Many gas sensors use spectroscopy to measure or infer physical properties of a gas sample. Examples of such physical properties include concentration, temperature, and pressure. These spectroscopic gas sensors use various signal processing techniques to convert raw spectroscopic data into estimates of the physical properties.
One technique that can be used to derive physical properties from raw spectroscopic data is fitting a measured spectrum to a mathematical model. For example, non-linear least-squares can be implemented with a Levenberg-Marquardt algorithm to identify a set of best-fit parameters that optimize agreement between the model and the measured spectrum. These best-fit parameters can then be processed to calculate the physical properties. Other nonlinear regression algorithms and techniques may be used
Nonlinear regression suffers from several drawbacks. First, it is computationally intensive because it typically involves many operations, like division, that are relatively time-consuming and inefficient. Second, many regression algorithms are iterative, continuing until some level of convergence has been reached. However, these algorithms sometimes do not converge, such as when the initial values of the parameters are not well selected. It can also be challenging to identify initial values with sufficient accuracy to ensure convergence. Third, the number of iterations needed to reach convergence can vary depending on the initial values. Accordingly, the algorithm may not always have the same execution time, which can lead to back-logs of data and delays in operation of the gas sensor.
To avoid these drawbacks, regression can be avoided altogether. For example, the measured spectrum can be compared to several “template” spectra that are stored in, and retrieved from, a look-up table. Each template spectrum is generated from the mathematical model using one unique set of values for the parameters. Calculating the discrepancy between the measured spectrum and the template spectrum (e.g., a residual sum of squares) can be performed quickly and efficiently (e.g., using a microprocessor). The template spectrum that gives rise to the smallest discrepancy may then be selected as a best-fit spectrum. The corresponding parameters used to generate the best-fit spectrum approximate the best-fit parameters that would have been obtained with non-linear regression. These parameters may then be processed to derive the properties of the sample.
In a simple implementation of a look-up table, the measured spectrum is compared to every template spectrum in the look-up table. The time complexity for this operation is O(N), where N is the number of template spectra in the look-up table. Although such linear scaling is generally considered efficient, N may be so large that this comparison becomes too time-consuming to be practical (e.g., several seconds, or longer). For example, the look-up table could store millions of template spectra, or more.
One way to avoid having to access every template spectrum in the look-up table is to implement the look-up table as a hash table. Here, the measured spectrum can be fed into a hash function that returns an integer hash value h. The template spectrum and parameters stored in the hth bin, or bucket, of the hash table are retrieved. These parameters may then be used as the best-fit parameters for deriving the physical properties of the gas sample. Advantageously, the use of a hash table dramatically improves time complexity to O(1).
One drawback to hash tables is that the resulting hash values are overly sensitive to noise in the measured spectrum. Specifically, a measured spectrum may be decomposed into a signal component and a noise component. Two measured spectra with the same signal component but different noise components should produce the same hash value (i.e., a collision), thereby leading to the same set of parameters stored in the same bin of the hash table. However, conventional hash functions are designed to avoid collisions between inputs that are not exactly identical. Accordingly, these two spectra will yield different hash values, and therefore two different sets of parameters stored in two different bins of the hash table.
The present embodiments solve this problem with a look-up table whose bins are accessed using a locality sensitive hash function. Locality sensitive hashing is designed to maximize the probability of a collision between two inputs that are similar, but not identical. In this case, each bin of the look-up table may store several template spectra and corresponding parameters. The time complexity of accessing one bin of the look-up table advantageously remains O(1). As described in more detail below, additional processing is needed to determine which of the template spectra in the one accessed bin best matches the measured waveform. However, this additional processing can be performed quickly.
The present embodiments include spectroscopic gas sensors that utilize locality sensitive hashing to vastly speed up signal processing of raw spectra obtained from an optical spectrometer. Advantageously, the present embodiments may be implemented with a host of spectroscopy techniques known in the art, including wavelength modulation spectroscopy, frequency modulation spectroscopy, and Doppler-free absorption spectroscopy. The present embodiments can operate at rates exceeding 1 kHz.
