left( \lambda \right){\text{d}}\lambda }\) while the transmitted beam has an intensity of \(\int_{{\lambda_{min} }}^{{\lambda_{max} }} {I_{T} \left( \lambda \right){\text{d}}\lambda }\). Hence, the transmission curve of the diode laser \(T\left( i \right)\) as a function of the laser injection current i at a fixed temperature can be calculated using Eqns. 1 and 2:

$$T\left( i \right) = \frac{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{T} \left( \lambda \right){\text{d}}\lambda }}{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{0} \left( \lambda \right){\text{d}}\lambda }} = \frac{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right)e^{ - Cl\sigma \left( \lambda \right)} {\text{d}}\lambda }}{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right){\text{d}}\lambda }}.$$
(3)

Here, \(I_{0} \left( \lambda \right)\) is the intensity spectrum of the laser. For a small absorbance, \(Cl\sigma \ll 1\), \(T\left( i \right)\) can be approximated to

$$T\left( i \right) \approx 1 - {\text{Cl}}\frac{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right)\sigma \left( \lambda \right){\text{d}}\lambda }}{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right){\text{d}}\lambda }},$$
(4)

where in this case, the transmission is a linear function of the concentration.

One way to experimentally measure the transmission is to split the laser beam into two beams: the signal beam and the reference beam. The signal beam passes through a region containing the sample, while the reference beam passes through a region free of the sample molecules. If the response of a light detector is assumed to be constant over the laser emission wavelength range, the voltage measured by the detector is proportional to the integrated intensity spectrum of the light falling on it and is given by \(V \propto \int_{{\lambda_{\min } }}^{{\lambda_{\max } }} {I\left( \lambda \right){\text{d}}\lambda }\). This is considered a good assumption since the tuning range of a typical diode laser is few nanometers much smaller than the smooth response curve of a typical photodiode. Hence, \(T\left( i \right)\) is proportional to the ratio of the voltage of the signal detector \(V_{sig} \left( i \right)\). to the voltage of the reference detector \(V_{{{\text{ref}}}} \left( i \right)\):

$$T\left( i \right) = \frac{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{T} \left( \lambda \right){\text{d}}\lambda }}{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{0} \left( \lambda \right){\text{d}}\lambda }} \propto \frac{{V_{{{\text{sig}}}} \left( i \right)}}{{V_{{{\text{ref}}}} \left( i \right)}}.$$
(5)

Although the constant of proportionality depends on many factors that are sometimes difficult to control, such as the splitting ratio of the two beams and the responsivity of the detectors, it can be determined by doing the transmission measurements with the sample region free of the sample molecules.

3 Experiment

Two Fabry–Perot multimode blue diode lasers are interchangeably used as a light source: one is from Toptica Photonics Inc., model LD-0445–0050-1, and the other is from Roithner LaserTechnick GmbH, model LD-445-50PD. Both lasers have a nominal emission wavelength of 445 nm, an output power of 50 mW, a threshold current of about 30 mA, and a maximum allowable injection current of 160 mA. Also, they can be operated over the temperature range from -10 °C to 60 °C. The diode laser is hosted in a TE-cooled mount, Thorlabs model TCLDM9, and its beam is collimated by an achromatic aspheric lens, Thorlabs model C230TMD-A. The laser temperature is controlled by a temperature controller, Thorlabs model TED200C, while its injection current is controlled by a current controller, Thorlabs model LDC205C. Both temperature and current can be set either manually or through a data acquisition card, National Instruments model NI USB-6251.

Although the two lasers have the same nominal wavelength, their actual tuning ranges are shifted by about 2 nm. It would be interesting to investigate the effect of this shift on the shape and variation of the NO2 transmission curves at different laser temperatures. For this reason, in this study, the diode laser with maximum variation in the transmission curve is determined.

