Influence of Spatial Inhomogeneity of Detector Temporal Responses On

sensors

Article Inﬂuence of Spatial Inhomogeneity of Detector Temporal Responses on the Spectral Fidelity in Continuous Wave Cavity Ringdown Spectroscopy

Zhensong Cao 1, Zhixin Li 2,*, Fei Xu 3,4, Yongqian Wu 5, Zixin Zhou 1, Zhaomin Tong 3,4 , Weiguang Ma 3,4,* and Wenyue Zhu 1

1 Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; [email protected] (Z.C.); [email protected] (Z.Z.); [email protected] (W.Z.) 2 School of Software, Shanxi University, Taiyuan 030006, China 3 State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; [email protected] (F.X.); [email protected] (Z.T.) 4 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China 5 Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China; [email protected] * Correspondence: [email protected] (Z.L.); [email protected] (W.M.); Tel.: +86-15835110491 (Z.L.); +86-13834595365 (W.M.) Received: 5 November 2019; Accepted: 25 November 2019; Published: 28 November 2019

Abstract: Due to their advantages of having a wide bandwidth, low cost, and being easy to obtain, traditional photodetectors (PDs) are being widely applied in measurements of transient signals. The spatial inhomogeneity of such PD temporal responses was measured directly to account for the PD spatial effect of decay rate due to poor alignment in continuous wave cavity ringdown spectroscopy (CW-CRDS) experiments. Based on the measurements of three PDs (i.e., model 1611 (Newport), model 1811 (Newport), and model PDA10CF-EC (Thorlabs)), all the temporal responses followed a tendency of declining first and then rising, and steady platforms existed for the last two PDs. Moreover, as we expected, the closer the PD center was, the faster the response. On the other hand, the initial shut-off amplitude generally reached a larger value for a faster temporal response. As a result, the spatial effect can strongly influence the spectral line shape and value, which will introduce more errors into the precise measurements of spectral parameters using the CRDS technique if this effect is not considered. The defined effective detection area (EDA) of the PDs, which was close to the active area given by manufacturers, was the key parameter that should be paid more attention by researchers. Therefore, the PD should be aligned perfectly to make sure that the EDA covers the laser spot completely.

Keywords: cavity ringdown spectroscopy; spatial eﬀect; temporal response; spectral ﬁdelity

1. Introduction Molecular spectroscopy techniques, which have advantages in terms of sensitivity, resolution, and linearity, are crucial in ﬁeld applications and fundamental physical measurements. For example, the line strengths of target transitions are required for ultra-trace gas detection in the semiconductor fabrication process [1] and the isotope ratio measurement of gaseous molecules in geological surveys [2], and their accuracies must be as precise as possible. The Boltzmann constant can be determined by accurately measuring the Doppler broadening width of an absorption line based on the Doppler broadening thermometry in the ﬁeld of precise measurement [3]. Accurate values for pressure broadening and

Sensors 2019, 19, 5232; doi:10.3390/s19235232 www.mdpi.com/journal/sensors Sensors 2019, 19, 5232 2 of 12 frequency shift coefficients of the target transitions of molecular gas are necessary to get a precise measurement of gas concentration in the lower stratosphere and upper troposphere based on a light detection and ranging (LIDAR) system [4]. Therefore, the measurement of an absorption line, with high fidelity in terms of frequency resolution, spectral line shape, and absorption coefficient, is necessary. Cavity ringdown spectroscopy (CRDS) is a sensitive and quantitative absorption spectroscopy method that is based on the decay rate measurement of a laser beam trapped in a high-finesse optical cavity. Since the first demonstration by O’Keefe and Deacon in 1988 [5], CRDS has been used for highly sensitive absorption measurements of weak transitions or rarefied species in various environments and configurations [6–23]. Benefiting from the high-finesse optical cavity, the interaction length between the light and target substances can be enhanced efficiently [24,25]. Compared with other sensitive absorption techniques, CRDS has an additional advantage that the absorption is measured on an absolute scale [26]. Initially, a wavelength tunable, pulsed laser is used for the determination of the cavity medium’s absorption spectrum. Generally, the laser bandwidth exceeds the cavity mode spacing, thereby giving rise to spectral overlap between the probe laser and several cavity resonances. Such a coupling between the broadband laser and the cavity causes a multimode excitation and results in a multi-exponential decay, which means the signal-to-noise ratio (SNR) and frequency resolution of the spectral signal are quite low. The conditions under which CRDS can be used for quantitative diagnostics of molecular species were examined and determined by Zalicki and Zare [27]. Hodges et al. found that failure to account properly for the laser bandwidth would lead to systematic errors in the number of densities determined from measured ring-down signals [28]. Therefore, a high-fidelity absorption spectrum cannot be realized by use of a wideband, laser-excited CRDS. In 1996, Lehmann proposed a CRDS setup using a narrow linewidth continuous wave (CW) laser instead of pulsed lasers, which can provide single mode excitation and high SNR [29]. In order to increase the spectral fidelity of continuous wave cavity ringdown spectroscopy (CW-CRDS), a series of works were performed by Hodges’ group [30–33]. Firstly, a refined CRDS, called frequency-stabilized CRDS (FS-CRDS), was proposed by stabilizing the cavity length to a laser reference, which can produce a linear, stable, and accurate frequency axis underneath the absorption spectra. Benefiting from the superior features of the FS-CRDS, the line strength and pressure broadening and shift coefficients of the five transitions were measured with a frequency resolution of 1 MHz [30]. In order to address weaker transitions in CRDS experiments, a pair of high-reflectivity cavity mirrors are required. However, the scattering due to cavity mirror surface defects will cause a wavelength-dependent loss in the order of ppm, and more importantly, it can produce an optical frequency-dependent finesse drop, which originates from the transverse mode coupling [34–37] and spatial inhomogeneity of mirror reflectivity due to coating [38]. In 2015, a pin hole was inserted into the cavity and the transverse mode coupling was reduced effectively in a noise-immune, cavity-enhanced, optical heterodyne molecular spectroscopy (NICE-OHMS) experiment [39]. As highlighted in the previous descriptions, although efforts had been undertaken to obtain high-fidelity and high-sensitivity spectra measurements, the temporal response of a photodetector (PD) is another key parameter in the decay time measurement of CRDS that had not been considered. Until now, multiple types of detectors [40], such as photon multiplier tubes (PMT) and avalanche PDs, have been provided commercially and used to detect weak light with sub-ns response times, which makes them perfectly matched for use in CRDS. Besides these types of photodetectors, traditional PDs are also good options for temporal measurements due to their advantages of have a wide response bandwidth, being low cost, and readily available. For such a PD with a given bandwidth, the rising time from 10% to 90% of the amplitude can be calculated as tr = 0.35/BW according to the rule of thumb, where BW is the bandwidth. As we know, the response time of a PD is limited by the capacitance of a p–n junction. In general, the larger the junction area means the larger the capacitance. A diameter smaller than 0.5 mm is required for a bandwidth in the order of 100 MHz. If such a detector is used in the related measurements, the Sensors 2019, 19, 5232 3 of 12 spatial effect of the PD temporal response should be evaluated systemically and a result should be given for the selection and alignment of a special PD. In this paper, the spatial effects of three PDs with different temporal responses are measured and evaluated, and then the PD spatial effects of the absorption spectrum in CW-CRDS experiments are measured. According to the measured results, we know that the highest detection efficiency and response bandwidth of PD can be guaranteed only in the effective detection area (EDA), which is slightly smaller than the area given by the datasheet. Outside of this range, the response characteristics decline, as moving away from the center position of the PD. On the other hand, neglecting the PD spatial effect leads to underestimations of intracavity loss in the CW-CRDS experiment. Therefore, for reliable and stable trace gas detection with CW-CRDS, one should make sure that the laser beam is aimed at the EDA of the PD and that the spot size is focused properly to match the size of this area.