One application of the present embodiments is reducing emissions and increasing efficiency of natural-gas-powered engines. Heavy-duty trucks and marine vessels operating on diesel and gasoline account for 7% of US energy consumption, a significant, addressable source of greenhouse gas (GHG) emissions. While GHG-reducing electrification is rising among light-duty vehicles, there remain challenges to electrifying long-haul heavy-duty vehicles due to demanding load and mileage requirements. Natural gas as fuel may help reduce GHG production. While natural gas can offer up to a 25% reduction in GHG emission over diesel fuel, reaching parity with diesel efficiency while meeting evolving modern emissions regulations is challenging and has slowed proliferation of this technology.
One strategy to reduce emissions and increase efficiency in commercial natural gas-powered engines is to precisely control the air-to-fuel ratio and exhaust gas recirculation (EGR) rates to maximize power density. This strategy can be implemented with a closed-loop control system coupled with fast gas sensors. The spectroscopic gas sensors herein are fast enough to use in such a closed-loop system, and therefore could be used as part of a high-efficiency natural-gas-powered engine.
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The measured spectrum 102 is a set of n spectroscopic values {α1, α2 . . . , αn}. Each spectroscopic value αi (1≤i≤n) is measured at a corresponding frequency fi of the laser beam 116. Each spectroscopic value αi may be a singular measurement of absorption or dispersion (i.e., phase shift), or a combination of such measurements. The n spectroscopic values may be stored in memory as an array S of n elements in which the ith array element S[i] stores the ith spectroscopic value αi. When the ith frequency fi can be derived from the index i, it does need not to be stored in the array S. The n spectroscopic values may be stored in the array S as a sequence ordered by the n frequencies f1, f2, . . . fn. The frequencies f1, f2, . . . fn may be uniformly spaced in frequency, although this is not necessary. Alternatively, the array may be ordered by the n wavelengths λ1, λ2, . . . λn. The wavelengths λ1, λ2, . . . λn may be uniformly spaced, although this is not necessary.
As an example of how the ith frequency fi can be derived from the index i, the ith spectroscopic value αi may have a corresponding time value ti indicating when the spectroscopic value αi was measured. In this case, the frequency fi can be derived from the time value ti (e.g., based on a predetermined frequency schedule). The n spectroscopic values may be stored in the array S as a sequence ordered by the n time values t1, t2, . . . , tn. In this case, the array S may be thought of as a time series. The time values t1, t2, . . . , tn may be uniformly spaced in time, although this is not necessary. Sweeping the laser frequency fL with a ramp signal (see signal 234 in
The measured spectrum 102 may additionally store the frequencies f1, f2, . . . fn, the time values t1, t2, . . . , tn, additional data, or any combination thereof. In these cases, the measured spectrum 102 is a set of tuples {a1, a2 . . . , an} in which the ith tuple ai contains two or more entries. For example, the ith tuple ai may be ai=(ai, fi, . . . ), where the first entry is the spectroscopic value di and the second entry is the frequency fi. The tuples may have alternative or additional entries without departing from the scope hereof. The tuples may be stored as a sequence ordered by any of their entries.
The spectroscopic gas sensor 100 includes a line-shape processor 122 that processes the measured spectrum 102 to determine and output the one or more properties 108. The line-shape processor 122 compares the measured spectrum 102 to a set of candidate spectra that are retrieved from a look-up table 154 storing a plurality of template spectra. The look-up table 154 may have thousands of bins (also referred to as buckets) or more, each storing one or more template spectra and corresponding parameters. In this case, the look-up table 154, due to its large size, may be stored in an external memory (e.g., a memory card or hard drive). More details about the look-up table 154 and line-shape processor 122 are presented below. In some embodiments, the gas sensor 100 excludes the optical spectrometer 104. For example, the optical spectrometer 104 may be operated or provided by a third party that sends the measured spectrum 102 to the line-shape processor 122 (e.g., via a computer network).
