Analyte concentration analysis with calibration-free wavelength modulated spectroscopy

Abstract

A calibration-independent method is disclosed for determining absorbance, and thereby concentration, of a target analyte using wavelength-modulated tunable diode laser spectroscopy. The method generates an excitation signal that includes a wavelength‑scan component superimposed with a periodic modulation component to drive a radiation source. Emitted radiation is directed through a sample, and transmitted radiation is detected to produce a detected signal. A reference incident intensity corresponding to the excitation signal is computed, and the detected signal is converted into an absorbance signal by logarithmic normalization relative to the reference intensity. The absorbance signal is then demodulated at a harmonic of the periodic modulation component to obtain a harmonic absorbance output. Because instrument-dependent multiplicative effects are removed prior to demodulation, the resulting harmonic absorbance output is directly proportional to analyte absorbance and concentration without requiring empirical calibration.

Description

ANALYTE CONCENTRATION ANALYSIS WITH CALIBRATION-FREE WAVELENGTH MODULATED SPECTROSCOPYStatement Regarding Federally Funded Research

[0001] This invention was made with government support under Grant No. 2233136 awarded by the National Science Foundation. The government has certain rights in the invention.Background

[0002] Tunable diode laser (TDL) spectroscopy has emerged as a cornerstone technology for high-sensitivity, high-selectivity gas sensing across atmospheric science, industrial monitoring, and laboratory measurement systems. TDL instruments offer high spectral resolution, continuous tunability, and non-invasive detection capabilities, enabling quantitative measurements of trace gas species at mixing ratios down to parts-per-trillion levels.

[0003] Early TDL-based approaches relied heavily on direct absorption spectroscopy (DAS), in which a monochromatic laser beam is tuned across a molecular absorption line, and the transmitted intensity is measured using the Beer-Lambert law. DAS enables absolute concentration retrieval without external calibration, provided that the absorption path length, pressure, temperature, and spectral line parameters are known. This method is straightforward and widely applied, but its sensitivity is often limited by dominant low-frequency noise sources, including laser intensity noise, mechanical vibrations, detector noise, and 1 / f noise.

[0004] Subsequently, wavelength-modulation spectroscopy (WMS) was developed. In WMS, a small sinusoidal modulation is added to the TDL injection current, enabling higher-frequency interrogation of the absorption feature and, consequently, reduction of as compared to the first harmonic analysis. The resulting second-harmonic (2f) or higher-harmonic signals provide superior sensitivity, particularly in the presence of weak absorption features. Modulation frequencies in the kHz to MHz regime have been shown to approach the quantum-noise limit under laboratory conditions.

[0005] However, traditional WMS methods require specialized electronics and periodic calibration because the WMS-2f signal amplitude depends on fluctuating quantities such as laser power, detector gain, and optics drift.Holzer Patel Drennan 1 Attorney Docket: CU2025-063-PCT1Summary

[0006] In some aspects, the techniques described herein relate to a method for calibrationindependent determination of absorbance of a target analyte in a sample, including: generating an excitation signal including a wavelength scan component and a period modulation component; driving a radiation source using the excitation signal to generate emitted radiation according to the excitation signal; directing the emitted radiation through the sample and detecting transmitted radiation to produce a detected signal; computing a reference incident intensity corresponding to the excitation signal; converting the detected signal to an absorbance signal based on the reference incident intensity; and demodulating the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output corresponding to the absorbance of the target analyte in the sample.

[0007] In some aspects, the techniques described herein relate to an apparatus for determining a concentration of a target analyte in a sample, including: a radiation source configured to generate emitted radiation based on an excitation signal including a wavelengthscan component and a periodic modulation component, a radiation path through which the emitted radiation is directed through the sample; a detector configured to detect radiation transmitted through the sample to generate a detected signal representing transmitted intensity of the emitted radiation through the sample; and a signal processor configured to: compute a reference incident intensity corresponding to the excitation signal, convert the detected signal into an absorbance signal by forming a logarithmic ratio of the reference incident intensity to the detected signal, demodulate the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output, and determine the concentration of the target analyte based on the harmonic absorbance output, which is directly proportional to absorbance.