2. Two-Dimensional Response Characteristics of Three Different PDs In order to clearly understand the spatial effects of PD temporal responses, a series of measurements for three different detectors (i.e., models 1611 and 1811 from Newport Corporation and model PDA10CF-EC from Thorlabs) were performed. The parameters given by the manufacturers for the three PDs are shown in Table1. Note that the DC output is evaluated for model 1611, the bandwidth of which is mainly limited by electronics.

Table 1. Detailed information of three diﬀerent photodetectors (PDs) employed in experiments.

Bandwidth Rising time Type of PD Manufacturer PD Diameter Window (BW) (0.35/BW) 1611(DC output) Newport 0.02 MHz 17.5 µs 0.1 mm Ball lens (d = 1.5mm) 1811 Newport 125 MHz 2.8 ns 0.3 mm ﬂat PDA10CF-EC Thorlabs 150 MHz 2.3 ns 0.5 mm ﬂat

The experimental system was based on a commercial erbium-doped fiber laser (Koheras Adjustik E15 PztS PM, NKT Photonics, Birkerød, Denmark) with a free running linewidth of 1 kHz (over 120 µs integration time) and a wavelength tuning range from 1530.8 nm to 1531.6 nm through temperature control. Firstly, we guided this laser emission passing through the fiber pigtailed acousto-optic modulator (AOM) (MT110-IIR20-Fio- PM0.5-J1-A, AA Opto Electronic, Orsay, France) with an announced rising–falling response time of 20 ns and its first-order diffraction emitted. The AOM was driven by a power-amplified voltage controlled oscillator (VCO) (MODA110-B51k-34, AA Opto-Electronic, Orsay, France), which was controlled by an integrated digital transistor transistor logic (TTL) radio frequency (RF) source to switch the laser beam on or off. In these measurements, the VCO was controlled by a 200 Hz square wave with an amplitude of 2 V. A spatially variable neutral density filter was used to control the laser power to desaturate the PD. Continuously, the laser beam was focused to a spot with a diameter of about 57 µm by a convex lens (f = 30 mm), which was measured by using a beam profiler (BP109-IR, Thorlabs, Newton, NJ, United States). In order to avoid the feedback interference, the optical devices were all tilted slightly away from the normal incidence. The PD mounted on a high-precision, three-dimensional translation stage was located at the focal point and the laser power was controlled to be about 0.4 mW. After each fixation of the position in the horizontal direction, the PD was moved from up to down with a fixed step. The data of transients were collected by a 200 MHz oscilloscope (TDS2024C, Tektronix, Shanghai, China) with a 2 GHz sampling rate. A series of transients of beam interruption were collected when the PD was located at different positions, or in other words, when the light spot impinged on different parts of the PD. The measured transients in three typical positions of three detectors (i.e., Figure1a–c for the DC output of model 1611, Figure1d–f for model 1811, and Figure1g–i for model PDA10CF-EC) are shown in Figure1. Among the figures, the data from Figure1a–i correspond to PD positions 1 to 9 in Figure2, and the sampling step is 100 µm for each detector. The red curves show the corresponding single exponential Sensors 2019, 19, 5232 4 of 12