The laser emission spectra are measured by a spectrometer which consists of a monochromator, SPEX model 500 M coupled to a CCD line camera, Thorlabs model LC1-USB. The monochromator has a resolution of 0.02 nm and a linear dispersion of 1.6 nm/mm and the CCD line camera has 3000 pixels, each pixel has a width of 7 µm and a length of 120 µm. A LabVIEW virtual instrument is used to record the laser spectra as a function of diode laser temperature and current.

Figure 1 shows a schematic diagram of the setup used to measure the transmission through a diluted NO2 gas sample. The blue diode laser (DL) emits a collimated beam which is split by a 50–50 beam splitter (BS) into two beams. One is called the reference beam, which is directed by a mirror (M) to one of the photodiode detectors (PD) of a balanced photodetector, Thorlabs model PDB210A/M. The second beam is called the signal beam, which travels through the absorption cell to the other photodiode detector in the balanced photodetector. Neutral density filters (ND) made from white printing paper are used to reduce the intensity of the laser beams to prevent detector saturation. To lower noise, the balanced photodetector and the density filters can be replaced with two low-noise photodetectors, Thorlabs model DET36A. The cylindrical absorption cell, of 40 cm length and 2.54 cm diameter, is made from stainless steel and has two BK7 glass windows at the inlet and outlet. The windows are tilted by an angle of about 45° to minimize interference between the incident beam and the reflected beams from the surfaces of the windows. Since the laser beam path is relatively short and the beam diameter is about 2 mm, which is smaller than the 5 mm active diameter of the photodetector, slight beam misalignments should not influence the measurement. However, in case of detection over long paths of hundreds of meters, careful optical alignment with the aid of steering optics, such as a telescope, is needed.

Fig. 1
figure 1

A schematic diagram of the experimental setup; DL blue diode laser, BS beam splitter, M mirror, ND neutral density filter, DAQ data acquisition card, PD photodiode detector, PC personal computer

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A pressurized pure N2 gas cylinder or a pressurized 200 ppm NO2/N2 gas mixture cylinder is used to supply gas to the cell with a flow rate regulated by a mass flow controller, Omega model FMASS14ST. The maximum flow rate of the mass flow controller is 1000 mL/min. The pressure in the cell is measured by an absolute capacitance manometer, MKS model 690A, and it is maintained at a pressure of 760 torr within 0.04% by a system consisting of a needle valve, vacuum pump and feedback mechanism between the flowmeter and the pressure gage controlled by the data acquisition card (DAQ) card, National Instruments model NI USB-6251. The card adjusts the flow rate of the mass flow controller and reads the pressure of the pressure gage. A LabVIEW virtual instrument is used to control the pressure and to acquire data for the measurement of NO2 transmission.

4 Results and discussion

To maximize signal-to-noise ratio, and hence improving the detection limit, the variation in the transmission curve T(i), which depends on the laser temperature, should be as large as possible. To select the optimal laser temperature, the transmission curves T(i) are obtained at different temperatures by direct measurement as well as by calculating them from the measured spectra of the laser. As will be seen later, the direct measurements agree reasonably well with the calculated transmission curves.

To calculate the transmission curve T(i) from Eq. 3, the spectra of the laser needs to be measured at different current values. Figure 2 shows samples of the measured laser emission spectra for the two lasers used in this study. The spectrum on the left is from the Roithner laser while the spectrum on the right is from the Toptica laser, which are taken at an operating temperature of 30 °C and an injection current of 100 mA. Both curves represent \(I_{0} \left( \lambda \right)\) in Eq. 3.

