Coupled-optimized dual-resonance photoacoustic sensor platform for detecting gases and their concentrations

Abstract

A photoacoustic spectroscopy system is provided, comprising an acoustic cell, an electromagnetic radiation unit, and a resonant transducer unit. The acoustic cell includes a resonant cavity supporting a first resonant mode having a first resonant frequency, and to which a sample fluid can be supplied. The resonant transducer supports a second resonant mode having a second resonant frequency and is functionally connected to the resonant cavity. The first and second resonant modes are configured to be coupled in a significant coupling region, and the adjustment of the first and second resonant modes is configured to result in an increase in signal intensity or signal-to-noise ratio.

Description

[Technical Field]

[0001] This application claims priority under U.S. Provisional Patent Application No. 63 / 509,211, filed on 20 June 2023, and U.S. Provisional Patent Application No. 63 / 626,927, filed on 30 January 2024, the contents of which are incorporated herein by reference.

[0002] This disclosure relates to the field of photoacoustic spectroscopy. [Background technology]

[0003] Rapid and highly accurate detection of analyte molecules in sample fluids in environments with fluctuating temperature, humidity, and background analytes is useful in a variety of applications. For example, gas detection is now an essential element in industrial process monitoring, occupational safety risk reduction, emissions monitoring, military applications, and air quality assessment. Continuous improvement of gas detection technologies is essential for their successful deployment in increasingly diverse applications. These stringent design constraints often lead to the need for lower detection limits as more and more applications require detection of gases at the parts per billion (ppb) or parts per trillion (ppt) level. The gold standard method for trace gas detection is gas chromatography-mass spectrometry, but this requires very expensive and large equipment and costly consumables. Several alternatives, such as semiconductor sensors and resistive sensors, are very small and inexpensive, but they lack sensitivity or specificity, and significant redevelopment may be required to adapt them to various target molecules. A recent trend in low-concentration gas detection systems is the use of direct absorption spectroscopy (DAS) (see, for example, Fathy et al., "Direct Absorption and Photoacoustic Spectroscopy for Gas Sensing and Analysis: A Critical Review. Laser & Photonics Reviews 2022, 16, 2100556"). In this method, electromagnetic radiation is transmitted through the gas to be analyzed, and the amount of electromagnetic radiation absorbed by this gas is measured using an electromagnetic radiation detector such as a photodiode, cadmium-mercury-tellurium (MCT) detector, thermopile, or other electromagnetic radiation detection device. The measured decrease in the intensity of electromagnetic radiation can then be correlated with the concentration of the target gas. However, this method is not background-free, and the detector is exposed to high-intensity electromagnetic radiation even when the target gas is absent, affecting the system's dynamic range and requiring a high-quality, low-noise detector.Furthermore, gas absorption spectroscopy is often desirable to operate using electromagnetic radiation in the infrared region, but this requires the use of a corresponding detector, and in certain wavelength bands of infrared radiation, detectors can be very expensive, consume a lot of power, and require large cooling systems. Another technique for detecting trace gases is photoacoustic spectroscopy (PAS). This technique is based on the detection of acoustic waves produced by light, and simultaneously mitigates the problem of high background signal and the noise, cost, and size constraints associated with electromagnetic radiation detectors. This disclosure describes a system and method for detecting, measuring, and identifying analyte molecules in a sample fluid using PAS. Outline.

[0004] One common approach to addressing modern gas detection engineering challenges is based on the principles of photoacoustic spectroscopy. This method allows for essentially background-free measurements and, in principle, a linear detection scheme. A typical photoacoustic spectroscopy system includes an electromagnetic radiation source, which can be absorbed by the target, such as the analyte gas molecules. When the target absorbs the electromagnetic radiation, it heats up, transferring its thermal energy to the surrounding medium (sample fluid), such as the gas matrix, thereby heating the medium. This heating increases the pressure within the medium. When the interaction between the electromagnetic radiation and the target is modulated, the pressure in the surrounding medium is also modulated, generating an acoustic pressure wave. Under normal operating parameters, the amplitude of the acoustic pressure wave is proportional to the energy absorbed by the target, which in turn is proportional to the output of the electromagnetic radiation and the absorption characteristics of the target. When the target is the analyte gas molecules, the amount absorbed is proportional to the concentration of the analyte gas molecules in the gas volume exposed to the electromagnetic radiation, and the amplitude of the acoustic pressure wave is similarly proportional. Acoustic pressure waves are typically measured by a mechanical transducer that converts the acoustic pressure waves in the surrounding medium into mechanical displacements of the transducer. Finally, a readout system converts these mechanical displacements into electrical signals that can be read by conventional electronic measuring devices.

[0005] Ultimately, the detection limit of a PAS system is determined by the noise floor of the entire apparatus, which in turn affects the signal-to-noise ratio at a given concentration of the target gas. The three main noise sources are (i) acoustic thermal noise in the medium through which the target gas is detected, (ii) thermal noise from pressure (acoustic) to the mechanical transducer, and (iii) noise in the readout system that converts the mechanical displacement of the transducer into the desired final form, such as a digital or analog electrical signal. The magnitude of the system's acoustic thermal noise is determined by the acoustic configuration of the apparatus. To increase the signal level, acoustic cells containing resonant cavities are often used in the implementation of the acoustic configuration. In this case, it is known that increasing the Q value (quality factor) of the resonant cavity reduces acoustic thermal noise, which is always desirable.

[0006] There are two main approaches to minimizing the noise floor in the output signal of a photoacoustic spectroscopy system and consequently increasing the signal-to-noise ratio. The first approach involves suppressing the noise of the acoustic-mechanical transducer and using a low-noise readout system. If the combined noise of these two noise sources is reduced to a level well below the acoustic-thermal noise, the signal-to-noise ratio will be determined solely by the acoustic configuration (see, for example, U.S. Patent No. 7,797,983). Implementing this approach requires a very stable laser light source and interferometer system, leading to complex readout system design (see, for example, U.S. Patents No. 9,170,397 and 8,497,996). Another viable approach is to amplify the signal measured from the acoustic domain, along with its inherent noise, to a level that exceeds the combined noise of the acoustic-mechanical transducer and the readout system.

[0007] This second method has been studied in conventional technology as double resonant photoacoustic spectroscopy, which combines acoustic amplification obtained by a resonant cavity with mechanical amplification obtained by a transducer that converts resonant acoustics to mechanical displacement (resonant transducer) to improve the sensitivity of the photoacoustic system. Such a double resonant photoacoustic spectroscopy system, which includes a resonant cavity and a resonant transducer, can be modeled as a coupled oscillator system, where the resonant cavity is the first oscillator and the resonant transducer is the second oscillator. Several examples of dual-resonance photoacoustic spectroscopy systems are described in the literature, such as on-beam quartz-enhanced photoacoustic spectroscopy (QEPAS) and off-beam QEPAS (e.g., Kosterev et al., "Applications of quartz tuning forks in spectroscopic gas sensing," Review of Scientific Instruments, 76(4):1-9 (2005), Liu et al., "Off-beam quartz-enhanced photoacoustic spectroscopy," Opt. Lett. 34(10):1594-1596). (See 2009 and U.S. Patent No. 10,908,129). Typically, on-beam QEPAS utilize a resonant cavity consisting of two aligned tubes in the gap between the claws of a quartz tuning fork (QTF) to increase the QTF's typically weak acoustic-mechanical coupling. As a result, on-beam QEPAS are highly sensitive to misalignment and vibration, and require a focused, high-quality laser beam to pass through the typically sub-millimeter gap between the QTF's claws, avoiding direct illumination of the claws due to the potential for significantly increased noise. Off-beam QEPAS utilize a resonant cavity formed by a single tube with side slits. The QTF is positioned near the side slits to maximize acoustic-mechanical coupling. Off-beam QEPAS do not require the same level of alignment precision as on-beam QEPAS, but tend to have weaker acoustic-mechanical coupling. Dual-resonance photoacoustic spectroscopy systems that are not sensitive to misalignment and vibration and exhibit high acoustic-mechanical coupling are useful for many applications.

[0008] An additional example of a dual-resonance photoacoustic system can be found in "Ruck (2017) Development, characterization and miniaturization of a trace gas detection system for NO2 in air based on photoacoustic spectroscopy. Thesis. University of Regensburg." This study uses an open-ended tube as the resonant cavity providing acoustic amplification and investigates both QTFs and resonant cantilevers as resonant transducers. Ruck mentions the challenge of using a high-Q QTF compared to a relatively low-Q resonant cavity when such a system is subjected to fluctuations in the speed of sound and the photoacoustic signal is attenuated. However, this study does not show a clear method for adjusting the coupling state of the two oscillators to maximize the displacement of the resonant transducer (and thus the output signal amplitude of the readout system), while considering manufacturing tolerances of the resonant cavity, manufacturing tolerances of the resonant transducer, or fluctuations due to environmental changes. For example, the detuning of the dual-resonance photoacoustic system shown by Ruck was not designed to be controllable. Furthermore, in fluid processing systems, it is not possible to equilibrium the temperatures of the sample fluid, resonant cavity, and resonant transducer, and this equilibrium is a crucial step in adjusting the coupling state of the two oscillators. While some adjustment may be possible by changing the gas composition, this is not the optimal method for detecting trace gases in non-laboratory environments. This lack of adjustability presents manufacturing problems. Specifically, to achieve high acoustic-mechanical coupling, each resonant cavity must be tested individually and carefully combined with the appropriate resonant transducer. This is not practical for mass production. Therefore, it is ideal to provide an adjustable dual-resonant photoacoustic spectroscopy system, as well as a method for adjusting the detuning of the resonant cavity and resonant transducer of the dual-resonant photoacoustic system after assembly or during operation.