The optical spectrometer 104 may implement any type of spectroscopy that can generate the measured spectrum 102.
The laser 110 may be a tunable diode laser. In this case, the driver 212 may be a current source that is modulated by the ramp signal 234. Examples of tunable diode lasers include, but are not limited to, a Fabry-Perot laser diode, a distributed feedback (DFB) laser, a distributed Bragg reflector (DBR) laser, and a vertical cavity surface emitting laser (VCSEL). The VCSEL may be a micro-electromechanical system VCSEL (MEMS-VCSEL). The laser 110 may alternatively be an external-cavity laser, in which case the frequency sweep can be implemented by modulating the length of the external cavity. The laser 110 may alternatively be a fixed-frequency laser, in which case the frequency fL can be adjusted using a phase or frequency modulator (e.g., an electro-optic modulator or acousto-optic modulator).
Other techniques for controlling the frequency fL that are known in the art may be used with the present embodiments. For example, the optical spectrometer 204 may include a reference laser that is locked to an optical frequency reference (e.g., a molecular or atomic transition, a resonance of a high-finesse Fabry-Perot cavity, etc.). The laser 110 may be offset phase-locked to the reference laser. Changing the offset frequency of the phase-lock loop changes the frequency fL relative to that of the reference laser. If the offset frequency is changed linearly in time (e.g., one period of a triangle or sawtooth wave), the frequency fL will similarly be swept linearly in time. However, the offset frequency can be varied in time in a different manner (e.g., randomly in time, linearly in corresponding wavelength, quadratically, etc.) without departing from the scope hereof.
Another technique for controlling the frequency fL is to offset phase-lock the laser 110 to a tooth of an optical frequency comb. The optical frequency comb may be stabilized to an optical or microwave frequency reference, thereby transferring the frequency stability of the reference to the frequency of the tooth. Changing the offset frequency of the phase-lock loop changes the frequency fL relative to that of the comb. The frequency fL can also be changed by adjusting one or both of the comb offset and comb repetition rate of the optical frequency comb. In this case, the offset frequency between the laser 110 and the tooth may be kept fixed.
The absorption spectroscopy implemented by the optical spectrometer 204 is relatively simple since there is no modulation and demodulation. In this case, the optical spectrometer 204 can alternatively be constructed using a tunable incoherent light beam instead of the laser beam 116. Such an incoherent light beam can be generated with a tunable incoherent light source, such as a lamp with a broadband output that is filtered with a tunable filter (e.g., a monochromator or similar type of grating-based optical filter). Accordingly, it should be recognized that many of the present embodiments may be implemented with incoherent light by replacing the laser 110 with a tunable source of incoherent light.
The optical spectrometer 304 also includes a lock-in amplifier 350 that uses the modulation signal 316 as a reference signal for demodulating the output 138 of the photodetector 120. The lock-in amplifier 350 may demodulate at the modulation frequency fm or a harmonic thereof (e.g., 2fm, 3fm, etc.). The lock-in amplifier 350 outputs an in-phase signal 322 and a quadrature signal 324 that a signal processor 314 processes to generate the measured spectrum 102. The signal processor 314 is an example of the signal processor 214 of
Without the ramp signal 234 (e.g., Ar is set to 0), the in-phase signal 322 and quadrature signal 324 would be constant in time (ignoring noise and drift of the laser frequency fL). With the ramp signal 234, the in-phase signal 322 and quadrature signal 324 both vary synchronously with the ramp signal 234. The signals 322 and 324 therefore form scans, over frequency, of the absorption feature, with each of the signals 322 and 324 containing different information (i.e., absorption and dispersion) about the absorption feature.