[0008] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

[0009] Other implementations are also described and recited herein.Holzer Patel Drennan 2 Attorney Docket: CU2025-063-PCT1Brief Description of the Drawings

[0010] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the present disclosure and, together with the description, serve to explain the principles of the disclosure. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the disclosure. Like reference numerals designate corresponding parts throughout the several views.

[0011] FIG. 1 illustrates an example implementation of a measurement platform as described in the present disclosure.

[0012] FIG. 2 illustrates a flowchart depicting an example method for calibration-free independent determination of the absorbance of a target analyte in a sample.

[0013] FIG. 3 illustrates example components of a tunable-diode-laser spectrometer (TDLS) scan cycle, including an example detected signal, a laser-drive voltage waveform, and a trigger pulse that synchronizes data acquisition.

[0014] FIG. 4 illustrates an example excitation signal that may be used for second harmonic analysis.

[0015] FIG. 5 illustrates example results obtained from a method according to the present disclosure, including a direct absorption spectrum and a 2f spectrum.

[0016] FIG. 6 illustrates an example plot of raw data vectors and an example of a calculated 2f spectrum.

[0017] FIGS. 7, 8, and 9 illustrate an example results and processing for strong water vapor absorption.

[0018] FIG. 10 illustrates an example computing system that may be operative to execute certain functionality described herein.Detailed Description

[0019] While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that it is not intended to limit the invention to the particular form disclosed, but rather, the invention is to cover all modifications, equivalents, and alternatives falling within the scope of the invention as defined by the claims.Holzer Patel Drennan 3 Attorney Docket: CU2025-063-PCT1

[0020] As noted above, TDL spectroscopy using a direct absorption spectrum provides reduced accuracy as compared to WMS methods. However, traditional signal-based WMS methods require periodic calibration, which restricts the measurement efficiency and adds to system complexity. This may limit the feasibility of use of such approaches in some measurement contexts. While significant advancements have been made to mitigate calibration requirements, the calibration requirement continues to limit TDL spectroscopy.

[0021] In conventional WMS approaches, harmonic demodulation is performed on an intensity -based signal, yielding a demodulated output containing unknown proportionality constants that depend on laser power, optical coupling efficiency, detector responsivity, and other variables. Accordingly, such systems require empirical calibration against known reference samples.

[0022] In contrast, the present disclosure relates to an approach that converts a detected signal into an absorbance signal prior to harmonic demodulation by applying a logarithmic normalization with respect to a reference incident intensity. This may be referred to as absorbance-based processing. This mathematical transformation removes variables, such as instrument-dependent terms, and converts them into additive constants. Because the additive constants possess no spectral or temporal variation at the harmonic demodulation frequency, they are rejected during harmonic demodulation. As a result, a final demodulated signal, referred to as a harmonic absorbance output, is proportional to absorbance and target analyte concentration without requiring empirical calibration.

[0023] Accordingly, the present disclosure provides a TDL -based spectroscopy approach for determining the absorbance (and, in turn, concentration) of a target analyte in a sample, using a calibration-free, absorbance-based method that leverages WMS methodology to improve accuracy. Specifically, the present disclosure provides approaches that are easily and efficiently implemented, enabling TDL-based spectroscopy with lightweight, low-power, and relatively inexpensive equipment. Thus, the applications and platforms to which the present disclosure may be applied are expanded compared to traditional approaches, in which cost-, weight-, or power-prohibitive approaches may not be feasible. For example, given the resulting simplicity of the present approach, relatively low-cost, low-weight, and low-power microprocessor hardware may be used. This may be particularly advantageous in atmospheric observation measurement that may be implemented with a system disclosed herein that may be easily provided as a payload toHolzer Patel Drennan 4 Attorney Docket: CU2025-063-PCT1an unmanned aerial vehicle (UAV or drone), weather balloon, or other aerial platform. However, other applications may also benefit from the approaches described herein, including laboratory uses due to reduced size, weight, power consumption, maintenance requirements, and cost, while preserving or improving accuracy and precision. These advantages enable deployment in research environments where space and resources are limited and facilitate integration into portable analytical instruments for field and laboratory analysis.