[0009] As mentioned above, quartz-enhanced photoacoustic spectroscopy (QEPAS) uses a quartz tuning fork (QTF) as a resonant transducer to measure pressure fluctuations amplified by a resonant cavity. Typically, QTFs have very high Q values, approximately 10,000 in air and approximately 100,000 in low vacuum. In systems with very weak coupling, the Q value is proportional to the resonant amplification coefficient and inversely proportional to the losses in the system. (These losses are related to the noise source via the fluctuation-dissipation theorem.) In dual-resonant photoacoustic spectroscopy, it is desirable to maximize the coupling between the resonant transducer and the acoustic region, and all other losses are undesirable. Therefore, rather than using QTFs or other transducers that have extremely high Q values ​​in both air and vacuum, it may be desirable to use a resonant transducer that satisfies the following conditions. Specifically, the requirements are: (i) the Q-factor should be as high as possible when there is no coupling with the fluid domain; (ii) the Q-factor should be substantially low in the sample fluid (e.g., air), showing strong coupling with waves in the fluid domain; and (iii) the coupling with dissipative vorticity waves and thermal waves within the fluid domain should be low. If a resonant transducer is designed to exhibit a much lower Q-factor in the sample fluid than in a vacuum, its losses will be predominantly in the fluid domain. Therefore, a high Q-factor in a vacuum compared to the sample fluid indicates that the energy lost by the resonant transducer through interaction with the sample fluid far exceeds any other losses inherent in the pure mechanical vibration of the resonant transducer. Furthermore, the low coupling with vorticity waves and thermal waves within the fluid domain indicates that the majority of the Q-factor loss observed when the resonant transducer is exposed to the sample fluid, compared to the case in a vacuum, is due to high coupling with acoustic waves within the fluid domain. It may be desirable to design a dual-resonant photoacoustic system that maximizes acoustic-mechanical coupling using this type of resonant transducer. Interestingly, commercially available dual-resonance photoacoustic spectroscopy systems often operate in a very weak coupling region. This very weak coupling region is characterized by the fact that the displacement of the resonant transducer (which is proportional to the signal amplitude transformed by the resonant transducer) is proportional to the product of the Q-factors of the two oscillators.There may be advantages to operating in significant binding regions, including strongly bound and semi-strongly bound regions, rather than in such very weak binding regions.

[0010] This disclosure presents a significant increase in signal intensity and a corresponding increase in the signal-to-noise ratio of the output signal of a photoacoustic spectroscopy system, which is achieved by (i) strengthening the coupling between the resonant cavity and the acoustic-mechanical transducer, and (ii) adjusting the resonant cavity and the resonant transducer to be in close proximity to leverage the signal enhancement achieved by the strengthened coupling. This signal enhancement is independent of, and complements, the signal enhancement obtained by using a high-Q resonator, such as in QEPAS. To fully realize the signal enhancement, it is desirable to increase the coupling strength and Q value of the resonant transducer until the signal-to-noise ratio of the resulting output signal is dominated by the intrinsic thermal noise contribution of the resonant cavity. This signal enhancement can be achieved without using a complex or expensive low-noise readout system by leveraging the large signal enhancement obtained by strengthening the coupling between the resonant cavity and the resonant transducer. This disclosure also provides methods and techniques for designing photoacoustic devices having a signal-to-noise ratio substantially determined solely by the fundamental limits of thermoacoustic noise resulting from the acoustic configuration of the photoacoustic spectroscopy system, using readout systems that are easy to manufacture, low-cost, and not state-of-the-art in terms of their intrinsic noise floor. Furthermore, this disclosure provides a dual-resonance photoacoustic spectroscopy system configured to operate in a way that can take advantage of the potential signal amplification enabled by a significant coupling region. These systems overcome many of the shortcomings of the prior art.

[0011] In one embodiment, a photoacoustic spectroscopy system is provided, comprising: an acoustic cell to which a sample fluid can be supplied, and which includes a resonant cavity configured to support a first resonant mode having a first resonant frequency; an electromagnetic radiation unit including an emitter and a control circuit, wherein the emitter is configured to transmit electromagnetic radiation through the resonant cavity; and a resonant transducer unit including a resonant transducer and a readout system, wherein the resonant transducer is configured to support a second resonant mode having a second resonant frequency, and the resonant transducer is functionally connected to the resonant cavity, wherein the first resonant mode and the second resonant mode are configured to be coupled in a significant coupling region.

[0012] In one embodiment, a method for performing photoacoustic spectroscopy is provided. The method includes: preparing the photoacoustic spectroscopy system described above; operating the emitter in a modulation mode so that the analyte molecules in the sample fluid within the resonant cavity undergo periodic absorption and heating at the operating frequency; configuring the acoustic cell such that the periodic heating induces an acoustic pressure wave having an amplitude proportional to the concentration of the analyte molecules in the sample fluid within the resonant cavity, thereby exciting the modes of the coupled resonant cavity and resonant transducer; detecting the excitation of the excited coupled resonant cavity and resonant transducer modes by measuring the displacement of the resonant transducer in a frequency-dependent manner using the readout system; and outputting a signal representing the concentration of the analyte molecules via the readout system.

[0013] Another broader aspect is a photoacoustic spectroscopy system. This photoacoustic spectroscopy system comprises an acoustic cell to which a sample fluid can be supplied, and which includes a resonant cavity configured to support a first resonant mode having a first resonant frequency; an electromagnetic radiation unit including an emitter and a control circuit, wherein the emitter is configured to transmit electromagnetic radiation through the resonant cavity; and a resonant transducer unit including a resonant transducer and a readout system, wherein the resonant transducer is configured to support a second resonant mode having a second resonant frequency, and the resonant transducer is functionally connected to the resonant cavity, wherein the first and second resonant modes are configured to be coupled in a significant coupling region.

[0014] In some embodiments, the system can be tuned to achieve at least one of (i) a proximity-tuned configuration and (ii) an optimally tuned configuration, for example, by configuring either or both of the first resonant frequency of the resonant cavity and the second resonant frequency of the resonant transducer to be adjustable.

[0015] In some embodiments, the system may include a control system configured to stabilize at least one or a combination of (i) the temperature of the sample fluid, (ii) the pressure of the sample fluid, (iii) the humidity of the sample fluid, (iv) the mass flow rate of the sample fluid passing through the acoustic cell, (v) the temperature of the resonant transducer, and (vi) the temperature of the acoustic cell.

[0016] In some embodiments, the first resonance frequency of the resonance cavity can be configured to be less than the second resonance frequency of the resonance transducer at a first temperature (T1), and the first resonance frequency of the resonance cavity can be configured to be greater than the second resonance frequency of the resonance transducer at a second temperature (T2), where T1 ≠ T2, and the control system can be configured to at least stabilize the temperature of the acoustic cell at any selected temperature between T1 and T2.

[0017] In some embodiments, the resonance transducer can be selected from one or a combination of (i) an out-of-plane resonator, (ii) a tuning fork resonator, (iii) a cantilever resonator, and (iv) a diaphragm resonator.

[0018] In some embodiments, the acoustic cell can further include at least one acoustic frequency filter functionally connected to the resonance cavity.

[0019] In some embodiments, the acoustic cell can further include at least one transducer housing, each of the at least one transducer housing enclosing a portion of the sample fluid surrounding at least one active surface of the resonance transducer and configured to isolate the at least one active surface of the resonance transducer from the external environment.

[0020] In some embodiments, the readout system can be at least configured to detect the resonance transducer using a piezoelectric material.

[0021] In some embodiments, the readout system can further include a preamplifier in the vicinity of the resonance transducer.

[0022] In some embodiments, the resonant transducer unit may further include, for example, a printed circuit board (PCB), the resonant transducer is mounted on the PCB, the PCB is attached to the acoustic cell such that the resonant transducer is functionally connected to the resonant cavity, and at least a part of the reading system can be disposed on the PCB.

[0023] In some embodiments, the acoustic cell can be configured using an integrated structure design and further includes at least one acoustic frequency filter and an acoustic port machined from a single piece of material.

[0024] In some embodiments, the acoustic cell configured using an integrated structure design may further include a heat exchanger machined within the acoustic cell that allows the sample fluid to reach thermal equilibrium with the acoustic cell before at least entering the resonant cavity.

[0025] In some embodiments, the Q (quality) value of the second resonance mode of the resonant transducer in vacuum can be configured to be substantially greater than the free Q value of the second resonance mode of the resonant transducer in the sample fluid. <00,00102>

[0026] In some embodiments, the Q value of the resonant transducer in vacuum can be configured to be greater than 1000. <00001,05>

[0027] In some embodiments, the coupling strength (Ω) between the resonant cavity and the resonant transducer is above a threshold value represented by the following equation (1).

Number

[0028] In some embodiments, the resonant transducer has a Q value Q2, the Q value being greater than or equal to a threshold represented by the following equation (2), the readout system has a noise amplitude spectral density β, and both the sample fluid in the resonant cavity and the resonant transducer have a temperature T.

number

[0029] In some embodiments, the acoustic cell may further include at least one acoustic port.

[0030] In some embodiments, the acoustic cell may further include at least one optical window.