Fig. 2
figure 2

Emission spectrum of the Roithner diode laser, on the right, and emission spectrum of the Toptica diode laser, on the left. Both lasers are operating at 30 °C with an injection current of 100 mA. λmin and λmax are the minimum and maximum wavelength of the laser emission spectrum, respectively

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Figure 3 shows the absorption cross section of NO2 per molecule and the wavelength tuning ranges with current at different temperatures for the two lasers. The ranges are shown below the cross section as horizontal lines. The Roithner laser ranges are shown on the left while the Toptica laser ranges are shown on the right. The laser wavelength shifts toward higher values with current and each line corresponds to changing the current from the threshold current of about 30 mA to the maximum allowed current of 160 mA. Just above the 60 °C line of the Toptica laser, the figure also shows a spectrum of the laser with an injection current of 90 mA. For both lasers, the width of the current tuning range does not change much with temperature, but it is wider for the Roithner laser. The width for the Roithner laser is about 3.0 nm whereas it is about 2.6 nm for the Toptica laser. For the same temperature, the current tuning range of the Roithner laser is lower by 2 nm compared to that of the Toptica laser. The current tuning range for both lasers shifts towards longer wavelength with temperature at roughly the same rate of 0.05 nm/°C or 0.5 nm for a temperature change of 10 °C. With current and temperature tuning, the Roithner laser can cover a range of a width of 5.5 nm from 443.2 to 448.7 nm, while the Toptica laser can cover a spectral range of a width of 5.2 nm from 445.3 to 450.5 nm.

Fig. 3
figure 3

NO2 absorption cross section along with the current wavelength tuning ranges, shown as horizontal lines, for the Roithner and Toptica laser for different temperatures. The insert shows the absorption cross section over a wider wavelength range. The range between the two vertical lines in the insert is the part of the cross section shown in the main figure

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It can be noted that the tuning ranges are wide enough to cover one of the largest peak-like features of the NO2 cross section. Hence, it is expected to observe big variations in transmission as the laser is tuned over one of the current tuning ranges. At one specific current i, the transmission function T(i), can be calculated from Eq. 3 by converting the integration into sum over the pixels of the CCD line camera:

$$T\left( i \right) = \frac{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right)e^{ - Cl\sigma \left( \lambda \right)} {\text{d}}\lambda }}{{\mathop \smallint \nolimits_{{\lambda_{\min } }}^{{\lambda_{\max } }} I_{o} \left( \lambda \right){\text{d}}\lambda }} \approx \frac{{\mathop \sum \nolimits_{{p = p_{\min } }}^{{p_{\max } }} I_{o} \left( p \right)e^{ - Cl\sigma \left( p \right)} }}{{\mathop \sum \nolimits_{{p = p_{\min } }}^{{p_{\max } }} I_{o} \left( p \right)}}.$$
(6)

Here, p is the pixel number, \(p_{\min }\) and \(p_{\max }\) are the pixel numbers that correspond to the \(\lambda_{\min }\), and \(\lambda_{\max }\), respectively. \(I_{o} \left( p \right)\) is the count of pixel p, and \(\sigma \left( p \right)\) is the molecular absorption cross section over the wavelength range covered by pixel p. The following calculations use a 40-cm gas cell, a 200-ppm NO2/N2 gas mixture ratio at room temperature and atmospheric pressure, while the absorption cross section is obtained from ref. [18].

Figure 4 shows the calculated transmission, using Eq. 6, as a function of the injection laser current for the Roithner laser on the left and for the Toptica laser on the right. Each of the six curves represents a fixed laser temperature ranging from 10 to 60 °C in steps of 10 °C. Because of different current tuning ranges, the two lasers have different transmission curves for the same temperature, while the same laser has different transmission curves for different temperatures.

Fig. 4
figure 4

Calculated transmission as a function of the laser injection current for the Roithner and Toptica lasers at different laser temperatures ranging from 10 to 60 °C in steps of 10 °C