Sensors 2019, 19, x FOR PEER REVIEW 4 of 12 fitting and the fitted decay times are shown as τ. The data curves in Figure1a–c are thicker because therethicker are no because averages. there The are transientsno averages. in theseThe transients panels give in these the decay panels times give in the the decay order times of µ sin due the to theorder slow responseof s due ofto the slow DC output response of of model the DC 1611. output For of Figure model1d,e,g, 1611. the For transients Figure 1d,e are and composed Figure 1g, of an initialthe transients quick interruption are composed and of an then initial a slow quick varied interruption tail. The and starting then a amplitude slow varied of tail. the The tail increasesstarting as theamplitude PD moves of the away. tail increases It is worth as the emphasizing PD moves away. that It the is worth initial emphasizing shut-off amplitude that the initial increases shut to‐off its maximum,amplitude but increases a relatively to its long maximum, decay tail but still a exists relatively in Figure long1 decayd,e for tail model still 1811.exists However, in Figure the1d,e initial for shut-omodelff amplitude 1811. However, barely the increases, initial shut but‐off the amplitude decay time barely decreases increases, to 7.16 but the ns indecay Figure time1e,f, decreases where theto initial7.16 shut-o ns in Figureff amplitude 1e,f, where is defined the initial as the shut amplitude‐off amplitude of the is detector defined as signal the amplitude at the shut-o of theff time. detector Such behaviorsignal confirmsat the shut the‐off fact time. that Such part behavior of the laser confirms beam the hits fact the that PD part active of area,the laser and beam the other hits partthe PD hits theactive outer area, range and in Figurethe other1d,e part and hits all the the outer light range incidents in Figure on the 1d,e active and area all the in Figurelight incidents1f. The formeron the contributesactive area the in voltage Figure amplitude1f. The former and contributes quick interruption the voltage to theamplitude signal due and to quick the higherinterruption photoelectric to the signal due to the higher photoelectric transformation efficiency and fast response, and the latter transformation efficiency and fast response, and the latter contributes the slow varied tail due to its contributes the slow varied tail due to its opposite performance. For the other two detectors, as the opposite performance. For the other two detectors, as the decay time shortens, the initial shut-off decay time shortens, the initial shut‐off amplitude increases. Generally, the experimental amplitude increases. Generally, the experimental measurement of the transient is a convolution over measurement of the transient is a convolution over the response time of the PD and the time delay of the response time of the PD and the time delay of the cutoff process. The decay of the tail qualitatively the cutoff process. The decay of the tail qualitatively represents the time response characteristic of representsPD, since the the time shut response‐off time characteristic of AOM is fairly of PD, quick since at thearound shut-o 20ff ns,time as ofgiven AOM by is the fairly datasheet. quick at aroundAlthough 20 ns, the as givenmeasured by the decay datasheet. times of Although transient responses the measured in Figure decay 1f, times Figure of transient1h, and Figure responses 1i are in Figure7.161 f,h,ins, 6.47 are ns, 7.16 and ns, 6.15 6.47 ns, ns, respectively, and 6.15 ns, respectively,the shut‐off times the shut-o taken fffromtimes 90% taken to 10% from of 90% the detector to 10% of theamplitudes detector amplitudes are all close are to all 20 closens. to 20 ns.

Figure 1. The transients in three typical positions of three detectors: (a–c) model 1611, (d–f) model Figure 1. The transients in three typical positions of three detectors: (a–c) model 1611, (d–f) model 1811, (g–i) model PDA10CF-EC. (a–i) The data correspond to the PD positions 1 to 9 in Figure2. 1811, (g–i) model PDA10CF‐EC. (a–i) The data correspond to the PD positions 1 to 9 in Figure 2. Figure 2 displays the two‐dimensional contour plot of initial shut‐off amplitudes (left column) and temporal responses (right column) as functions of vertical and horizontal positions of three different PDs, namely model 1611 (Newport), model 1811 (Newport), and model PDA10CF‐EC

Sensors 2019, 19, x FOR PEER REVIEW 5 of 12

(Thorlabs) from the upper to the lower rows, respectively. The units for color scales on the right side of the columns are voltage and seconds, respectively. In these panels, the data were acquired when Sensorsthe detectors2019, 19, 5232 were located at a serials of horizontal (x) and vertical (y) coordinates with a fixed5 of step. 12 The steps for the last two detectors were 50 μm and for the first detector it was 100 μm.

FigureFigure 2. 2.The The two-dimensional two‐dimensional contour contour plot plot of of initial initial shut-o shut‐offff amplitudesamplitudes and temporal responses responses as asfunctions functions of of vertical vertical and and horizontal horizontal positions positions of of three three different different PDs. PDs. Panels Panels (a), (a ),(c) ( cand) and (e ()e show) show the theinitial initial shut shut-o‐off ffamplitudesamplitudes for for the detectors ofof modelsmodels 1611 1611 (Newport), (Newport), 1811 1811 (Newport), (Newport), and and PDA10CF-ECPDA10CF‐EC (Thorlabs), (Thorlabs), respectively, respectively, and Panelsand Panels (b), (d )( andb), ((fd)) show and their(f) show corresponding their corresponding ringdown times.ringdown The numbers times. The 1 to numbers 9 represent 1 to the 9 represent measurement the measurement positions of Figure positions1a–i. of Figure 1a to Figure 1i.