[0031] In some embodiments, the emitter may include one of the following options: (i) a quantum cascade laser (QCL), (ii) a continuous wave (CW) laser, (iii) a pulsed laser, (iv) an interband cascade laser (ICL), (v) a vertical cavity surface-emitting laser (VCSEL), and (vi) a thermal emitter.

[0032] In some embodiments, the control circuit may be configured to modulate at least the output of the emitter, and modulating the output of the emitter includes modulating one or a combination of (i) the emission wavelength of the electromagnetic radiation, (ii) the emission intensity of the electromagnetic radiation, (iii) the pulse repetition rate of the electromagnetic radiation, and (iv) one or a combination of patterned pulse trains of the electromagnetic radiation.

[0033] In some embodiments, the readout system may further include a preamplifier, which may include one of (i) a differential charge amplifier, (ii) a differential transimpedance amplifier, (iii) a single-ended voltage amplifier, (iv) a single-ended charge amplifier, (v) a single-ended transimpedance amplifier, and (vi) an instrumentation amplifier.

[0034] In some embodiments, the readout system may be configured to convert the displacement of the resonant transducer into one or more electrical signals, and to amplify and process the one or more electrical signals.

[0035] In some embodiments, the acoustic cell can be configured to be sealed with the sample fluid contained inside.

[0036] In some embodiments, the acoustic cell may further include at least one port connected to a fluid processing system.

[0037] In some embodiments, the fluid processing system may consist of at least a portion of low-adsorption tubes.

[0038] Another broader aspect is a method for performing photoacoustic spectroscopy. This method includes providing the photoacoustic spectroscopy system described herein; operating the emitter in a modulation mode so that the analyte molecules in the sample fluid within the resonant cavity undergo periodic absorption and heating at the operating frequency; configuring the acoustic cell such that the periodic heating induces an acoustic pressure wave having an amplitude proportional to the concentration of the analyte molecules in the sample fluid within the resonant cavity, thereby exciting the modes of the coupled resonant cavity and resonant transducer; detecting the excitation of the excited coupled resonant cavity and resonant transducer modes by measuring the displacement of the resonant transducer in a frequency-dependent manner using the readout system; and outputting a signal representing the concentration of the analyte molecules via the readout system.

[0039] In some embodiments, the method further includes configuring a control system to stabilize the temperatures of the sample fluid, the resonant transducer unit, and the resonant cavity, thereby actively stabilizing the detuning between the first and second resonant modes and maintaining either a proximity-tuned configuration or an optimally tuned configuration.

[0040] In some embodiments, the method further includes increasing the amplitude of the signal transformed by the resonant transducer to improve the signal-to-noise ratio of the readout system, which is achieved by increasing the coupling strength by one or a combination of i) selecting a shape of the resonant transducer having a large active area, ii) positioning the resonant transducer and acoustic port at the pressure maximum position within the resonant cavity, and increasing the Q factor of the resonant transducer by reducing coupling to vorticity waves and heat waves, thereby operating the photoacoustic spectroscopy system in a proximity-tuned or optimally-tuned configuration.

[0041] In some embodiments, the readout system has, for example, an input-referred noise amplitude spectral density β, the sample fluid in the resonant cavity and the resonant transducer are at temperature T, and the method may further include providing a photoacoustic spectroscopy system such that the contribution of the intrinsic thermoacoustic noise of the resonant cavity to the total output noise of the resonant transducer unit is greater than the sum of the contribution of the intrinsic thermomechanical noise of the resonant transducer and the noise of the readout system to the total output noise of the resonant transducer unit, so that the noise of the electrical signal converted by the resonant transducer unit consists mostly of the contribution of the intrinsic thermoacoustic noise of the resonant cavity 204. This is achieved by selecting a resonant transducer having a sufficiently high Q value that satisfies equation (3), selecting a resonant transducer having a sufficiently high coupling strength that satisfies equation (4), tuning the photoacoustic spectroscopy system to zero detuning, and operating the photoacoustic spectroscopy system at an operating frequency corresponding to the crossover frequency ω0 in the uncoupled state.

number

number

[0042] In some embodiments, the method may further include operating a control circuit to modulate the emitter wavelength at a frequency of half the operating frequency of the resonant cavity and resonant transducer, while simultaneously reducing unwanted background photoacoustic signals by measuring the signal output of the resonant transducer unit at the operating frequency using a signal band selection system. [Brief explanation of the drawing]

[0043] Embodiments of this disclosure will be described for illustrative purposes only, with reference to the following accompanying drawings.

[0044] [Figure 1A] This figure shows a dual-resonance photoacoustic spectroscopy system, including a resonant transducer and a resonant cavity, as a coupled oscillator system.

[0045] [Figure 1B] This shows the theoretical MEMS displacement |x2| as a function of the normalized bond strength Ω / Ω0.

[0046] [Figure 1C] This shows the location of the local maximum value of the resonant transducer displacement as a function of the detuning δ between the resonant transducer and the resonant cavity of the acoustic cell in a strongly coupled system exhibiting frequency anticrossing.

[0047] [Figure 1D] This shows the experimentally measured frequency anticrossing behavior of two hybrid coupled modes in a dual-resonance photoacoustic system.

[0048] [Figure 2A] This figure shows a dual-resonance photoacoustic spectroscopy system.

[0049] [Figure 2B] This figure shows a dual-resonance photoacoustic spectroscopy system with a fluid processing system and a control system.

[0050] [Figure 3] This figure shows an example of an acoustic cell.

[0051] [Figure 4] This example shows how temperature can be used as a control parameter.

[0052] [Figure 5] A flowchart illustrating an exemplary method for performing photoacoustic spectroscopy is shown. Detailed explanation

[0053] I. Overview Please note that this specification describes and illustrates multiple inventions. The following description is intended to illustrate the general principles of the invention and is not intended to limit the concepts of the inventions described in the claims. This disclosure provides a system and method for detecting analyte molecules in a sample fluid using PAS technology.

[0054] This disclosure refers to individual circuit components and elements such as capacitors, inductors, resistors, diodes, transformers, and switches, combinations of these elements as networks, topologies, circuits, etc., and objects with inherent properties such as “resonant” objects. Those skilled in the art will understand that the performance of a circuit or network can be adjusted by adjusting and controlling the variable components within the circuit or network, and that such adjustments may generally be expressed as tuning, adjustment, matching, correction, etc. Furthermore, those skilled in the art will recognize that the specific topologies described in this disclosure can be implemented in various ways without departing from this disclosure.

[0055] The terms "circuit" and "circuit configuration" may include a single component or a group of components, which are active and / or passive, and are connected in ways such as connections to achieve the described function.

[0056] The various exemplary logics, logic blocks, modules, circuits, and algorithmic processes described herein in relation to embodiments disclosed herein can be implemented as electronic hardware, computer hardware, or a combination of both. The interchangeability of hardware and software is described in general terms from a functional standpoint and is illustrated throughout this specification in the various exemplary components, blocks, modules, circuits, and processes described herein. Whether such functionality is implemented in hardware or software depends on the specific application and design constraints of the overall system.

[0057] One method for detecting trace gases is photoacoustic spectroscopy (PAS), a technique based on detecting acoustic waves generated by photoexcitation. The main advantages of PAS-based systems include their compact size, the absence of consumables, and the ability to generate real-time data. Therefore, PAS-based systems are suitable for continuous monitoring, mobile applications, or large-scale applications requiring high sample processing capacity. Furthermore, laser-based PAS systems can be easily adapted to detect virtually any molecule while maintaining extremely high specificity. By using broadband tunable lasers or laser arrays, it is also possible to simultaneously detect a large number of different molecules to suit specific applications. Thus, PAS-based systems are easily customizable.

[0058] A typical PAS system includes an electromagnetic radiation source, an acoustic cell which may include a resonant cavity, means for modulating the electromagnetic radiation reaching the acoustic cell, an acoustic-mechanical transducer functionally connected to the resonant cavity, and a readout system which measures the displacement of the transducer and converts it into a usable electronic signal. Throughout this specification and disclosure, the acoustic configuration of the acoustic cell and resonant cavity is assumed to be state-of-the-art and fixed.

[0059] In PAS, the wave number υ[cm- 1The electromagnetic radiation of ρ[mol cm-] is absorbed by the analyte molecules in the sample fluid as it passes through the sample fluid, and this absorption is due to the molar density ρ[mol cm-] of the analyte molecules. 3 ], absorption cross-section σ(υ)[cm] at wavenumber υ 2 mol- 1 ], and the intensity I[W cm-] of the electromagnetic radiation source at wavenumber υ 2 This occurs at a rate proportional to ]. Subsequent relaxation to the molecular ground state can occur through multiple processes, namely, radiation (stimulated or spontaneous emission of photons), chemical reactions, non-radiative relaxation, or a combination of these processes. Non-radiative relaxation can result in an increase in the kinetic energy of surrounding molecules, which can lead to local heating and a corresponding local pressure drop. If the absorption process is periodically modulated by a radiation source (intensity or wavelength) or by shifting the absorption line, the induced periodic heating generates a pressure wave (synonymous with an acoustic wave) at the same frequency or its harmonics. If the frequency ω of the resulting pressure wave matches the resonant frequency of the resonant cavity, it leads to amplification of the acoustic wave generated within the resonant cavity. In this disclosure, instead of always making the acoustic wave generated within the resonant cavity exactly the same frequency as the resonant frequency of the resonant cavity, different acoustic wave frequencies can be selected for various reasons, such as maximizing the output signal amplitude or the signal-to-noise ratio. Throughout this specification and disclosure, the operating frequency is defined as the frequency of the pressure wave generated in the resonant cavity as modulated electromagnetic radiation is absorbed by the molecule under analysis. This periodic thermal excitation induces acoustic resonance within the resonant cavity, which is measured as pressure by the transducer. The pressure p [Pa] at the transducer position is proportional to the density, absorption cross-section, and radiation source intensity, and is expressed by equation (5).

number

[0060] There are several types of transducers suitable for PAS, including both resonant and non-resonant transducers. Suitable resonant transducers include resonant microelectromechanical system (MEMS) transducers and quartz tuning forks (QTFs). In addition, non-resonant transducers such as broadband MEMS microphones and electret microphones may be used. Using resonant transducers can be beneficial in some cases. In addition to acoustic amplification using a resonant cavity, photoacoustic signals can also be amplified by using a resonant transducer with a high Q factor. This is known as a dual-resonant system. The physical interpretation of the Q factor of an oscillator is the ratio of stored energy to dissipated energy in one period of oscillation.