In some embodiments, the spectroscopic gas sensor 300 includes multiple lasers that are modulated at different modulation frequencies. These lasers may have different wavelengths so that they simultaneously interact with different absorption features of the gas sample 106. The outputs of the lasers may be combined into a single laser beam that, after transmission through the sample 106, is detected by the photodetector 120. The output 138 is then demodulated by at least one lock-in amplifier for each modulation frequency, thereby allowing spectroscopic values to be measured for each laser (i.e., each absorption feature).
The optical spectrometer 404 is an example of the optical spectrometer 304 of
The lock-in amplifiers 450(1) and 450(2) demodulate the output 138 at different harmonics of the modulation signal 316. Specifically, the first lock-in amplifier 450(1) is configured to demodulate at the jth harmonic jfm while the second lock-in amplifier 450(2) is configured to demodulate at the kth harmonic kfm, where j≠k. In one example, j=1 and k=2, i.e., the first lock-in amplifier 450(1) operates at the first harmonic 1fm and the second lock-in amplifier 450(2) operates at the second harmonic 2fm. In another example, j=2 and k=3. The integers j and k may have other values without departing from the scope hereof.
The optical spectrometer 404 also includes a signal processor 414 that is an example of the signal processor 314 of
In
In embodiments, the line-shape processor 122 is implemented as a digital circuit. In some of these embodiments, the line-shape processor 122 may advantageously be implemented using the same digital circuit as other components. For example, in
Those trained in the art will recognize that it is not necessary for lock-in amplifiers, function generators, oscillators, and other components of the present embodiments to be implemented digitally. Accordingly, the present embodiments include any combination of digital and analog implementations of these components. For example, the lock-in amplifiers 450(1) and 450(2) can be implemented as analog circuits while the signal processor 122 is digital. In this case, analog-to-digital converters may be used to digitize the signals 422(1), 424(1), 422(2), and 424(2) for subsequent processing by the signal processor 122.
The gas sample 106 need not be physically confined. For example, the gas sample 106 could be air or gas in the atmosphere. Alternatively, the gas sample 106 can be confined in a chamber. The chamber may be a vapor cell (e.g., made of optically transparent glass or sapphire) or a stainless-steel vacuum system with optical viewports. In any case, the chamber may include a first window through which light from the tunable laser 110 enters the chamber. The chamber may also include a second window through which the light, after passing through the gas sample 106, exists the chamber to reach the photodetector 120.
In
The gas sample 106 may be located remotely from some or all of the components of the spectroscopic gas sensor 100. For example, the gas sample 106 may be located in a space-limited and environmentally demanding location, such as the exhaust of an engine or inside an industrial furnace. One or more components of the present embodiments (e.g., the line-shape processor 122, the signal processor 114, the lock-in amplifier 350, the function generator 262, the oscillator 318, the driver 212, etc.) may be located away from this location, where the environment is less extreme (e.g., cooler temperatures, less vibration, etc.). In this case, optical fibers and electrical cables may be used, as needed, for transmitting optical and electrical signals, respectively, between those components near the gas sample 106 with those components that are remotely located. Since the laser beam 116 can travel several kilometers, it is possible for all of the components of the gas sensor 100, including the laser 110 and photodetector 120, to be located remotely (e.g., more than 10, 100, or 1000 meters away) from the gas sample 106.
One aspect of the present embodiments is the realization that locality-sensitive hashing can be efficiently implemented with a measured spectrum by summing the elements of the measured spectrum and truncating one or more of the least-significant digits of the sum. Applying this to the method 500, the elements of the measured-spectrum array M are summed i.e., s=Σi=1nM[i]. One or more of the less-significant digits of the sum s are then truncated to obtain the integer hash value h, e.g., h=trunc (s,c)=└10cs┘/10c, where c is the number of digits to truncate and the notation └x┘ indicates the floor of x. Referring to the example above, the arrays M1 and M2 have respective sums s1 and s2 that would be identical if it were not for their different noises. Truncating some or all of the less-significant digits of the sums s1 and s2, whose values are more sensitive to noise, leaves the more-significant digits that are less sensitive to noise. If a sufficient number of less-significant digits are truncated from both the sums s1 and s2, then the resulting hash values h1 and h2 will be equal.