FigureThe 2settings displays for the color two-dimensional scales and axis contour ranges plot for ofmodel initial 1611 shut-o areff differentamplitudes from (left those column) of models and temporal1811 and responses PDA10CF (right‐EC, column)while the as latter functions two are of vertical manually and set horizontal to the same positions settings. of threeFor model different 1611 PDs,(Figure namely 2a,b), model both 1611 responses (Newport), are modellower 1811compared (Newport), to the and other model two PDA10CF-EC PDs, since its (Thorlabs) DC bandwidth from theoutput upper is to only the lower20 kHz. rows, The respectively. closer the detector The units center for coloris, the scales faster on the the response right side will of be. the Moreover, columns are the voltageshortest and temporal seconds, response respectively. is larger In these than panels,3 μs, which the data indicates were acquiredthat this whendetector the could detectors cause were large locatederror atwhen a serials measuring of horizontal time decay (x) and signals vertical with (y) coordinatestime constants with of a fixedseveral step. μs. The The steps calculated for the rising last twotime detectors is 17.5 μ weres according 50 µm and to the for theprevious first detector empirical it was formula, 100 µ m.which is around six times longer than theThe shortest settings measured for color value. scales Although and axis ranges the PD for diameter model 1611 is around are diff erent100 μ fromm, there those is of still models signal 1811amplitude and PDA10CF-EC, when the beam while is the500 μ latterm away two arefrom manually the center set due to theto the same ball settings. lens having For modela diameter 1611 of (Figure2a,b), both responses are lower compared to the other two PDs, since its DC bandwidth output is only 20 kHz. The closer the detector center is, the faster the response will be. Moreover, the shortest temporal response is larger than 3 µs, which indicates that this detector could cause large error when Sensors 2019, 19, 5232 6 of 12 measuring time decay signals with time constants of several µs. The calculated rising time is 17.5 µs according to the previous empirical formula, which is around six times longer than the shortest measured value. Although the PD diameter is around 100 µm, there is still signal amplitude when the beam is 500 µm away from the center due to the ball lens having a diameter of 1.5 mm. However, for models 1811 and PDA10CF-EC, the calculated rising times are 2.8 ns and 2.3 ns, which are close to, but smaller than, the shortest measured temporal responses of 7.16 ns and 6.15 ns in Figure2d,f, respectively. The reason for the larger measured values is due to the relatively slow response of AOM. As can be seen from Figure2c,d, the measured initial shut-o ff amplitude shows a platform and a relatively steep edge for model 1811, however the contour lines for the temporal responses show square shapes in the detector’s outer range and circular shapes around the center. The response times are faster than 1 µs in the square area and are even faster than 0.1 µs in the circular area, with a diameter of 200 µm. For model PDA10CF-EC (Figure2e,f), the initial shut-o ff amplitude increases slower than that of model 1811 when the laser spot is moved from the outside to the center of the PD. However, the response times show a sharp decrease within the circumference at about 150 µm from the center. Inside this circumference, the response times are faster than 0.1 µs. If we define the zones with response times smaller than 0.1 µs as the effective detectable areas (EDAs) of models 1811 and PDA10CF-EC, the EDAs are slightly smaller than the detectors’ officially stated active areas, which is partially explained by the remarkable size of the laser spots in both detectors.

3. PD Spatial Eﬀect in the CW-CRDS Experiment

3.1. Experimental Setup The experimental design of our CW-CRDS setup for the PD spatial effect measurement is schematically depicted in Figure3. The system was still based on the previously mentioned fiber laser, fiber pigtailed AOM, and the shut-off scheme. After the laser passed through the AOM, the light was mode-matched to the fundamental transverse electromagnetic (TEM00) mode of the cavity by lens 1, with a focal length of 50 cm. The ringdown cavity consisted of two mirrors separated by a distance of 39.4 cm, in which the input mirror was flat and the output one had a radius of curvature Rc = 1 m. This gave a free spectral range (FSR) of 380.7 MHz. The reflectivity of each mirror was 99.94%, which gave a cavity finesse of around 5200. After the mode matching calculation, the beam radius on the flat input and concave output mirrors were 0.488 mm and 0.627 mm, respectively. The piezoelectric transducer (PZT) (HPSt 150/20-15/25, Piezomechanik GmbH, Munich, Germany) mounted on the output mirror was used to dither the cavity length to increase data points in a single spectrum for CRDS experiments. The transmitted light from the cavity was focused on the PD by using lens 2, with a focal length of 30mm. Lens 2 and the PD were tilted away from normal incidence to prevent the feedback coupling. A threshold circuit, working in a monostable design based on a 555 timer, was used to turned off the RF power to the AOM when the measured output voltage of the PD exceeded the preset value. The duration of the beam interruption, set to 0.5 ms, was controlled by the resistor and capacitor included in the threshold circuit. A 10-MHz, a 12-bit data acquisition card (PCI-6115, National Instruments, Austin, TX, United States) sampled the cavity transmission (i.e., ringdown signal), which was fitted to a single exponential decay by using the Levenberg–Marquardt method. The LabVIEW program was used to record data and show the absorption spectrum. By careful alignment of the incident laser beam, the higher order transverse modes were reduced to less than 2% of the TEM00 mode. In this CW-CRDS experiment, a time delay of around 370 ns, including the response time of the threshold circuit, RF turn-off time, and the transit time of the acoustic wave traveling through the laser spot in the crystal, existed between the trigger signal to the AOM driver and the generation of the ringdown event. This delay results in amplitude variation of the ringdown event in the starting time, since the laser cutoff optical frequency is varied during this delay time, which does not seriously affect the intrinsic characteristics of the decay. According to Sensors 2019, 19, x FOR PEER REVIEW 6 of 12

1.5 mm. However, for models 1811 and PDA10CF‐EC, the calculated rising times are 2.8 ns and 2.3 ns, which are close to, but smaller than, the shortest measured temporal responses of 7.16 ns and 6.15 ns in Figure 2d,f, respectively. The reason for the larger measured values is due to the relatively slow response of AOM. As can be seen from Figure 2c,d, the measured initial shut‐off amplitude shows a platform and a relatively steep edge for model 1811, however the contour lines for the temporal responses show square shapes in the detector’s outer range and circular shapes around the center. The response times are faster than 1 μs in the square area and are even faster than 0.1 μs in the circular area, with a diameter of 200 μm. For model PDA10CF‐EC (Figure 2e,f), the initial shut‐off amplitude increases slower than that of model 1811 when the laser spot is moved from the outside to the center of the PD. However, the response times show a sharp decrease within the circumference at about 150 μm from the center. Inside this circumference, the response times are faster than 0.1 μs. If we define the zones with response times smaller than 0.1 μs as the effective detectable areas (EDAs) of models 1811 and PDA10CF‐EC, the EDAs are slightly smaller than the detectors’ officially stated active areas, which is partially explained by the remarkable size of the Sensorslaser2019 spots, 19, in 5232 both detectors. 7 of 12

3. PD Spatial Effect in the CW‐CRDS Experiment Figure1i, the measured shut-o ﬀ time for the laser power was less than 6.15 ns, which can be neglected if compared3.1. Experimental to the Setup ringdown time in the order of µs.