[0061] Figure 1A shows a dual-resonance photoacoustic spectroscopy system including a resonant transducer and a resonant cavity, represented as a coupled oscillator system 100 with a simple coupling configuration. More complex coupling methods exist, and the application of more complex coupling mechanisms is also within the scope of this disclosure. Here, the acoustic vibration in the resonant cavity has an effective mass m1, an effective spring constant k1, an effective damping constant α1, and an effective displacement x1, and the resonant transducer has a spring mass m2, a spring constant k2, a damping constant α2, and a displacement x2. The coupling is modeled as a spring of constant κ connecting the two masses. For both masses, the displacement is positive in the rightward direction. The equations of motion are given by equations (6) and (7) below.

number

number

[0062] In a typical use case of the system for performing PAS, modulated electromagnetic radiation excites the sample fluid in the resonant cavity, and the resonant transducer is detected. Therefore, as will be apparent to those skilled in the art, for a coupled oscillator system, F1 = F i e iωt Assuming that F2=0, the transfer function can be determined. The transfer function H represents the displacement x2 of the resonant transducer when the acoustic vibration in the resonant cavity is excited by force F1. x2 This is given by equation (8) below.

number

number

[0063] The analytical model of a dual-resonance system such as the coupled oscillator system 100 can be most easily understood by considering one oscillator to have a fixed resonance frequency and the other oscillator to have a resonance frequency that can be adjusted by various parameters. As a non-limiting example, one skilled in the art reading this might consider a scenario where the temperature is the adjustment parameter. In this scenario, the resonance frequency of the resonance transducer has a medium degree of temperature dependence, while the resonance frequency of the resonance cavity strongly depends on temperature. Thus, temperature can function as an adjustment parameter that controls the detuning between the two oscillators. Therefore, as a simple model, without losing the mathematical generality of the model, it can be considered that ω2 is a fixed value equal to ω0, and ω1(δ) = ω0 + δ is treated as a function of the temperature-dependent detuning δ. One skilled in the art reading this will understand that there are also various other adjustment parameters, such as pressure, humidity, the composition of the sample fluid, shape, etc.

[0064] In FIG. 1B, the behavior of the coupled oscillator system 100 is shown in plot 104. The coupled oscillator system exchanges energy between the oscillators and dissipates energy to the surrounding environment. Qualitatively different behaviors appear when energy exchange is dominant and when energy dissipation is dominant. These different behaviors are respectively referred to as the strong coupling region indicated by bracket 504 in plot 104 and the weak coupling region indicated by bracket 505 in plot 104. In the weak coupling region, the transfer function H of the coupled oscillator system 100 x2 has only one maximum at the point where the frequencies of the two oscillators are equal (δ = 0). When ω = ω1 = ω2 = ω0, the transfer function H x2 can be simplified as shown in the following equation (1)0).

Equation

[0065] In the weak coupling region, the total maximum transducer displacement is obtained at the point where the frequencies of the two oscillators are equal. The solid curve 500 in plot 104 shows the normalized theoretical transducer displacement |x2| in the case of zero detuning (δ=0) as a function of the normalized coupling strength Ω / Ω0 under the condition ω0=ω1=ω2, where Ω0 is the coupling strength threshold for strong coupling. As shown by the vertical dashed line 502 in plot 104, the maximum value shown in equation (11) is reached when the condition of equation (12) is satisfied.

number

number

[0066] Frequency anti-crossing behavior is a phenomenon observed in the response of symmetric coupled oscillator systems, where two different local resonant maximums can be observed even if the detuning between the two coupled oscillators is zero. In asymmetric coupled oscillator systems, such as those with differential loss or common-mode loss mechanisms, or when the two oscillators exhibit different Q-factors, this concept is naturally extended by considering the splitting of the peaks (maximas) of the fitted Lorentz curve, rather than local maximums, as will be discussed later. When this phenomenon occurs, well-coupled modes take on a hybridized nature when the resonant frequency of the first oscillator is sufficiently close to that of the second oscillator. Both of the hybridized coupled modes exhibit components originating from both oscillators. In other words, in a system having a strongly coupled resonant transducer and a resonant cavity, if the resonant frequency of the resonant transducer is sufficiently close to the resonant frequency of the resonant cavity (or vice versa), the hybrid coupled modes will exhibit both a significant displacement of the resonant transducer and a significant displacement of the pressure wave.

[0067] As mentioned above, when frequency anticrossing behavior exists, the frequency response of a coupled harmonic oscillator splits into two Lorentz peaks, even at low detuning conditions where the resonant frequencies of both oscillators are nearly equal when uncoupled. The sum of these peaks may or may not show two local maximums. This is due to the transfer function H x2 This means that the global maximum value no longer exists at the point ω1=ω2, as was observed in the weakly coupled region. Therefore, one definition of the strongly coupled region in the literature is given by equation (13), where ω0 is the frequency at which the uncoupled resonant frequencies coincide, and the condition of equation (14) is satisfied. (See, for example, Rodriguez, "Classical and quantum distinctions between weak and strong coupling," Eur. J. Phys., 31 (2), 025802). For a symmetric coupled oscillator system, this definition ensures that the strongly coupled region begins precisely at the point where the zero detuning point is no longer the global maximum value. In this specification and throughout this disclosure, the strongly coupled region means the coupling region where the coupling strength Ω is greater than that given by equation (15). Since it is known that the geometric mean of positive numbers is less than or equal to the arithmetic mean, we can derive equation (16), which shows that the threshold of the strongly coupled region is greater than or equal to the coupling strength that yields the maximum transfer function of the weakly coupled region. The maximum value shown in curve 500 of plot 104 is Ω ≥ Ω over most of the weakly coupled region. p Within this range, it is the global maximum value, and due to continuity, the maximum value entering the strongly coupled region is also the same. In this case, the analytical expression is not easy to handle because it requires solving a quartic equation. However, the maximum value is not only relatively continuous, but it also remains substantially the same even when the coupling strength is further increased beyond the strongly coupled threshold. This is shown by the dashed curve 501 in plot 104, which numerically determines the maximum value of the transducer displacement.

number

number

number

number

[0068] In the strongly coupled region, the positions of the two Lorentz-type peaks in the changing detuning can be found by determining the resonant frequency of the coupled oscillator system 100. This is achieved by solving the characteristic equation of the system given by equation (17).

number

number

[0069] Referring to plot 106 in Figure 1C, the behavior of the equation describing the strongly coupled oscillator obtained is shown as a continuous line indicating the resonant frequency as a function of detuning δ, exhibiting frequency anti-crossing behavior. In contrast, the dashed line shows the resonant frequencies of both oscillators as a function of detuning in a system that does not exhibit anti-crossing behavior. At the zero detuning point, i.e., ω0=ω1=ω2, the resonant frequency is given by the following equation (19).

number

number

[0070] In the limit where the bond strength is very small, the series expansion around Ω=0 yields the following equation (21).

number

[0071] Throughout this specification and disclosure, “significant coupling regime” refers to a region encompassing the upper portions of the strong coupling regime and the weak coupling regime, where the coupling strength Ω of the two coupled oscillators is considered to represent a significant proportion of the coupling strength threshold (Ω0) of the strong coupling regime. In some embodiments, this significant proportion may be at least 10%, or at least 20%, 30%, 40%, 50%, 60%, 70%, or 80% of the coupling strength threshold (Ω0) of the strong coupling regime. The bracketed 503 in Figure 1B shows the significant coupling regime at the significant coupling threshold corresponding to 10% of Ω0. In the significant coupling regime, the amplitude of the displacement of one oscillator, which is part of a system of two coupled oscillators, deviates from the relationship that is proportional to the product of the Q values, which is characteristic of the very weak coupling regime.