To convert the hash value h into an integer index for accessing the look-up table 154, the sum s may be divided by a constant to obtain the integral part of the quotient. This may be implemented using the DIV function that is commonly used in many programming languages. Alternatively, the sum s may be divided by the constant to obtain a real-valued quotient that is converted to an integer either by truncating the decimal points (e.g., using a floor function) or rounding. The value of the constant may be selected, based on the expected range of values of the sum s that is expected, such that the resulting values of h span the number of bins in the look-up table 154.
In step 506 of the method 500, the memory 152 is accessed to retrieve template spectra stored in the hth bin, or bucket, of the look-up table 154. The template spectra retrieved from the look-up table 154 form a set of candidate spectra.
As shown in
In step 508 of the method 500, each candidate spectrum W, of the set of candidate spectra, is compared to the measured-spectrum array M to find a best-fit spectrum WBF that best matches M. Each candidate spectrum W may be thought of as a fixed-parameter mathematical model to which the array M can be fitted. A metric may be calculated to quantify the discrepancy between each candidate spectrum W and the array M. For example, the metric may be the residual sum of squares RSS, given mathematically by
In this case, the candidate spectrum W with the lowest RSS is selected as the best-fit spectrum WBF. Other examples of the metric include, but are not limited to, mean square error, mean absolute error, and root mean square error. Some metrics (e.g., mean square error) include division by the number of elements n. Such division is not necessary in embodiments where n does not change. Given that division is a computationally intensive operation, avoiding this division can help conserve computational resources.
In some embodiments, the template spectra stored in one or both of the (h−1)th and (h+1)th bins are also retrieved and added to the set of candidate spectra as part of the step 506. Similarly, the template spectra stored in one or both of the (h−2)th and (h+2)th bins may be retrieved and added to the set of candidate spectra. Retrieving template spectra from more than one bin accounts for the fact that truncation of the sum s may not remove all of the less-significant digits whose values are susceptible to noise. As a result, while there may be a high probability that the best-fit spectrum WBF is one of the template spectra stored in the hth bin, this probability is not unity. If the best-fit spectrum WBF is not stored in the hth bin, then there is a high probability, due to the locality-sensitive hashing, that it is stored in one of the two neighboring (h−1)th and (h+1)th bins, a lower probability that it is stored one of the two next-to-neighboring (h−2)th and (h+2)th bins, and so on. Accordingly, adding, to the set of candidate spectra, the template spectra stored in two or more bins of the look-up table 154 improves the likelihood that the best-fit spectrum WBF is the one template spectrum, of the entire look-up table 154, that best matches the array M.
In step 510 of the method 500, the parameter set PBF of the best-fit spectrum WBF is retrieved. For example, when the look-up table 154 is accessed the first time in the step 506 to retrieve candidate spectra, the parameter set P associated with each template spectrum may be retrieved with the template spectrum. Alternatively, the look-up table 154 may be accessed a second time, after the best-fit spectrum WBF has been identified, to retrieve only the one parameter set PBF of the best-fit spectrum WBF. In step 512, one or more of the parameters of the parameter set PBF are outputted. These parameters may be outputted as the one or more properties 108 of the gas sample 106 in
The method 500 may be repeated as the measured-spectrum array M is updated. Repeating the method 500 for a sequence of such arrays M1, M2, . . . gives rise to a sequence of the one or more properties 108. Performing the method 500 repeatedly in this manner can be used to identify changes in the one or more properties, from which a change in the gas sample 106 can be inferred. Alternatively, when the gas sample 106 is stable, each of the one or more properties 108 may be averaged over time to reduce statistical uncertainty.