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The general behavior of the calculated curves for a multimode laser in Fig. 4 can be understood and compared with the transmission values obtained from a single-mode laser. One expects to get the maximum transmission at a wavelength near 446.7 nm, between the two peak-like features in the cross section, where the value of the cross section is minimum and of about \(0.39 \times 10^{ - 18} \;{\text{cm}}^{2} /{\text{molecule}}\). This leads to a transmission of about 0.93 for a single-mode laser. This value is nearly reached by the Roithner laser for the temperatures: 40, 50 and 60 °C and for the Toptica laser for the temperatures: 10, 20 and 30 °C. However, because of the width of their spectra, the calculated transmission for the two lasers is slightly lower than that of a single-mode laser. Also, it might be noted that the maximum of transmission occurring at lower currents is slightly higher than that occurring at higher currents. This behavior is related to the fact that the width of intensity spectrum of a diode laser becomes wider with the injection current. With a wider laser spectrum, the transmission is lowered by the contributions from regions of spectrum with higher cross sections. Likewise, with careful inspection, one might note that the maximum transmission from the Toptica laser is slightly higher than that of the Roithner laser. This is because the intensity spectra of the Toptica laser is, in general, narrower by about half a nanometer than that of the Roithner laser, as exemplified by Fig. 2.

For a single-mode laser, the minimum transmission is expected to be at a wavelength that corresponds to the maximum cross section. This occurs at around 448 nm with a cross section of about \(0.72 \times 10^{ - 18} \;{\text{cm}}^{2} /{\text{molecule}}\), corresponding to a transmission of about 0.87. This value is nearly reached by the Toptica laser for the temperatures: 30, 40 and 50 °C. For these three operating temperatures, the minimum of transmission occurring at lower currents is lower than that occurring at higher currents. This behavior can be explained by the fact that the laser spectrum is narrower at lower injection currents. The variation in the minimum transmission is clearer than that of the maximum transmission because the corresponding cross section variation for the minimum transmission is sharper, as can be seen in Fig. 3.

For the Roithner laser, the minima in the transmission curves of the temperatures: 10, 20 and 30 °C are much higher than that of the Toptica laser because they correspond to the less pronounced peak-like feature in the cross section occurring at about 444.8 nm. The behavior of the transmission curve at 30 °C for the Roithner laser is interesting. It seems that there is a sudden jump in the transmission when changing the laser current from 30 to 40 mA. This occurs because, at 30 mA near threshold, the Roithner laser lases almost equally at two neighboring modes at wavelength of 444.2 nm. Upon increasing the current, few additional strong neighboring modes appear at about 444.8 nm, which happens to be just at the maximum of the peak-like feature. At 40 mA, the intensity of the laser at 444.8 nm is about six times stronger than that at 444.2 nm and, therefore, the transmission is effectively caused by the higher intensity light at 444.8 nm.

To measure the transmission curve T(i) for a known concentration of NO2 gas, NO2/N2 gas mixture needs to be flowed in the cell while keeping the gas pressure constant. It is observed that if the NO2 gas mixture inside the absorption cell is not flowing, the transmission due to NO2 increases with time. This indicates that some of NO2 gas is slowly lost with time. Since there is no leakage in the cell, the loss might be due to adsorption of NO2 onto the walls of the cell or due to chemical reaction of NO2 with the cell or with other NO2 molecules to form N2O4 dimers [21]. To determine an appropriate flow rate that is high enough to eliminate the increase in the transmission signal due to the loss of NO2 in the cell, but low enough to reduce the consumption of the NO2/N2 gas mixture, transmission at specific wavelength for different flow rates is observed as a function of time. The following flow rates are tested: 50, 100, 200, 400, 600, and 800 ml/min. Before testing a specific flow rate, the cell is cleaned by flowing pure N2 gas into the cell for a long time, about an hour. Then, the N2 gas valve is closed and simultaneously the NO2/N2 gas mixture valve is opened. Figure 5 shows the transmission as a function of time for the six flow rates. It is expected that the steady state takes some time to be reached. For the 50 ml/min flow rate, the flow rate is relatively small to the extent that the steady state is not reached after more than two hours. For the 100 and 200 ml/min, the steady state is reached after 20 and 10 min, respectively. However, there are two different steady states for these two flow rates indicating that they are not sufficiently large. In addition, the transmission values at these steady states are less than the expected values. For the 600 and 800 ml/min, the steady state is reached within about 5 min and their steady-state transmission values are almost the same which is in good agreement with the predicted value. Hence, the 600 ml/min flow rate is used in the measurements of transmission curve T(i).