[0072] It should be noted that any potential signal gain obtainable by a photoacoustic spectroscopy system operating in the significant coupling region cannot be realized if the detuning δ between the resonant cavity and the resonant transducer is too large. This is because resonant energy transfer between the two oscillators occurs only when their frequencies match sufficiently, i.e., when the system is optimally tuned. In this specification and throughout this disclosure, an optimally-tuned configuration refers to a system in which the detuning between the uncoupled resonant frequencies of both oscillators (here, the resonant cavity and the resonant transducer) is adjusted so that the resulting displacement of the resonant transducer, and consequently the signal intensity, reaches its global maximum value. This optimal detuning value δ0 is close to zero, but in some strongly coupled systems, or in the presence of additional phenomena not considered in the models presented herein, δ0 may be a non-zero value, however, its value is usually limited by equation (22).

number

[0073] To experimentally verify the coupling strength of a dual-resonance photoacoustic spectroscopy system, it is first necessary to measure the dissipation coefficient γ1 of the resonant cavity oscillator and the dissipation coefficient γ2 of the resonant transducer in the uncoupled state, and then to determine the peak splitting Γ of the tuned and coupled oscillator. This can be achieved by measuring the excitation response power of the system for multiple detuning values ​​and fitting the Lorentz function shown in equation (23) to the response power peaks obtained from the resonant cavity and resonant transducer. Here, ω c θ is the center frequency of the peak, γ is the dissipation coefficient, which corresponds to the full width at half maximum (FWHM) of the peak, and A is the peak area. It is also necessary to measure a quantity corresponding to the signal power, which is, for example, the square of the signal amplitude.

number

[0074] Figure 1D shows an example of such measurements in plot 107, where the center frequencies ωc of both measured peaks are shown. 1,2 However, it is shown as a function of temperature, and temperature functions as a detuning control parameter. It should be noted that the peak frequency follows two non-intersecting curves, and the peak fitted near zero detuning does not reflect the behavior of the uncoupled resonant cavity and uncoupled resonant transducer, shown by the dashed line. Dissipation coefficient (γ) in the uncoupled state of each oscillator 1,2 =FWHM 1,2 To obtain an effective approximation for the (corresponding to) the following, the fitting data must be selected under detuning conditions such that the separation of the two peak center frequencies is greater than or equal to the sum of the two FWHMs and less than or equal to twice that sum. By selecting weakly mixed modes not far from the intersection within such a limited range, the fitting data can accurately approximate the actual uncoupled state behavior in the region around the frequency crossover. The second parameter to be extracted from this data is the peak splitting in equation (24) obtained during zero detuning, which corresponds to the smallest peak splitting observed on the graph. The crossover frequency ω0 in the uncoupled state can be estimated as the average of the two peak center frequencies during zero detuning using equation (25). Finally, the coupling strength between the resonant cavity and the resonant transducer can be estimated using equation (26), which allows for the determination of the system's coupling region. In the measurement data of plot 107 in Figure 1D, the calculated coupling strength is Ω = 1593 Hz, which corresponds to 82% of the coupling strength Ω0 required for strong coupling and falls within the significant coupling region.

number

number

number

[0075] In a dual-resonance PAS (photoacoustic spectroscopy) system, it is sometimes desirable to use a resonant transducer that (i) exhibits a high Q-factor in a vacuum and (ii) exhibits a lower free Q-factor in a sample fluid (e.g., air) compared to the vacuum. Here, the free Q-factor refers to the Q-factor measured when the resonant transducer is not coupled to a resonant cavity. This indicates that energy dissipation (loss) is determined more by losses in the fluid domain than by mechanical losses, etc. In other words, the Q-factor of the resonant transducer in a vacuum is configured to be substantially larger than the free Q-factor of the resonant transducer in the sample fluid. In this case, "substantially larger" includes the ratio of the Q-factor of the resonant transducer in a vacuum to the free Q-factor of the resonant transducer in the sample fluid being greater than 2, greater than 5, or greater than 20. For example, it may be desirable to use a MEMS-based resonant transducer with a Q-factor of approximately 4500 in a vacuum and a free Q-factor of approximately 150 in air (sample fluid). In other parts of this specification, “substantially large” includes a ratio of the first Q value to the second Q value that is greater than 2, greater than 5, or greater than 20.

[0076] The Q-factor of a resonant transducer decreases due to any energy loss or dissipation mechanism affecting the resonant transducer. Therefore, a higher Q-factor in a vacuum than in a sample fluid such as air means that the energy lost by the resonant transducer through interaction with the sample fluid far exceeds other losses inherent in the pure mechanical vibration of the resonant transducer itself. Furthermore, the energy lost by the resonant transducer through coupling with the fluid domain can dissipate into the surrounding sample fluid in various forms. Only three types of linear waves can exist in a gaseous fluid: acoustic waves, vorticity waves, and thermal waves (see, for example, Chu et al., "Non-linear interactions in a viscous heat-conducting compressible gas," J. Fluid Mech., 3, pp. 494-514), and these constitute the total energy loss from the resonant transducer to the air or gaseous medium due to linear phenomena. Thus, for small amplitudes, the decrease in the Q-factor of a resonant transducer between a vacuum environment and a sample fluid environment (e.g., air) is due to the introduction of these three additional energy loss pathways. In photoacoustic systems, coupling with acoustic waves is essential for the use of resonant transducers. This coupling can be considered not as a loss path, but as a signal path between the acoustic waves in the resonant cavity and the resonant transducer itself. This effect is taken into account when measuring the Q-factor while coupled to an acoustic resonator, as mentioned above. On the other hand, vorticity waves and thermal waves have strong dissipative properties, so coupling with these two types of waves should be minimized as much as possible. Coupling with these three types of waves can be estimated using finite element analysis (FEA) with a thermoviscoacoustic model, or other appropriate methods currently known or to be developed in the future. Using such analyses, it is possible to optimize the shape and design of the resonant transducer and improve the Q-factor in the sample fluid. The methods for doing so include the following.Specifically, this involves: i) designing the support structure to minimize coupling with the surrounding environment in order to increase the Q-factor in a vacuum; ii) suppressing the tangential component of the fluid velocity field at all surfaces caused by mechanical vibration of the resonant transducer in the sample fluid; iii) reducing the thermal conductivity and heat capacity of the resonant transducer by carefully selecting the constituent materials and shape; and iv) minimizing the gap between the movable surfaces and avoiding the use of capacitive readout systems that involve squeeze film damping.

[0077] In any measuring device, the readout system has a noise floor that depends on its operating principle, structural quality, temperature, etc. To prevent the noise floor from affecting the signal-to-noise ratio of the PAS system, maximization of the displacement of the resonant transducer due to the pressure signal from the acoustic cell can be applied, as described in this disclosure. Amplification of the resonant transducer displacement due to the pressure signal from the acoustic cell is also applied simultaneously to noise originating from the coupling system. When efficient energy transfer occurs through resonant coupling between a significantly coupled and closely coupled, or ideally optimally coupled, resonant cavity and resonant transducer, the displacement amplitude of one or more active surfaces of the resonant transducer for a given excitation of the resonant cavity can be significantly increased compared to a very weakly coupled system. In such a configuration, if the coupling strength Ω is sufficiently large, satisfies the conditions of equation (27), and the displacement amplitude of the resonant transducer is maximized, and furthermore, if the Q value Q2 of the resonant transducer is sufficiently high and satisfies the conditions of equation (28) (where T is the temperature of both the sample fluid in the resonant cavity and the resonant transducer), then the input-referred noise amplitude spectral density β associated with the readout system contributes less than 12% to the total output noise of the resonant transducer unit, which is composed of the noise of the readout system and thermal noise. In this case, in contrast to an ultra-low noise readout system, even a relatively noisy and potentially low-cost readout system, such as one employing piezoelectric conversion, will have the majority of the total output noise consisting of noise originating from the coupling system. To obtain the numerical value of this inequality, it is necessary to use the value of m2, which is the sprung mass of the resonant transducer, and this value can be calculated from the shape of the resonant transducer and the density of the constituent materials.

number

number

[0078] According to the fluctuation dissipation theorem, the source of thermal noise in a system corresponds to losses. Referring to the coupled oscillator system 100 in Figure 1A, the noise in Newtons due to all dissipation mechanisms is given by equation (29).

number

number

[0079] A PAS system in which the signal-to-noise ratio is determined solely by the acoustic thermal noise of the acoustic cell can be designed, as described in this disclosure, to maximize the displacement of the resonant transducer caused by the pressure signal from the acoustic cell while minimizing the noise contribution of the resonant transducer. In some embodiments, by selecting the operating frequency to be the resonant frequency of the resonant cavity and setting the detuning to zero, the inequality (31) below holds.

number

[0080] Figure 2A shows one embodiment of a dual-resonance photoacoustic spectroscopy system 200. The photoacoustic spectroscopy system 200 includes: an acoustic cell 202 including a resonant cavity 204, the resonant cavity 204 supporting a first resonant mode having a first resonant frequency, and the acoustic cell 202 is capable of supplying a sample fluid 206; an electromagnetic radiation unit 208 including an emitter 210 and a control circuit 212, the emitter 210 transmitting electromagnetic radiation through the resonant cavity 204; and a resonant transducer unit 214 including a resonant transducer 216 and a readout system 218, the resonant transducer 216 supporting a second resonant mode having a second resonant frequency, and the resonant transducer 216 is functionally connected to the resonant cavity 204. The first and second resonant modes are configured to be coupled in a significant coupling region.

[0081] The acoustic cell 202 is configured to support resonant acoustic waves within the resonant cavity 204. The electromagnetic radiation unit 208 is configured to control the transmission of electromagnetic radiation passing through the resonant cavity 204. In particular, the control circuit 212 is configured to controllably operate the emitter 210. The resonant transducer unit 214 is configured to convert a pressure signal into a mechanical displacement, and that mechanical displacement into an electrical signal. In particular, the readout system 218 is configured to output a signal corresponding to the signal converted by the resonant transducer 216 (i.e., converted by converting the mechanical displacement of the resonant transducer into an electrical signal).

