1. Introduction

Online determination of substances in industrial processing liquids can facilitate continuous processing, enable real-time information flow, save power energy, and improve material use, which are high on the list of priorities of industrial manufacture requiring concentration measurements and process control. Thanks to well-developed techniques and inexpensive devices, optical and ultrasound measurements have been successfully applied to these tasks. However, optical techniques usually measure optical parameters (absorption, scattering, or refractive index) and ultrasound determines acoustic speed or attenuation. Moreover, simultaneous monitoring of both optical and acoustic properties necessitates two or more sensing systems [1–7]. Naturally, the more parameters a technique can measure, the more information it reveals of the studied material. To that end, a hybrid technique was developed utilizing a single optical, electrical, and ultrasonic sensor to measure optical intensity, electrical impedance, and ultrasonic speed in order to determine ingredient concentrations in liquids [8]. This sensor comprises a pair of optical devices, a pair of electrodes, and a pair of ultrasonic devices.

We have previously proposed a hybrid technique utilizing a pair of laser-detectors to determine optical parameters and acoustic attenuation in turbid suspensions. This technique has been successfully applied to the measurement of fiber and fines consistencies in paper pulp [9–11]. In this study, we explore a new hybrid technique based on time-resolved photoacoustics (TR-PA), capable of measuring simultaneously the optical, acoustic, and thermal-acoustic transformation properties of an absorbing liquid. It is well known that the photoacoustic (PA) effect [12] is the phenomenon of acoustic wave generation by a pulsed laser or a modulated light source. When a pulsed laser irradiates an absorbing material, the optical energy of the laser is absorbed by the absorbing material, where it transforms into heat energy, causing a thermal expansion of the illuminated region. Owing to inertial effects within the material, this type of modulated thermal expansion causes the illuminated region to extend and compress. As a result of this action, an acoustic wave is generated. The thus produced PA wave propagates out from the generation region (PA source) and can subsequently be detected by an ultrasonic transducer. Hence, there are three processes from PA generation to detection: optical energy absorption, thermal expansion, and acoustic propagation. With its custom-tailored design, our new apparatus, consisting only of a laser-detector pair, has the ability to simultaneously measure the optical absorption coefficient, thermal-acoustic transformation coefficient, and acoustic speed in an absorbing liquid. To the authors’ knowledge, no other publication exists that describes the simultaneous measurement of these three parameters.

The developed technique is particularly suitable for online measurement of constituent concentrations in liquid mixtures, as the three physical parameters (optical absorption, acoustic speed, and thermal-acoustic transformation) can be quickly and simultaneously determined by analyzing recorded time-resolved PA signals. No doubt, this technique will prove very useful for the chemical, food, and paper industries, as well as for environmental protection. For instance, it could be used in the pulping industry to determine lignin, sugar, and dissolved alkaline contents in cooking liquids. It may also be applied by the offshore oil industry to measure concentrations of dissolved oil, salts, and oil field chemicals in water.

2. Theoretical Aspects

When a pulsed laser beam irradiates a homogeneously absorbing medium, as shown in Fig. 1(a), the optical energy is absorbed in the illuminated region of the medium and then transformed into heat in the thermal de-exciting mechanism [12]. Transient heat, produced by thermal expansion of the heated volume, will generate an initial stress. Since thermal diffusion from the heated volume can be ignored during nano- or microsecond laser pulses, the initial stress distribution equals that of the absorbed optical energy fulfilling the stress confinement condition [13]. This stress is relaxed by generating an outward propagating acoustic wave. If the light beam diameter $w$ is much larger than the optical penetration depth $d$ (i.e., the thickness of the heated volume) in the absorbing medium, the PA source (i.e., the heated volume) is planar and the PA wave propagates along the depth direction of the medium. The acoustic pressure at the depth of $z_0$ can be described by

 

Fig. 1. Principle of time-resolved photoacoustic measurement: (a) radiation and detection, (b) measurands of received signals.

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Figure 1(b) shows a typical signal recorded by a wideband ultrasonic detector used to receive acoustic waves at depth $z_0$. This signal can be described as $S(t)=kRp(t)$, where $k$ is a system constant and $R$ is a function of detector response. Substituting Eq. (1) and doing the logarithm, the formula takes the form

In general, the detector response $R$ is a function of acoustic frequency. In the case of PA generation of a planar source, the center frequency of the generated PA wave can be calculated as $f_{\mathrm{ac}}\approx v/(2d)=\alpha v/2$ for an absorbing medium fulfilling the stress confinement condition [14]. The detector response can therefore be written as $R(\alpha )$, a function of optical absorption coefficient. In this study, very small quantities of an absorbing material (${\mathrm{k}}_2{\mathrm{CrO}}_4$) were added into distilled water to make calibration solutions, allowing $k^{\prime }R(\alpha )$ of the detection system to be calibrated:

In summary, acoustic speed and optical absorption coefficient can be deduced directly from the time-of-flight of a time-resolved PA signal and its front profile. The thermal-acoustic transformation coefficient, on the other hand, can be calculated from signal amplitude, optical absorption coefficient, and the calibrated curve of the measurement system, determined by a suitable calibration liquid. If the transducer has a flat response in the studied acoustic frequency range, the relative value of the thermal-acoustic transformation coefficient can be deduced without calibration from optical absorption and signal amplitude.