Fig. 5
figure 5

Transmission variation with time for different NO2/N2 mixture flow rates, ranging from 50 to 800 ml/min

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The transmission curve for NO2 is obtained by dividing the voltage ratio of the signal and reference beams for N2/NO2 gas mixture sample to that for pure N2 gas sample. Figure 6 shows typical voltage ratios as a function of laser current for N2/NO2 gas mixture sample and for pure N2 gas sample using the Roithner laser operated at 30 °C. The acquisition time for each ratio is about 10 s. As can be seen, the ratios are nosier at lower currents due to low laser intensity.

Fig. 6
figure 6

Typical voltage ratios of the signal and reference detectors as a function of the laser injection current for NO2/N2 gas mixture and for pure N2 gas

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Figure 7 shows examples of measured transmission curves along with the corresponding calculated transmission curves of Fig. 4 for both lasers. On the left is the case for the Roithner laser when it is operated at 30 °C while on the right is the case for the Toptica laser at 50 °C. The figure for the Roithner laser demonstrates the abrupt change in the transmission when the current is tuned from 30 to 40 mA, while the figure for the Toptica laser shows the case for a temperature with the largest variation in transmission curve that has a clear minimum. The agreement between the measured and the calculated absorptions is quite good with a deviation of less than 5%. This small difference is mainly due to the calculated absorption which is obtained using laser spectra with limited resolution, as shown in Fig. 2.

Fig. 7
figure 7

Measured transmission curves, in red, and calculated transmission curves, in black, for the Roithner and Toptica lasers. The Roithner laser is operated at 30 °C while the Toptica laser is operated at 50 °C

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The following experiment is preformed to test the precision and stability of the setup. Since the concentration of NO2 in the gas mixture is proportional to the pressure of the gas, the concentration of NO2 is varied by varying the pressure for a fixed gas mixture ratio instead of changing the mixing ratio of the gas at a fixed pressure. The pressure inside the gas cell is varied up and down near the atmospheric pressure in small steps and the transmission curves are measured. One of the transmission curve measurements at the atmospheric pressure is used as a reference while the other transmission curve measurements are used to extract the pressure by comparing them with the reference transmission curve. The extracted pressure values are then compared with the pressure values measured independently by the pressure gage. It should be noted that the pressure inside the cell is maintained constant with a standard deviation of 0.02% near the atmospheric pressure by the feedback system between the pressure gage and the flowmeter.

The Toptica laser is operated at 50 °C and its injection current is scanned up and down continuously between 25 and 155 mA. The variation in the current is done in a step manner with a step size of 1 mA and the time for scanning the laser current in one direction is 6.63 s. To reduce noise, the balanced photodetector and the density filters are replaced with two photodetectors having much lower noise, Thorlabs model DET36A. Furthermore, for each detector, 1000 sample points are acquired and averaged at each current step. For NO2 gas mixture in the cell, the pressure is changed up and down in a small step of 1.3% as follows; 760, 750, 740, 750, and 760 mmHg. The duration of each pressure step is about five minutes, and it takes about one minute for the pressure to stabilize around the new pressure value. After that, NO2 gas mixture is changed by pure N2 gas and the same pressure steps are repeated. A transmission curve can be obtained from two current scans; one from an NO2 current scan and the other is from its corresponding N2 current scan.

The transmission curve of the first current scan is arbitrarily assigned as a reference. The pressure is extracted from another transmission curve by the least square regression method by minimizing the following sum:

$$\mathop \sum \limits_{k} \left( {T\left( k \right) - \exp \left( {p_{f} \frac{{\ln T_{r} \left( k \right)}}{{p_{r} }}} \right)} \right)^{2} .$$
(7)

Here, \(T\left( k \right)\) and \(T_{r} \left( k \right)\) are transmissions at current step k in the measured curve and the reference curve, respectively. \(p_{f}\) is a fitting parameter and \(p_{r}\) is the pressure at the reference curve. At \(p_{r}\) = 760 mmHg, the concentration of NO2 in the gas mixture is 200 ppm, according to the manufacture, and thus the concentration obtained from the fit is \(C_{f} = 200\;{\text{ppm}} \times p_{f} /p_{r}\). This should be compared with the expected concentration value \(C_{e} = 200\;{\text{ppm}} \times p_{m} /p_{r}\), where \(p_{m}\) is the pressure measured by the pressure gauge.