The signals 422(1), 424(1), 422(2), and 424(2) are assumed to be digitized discrete-time signals of length n (e.g., 128 or 256 points). The length n, which determines the temporal duration of the block 700, may be selected to equal one period of the ramp signal 234 (e.g., when the ramp signal 234 is a sawtooth wave) or one-half of the period of the ramp signal 234 (e.g., when the ramp signal 234 is a triangle wave). As shown in
Mathematically, the harmonic-ratio time series H may be defined by
where the notation [i] indicates the ith element, or sample, of the corresponding time series. As can be seen from Eqn. 1, the elements X1[i] and Y1[i] are squared and added to obtain a first amplitude-squared value. Similarly, the elements X2[i] and Y2[i] are squared and added to obtain a second amplitude-squared value. The first amplitude-squared value is then divided by the second amplitude-squared value, thereby normalizing the first amplitude-squared value with the second amplitude-squared value. The square-root of this ratio may be taken, although this adds computational complexity.
Because of the squaring in Eqn. 1, all elements of the harmonic-ratio time series H are non-negative. This property is advantageous for hashing as it prevents cancelation that occurs when some of the elements are positive and some are negatives. Another definition of the time series H that results in non-negative elements is
As can be seen from Eqns. 1 and 2, making each of the elements X1[i], Y1[i], X2[i], and Y2[i] non-negative (e.g., by squaring or taking the absolute value) prior to adding and division is one way to ensure that all elements of H are non-negative. Another definition of H may be used without departing from the scope hereof.
For each parameter p1, p2, . . . , a finite number of values of the parameter are sampled over a range of interest associate with that parameter. For example, if the parameter is concentration of a particular species of gas, the range of interest may range from zero to a maximum concentration to be detected by the spectroscopic gas detector 100. The number of values in the range of interest, and their spacing, may be determined by a target resolution of the gas detector 100. A superset of parameter sets is then constructed by adding to the superset one parameter set Pk formed from each unique combination of the sampled values of all the one or more parameters. Here, k indexes the parameter sets in the superset.
For each parameter set Pk in the superset, the mathematical model 802 is used to construct one corresponding template spectrum Wk by evaluating the model 802 at the same n frequencies f1, f2, . . . fn used for the measured spectrum 102. The model 802 also uses the one parameter set Pk for all n evaluations. The model 802 returns n predicted spectroscopic values {α1*, α2* . . . , αx*} in one-to-one correspondence with the n frequencies f1, f2, . . . fn, where the superscript * indicates that the spectroscopic value is the result of a mathematical calculation (as opposed to a measurement). The n predicted spectroscopic values {α1*, α2* . . . , αx*} are then stored in an array Wk in the same order that the measured spectroscopic values {α1, α2 . . . , αn} are stored in the measured-spectrum array M, i.e., like-numbered elements of the two arrays Wk and M correspond to the same frequency.
Each template spectrum Wk is then hashed using the same locality-sensitive hashing described above (e.g., see step 504 in
In
Step 504 of the method 500 (see
On the other hand, it is advantageous to reduce bin size, which speeds up operation of the spectroscopic gas sensor 100 by reducing the number of candidate spectra that must be processed to find the best-fit spectrum. For example, reducing the bin size by a factor of five from 110 to 22 will reduce the amount of time needed to process the candidate spectra by the same factor of five. However, making the bin size too small increases the probability of getting the wrong bin number. Accordingly, there is a trade-off between speed and accuracy.