[0082] A person skilled in the art will understand, both in this specification and throughout this disclosure, that the first resonant mode of the resonant cavity 204 does not necessarily refer to the first normal mode of the resonant cavity 204, but rather to a particular resonant mode among many possible resonant modes. Similarly, the second resonant mode of the resonant transducer 216 does not necessarily refer to the second normal mode of the resonant transducer 216, but rather to a particular resonant mode among many possible resonant modes.

[0083] Figure 2B shows a dual-resonance photoacoustic spectroscopy system 250 of a further embodiment. The system 250 further includes a fluid processing system 302 and a control system 232. The fluid processing system 302 is configured to supply a sample fluid 206 to an acoustic cell 202. The fluid processing system further includes at least one heat exchanger 230, which is configured to allow the supplied sample fluid 206 to reach thermal equilibrium with the acoustic cell 202 before entering the resonant cavity 204. In some embodiments, the heat exchanger 230 is functionally connected to an inlet port 112a.

[0084] The control system 232 may monitor and / or control one or a combination of (i) the temperature of the sample fluid 206, (ii) the pressure of the sample fluid 206, (iii) the humidity of the sample fluid 206, (iv) the mass flow rate of the sample fluid 206 passing through the acoustic cell 202, (v) the temperature of the resonant transducer 216, and (vi) the temperature of the acoustic cell 202. In some embodiments, one or a combination of (i) the temperature of the sample fluid 206, (ii) the pressure of the sample fluid 206, (iii) the humidity of the sample fluid 206, and (iv) the mass flow rate of the sample fluid 206 passing through the acoustic cell 202 is measured at the outlet port 112b of the acoustic cell 202. In some embodiments, the control system 232 controls at least a heating device 234 capable of heating the acoustic cell 202, and the control system 232 also measures at least the temperature of the resonant cavity 204 by measuring the temperature of the acoustic cell 202 at one or more locations 238 that are close to the resonant cavity 204 and have good thermal contact with the resonant cavity 204.

[0085] Figure 3 shows an example of an interface between an acoustic cell 202 and a resonant transducer unit 214. The acoustic cell 202 includes a resonant cavity 204. The acoustic cell 202 is capable of receiving a sample fluid 206. In this example, the acoustic cell 202 further includes at least one acoustic port 220, at least one transducer housing 222, at least one acoustic frequency filter 226, at least one optical window 224, and at least one port 112 for supplying the sample fluid 206.

[0086] At least one acoustic port 220 extends from the resonant cavity 204 and is functionally connected to at least one active surface of the resonant transducer 216. The at least one acoustic port 220 can take various forms, including i) a hollow tube extending from the resonant cavity 204 as shown in Figure 3, ii) a hole formed in the wall of the resonant cavity 204, or iii) any other form that allows the active surface of the resonant transducer 216 to be functionally connected to the acoustic waves in the resonant cavity 204. At least one transducer housing 222 can serve several purposes, including: Specifically, i) sealing at least one encapsulation volume covering at least one active surface of the resonant transducer 216 to isolate it from the external environment; ii) shielding the resonant transducer unit 214 from electromagnetic noise; iii) minimizing vulnerability to ambient acoustic noise by mechanically shielding the resonant transducer 216 from external pressure waves; iv) protecting the resonant transducer 216 from contamination and damage; and v) minimizing steady gas flow generated around or inside the structure of the resonant transducer 216 due to pressure differences that may occur between the acoustic cell 202 and the surrounding fluid. At least one acoustic frequency filter 226 in this example includes two buffer volumes. The buffer volumes reduce background noise generated by laser absorption in at least one optical window 224. At least one optical window 224 may be formed from quartz, zinc selenide (ZnSe), ultraviolet fused silica, sapphire, silicon, germanium, or other material that reduces the absorption of energy from an electromagnetic radiation source, and may also be coated with an anti-reflective optical coating. At least one optical window 224 serves to isolate the acoustic environment inside the acoustic cell 202 from the external environment. The acoustic cell 202, in particular the transducer housing 222, may be made airtight using sealing gaskets as needed. At least one port 112 includes an inlet port 112a and an outlet port 112b.

[0087] Continuing to refer to Figure 3, in this example, the resonant transducer unit 214 includes a resonant transducer 216 mounted on a printed circuit board (PCB) 228. The PCB 228 can be mounted on the acoustic cell 202 so that the resonant transducer 216 is correctly positioned and functionally connected to the resonant cavity 204. At least a portion of the readout system 218 may be located on the PCB 228. V. Gas Processing Systems

[0088] Operating the dual-resonance photoacoustic spectroscopy systems 200 and 250 at a constant temperature may be optimal for several reasons. Firstly, resonant MEMS transducers are typically made of silicon, which exhibits significantly larger temperature-induced frequency drift compared to other materials commonly used in resonator fabrication, such as AT-cut quartz (3750 ppm for silicon and 20 ppm for AT-cut quartz in the temperature range of -40°C to 85°C). Furthermore, the resonant frequency of the resonant cavity 204 also drifts significantly due to changes in the sound velocity of the sample fluid 206 contained within it. Therefore, heating and maintaining the acoustic cell 202 and resonant transducer 216 at precise temperatures is necessary to achieve reliable performance. The temperature-induced drift of the resonant frequencies of the resonant cavity 204 and the resonant transducer 216 can also be used to compensate for frequency variations that may occur due to manufacturing tolerances of these components, thereby enabling operation close to the optimal detuning δ0. Heating the acoustic cell 202 also has the additional advantage of reducing the adsorption of the analyte to the inner walls of the acoustic cell 202 and the resonant cavity 204. A heat exchanger 230 may be fabricated and formed within the external structure of the acoustic cell 202 to maintain the temperatures of the resonant cavity 204, the resonant transducer 216, and the sample fluid 206 in a stable and controlled state.

[0089] Plot 400 in Figure 4 shows an example where temperature is used as a tuning parameter, illustrating the effect of the temperatures of the acoustic cell 202, the resonant transducer 216, and the sample fluid 206 (assuming they are equal in this example) on the measured photoacoustic system response as a function of frequency. The curve shown corresponds to the case where the temperature increases from bottom to top and is vertically offset for improved visibility. Both the frequency of the resonant cavity 204 and the frequency of the silicon-based resonant transducer 216 change with temperature, but the frequency shift of the resonant transducer 216 is not solely due to the change in the temperature-dependent elastic constant of silicon. The resonant transducer 216 (a piezoelectric MEMS pressure transducer in this example) is expected to shift by only about -30 ppm / °C, while the actually observed shift is approximately -540 ppm / °C. The majority of this shift is due to the change in the acoustic properties of the sample fluid 206 located behind the resonant transducer 216 in the sealed space 222.

[0090] In some embodiments, the first resonant frequency of the resonant cavity 204, the second resonant frequency of the resonant transducer 216, or both resonant frequencies are configured to be adjustable, so that the system can be adjusted to at least one of (i) a proximity-tuned configuration and (ii) an optimally tuned configuration.

[0091] Throughout this specification and disclosure, “tunable” refers to parameters that are intentionally controlled to produce a desired output. The material properties of the sample fluid 206, acoustic cell 202, resonant cavity 204, and resonant transducer 216 may change with environmentally induced changes such as temperature, pressure, or humidity, but these parameters must be controlled externally in some way in order to be considered tunable.

[0092] In some embodiments, the system further includes a control system 232 configured to stabilize at least one or a combination of (i) the temperature of the sample fluid 206, (ii) the pressure of the sample fluid 206, (iii) the humidity of the sample fluid 206, (iv) the mass flow rate of the sample fluid 206 passing through the acoustic cell 202, (v) the temperature of the resonant transducer 216, and (vi) the temperature of the acoustic cell 202.

[0093] In some further embodiments, the first resonant frequency of the resonant cavity 204 is configured to be lower than the second resonant frequency of the resonant transducer 216 at a first temperature (T1), and higher than the second resonant frequency of the resonant transducer 216 at a second temperature (T2). Here, T1 ≠ T2, and the control system 232 is configured to stabilize the temperature of the acoustic cell 202 to at least an arbitrary selected temperature between T1 and T2. Throughout this specification and disclosure, “stabilizing the temperature of the acoustic cell 202” can be understood to mean stabilizing the temperature of one or a combination of i) the resonant transducer 216, ii) the resonant cavity 204, iii) the sample fluid 206 in the resonant cavity 204, and iv) the entire acoustic cell 202.

[0094] In some embodiments, the resonant transducer 216 is selected from one or a combination of (i) an out-of-plane resonator, (ii) a tuning fork resonator, (iii) a cantilever resonator, and (iv) a diaphragm resonator.

[0095] In a preferred embodiment, the resonant transducer 216 is a MEMS device.

[0096] In some embodiments, the acoustic cell 202 further includes at least one acoustic frequency filter 226 functionally connected to the resonant cavity 204. Throughout this specification and disclosure, “acoustic frequency filter” means any type of filter configured to reduce the transmission of noise to the resonant cavity 204. This at least one acoustic frequency filter 226 is selected from i) a bandstop filter, ii) a low-pass filter, or iii) an attenuation filter, which can be implemented as one or a combination of a quarter-wave tube, a buffer space, or an acoustic attenuator. This at least one acoustic frequency filter 226 can be connected to at least one port 112 and / or the resonant cavity 204.

[0097] In some embodiments, the acoustic cell 202 further includes at least one transducer housing 222, each transducer housing 222 configured to enclose a portion of the sample fluid 206 surrounding at least one active surface of a resonant transducer 216, thereby isolating that at least one active surface of the resonant transducer 216 from the external environment.