FigureFigure 3. Setup3. Setup designed designed for continuous for continuous wave cavitywave ringdown cavity ringdown spectroscopy spectroscopy (CW-CRDS) (CW experiments.‐CRDS) Note:experiments. AOM = acoustic-optic Note: AOM modulator;= acoustic‐ DAQoptic =modulator;data acquisition DAQ card;= data PD acquisition= photodetector. card; PD = photodetector. 3.2. Observation of the Spatial Effect in the CRDS Measurement The experimental design of our CW‐CRDS setup for the PD spatial effect measurement is In order to investigate the dependence of ringdown time on the spatial position of PD, a series of schematically depicted in Figure 3. The system was still based on the previously mentioned fiber measurements were performed. The incident laser power to the cavity was about 2.5 mW, and the laser, fiber pigtailed AOM, and the shut‐off scheme. After the laser passed through the AOM, the preset value of the threshold circuit was set to around 2 V for generation of ringdown events. During light was mode‐matched to the fundamental transverse electromagnetic (TEM00) mode of the cavity the experiments, the PD was assembled on a three-dimensional translation stage and moved from by lens 1, with a focal length of 50 cm. The ringdown cavity consisted of two mirrors separated by a updistance to down of in 39.4 the cm, cross-section in which the perpendicular input mirror was to the flat light and propagation the output one direction, had a radius with of a fixedcurvature step of 50 µm. The movement of the PD always ensured that the detected light signal was higher than the Rc = 1 m. This gave a free spectral range (FSR) of 380.7 MHz. The reflectivity of each mirror was preset99.94%, voltage. which In gave the horizontal a cavity finesse direction, of around the PD 5200. was After aligned the at mode the center matching position calculation, by maximizing the beam the detectedradius lighton the signal. flat input In the and following concave output experiments, mirrors a were 150 MHz 0.488 bandwidthmm and 0.627 InGaAs mm, respectively. PD (PDA10CF-EC, The Thorlabs,piezoelectric Newton, transducer NJ, United (PZT) States) (HPSt with 150/20 the manufacturer-marked‐15/25, Piezomechanik diameterGmbH, ofMunich, 0.5 mm Germany) was used. mountedTo confirm on the this output spatial mirror effect, was we used first to evaluated dither the the cavity performance length to increase of the single data points exponential in a single fitting model.spectrum Four for individual CRDS experiments. ringdown decayThe transmitted signals gathered light from during the thecavity translation was focused of the on PD the are PD shown by inusing Figure lens4, represented 2, with a focal by length solid squares, of 30mm. solid Lens circles, 2 and the solid PD triangle, were tilted and away solid from stars, normal together incidence with the single exponential fits (red line) and the residuals (the lower panel). For clarity, the measured ringdown decays are displayed every at second point. Here, the laser beam at position 1 was tightly focused on the center of the photon-sensitive area of PD. The PD centers at positions 2, 3, and 4 were away from the laser focus in the vertical direction. However, the initial shut-off amplitudes for all the positions were larger than the preset threshold value of 2 V, due to the time delay between the trigger signal and laser shutdown, since the laser frequency was continued to scan during the delay. The initial shut-off amplitude of the decay at position 4 was smaller than other events, since the temporal response at this detection position is slower than those of others, according to the later analysis. The residuals indicate that the cavity decays were accurately demonstrated by the simple, single exponential fitting model. Then, the distances between the PD and lens 2 were adjusted to 20 mm, 35 mm, and 50 mm, while the corresponding beam diameters at these distances were 490 µm, 57 µm, and 530 µm, respectively, which were measured with the previously mentioned beam profiler under the condition of laser frequency stabilization to the cavity mode via the Pound–Drever–Hall (PDH) technique. The measured ringdown times as a function of relative vertical positions are shown in Figure5a. As can be seen, the measured ringdown times at all three distances varied with the translation of the PD, following the tendency of decreasing first and then increasing. It also shows that the farther the PD deviated Sensors 2019, 19, x FOR PEER REVIEW 7 of 12 to prevent the feedback coupling. A threshold circuit, working in a monostable design based on a 555 timer, was used to turned off the RF power to the AOM when the measured output voltage of the PD exceeded the preset value. The duration of the beam interruption, set to 0.5 ms, was controlled by the resistor and capacitor included in the threshold circuit. A 10‐MHz, a 12‐bit data acquisition card (PCI‐6115, National Instruments, Austin, TX, United States) sampled the cavity transmission (i.e., ringdown signal), which was fitted to a single exponential decay by using the Levenberg–Marquardt method. The LabVIEW program was used to record data and show the absorption spectrum. By careful alignment of the incident laser beam, the higher order transverse modes were reduced to less than 2% of the TEM00 mode. In this CW‐CRDS experiment, a time delay of around 370 ns, including the response time of the threshold circuit, RF turn‐off time, and the transit time of the acoustic wave traveling through the laser spot in the crystal, existed between the trigger signal to the AOM driver and the generation of the ringdown event. This delay results in amplitude variation of the ringdown event in the starting time, since the laser cutoff optical frequency is varied during this delay time, which does not seriously affect the intrinsic characteristics of the decay. According to Figure 1i, the measured shut‐off time for the laser power was less than 6.15 ns, which can be neglected if compared to the ringdown time in the order of μs.