It is expected that relatively large bin sizes are needed when one or more of the parameters have little impact on the sum s. One such parameter is the line center, i.e., the frequency of the center of the absorption feature. The position of the line center in the measured spectrum 102 can vary as the laser frequency fL drifts. Consider template spectra that have different values of the line center but are otherwise the same. All of these template spectra will hash to similar bin numbers since changes in line center have little impact on the sum s. Accordingly, locality-sensitive hashing may not be as effective at finding the one template spectrum whose line center is closest to that of the measured spectrum 102. Instead, the template spectra may all be added to the set of candidate spectra (see the step 506 in
Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate possible, non-limiting combinations of features and embodiments described above. It should be clear that other changes and modifications may be made to the present embodiments without departing from the spirit and scope of this invention:
(A1) A method for spectroscopic gas sensing includes operating a spectrometer to generate a measured spectrum of a gas sample and transforming, with a locality-sensitive hash function, the measured spectrum into an integer hash value h. The method also includes adding, to a candidate set of candidate spectra, template spectra stored in an hth bin of a look-up table. The method also includes calculating, based on each candidate spectrum in the candidate set, a measure that quantifies discrepancy between the measured spectrum and said each candidate spectrum. The method also includes identifying, based on the measure, a best-match spectrum of the candidate spectra, and retrieving, from the hth bin of the look-up table, a parameter set corresponding to the best-match spectrum. The method also includes deriving, based on the parameter set, one or more properties of the gas sample.
(A2) In the method denoted (A1), said operating the spectrometer includes scanning a frequency of a laser beam across an absorption feature of the gas sample, transmitting the laser beam through the gas sample, and photodetecting the laser beam after transmission through the gas sample.
(A3) In the method denoted (A2), the template spectra identically have a template length corresponding to a period of said scanning and the measured spectrum has a length equal to the template length.
(A4) In any of the methods denoted (A1) to (A3), said operating the spectrometer includes performing wavelength modulation spectroscopy.
(A5) In the method denoted (A4), said performing wavelength modulation spectroscopy includes performing calibration-free wavelength modulation spectroscopy.
(A6) In any of the methods denoted (A1) to (A5), said transforming includes summing elements of the measured spectrum to obtain a sum and truncating one or more least-significant digits of the sum.
(A7) In any of the methods denoted (A1) to (A6), said operating the spectrometer includes demodulating a spectroscopic signal with a local-oscillator signal to generate an in-phase signal and a quadrature signal, the local-oscillator signal having a frequency equal to a harmonic of a modulation frequency. Said operating the spectrometer also includes processing the in-phase signal and quadrature signal to generate the measured spectrum.
(A8) In the method denoted (A7), said processing includes normalizing the measured spectrum based on one or both of the in-phase signal and the quadrature signal.
(A9) In either of the methods denoted (A7) and (A8), said operating the spectrometer includes (i) frequency modulating a laser beam, prior to transmission through the gas sample, at both the modulation frequency and a ramp frequency different from the modulation frequency, (ii) transmitting the laser beam through the gas sample, and (iii) photodetecting the laser beam after transmission through the gas sample. Said demodulating occurs synchronously with said frequency modulating.
(A10) In any of the methods denoted (A1) to (A9), said operating the spectrometer includes (i) demodulating a spectroscopic signal with a first local-oscillator signal to generate a first in-phase signal and a first quadrature signal, the first local-oscillator signal having a first frequency equal to a harmonic of a modulation frequency, (ii) demodulating the spectroscopic signal with a second local-oscillator signal to generate a second in-phase signal and a second quadrature signal, the second local-oscillator signal having a second frequency equal to a harmonic of the modulation frequency, the second frequency being different from the first frequency, and (iii) processing the first in-phase signal, first quadrature signal, second in-phase signal, and second quadrature signal to generate the measured spectrum.
(A11) In the method denoted (A10), the first frequency is a first harmonic of the modulation frequency and the second frequency is a second harmonic of the modulation frequency.
(A12) In either of the methods denoted (A10) and (A11), said operating the spectrometer includes (i) frequency modulating a laser beam, prior to transmission through the gas sample, at both the modulation frequency and a ramp frequency different from the modulation frequency, (ii) transmitting the laser beam through the gas sample, and (iii) photodetecting the laser beam after transmission through the gas sample. Said demodulating the spectroscopic signal with the first local-oscillator signal and said demodulating the spectroscopic signal with the second local-oscillator signal occur synchronously with said frequency modulating.