3. Experimental Apparatus and Samples

Figure 2 shows the scheme of the experimental apparatus used for measuring liquid samples. A tunable laser (Opolette HE 355 II, OPOTEK Inc.) with a 5 ns pulse duration and a 355 nm pumping wavelength is used as the exciting source to produce PA waves. To satisfy the requirement of generating a planar PA source, optical lenses expand the laser beam to a diameter of 20 mm, before it passes through an optical aperture with a diameter of 15 mm. A rough glass slide is put in the optical path for further smoothing the optical energy distribution in the beam’s cross-section, before it enters a cuvette where the sample is placed. A plane of fused silica with a thickness of 5 mm functions as cuvette window to produce a limiting boundary condition for highly-efficient PA generation. Measuring 1 cm in thickness, the cuvette is capable of eliminating the effects of acoustic diffraction and attenuation. Aligned with the excited laser beam is a homemade detector, combining a piezoelectric PVDF transducer with a preamplifier. This detector is acoustically coupled to the back surface of the cuvette by a drop of silicon oil. The thickness of the PVDF foil is 52 µm, the gain of the preamplifier is 40 dB, and the 6 dB bandwidth is about 200 kHz—5 MHz. To prevent the laser beam from directly irradiating the detector surface when using a sample with low optical extinction, the back surface of the cuvette is covered by a reflecting layer of aluminum film with a thickness of 150 nm. A thermocouple is inserted into the cuvette for monitoring the temperature of the solution. In addition, a photodiode is used to monitor the energy fluctuation of the laser pulses. The output from the detector is connected to a two-channel digital card (PCI-1250, NI, sampling at $200MS/\mathrm{s}$) in a PC and, to compensate for the energy fluctuation effect of the laser pulses, the output is divided by the amplitude of the photodiode’s output. One hundred twenty-eight compensated signals are averaged by LabView software to decrease random noise in the detection channels and the amplitude and wave-shape of the averaged signals are recorded in the PC for postprocessing.

 

Fig. 2. Experimental scheme of time-resolved photoacoustic measurement.

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As samples, this study used aqueous solutions of potassium chromate (${\mathrm{K}}_2{\mathrm{CrO}}_4$) and mixtures of potassium chromate and glucose, because their properties are well known. Potassium chromate has a very high optical absorption coefficient at 355 nm (about $1000{\mathrm{cm}}^{-1}$ at a concentration of $35\mathrm{mg}/{\mathrm{cm}}^3$ [13]). Moreover, potassium chromate solutions do not fluoresce and their optical properties are not altered by strong laser exposure. As a result, potassium chromate is suitable for the calibration of the PA measurement system and for the quantitative PA detection of absorption coefficients in solutions. Glucose, on the other hand, exhibits considerably weaker optical absorption characteristics at this wavelength. However, it will change the thermal parameters [15,16] and density of the solutions it is added to.

4. Experiments and Results

Before measurements, all liquid samples were prepared and put on the laboratory table at room temperature (22 °C) and the experimental apparatus was preheated for 30 minutes. The experiments included three steps. Potassium chromate solutions with concentrations from 0.02 wt. % to 0.1 wt. % were successively loaded into the cuvette. Then, to make glucose solutions, varying amounts of glucose (0.2 g, 0.4 g, 0.6 g, 0.8 g, and 1 g, respectively) were added into 10 ml of potassium chromate solutions with a concentration of 0.02%. Potassium chromate was used here as background absorber in the glucose solutions for PA generation, because glucose and distilled water have little optical absorption at the investigating wavelength—355 nm. Finally, five mixed solutions, each with a different concentration of potassium chromate and glucose, were measured. In every measurement, the signal amplitude was recorded ten times to calculate the standard deviation of the amplitude. The sample was then sucked out by a plastic pastette and the cuvette was washed twice using distilled water, before a new sample was loaded. When measured, the temperature difference, due to room temperature fluctuations during the experiment, was less than 0.3 °C in all samples.