3.2.Sensors Observation2019, 19, 5232 of the Spatial Effect in the CRDS Measurement 8 of 12 SensorsIn 2019order, 19 to, x FORinvestigate PEER REVIEW the dependence of ringdown time on the spatial position of PD, a series8 of 12 offrom measurements the laser beam, were the performed. larger the The ringdown incident time laser was. power Moreover, to the cavity even if was the about laser injection 2.5 mW, positionand the and 4 were away from the laser focus in the vertical direction. However, the initial shut‐off preseton the value PD surface of the wasthreshold identical, circuit diff waserent set ringdown to around times 2 V for were generation observed of at ringdown different events. distances During from amplitudes for all the positions were larger than the preset threshold value of 2 V, due to the time thelens experiments, 2. Differing from the PD the was results assembled at 20 mm on and a three 50 mm,‐dimensional the ringdown translation time profile stage at and 35 mm moved exhibited from delay between the trigger signal and laser shutdown, since the laser frequency was continued to upa steady to down platform in the cross (an average‐section ofperpendicular 2.12 µs) in the to the range light of propagation about 400–800 direction,µm, which with was a fixed very step close of scan during the delay. The initial shut‐off amplitude of the decay at position 4 was smaller than 50to μ them. theoretical The movement empty of cavity the PD ringdown always ensured time of 2.19that µthes. Indetected these measurements, light signal was the higher uncertainty than the of other events, since the temporal response at this detection position is slower than those of others, presetthe ringdown voltage. time In the was horizontal in the order direction, of tens the of ns.PD Figurewas aligned5b presents at the the center PD-detected position by initial maximizing shut-o ff according to the later analysis. The residuals indicate that the cavity decays were accurately theamplitudes detected at light those signal. three distances.In the following As with theexperiments, ringdown a time 150 measurements MHz bandwidth at the InGaAs distance PD of demonstrated by the simple, single exponential fitting model. (PDA10CF35 mm, the‐ amplitudeEC, Thorlabs, profile Newton, also exhibited NJ, United a constant States) valuewith the in a manufacturer certain range.‐marked The dark diameter shapes shown of 0.5 Then, the distances between the PD and lens 2 were adjusted to 20 mm, 35 mm, and 50 mm, mmin two was panels used. indicate the PD-sensitive area range. while the corresponding beam diameters at these distances were 490 μm, 57 μm, and 530 μm, respectively, which were measured with the previously mentioned beam profiler under the condition of laser frequency stabilization to the cavity mode via the Pound–Drever–Hall (PDH) technique. The measured ringdown times as a function of relative vertical positions are shown in Figure 5a. As can be seen, the measured ringdown times at all three distances varied with the translation of the PD, following the tendency of decreasing first and then increasing. It also shows that the farther the PD deviated from the laser beam, the larger the ringdown time was. Moreover, even if the laser injection position on the PD surface was identical, different ringdown times were observed at different distances from lens 2. Differing from the results at 20 mm and 50 mm, the ringdown time profile at 35 mm exhibited a steady platform (an average of 2.12 μs) in the range of about 400–800 μm, which was very close to the theoretical empty cavity ringdown time of 2.19 μs. In these measurements, the uncertainty of the ringdown time was in the order of tens of ns. Figure 5b presents the PD‐detected initial shut‐off amplitudes at those three distances. As with the ringdown time measurements at the distance of 35 mm, the amplitude profile also exhibited a constantFigureFigure value 4. AA group groupin a certain of of gathered gathered range. cavity cavity The decay decaydark signalsshapes signals when whenshown the the in laser laser two focus focus panels of of the the indicate PD was the located PD‐sensitive in areadifferentdi range.fferent positions. The The red red curve curve on on the the top top of of each each decay decay signal signal shows shows the the single single exponential exponential fitting fitting andand the the residual is shown in the lower panel.

To confirm this spatial effect, we first evaluated the performance of the single exponential fitting model. Four individual ringdown decay signals gathered during the translation of the PD are shown in Figure 4, represented by solid squares, solid circles, solid triangle, and solid stars, together with the single exponential fits (red line) and the residuals (the lower panel). For clarity, the measured ringdown decays are displayed every at second point. Here, the laser beam at position 1 was tightly focused on the center of the photon‐sensitive area of PD. The PD centers at positions 2, 3,

FigureFigure 5. 5.Measurements Measurements of (ofa) ringdown(a) ringdown time time and (andb) initial (b) initial shut-o ffshutamplitude‐off amplitude as a function as a function of relative of verticalrelative PD vertical position PD when position the PD when was the located PD was behind located lens behind 2 at a distance lens 2 at of a 20 distance mm, 35 of mm, 20 andmm, 50 35 mm. mm, and 50 mm. 3.3. Analysis of the Spatial Effect 3.3. FigureAnalysis6 shows of the Spatial the measured Effect ringdown time or response times in Figure6a and initial shut-o ff amplitudesFigure in 6 Figure shows6 bthe for measured CRDS (solid ringdown square) time and PDor response (solid circle), times respectively. in Figure 6a The and data initial for shut CRDS‐off isamplitudes shown by thein Figure red solid 6b circlefor CRDS in Figure (solid5. square) The data and for PD CRDS (solid show circle), a small respectively. right shift The in abscissa data for andCRDS a slightly is shown wider by platformthe red solid range circle than in those Figure for 5. PD The because data for of CRDS the positioning show a small error right of the shift two in measurements.abscissa and a slightly The dark wider shapes platform shown range in the than two those panels for indicate PD because the sensitive of the positioning area range. error It can of bethe seentwo frommeasurements. Figure6a that The the dark measured shapes responseshown in time the oftwo the panels PD and indicate the ringdown the sensitive time show area similarrange. It behaviorscan be seen over from the Figure relative 6a vertical that the position measured (i.e., response there is atime range of the of relative PD and positions the ringdown for which time bothshow thesimilar PD response behaviors time over and the the relative ringdown vertical time position are at their (i.e., minimums,there is a range and whenof relative the laser positions beam for is movedwhich outboth of the this PD range, response both responsestime and the get ringdown worse with time further are distanceat their minimums, from the center and ofwhen the detector the laser area).beam Moreover, is moved theout ringdown of this range, time both and theresponses PD response get worse time havewith almostfurther similar distance dependences from the center on the of the detector area). Moreover, the ringdown time and the PD response time have almost similar dependences on the distance from the detector center, which gives indirect evidence that the