(A13) In any of the methods denoted (A10) to (A12), each of the first in-phase signal, the first quadrature signal, the second in-phase signal, the second quadrature signal, and the measured spectrum is a sequence of n elements. Said processing includes, for each element of the sequence of n elements, (i) squaring each element of the first in-phase signal to obtain a first in-phase-squared element, (ii) squaring each element of the first quadrature signal to obtain a first quadrature-squared element, (iii) adding the first in-phase-squared element and the first quadrature-squared element to obtain a first amplitude-squared element, (iv) squaring each element of the second in-phase signal to obtain a second in-phase-squared element, (v) squaring each element of the second quadrature signal to obtain a second quadrature-squared element, (vi) adding the second in-phase-squared element and the second quadrature-squared element to obtain a second amplitude-squared element, and (vii) dividing the second amplitude-squared element by the first amplitude-squared element to obtain a corresponding element of the measured spectrum.
(A14) In any of the methods denoted (A10) to (A13), the spectroscopic signal is a digital signal. Said demodulating the spectroscopic signal with the first local-oscillator signal includes digitally multiplying the digital signal with a first digital local-oscillator waveform to generate a first digital in-phase waveform and a first digital quadrature waveform. Said demodulating the spectroscopic signal with the second local-oscillator signal includes digitally multiplying the digital signal with a second digital local-oscillator waveform to generate a second digital in-phase waveform and a second digital quadrature waveform. Said processing comprises digitally processing the first digital in-phase waveform, the first digital quadrature waveform, the second digital in-phase waveform, and the second digital quadrature waveform.
(A15) In any of the methods denoted (A1) to (A14), said calculating the measure includes calculating a residual sum of squares.
(A16) In any of the methods denoted (A1) to (A15), the method further includes storing the look-up table in a memory, the hth bin being one a plurality of bins of the look-up table, each of the plurality of bins storing one or more template spectra and a parameter set corresponding to each of the one or more template spectra.
(A17) In any of the methods denoted (A1) to (A16), said adding includes adding, to the candidate set, template spectra stored in one or both of an (h-1)th bin of the look-up table and an (h+1)th bin of the look-up table.
(A18) In any of the methods denoted (A1) to (A17), the method further includes outputting the one or more properties of the gas sample.
(A19) In the method denoted (A18), said outputting includes outputting one or more of a temperature, a pressure, a velocity, and a concentration of a gas species.
(A20) In either of the methods denoted (A18) and (A19), said outputting includes one or both of (i) displaying the one or more properties on a screen and (ii) transmitting the one or more properties to a computing device.
(A21) In any of the methods denoted (A1) to (A20), said deriving includes outputting one or more parameters of the parameter set as the one or more properties of the gas sample.
(B1) A spectroscopic gas sensor comprising a signal processor configured to perform the method of any one or more of the methods denoted (A1) to (A21).
(B2) In the spectroscopic gas sensor denoted (B1), the signal processor includes a microprocessor core, a field-programmable gate array, and a memory in electronic communication with the microprocessor core and the field-programmable gate array, the memory storing the look-up table.
(B3) In either of the spectroscopic gas sensors denoted (B1) and (B2), the spectroscopic gas sensor further includes a photodetector configured to detect a laser beam transmitted through the gas sample.
(B4) In any of the spectroscopic gas sensors denoted (B1) to (B3), the spectroscopic gas sensor further includes a laser.
(B5) In any of the spectroscopic gas sensors denoted (B1) to (B4), the signal processor is further configured to output the one or more properties of the gas sample.
Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.
This application claims priority to U.S. Provisional Patent Application No. 63/266,946, filed on Jan. 20, 2022, the entirety of which is incorporated herein by reference.
Filing Document | Filing Date | Country | Kind |
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PCT/US2023/011240 | 1/20/2023 | WO |
Number | Date | Country | |
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63266946 | Jan 2022 | US |