[0098] In some embodiments, the readout system 218 is configured to detect the resonant transducer 216 using a piezoelectric material.

[0099] In some embodiments, the readout system 218 may be configured to detect the resonant transducer 216 using a piezoelectric material.

[0100] In some embodiments, the readout system 218 further includes a preamplifier in the vicinity of the resonant transducer 216.

[0101] In some embodiments, the resonant transducer 216 is mounted on a printed circuit board (PCB) 228, which is attached to the acoustic cell 202 such that the resonant transducer 216 is functionally connected to the resonant cavity 204, and at least a portion of the readout system 218 is located on the PCB 228.

[0102] In some embodiments, the acoustic cell 202 is constructed using a one-piece design that includes a resonant cavity 204, at least one acoustic frequency filter 226, and an acoustic port 220, which are machined from a single piece of material. The one-piece design may be desirable in reducing assembly steps and ensuring fixed positional relationships and good thermal contact between the components and between parts of the resonant transducer unit 214, including the resonant transducer 216 mounted on the one-piece acoustic cell.

[0103] In some embodiments, the acoustic cell 202, configured using an integrated structural design, further includes a machined heat exchanger 230 within the acoustic cell 202, which allows the sample fluid 206 to reach thermal equilibrium with the acoustic cell 202 before entering the resonant cavity 204.

[0104] In some embodiments, the Q-factor of the resonant transducer 216 in a vacuum is configured to be substantially greater than the Q-factor of the resonant transducer 216 in the sample fluid 206.

[0105] Furthermore, in some embodiments, the Q value of the resonant transducer 216 in a vacuum is configured to be greater than 1000.

[0106] In some embodiments, the coupling strength Ω between the resonant cavity 204 and the resonant transducer 216 is greater than or equal to the threshold shown in equation (32).

number

[0107] In some embodiments, the readout system 218 has an input-referred noise amplitude spectral density β, the sample fluid 206 in the resonant cavity 204 and the resonant transducer 216 have a temperature T, and the Q value Q2 of the resonant transducer 216 is greater than or equal to the threshold shown in equation (33).

number

[0108] Furthermore, in some embodiments, the coupling strength Ω is greater than or equal to the threshold shown in equation (34), so that the noise from the readout system 218 contributes less than 12% to the total output noise of the resonant transducer unit 214, which is composed of the noise from the readout system 218 and the thermal noise of the resonant cavity 204 and the resonant transducer 216.

number

[0109] In some embodiments, both the sample fluid 206 in the resonant cavity 204 and the resonant transducer 216 are at temperature T, the operating frequency is set to the first resonant frequency of the resonant cavity 204, the detuning is set to zero, the coupling strength satisfies the condition of equation (35), and the Q value of the resonant transducer 216 is configured to be greater than or equal to the threshold shown in equation (36). As a result, most of the noise in the electrical signal converted by the resonant transducer unit 214 is attributable to the inherent thermoacoustic noise of the resonant cavity 204.

number

number

[0110] In some embodiments, the acoustic cell 202 further includes at least one acoustic port 220.

[0111] In some embodiments, the acoustic cell 202 further includes at least one optical window 224.

[0112] In some embodiments, the emitter 210 includes one of the following options: (i) a quantum cascade laser (QCL), (ii) a continuous wave (CW) laser, (iii) a pulsed laser, (iv) an interband cascade laser (ICL), (v) a vertical cavity surface-emitting laser (VCSEL), and (vi) a thermal emitter.

[0113] In some embodiments, the control circuit 212 is configured to modulate at least the output of the emitter 210, wherein modulating the output of the emitter 210 includes modulating one or a combination of (i) the emission wavelength of the electromagnetic radiation, (ii) the emission intensity of the electromagnetic radiation, (iii) the pulse repetition rate of the electromagnetic radiation, and (iv) one or a combination of patterned pulse trains of the electromagnetic radiation.

[0114] In some embodiments, the readout system 218 further includes a preamplifier, which comprises any one of the following: (i) a differential charge amplifier, (ii) a differential transimpedance amplifier, (iii) a single-ended voltage amplifier, (iv) a single-ended charge amplifier, or (v) a single-ended transimpedance amplifier, (vi) an instrumentation amplifier, or (vii) other preamplifier configurations currently known or to be developed in the future.

[0115] In some embodiments, the readout system 218 is configured to convert the displacement of the resonant transducer 216 into one or more electrical signals, and to amplify and process these one or more electrical signals.

[0116] In some embodiments, the acoustic cell 202 is configured to be sealed with the sample fluid 206 contained inside.

[0117] In some embodiments, the acoustic cell 202 further includes at least one port 112 connected to the fluid processing system 302.

[0118] In some embodiments, the fluid processing system 302 is composed of at least a portion of a low-adsorption material such as glass, ceramic, aluminum, stainless steel, or fluoropolymer (PTFE, PFA, etc.). In some embodiments, at least a portion of these components is coated with a passivation layer. In a preferred embodiment, the fluid processing system 302 is composed of at least a portion of metal components coated with a silicon-based passivation layer.

[0119] In some embodiments, the resonant cavity 204 has an absolute rate of change of a first resonant frequency as a function of temperature (|∂ω1 / ∂T|), and the resonant transducer 216 has an absolute rate of change of a second resonant frequency as a function of temperature (|∂ω2 / ∂T|), where |∂ω1 / ∂T| ≠ |∂ω2 / ∂T|.

[0120] In some embodiments, one or both of the first resonant frequency of the resonant cavity 204 and the second resonant frequency of the resonant transducer 216 are configured to be adjustable by pressure.

[0121] In some embodiments, one or both of the first resonant frequency of the resonant cavity 204 and the second resonant frequency of the resonant transducer 216 are configured to be adjustable by humidity.

[0122] In some embodiments, the Q-factor of the uncoupled resonant transducer 216 in the sample fluid 206 is configured to be substantially greater than the Q-factor of the resonant cavity 204.

[0123] In some embodiments, the method further includes operating the system in an optimally tuned configuration.

[0124] In some embodiments, a resonant cavity supporting a first resonant mode having a first resonant frequency further comprises a plurality of resonant cavities supporting a first resonant mode having a first resonant frequency, and a resonant transducer supporting a second resonant mode having a second resonant frequency further comprises a plurality of resonant transducers supporting a second resonant mode having a second resonant frequency, wherein the coupling between the first resonant mode of the plurality of resonant cavities and the second resonant mode of the plurality of resonant transducers is configured to be within a significant coupling region and to be proximity-tuned, the emitter transmits electromagnetic radiation through the plurality of resonant cavities, and the gas processing system is configured to circulate the sample fluid across the plurality of resonant cavities.

[0125] In some embodiments, a resonant cavity supporting a first resonant mode having a first resonant frequency further comprises a plurality of resonant cavities supporting a first resonant mode having a first resonant frequency, a resonant transducer supporting a second resonant mode having a second resonant frequency further comprises a plurality of resonant transducers supporting a second resonant mode having a second resonant frequency, an electromagnetic radiation unit including an emitter and a control circuit further comprises a plurality of emitters, the coupling between the first resonant mode of the plurality of resonant cavities and the second resonant mode of the plurality of resonant transducers is configured to be within a significant coupling region and to be proximity-tuned, each of the plurality of emitters transmits electromagnetic radiation through one of the plurality of resonant cavities, and the gas processing system is configured to circulate a sample fluid across the plurality of resonant cavities.

[0126] Figure 5 shows a method for performing photoacoustic spectroscopy. In step 512, the photoacoustic spectroscopy system 200 or 250 described above is prepared. In step 514, the emitter 210 is operated in modulation mode, thereby causing the analyte molecules in the sample fluid 206 within the resonant cavity 204 to undergo periodic absorption and heating at the operating frequency. In step 516, the acoustic cell 202 is configured such that this periodic heating induces an acoustic pressure wave having an amplitude proportional to the concentration of the analyte molecules in the sample fluid 206 within the resonant cavity 204, exciting the coupled resonant cavity and resonant transducer modes (i.e., the coupled mode of the first and second resonant modes). In step 518, the excitation of the coupled resonant cavity and resonant transducer modes is detected by measuring the displacement of the resonant transducer 216 in a frequency-dependent manner using the readout system 218. In step 520, a signal representing the concentration of the analyte molecules is output via the readout system 218.

[0127] In some embodiments, the method further includes configuring a control system 232 to stabilize the temperatures of the sample fluid 206, the resonant transducer unit 214, and the resonant cavity 204, thereby actively stabilizing the detuning between the first and second resonant modes and maintaining either a proximity-tuned configuration or an optimally tuned configuration.

[0128] In some embodiments, the method further includes increasing the amplitude of the signal transformed by the resonant transducer 216 to improve the signal-to-noise ratio of the readout system 218, which is achieved by increasing the coupling strength by one or a combination of i) selecting a shape for the resonant transducer 216 having a large active area, ii) positioning the resonant transducer 216 and its associated acoustic port 220 at the pressure maximum position within the resonant cavity 204, and iii) increasing the Q value of the resonant transducer 216 by reducing coupling to vorticity waves and thermal waves, thereby operating the photoacoustic spectroscopy system in proximity-tuned or optimally-tuned configuration.