Sensors 2019, 19, 5232 9 of 12 Sensors 2019, 19, x FOR PEER REVIEW 9 of 12 variationdistance fromof ringdown the detector time center, (Figure which 5) was gives caused indirect by the evidence PD response. that the Therefore, variation the of ringdown time measurements(Figure5) was caused are affected by the by PD both response. the temporal Therefore, response the ringdown of the PD time and measurements the true value are of atheffected photon by lifetime.both the temporalIn addition, response as can of be the seen PD andfrom the Figure true value 6b, the of theinitial photon shut lifetime.‐off amplitudes In addition, are asnot can only be affectedseen from by Figure the cavity,6b, the but initial also shut-oby the ffPDamplitudes response. All are of not this only shows affected that by the the measured cavity, but decay also time by the is thePD true response. cavity All ringdown of this shows time when that the the measured light impinges decay timeupon is the the PD true at cavitya position ringdown at which time the when PD responsethe light impingesis sufficiently upon fast. the PDWhen at a the position response at which functions the PD of responsethe cavity is and suffi theciently PD fast.are on When similar the timeresponse scales, functions the resulted of the ringdown cavity and time the measurements PD are on similar will timebe strongly scales, theinfluenced resulted by ringdown PD response. time Allmeasurements of this indicates will be that strongly it is important influenced to by focus PD response.the light well All of on this the indicates central part that itof is the important depletion to regionfocus the of the light p–n well junction on the of central the PD. part of the depletion region of the p–n junction of the PD.

Figure 6. The The measured measured response response times times (a )( anda) and initial initial shut-o shutﬀ amplitudes‐off amplitudes (b) as ( ab function) as a function of relative of relativevertical vertical position position for CRDS for (solid CRDS squares) (solid squares) and PD (solidand PD circles), (solid respectively.circles), respectively.

3.4. Influences on Trace Gas Detection 3.4. Influences on Trace Gas Detection In order to evaluate the influences of this spatial effect on the spectral line shape measurement, the 1 P(10)e rotational transition of the ν1+ν3 overtone band of C2H2 at the wavenumber of 6531.7805 cm− was analyzed [41]. In order to obtain a spectral signal, the laser frequency was tuned by a triangular wave at a frequency of 0.1 Hz, with an optical tuning range of 2 GHz. Meanwhile, in order to improve the spectral resolution, the cavity length was dithered at a frequency of 10 Hz, and an amplitude of cavity mode shift of around 400 MHz was applied to ensure a cavity mode in the dithering range. Another cavity with a length of 40 cm and a finesse of 300 was used to calibrate the spectral signal. The cavity was filled with the 507 ppm C2H2 gas balanced with nitrogen and the total sample pressure was controlled to be about 1.88 mbar. Figure7a shows the measured absorption profiles expressed in ringdown times at different vertical positions when the detector was located at a distance of 35 mm from lens 2. In these measurements, the PDA10CF-EC detector from Thorlabs was used and the uncertainty of the individual ringdown time was in the order of tens of ns. The initial position (0 µm) was adjusted Figure 7. Measured absorption lines of C2H2 gas at the wavenumber of 6531.7805 cm−1. The cavity to ensure perfect alignment and coverage of the light spot. The distances of 240 µm, 280 µm, and 320 was filled with the 507 ppm C2H2 gas balanced with nitrogen and the total sample pressure was µm were implemented by moving the PD away from the initial position as was previously done in the controlled to be about 1.88 mbar: (a) ringdown times; (b) absorption coefficients. translation. According to the beam focus size of 57 µm and the detector active area diameter of 500 µm, thereIn should order notto evaluate have been the any influences signal whenof this the spatial beam effect position on the was spectral 257 µm line away shape from measurement, the detector thecenter. P(10)e However, rotational according transition to Figure of 6b,the the ν initial1+ν3 overtone shut-o ff valuesband stillof C had2H2 a at certain the amplitude,wavenumber which of 6531.7805means the cm 1/e− laser1 was power analyzed outside [41]. the In beamorder focusto obtain size a played spectral a role signal, in this the situation. laser frequency As can bewas seen, tuned the byresults a triangular at different wave positions at a frequency have a similar of 0.1 Hz, profile with and an optical the profile tuning depths range at theof 2 line GHz. center Meanwhile, are almost in orderthe same. to improve However, the thespectral profiles resolution, have diff theerent cavity offsets. length By adoptingwas dithered the ringdownat a frequency times of of 10 an Hz, empty and ancavity amplitude (i.e., 2.12 ofµ cavitys, 2.22 modeµs, 2.45 shiftµs, of and around 2.84 µ s,400 respectively) MHz was applied for the four to ensure different a cavity detected mode positions, in the the absorption coefficient α (in cm 1) can be calculated based on the formula α = (1/τ 1/τ )/c, dithering range. Another cavity with− a length of 40 cm and a finesse of 300 was used to calibrate− 0 the τ τ spectralwhere c signal. is the lightThe cavity speed, was and filledand with0 arethe 507 the ringdownppm C2H2 gas times balanced with absorption with nitrogen inside and the the cavity total sampleand an emptypressure cavity, was respectively.controlled to Thebe about converted 1.88 mbar. absorption Figure profiles 7a shows are shownthe measured in Figure absorption7b. As is profilesshown, expressed the peak absorption in ringdown coe timesfficients at different of the profiles vertical are positions different, when which the is detector caused was by the located almost at aequal distance dip depthof 35 mm and from different lens o2.ff setsIn these in ringdown measurements, time profiles. the PDA10CF Considering‐EC detector the Voigt from broadening Thorlabs scheme, the calculated peak absorption coefficient of this transition is 5.47 10 6 cm 1, by adopting was used and the uncertainty of the individual ringdown time was in the× order− of −tens of ns. The initial position (0 μm) was adjusted to ensure perfect alignment and coverage of the light spot. The distances of 240 μm, 280 μm, and 320 μm were implemented by moving the PD away from the initial