[0024] In at least some examples presented herein, methodologies determine calibration-free second harmonic (or 2f) spectra by explicitly incorporating Beer-Lambert absorbance into the harmonic calculation itself. By deriving both direct absorption and 2 / spectra from the same detected signal (e.g., the same raw data vector) and performing absorbance computation prior to harmonic demodulation, the approach described herein eliminates dependence on absolute signal magnitude and enables accurate high-speed computation on low-cost microprocessors. This creates measurement systems that are robust to optical contamination, thermal drift of distributed-feedback (DFB) lasers, and changes in detector responsivity.

[0025] Together, the advances provided herein facilitate TDL-based DAS and WMS that are merged into a unified, calibration-free architecture that offers high precision, low noise, and operational simplicity. The combination of high-resolution tunability, robustness against environmental and instrumental variability, and the capability for real-time quantitative spectroscopy continues to expand the applicability of TDL systems in atmospheric chemistry, industrial safety monitoring, and multi-species gas sensing applications, such as industrial monitoring applications including clean rooms, hazardous detection, mitigation, etc.

[0026] An implementation of the present disclosure, including a measurement platform 100, is shown in FIG. 1. The example implementation includes a signal processing microcontroller 102 and a radiation source microcontroller 104, which may be operably connected. Optionally, the signal processing microcontroller 102 and radiation source microcontroller 104 can be configured to transmit information between them, such as a timing signal 122 or excitation signal 124 information.

[0027] A measurement system 110 can be coupled to the signal processing microcontroller 102 so that the signal processing microcontroller 102 can receive a detected signal 130 (e.g., sampled data) from the measurement system 110. The measurement system 110 can optionally include a radiation path 112 (e.g., an optical cell) and a detector 114 (e.g., an InGaAs detector)Holzer Patel Drennan 5 Attorney Docket: CU2025-063-PCT1configured to measure the detected signal 130 from the detector 114 after emitted radiation 128 from a radiation source 108 passes through a sample disposed in the radiation path 112. The sample in the measurement system 110 may be a gas sample having a target analyte.

[0028] Additional example components of the measurement system 110 may include a thermoelectric cooler, Herriott cell, multipath optical cell, folded optical path(s) (e.g., greater than or equal to 5 meters of optical path), mirrors (e.g., spherical mirrors configured to illuminate the detector 114), a collimating lens, and / or any other optical features.

[0029] A radiation source 108 can be used to illuminate the measurement system 110, and the radiation source 108 can be powered by a driver 106 that is controlled by the radiation source microcontroller 104. Using the driver 106, the radiation source microcontroller 104 can control the emitted radiation 128 of the measurement system 110. In at least one example, the radiation source 108 may be a TDL laser. In this regard and as discussed further in the description below, the radiation source 108 may be controlled using an excitation signal provided to the driver 106 to generate a drive current to the radiation source 108.

[0030] The measurement system 110 can be configured to receive the sample of gas (e.g., atmospheric gas), illuminate the gas with the radiation source 108, and measure the content or concentration of a target analyte in the sample by analyzing the light received at the detector 114, as represented by the detected signal 130.

[0031] It should be understood that a different radiation source 108, detector 114, and radiation path 112 can be combined in various implementations of the present disclosure to measure different target analytes. In implementations configured to measure water as the target analyte in the sample, the output wavelength of a laser acting as the radiation source 108 can be about 1392.5 nm, but it should be understood that this is only a non-limiting example of a laser that can be used in implementations of the present disclosure.