Figure 3 shows a typical TR-PA signal recorded in a ${\mathrm{K}}_2{\mathrm{CrO}}_4$ solution. In agreement with Eq. (2), the inserted graph, drawn in the semilogarithm scale, illustrates good linearity at the signal front. As the ${\mathrm{K}}_2{\mathrm{CrO}}_4$ concentration increases, so does the recorded signal amplitude, while the arriving time of the amplitude remains almost unchanged. Figure 4 illustrates the measurement result. It demonstrates an optical absorption coefficient of $7.8\pm 0.2{\mathrm{cm}}^{-1}$ and an acoustic speed of $1486+4\mathrm{m}/\mathrm{s}$ for a 0.02% ${\mathrm{K}}_2{\mathrm{CrO}}_4$ solution. Both of these values are nearly identical to those presented in [13]. With increasing concentration, the absorption coefficient grows linearly with a huge slope rate, whereas acoustic speed is unaffected within the measurement error range. As the solutions were highly diluted, their Grüneisen coefficients should be identical and equal to that of water (${\mathrm{\Gamma }}_w=0.12$ at 22 °C). Based on this consideration, the $k^{\prime }R(\alpha )$ of the measurement system can be calculated for solutions with different concentrations (or optical absorption), as shown in Fig. 4. Doing a polynomial fit to these data allowed us to obtain a calibrated curve for computing the Grüneisen coefficient of the current measurement system:

 

Fig. 3. Typical TR-PA signals recorded in ${\mathrm{K}}_2{\mathrm{CrO}}_4$ solutions with different concentrations (the inserted graph is shown in the semilogarithm axis).

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Fig. 4. Experimental results of calibration solutions (standard deviations are smaller than the marks).

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Figure 5 monitors how the three parameters changed with glucose concentration in aqueous solutions containing 0.02% ${\mathrm{K}}_2{\mathrm{CrO}}_4$. As seen, a 1% increase in glucose concentration increased the Grüneisen coefficient by about 3.4% and acoustic speed by 0.26%. These values are in good agreement with previously published data [7,16]. The error bars for the relative change of the Grüneisen coefficient in response to concentration increase are mainly caused by fluctuations in laser pulse energy and the error in measuring the absorption coefficient. Yet another contributing factor is temperature; the Grüneisen coefficient of the solutions increased by 1.3% when room temperature increased by 0.3 °C [13]. In addition, the absorption coefficient decreased about 0.72%, due to the diluting effect of glucose on potassium chromate.

 

Fig. 5. Relative change of the three parameters with glucose concentration (error bars for acoustic speed and absorption coefficient are smaller than the marks).

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Figure 6 gives the experimental result of the three parameters obtained from five mixed solutions, consisting of ${\mathrm{k}}_2{\mathrm{CrO}}_4$ and glucose. Shown in square brackets under the horizontal axis are the used concentrations (for example, [0.091_9.1], indicating a mixed solution consisting of 0.091% of potassium chromate and 9.1% of glucose). It is easy to understand that the values of the three parameters increase with concentration and Table 1 illustrates the relative increase of each parameter. For comparison, the table also lists the results contributed by the sum of the ${\mathrm{K}}_2{\mathrm{CrO}}_4$ solution and glucose solution (calculated from the data presented in Figs. 4 and 5). It is evident that the result in Fig. 6 is practically identical to the sum of the results in Figs. 4 and 5.

 

Fig. 6. Measurement results of the three parameters obtained from mixed solutions containing ${\mathrm{K}}_2{\mathrm{CrO}}_4$ and glucose.

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Table 1. Comparing Relative Changes in the Three Parameters Deduced from Fig. 6 and the Sum of Figs. 4 and 5

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5. Discussion

Although the constituents of most processing liquids are known, determining the concentration of each constituent may require real-time measurements. This became our motivation to develop the multiparameter measurement technique presented in this study. Table 1 demonstrates that ${\mathrm{k}}_2{\mathrm{CrO}}_4$ and glucose concentrations in mixed solutions can be deduced by measuring three parameters, provided that the effects of ${\mathrm{K}}_2{\mathrm{CrO}}_4$ and glucose on these parameters are determined beforehand. In general, this technique is applicable to absorbing liquids consisting of three constituents in which no chemical reactions take place. The technique allows determining the concentration of each constituent, if they all contribute to optical absorption, acoustic speed, or thermal-acoustic transformation with a different weight factor.

Our experiment demonstrates that the absorption coefficient can be deduced with measurement error no larger than 3% (when measuring a sample three times), without calibration. It is worth mentioning that the result remains accurate, even if only a part of the signal’s front profile satisfies the exponential distribution. This offers the extra benefit that a high absorption coefficient can be correctly measured by a transducer whose frequency bandwidth does not cover the higher frequency components of the PA wave produced in the sample (of course, the deduced Grüneisen coefficient is not correct in this case). Dominating error sources in the absorption coefficient measurement are the following: 1) energy fluence in the cross-section of the laser beam is not strictly homogeneous, 2) the laser beam is probably not well collimated, and 3) the detector and the laser beam are not exactly aligned.