Figure 8a shows the concentrations obtained from transmission curve measurements, shown as red dots, and the expected concentration, represented as black lines. Each dot corresponds to a transmission curve measured during a current scan. Over few minutes, the concentration measurements are reproducible within 0.1 ppm. However, over a longer time span, there is a linear drift of about 1 ppm per hour. This drift is mainly observed in the output voltage of the signal detector when NO2 is present in the cell. This probably due to a slow desorption process of NO2 molecules from the surface of the gas cell. It is interesting to investigate the cause of the drift using gas cells made of other materials such as glass or aluminum instead of stainless steel. The green dots in Fig. 8a show the result when the measurements are corrected for the linear drift. The good agreement between the measured and expected (nominal) concentrations confirms the accuracy of the setup. Figure 8b shows Allan deviation for the ratio of the signal to reference detectors. As can be seen, the lowest deviation of \(6.5 \times 10^{ - 6}\) occurs at about 150 s after which that the ratio starts to drift.

Fig. 8
figure 8

a Concentrations obtained from transmission measurements, red dots; concentrations corrected for a slow linear drift, green dots; and the expected concentration, black lines. b Allan deviation for the ratio of the signal to reference detectors

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The minimum detectable limit of 0.1 ppm for the 40-cm gas cell used corresponds to a detection limit of about 0.1 ppb if an absorption path length of 400 m is used. It is worth mentioning that the detection limit of 0.1 ppb is much lower than the maximum allowed safe limits for NO2 concentrations in ambient air. The World Health Organization, for example, sets 200 \({\mu g}/{\text{m}}^{3}\) or 106 ppb for the annual exposure limit and 40 \({\mu g}/{\text{m}}^{3}\) or 21 ppb for hourly exposure limit [22].

It should be emphasized that the method proposed in this work does not require using a spectrometer nor does it require calculating the transmission curves. It only requires a laser and two detectors. However, if the method is intended for detecting trace amounts of NO2 in ambient air, it might be easier to use a spectrometer with a high enough resolution to find the optimal operating temperature for the laser. If a suitable spectrometer is available, it is much easier and cheaper to measure the laser spectra and to calculate the transmission curves than finding the transmission curves experimentally by building or operating a gas cell with a calibrated amount of NO2/N2 gas mixture. Additionally, the method utilizes transmission signature of NO2 gas over a range of 1 nm rather than relying on transmissions at one or two wavelengths. Hence, it is not affected by undesired interferences which have broad transmissions that are much wider than 1 nm, like those originating from particles, liquid droplets, and window fouling. Also, in the used spectral region around 450 nm, there are no interferences from other common gas pollutants [4].

5 Conclusion

A new simple and low-cost spectroscopic method based on direct absorption spectroscopy is successfully applied on the broad absorption band of NO2 gas centered around 400 nm using a multimode Fabry–Perot blue diode laser. The laser transmission as a function of the injection current provides a unique signature that is utilized to positively identify and measure trace amounts of NO2 gas under standard atmospheric conditions. The laser transmission is directly measured through a calibrated NO2 gas sample and is also calculated from the measured laser spectra and NO2 absorption cross section. At six different laser temperatures, the transmission curves are measured and calculated for two Fabry–Perot blue diode lasers where the agreement between the measured and calculated absorption curves is found to be within 5%. A detection limit of 0.1 ppm can be achieved in a 40-cm absorption gas cell and, hence, atmospheric NO2 pollution can be monitored over long path lengths. For example, over a path length of 400 m, a detection limit of 0.1 ppb can be achieved.