[0129] In some embodiments, the readout system 218 has an input-referred noise amplitude spectral density β, and the method is further applied such that the coupling strength satisfies the condition of equation (37) and the Q value of the resonant transducer 216 is at least equal to the threshold shown in equation (38), so that the noise from the readout system 218 contributes less than 12% to the total output noise of the resonant transducer unit 214, which is composed of the noise from the readout system 218 and the thermal noise of the resonant cavity 204 and the resonant transducer 216.

number

number

[0130] In some embodiments, the readout system 218 has an input-referred noise amplitude spectral density β, the sample fluid 206 in the resonant cavity 204 and the resonant transducer 216 are at temperature T, and the method further includes providing a photoacoustic spectroscopy system such that the contribution of the intrinsic thermoacoustic noise of the resonant cavity 204 to the total output noise of the resonant transducer unit 214 is greater than the sum of the contribution of the intrinsic thermomechanical noise of the resonant transducer 216 and the noise of the readout system 218 to the total output noise of the resonant transducer unit 214, so that the noise of the electrical signal converted by the resonant transducer unit 214 is largely attributable to the intrinsic thermoacoustic noise of the resonant cavity 204. This is achieved by selecting a resonant transducer 216 having a sufficiently high Q value that satisfies the condition of equation (39), selecting a resonant transducer 216 having a sufficiently high coupling strength that satisfies the condition of equation (40), tuning the photoacoustic spectroscopy system to zero detuning, and operating the photoacoustic spectroscopy system at an operating frequency corresponding to the crossover frequency ω0 in the uncoupled state.

number

number

[0131] In some embodiments, the method further includes operating the control circuit 212 to modulate the wavelength of the emitter 210 at a frequency half the operating frequency of the resonant cavity 204 and the resonant transducer 216, while simultaneously reducing unwanted background photoacoustic signals by measuring the signal output of the resonant transducer unit 214 at the operating frequency using a signal band selector.

[0132] This disclosure describes several embodiments, and many modifications of the invention can be easily conceived by those skilled in the art by reading this disclosure, and the scope of the invention should be determined by the following claims.

[0133] Although the present invention has been described with reference to preferred embodiments, various modifications are possible, as will be apparent to those skilled in the art. Such modifications and variations are within the scope of the present invention.

[0134] Representative and non-limiting embodiments of the present invention have been described in detail with reference to the accompanying drawings. This detailed description is intended solely to teach those skilled in the art further details for carrying out preferred embodiments of the present invention and is not intended to limit the scope of the invention. Furthermore, each of the additional features and teachings described above and below may be used individually or in combination with other features and teachings.

[0135] Furthermore, the combinations of features and processes disclosed in the above detailed description and examples are not necessarily required to carry out the invention in its broadest sense, but rather are provided to specifically illustrate representative examples of the invention. Moreover, various features of the above representative examples, as well as the various independent and dependent claims below, can be combined in ways not specifically and explicitly enumerated to provide additional useful embodiments of this teaching.

Claims

1. A photoacoustic spectroscopy system, An acoustic cell comprising a resonant cavity configured to support a first resonant mode having a first resonant frequency, and to which a sample fluid can be supplied, An electromagnetic radiation unit including an emitter and a control circuit, wherein the emitter is configured to transmit electromagnetic radiation through the resonant cavity, A resonant transducer unit comprising a resonant transducer and a readout system, wherein the resonant transducer is configured to support a second resonant mode having a second resonant frequency, and the resonant transducer is functionally connected to the resonant cavity, A photoacoustic spectroscopy system configured such that the first resonance mode and the second resonance mode are coupled in a significant coupling region.

2. The system according to claim 1, wherein either or both of the first resonant frequency of the resonant cavity and the second resonant frequency of the resonant transducer are configured to be adjustable, so that the system can be adjusted to achieve at least one of (i) a proximity-tuned configuration and (ii) an optimally tuned configuration.

3. The system according to claim 1 or 2, further comprising a control system configured to stabilize at least one or a combination of (i) the temperature of the sample fluid, (ii) the pressure of the sample fluid, (iii) the humidity of the sample fluid, (iv) the mass flow rate of the sample fluid passing through the acoustic cell, (v) the temperature of the resonant transducer, and (vi) the temperature of the acoustic cell.

4. The system according to claim 3, wherein the first resonant frequency of the resonant cavity is configured to be smaller than the second resonant frequency of the resonant transducer at a first temperature (T1), and the first resonant frequency of the resonant cavity is configured to be larger than the second resonant frequency of the resonant transducer at a second temperature (T2), where T1 ≠ T2, and the control system is configured to stabilize the temperature of the acoustic cell at least to any selected temperature between T1 and T2.

5. The system according to any one of claims 1 to 4, wherein the resonant transducer is selected from one or a combination of (i) an out-of-plane resonator, (ii) a tuning fork resonator, (iii) a cantilever resonator, and (iv) a diaphragm resonator.

6. The system according to any one of claims 1 to 5, wherein the acoustic cell further comprises at least one acoustic frequency filter functionally connected to the resonant cavity.

7. The system according to any one of claims 1 to 6, wherein the acoustic cell further comprises at least one transducer housing, each of which is configured to enclose a portion of the sample fluid surrounding at least one active surface of the resonant transducer, thereby isolating the at least one active surface of the resonant transducer from the external environment.

8. The system according to any one of claims 1 to 7, wherein the readout system is configured to detect the resonant transducer using a piezoelectric material.

9. The system according to claim 8, wherein the readout system further includes a preamplifier in the vicinity of the resonant transducer.

10. The system according to any one of claims 1 to 9, wherein the resonant transducer unit further includes a printed circuit board (PCB), the resonant transducer is mounted on the PCB, the PCB is attached to the acoustic cell such that the resonant transducer is functionally connected to the resonant cavity, and at least a portion of the readout system is arranged on the PCB.

11. The system according to any one of claims 1 to 10, wherein the acoustic cell is constructed using a one-piece structural design and further comprises at least one acoustic frequency filter and an acoustic port machined from a single piece of material.

12. The system according to claim 11, wherein the acoustic cell, configured using a one-piece structural design, further includes a machined heat exchanger within the acoustic cell, which enables the sample fluid to reach thermal equilibrium with the acoustic cell at least before entering the resonant cavity.

13. The system according to any one of claims 1 to 12, wherein the Q value of the second resonance mode of the resonant transducer in a vacuum is configured to be substantially greater than the free Q value of the second resonance mode of the resonant transducer in the sample fluid.

14. The system according to any one of claims 1 to 13, wherein the Q value of the resonant transducer in a vacuum is configured to be greater than 1000.

15. The system according to any one of claims 1 to 14, wherein the coupling strength (Ω) between the resonant cavity and the resonant transducer is greater than or equal to the threshold shown in the following formula (1). [Math 1]

16. The aforementioned resonant transducer has a Q value Q 2 The system according to any one of claims 1 to 15, wherein the Q value is greater than or equal to the threshold shown in the following equation (2), the readout system has a noise amplitude spectral density β, and both the sample fluid in the resonant cavity and the resonant transducer have a temperature T. [Math 2]

17. The system according to any one of claims 1 to 16, wherein the acoustic cell further comprises at least one acoustic port.

18. The system according to any one of claims 1 to 17, wherein the acoustic cell further comprises at least one optical window.

19. The system according to any one of claims 1 to 18, wherein the emitter includes one of the following options: (i) a quantum cascade laser (QCL), (ii) a continuous wave (CW) laser, (iii) a pulsed laser, (iv) an interband cascade laser (ICL), (v) a vertical cavity surface-emitting laser (VCSEL), and (vi) a thermal emitter.

20. The system according to any one of claims 1 to 19, wherein the control circuit is configured to modulate at least the output of the emitter, and modulating the output of the emitter includes modulating one or a combination of (i) the emission wavelength of the electromagnetic radiation, (ii) the emission intensity of the electromagnetic radiation, (iii) the pulse repetition rate of the electromagnetic radiation, and (iv) the patterned pulse train of the electromagnetic radiation.

21. The system according to any one of claims 1 to 20, wherein the readout system further includes a preamplifier, the preamplifier comprising one of (i) a differential charge amplifier, (ii) a differential transimpedance amplifier, (iii) a single-ended voltage amplifier, (iv) a single-ended charge amplifier, (v) a single-ended transimpedance amplifier, and (vi) an instrumentation amplifier.

22. The system according to any one of claims 1 to 21, wherein the readout system is configured to convert the displacement of the resonant transducer into one or more electrical signals, and to amplify and process the one or more electrical signals.

23. The system according to any one of claims 1 to 22, wherein the acoustic cell is configured to be sealed with the sample fluid contained inside.

24. The system according to any one of claims 1 to 23, wherein the acoustic cell further includes at least one port connected to a fluid processing system.

25. The system according to claim 24, wherein the fluid processing system is composed of at least a portion of low-adsorption tubes.

26. A method for performing photoacoustic spectroscopy, A photoacoustic spectroscopy system according to any one of claims 1 to 25 is provided, The emitter is operated in modulation mode, thereby causing the analyte molecules in the sample fluid within the resonant cavity to undergo periodic absorption and heating at the operating frequency. The acoustic cell is configured such that the periodic heating induces an acoustic pressure wave having an amplitude proportional to the concentration of the analyte molecule in the sample fluid within the resonant cavity, thereby exciting the modes of the coupled resonant cavity and resonant transducer. By measuring the displacement of the resonant transducer in a frequency-dependent manner using the readout system, the excitation of the excited coupled resonant cavity and the modes of the resonant transducer can be detected. A method comprising outputting a signal representing the concentration of the analyte via the readout system.

Images