Acoustic speed was deduced by measuring the arrival time of a PA amplitude signal with a measuring error of up to 0.3%. Errors arise mainly from a slight difference in the transducer’s response to a wide range of PA frequencies and a possible change of acoustic coupling between the detector and cuvette wall when uploading and downloading samples during the measurement.

The measurement error of thermal-acoustic transformation coefficient in this study is mainly due to an error in determining the absorption coefficient or calibration curve and to fluctuations of laser pulse energy and the temperature of the solution. In contrast to measuring the absorption coefficient and acoustic speed, correctly determining the thermal-acoustic transformation coefficient sets higher requirements for the experimental setup as it also needs to measure the amplitude value of the PA pressure. In practice, the pressure amplitude is measured by the amplitude of the PA signal, but it must be noted that the two are not identical. Although signal amplitude is proportional to pressure amplitude, it is also related to the response sensitivity and frequency bandwidth of the detector, energy fluctuation of laser pulses, as well as to acoustic diffraction and attenuation within the sample. If the frequency spectrum of a PA wave exceeds the detector bandwidth, the PA signal amplitude will be cut and is no longer proportional to the pressure amplitude. In this study, the lower and upper frequencies of the detector's 6 dB bandwidth are about 200 kHz and 5 MHz, respectively, corresponding to optical absorption coefficients of $0.3{\mathrm{mm}}^{-1}$ and $6.7{\mathrm{mm}}^{-1}$ in aqueous solutions. This is the reason why ${\mathrm{K}}_2{\mathrm{CrO}}_4$ solutions with concentrations from 0.02% to 0.1% were used in the measurement (the absorption coefficients of these solutions are within the range mentioned above). Moreover, since the detector response in the 6 dB bandwidth is not flat with frequency change, it tends to modulate the signal amplitude, following changes in optical absorption in the solution. The effect of detector response and the effect of the system constant on signal amplitude were jointly compensated for by using a calibration curve (see $k^{\prime }R(\alpha )$ in Fig. 4). This eliminates the need to measure the detector response by other acoustic instruments. It is worth mentioning that, in the experimental condition reported here, the diffraction parameter $D$ was larger than 0.62 and the acoustic frequencies were lower than 5 MHz, allowing acoustic diffraction and attenuation to be ignored [13].

Finally, determining three parameters simultaneously in liquid necessitates using a purely absorbing liquid, because Eq. (1) only applies to purely absorbing materials. In the case of turbid samples, the TR-PA technique, as described above, has the capacity to measure the optical extinction coefficient (including the optical absorption and scattering coefficients) and acoustic speed, but fails at measuring the thermal-acoustic transformation coefficient, due to backscattering of the incident optical beam. However, if the laser is wavelength-tunable such that the optical absorption of the sample is much stronger at some wavelengths than optical scattering, the technique is still capable of correctly deducing the thermal-acoustic transformation coefficient. This is because the extinction coefficient approximately equals the absorption coefficient and backscattering can be ignored. Another benefit of applying a tunable laser is that it probably tunes the frequencies of the generated PA waves into the bandwidth of the detector. This not only expands the application range of the sample category, but also lowers detector requirements, since there is a trade-off between detector bandwidth and amplifying gain.

6. Conclusion

A hybrid technique was developed to simultaneously measure the optical absorption coefficient, acoustic speed, and thermal-acoustic transformation coefficient in an absorbing liquid, based on the TR-PA detection of the profile, amplitude, and flight time of PA signals. Conducted experiments utilized potassium chromate as absorber and glucose as nonabsorbing substance in mixed solution samples. The current experimental setup achieves measurement errors of 3%, 0.3%, and 8% in determining the optical absorption coefficient, acoustic speed, and thermal-acoustic transformation coefficient, respectively. The setup is suitable for measuring absorbing liquids with an absorption coefficient in the range of $0.3{\mathrm{mm}}^{-1}$ to $6.7{\mathrm{mm}}^{-1}$ (the range is limited by the detector bandwidth, not by the technique itself). Our experimental results show that, in mixed solutions, the value of each of these parameters is approximately equal to the sum value of the same parameter measured in a potassium chromate solution and a glucose solution. Hence, potassium chromate and glucose concentrations in mixed solutions can be deduced by measuring these parameters in constituent and mixed solutions. To sum up, the technique described here has the ability to monitor three constituent concentrations in an absorbing liquid, provided that these substances have different optical absorption, acoustic speed,brvgf or thermal-acoustic transformation properties. At the next step, the apparatus will be further improved to increase its measurement accuracy. Then it will be applied to measuring actual industrial processing liquids.