Sensors 2019, 19, x FOR PEER REVIEW 9 of 12

variation of ringdown time (Figure 5) was caused by the PD response. Therefore, the ringdown time measurements are affected by both the temporal response of the PD and the true value of the photon lifetime. In addition, as can be seen from Figure 6b, the initial shut‐off amplitudes are not only affected by the cavity, but also by the PD response. All of this shows that the measured decay time is the true cavity ringdown time when the light impinges upon the PD at a position at which the PD response is sufficiently fast. When the response functions of the cavity and the PD are on similar time scales, the resulted ringdown time measurements will be strongly influenced by PD response. All of this indicates that it is important to focus the light well on the central part of the depletion region of the p–n junction of the PD.

Sensors 2019, 19, 5232 10 of 12 the line strength of 4.0 10 21 cm 1/(molecule cm 2) from the high-resolution transmission molecular × − − · − absorption (HITRAN) database, which has a stated uncertainty of 1%–2% [41]. The peak absorption coefficient of the profile at the position of 0 µm was 5.54 10 6 cm 1, which was very close to the × − − theoretical calculation. The relative error of 1% was mainly induced by the inaccurate concentration of C H gas, the imprecise control of gas pressure, and the relative uncertainty of the line strength. 2 Figure2 6. The measured response times (a) and initial shut‐off amplitudes (b) as a function of We can infer that the larger ringdown times obtained when the light spot did not impinge on the EDA relative vertical position for CRDS (solid squares) and PD (solid circles), respectively. of the PD was not the true value of the cavity decay rate. Consequently, the spatial effect will lead to inaccurate3.4. Influences estimations on Trace ofGas intracavity Detection loss and gas absorption when the PD is not aligned perfectly.

1 −1 FigureFigure 7. 7.Measured Measured absorption absorption lines lines of Cof2H C22Hgas2 gas at the at wavenumberthe wavenumber of 6531.7805 of 6531.7805 cm− .cm The. cavity The cavity was ﬁlledwas withfilled the with 507 the ppm 507 C 2ppmH2 gas C2 balancedH2 gas balanced with nitrogen with andnitrogen the total and sample the total pressure sample was pressure controlled was tocontrolled be about 1.88to be mbar: about ( a1.88) ringdown mbar: (a) times; ringdown (b) absorption times; (b) coeabsorptionﬃcients. coefficients.

4. ConclusionsIn order to evaluate the influences of this spatial effect on the spectral line shape measurement, the AlthoughP(10)e rotational multiple typestransition of fast-response of the ν1+ detectorsν3 overtone are available band of for C the2H2 measurement at the wavenumber of transient of signals,6531.7805 such cm as−1 cavitywas analyzed ringdown [41]. decay In order signals, to obtain traditional a spectral PDs are signal, also goodthe laser options frequency for the was temporal tuned timeby a measurement triangular wave due at toa frequency their advantages of 0.1 Hz, of with having an aoptical wide responsetuning range bandwidth, of 2 GHz. being Meanwhile, low cost, in andorder easy to toimprove obtain. the The spectral inhomogeneous resolution, temporalthe cavity and length initial was amplitude dithered at responses a frequency of di offf erent10 Hz, PDs and werean amplitude studied in of this cavity work, mode which shift caused of around a detector 400 MHz spatial was eff ectapplied in the to CW-CRDS ensure a cavity experiments. mode in The the spatialdithering effect range. can strongly Another influence cavity with the a spectral length of line 40 shape cm and and a amplitude,finesse of 300 which was willused introduce to calibrate more the errorsspectral into signal. precise The measurements cavity was filled of spectral with the parameters 507 ppm when C2H2 gas using balanced CRDS technique with nitrogen if the and effect the is total not considered.sample pressure Therefore, was tocontrolled obtain reliable to be about and stable 1.88 measurementsmbar. Figure 7a in shows CW-CRDS the measured experiments, absorption the PD shouldprofiles be expressed aligned perfectly, in ringdown making times sure at thatdifferent the laser vertical beam positions is focused when properly the detector to match was the located size of at thea distance EDA of theof 35 PD. mm The from CRDS lens experimentalists 2. In these measurements, must pay attention the PDA10CF to this e‐ffECect, detector and one from should Thorlabs check thewas response used and characteristic the uncertainty of the of PD the before individual CRDS experiments.ringdown time The was research in the into order the of spatial tens of eff ns.ects The of ringdowninitial position event detection(0 μm) was will adjusted help to to precisely ensure evaluateperfect alignment the reflectivity and coverage of super mirrors of the light and tracespot. gasThe concentrations,distances of 240 and μm, will 280 also μm, serve and 320 as an μm alert were for implemented CRDS experimentalists. by moving the PD away from the initial

Author Contributions: Conceptualization, W.M. and Z.C.; methodology, Z.L.; formal analysis, Z.C., Z.L., Y.W., and W.M.; data curation, F.X. and Z.Z.; writing—original draft preparation, Z.L. and Z.C.; writing—review and editing, W.M., Y.W. and Z.T.; project administration, W.M.; funding acquisition, W.Z. and Z.T. Funding: This research was funded by the National Key R&D Program of China, grant number 2016YFB0401903; Open Research fund of Key Laboratory of Atmospheric Optics, Chinese Academy of Sciences, grant number JJ-2018-02; the Shanxi Scholarship Council of China, grant number 2017-016; and the National Natural Science Foundation of China, grant numbers 61675122, 61875107, 61905134, and 11704236. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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