[0032] Implementations of the present disclosure can be configured for mobile / remote sensing of a target analyte in a gas sample, including a water content of a gas, a carbon dioxide content of a gas, a methane content of a gas, and / or other target analytes in a sample. For example, implementations of the present disclosure include applications where the measurement platform 100 shown in FIG. 1 can be coupled to an aerial vehicle (drone, unmanned aerial vehicle, balloon, space vehicle, etc.). Optionally, the coupling can be an extension tube that separates the system from the body of the aerial vehicle.Holzer Patel Drennan 6 Attorney Docket: CU2025-063-PCT1

[0033] In the measurement platform 100, the signal processing microcontroller 102 may be configured as the main system for instrument control and monitoring status, acquiring and processing data, and transmission and storage of results. The radiation source microcontroller 104 may be configured for precision control of the radiation source 108 via rapid, coordinated communication with the driver 106 and signal processing microcontroller 102.

[0034] An input / output interface 120 of the signal processing microcontroller 102 can be used to coordinate timing with the radiation source microcontroller 104 and / or communicate with external devices. A timing signal 122 transmitted by signal processing microcontroller 102 on a digital I / O line to radiation source microcontroller 104 can synchronize the signal processing microcontroller 102 and the radiation source microcontroller 104. Alternatively, one may utilize an alternative timing signal, such as the use of a short pulse of the laser, or a series of pulses, lasting only a few microseconds, to alert the monitoring algorithm that the main scan is about to begin. This approach provides a clear optical signal for synchronization.

[0035] An excitation signal embedded on the radiation source microcontroller 104 can initiate the output of a custom -generated waveform used to scan the radiation source 108.

[0036] The system can further be configured to perform an update scan step where the timing signal 122 is synchronized with the signal processing microcontroller 102 for stepwise generation of a custom software-generated waveform (e.g., based on a driving equation). The status of the radiation source microcontroller 104 can be continuously transmitted to the signal processing microcontroller 102 via a digital I / O line. A custom software-generated waveform to scan the radiation source 108 can be sent to the driver 106 as a high -resolution voltage output with analog filtering.

[0037] High-resolution voltage output with analog filtering can be an input to generate a precision drive current 126 by the driver 106. The driver 106 can convert high-resolution voltage in the form of the excitation signal 124 from the radiation source microcontroller 104 into the current 126.

[0038] The current 126 can cause the radiation source 108 to generate the emitted radiation 128. In one example, the excitation signal 124 includes a wavelength scan and a period modulation component. The wavelength-scan component may be a slow, typically linear ramp in the current 126, where the ramp slope controls how quickly the laser wavelength is tuned across an absorption feature for a target analyte and produces the underlying spectral scan used forHolzer Patel Drennan 7 Attorney Docket: CU2025-063-PCT1measurement. This repetitive ramp waveform is applied to the diode-laser injection current to sweep the wavelength over the target absorption line for the target analyte in a controlled and repeatable manner. Superimposed on this ramp may be a periodic modulation component, implemented as a high-frequency sinusoidal waveform whose amplitude sets the extent of wavelength modulation and whose frequency determines how rapidly the laser wavelength oscillates around the instantaneous ramp position, thereby causing the laser to scan back and forth across a portion of the absorption feature twice per modulation cycle and generating the harmonic (e.g., 2f) components used for sensitive demodulation and noise-rejection processing. Optionally, the laser can be a commercial infrared diode laser with an integrated thermoelectric cooler, temperature monitor, and photodiode that produces a coherent light output. One example of the excitation signal 124, including the wavelength scan component and the periodic modulation component, is represented as example excitation signal 400 in FIG. 4.

[0039] Optionally, the measurement system 110 can include any or all of: gas handling, optics, detector, and / or custom-built amplified s).

[0040] A detected signal 130 from the detector amplifier circuit can represent the signal that is processed into a measurement by custom software on the signal processing microcontroller 102. As described in greater detail below, a custom spectral processing algorithm can convert the detected signal 130 from the measurement system 110 into a concentration for the target analyte in the sample. The processed results from the custom spectral processing algorithm can be transmitted as the primary observable of the measurement platform 100.

[0041] With reference to FIG. 2, a method 200 for calibration-free independent determination of absorbance of a target analyte in a sample is illustrated as a flowchart. The method 200 may be implemented by a measurement platform 100 as described in FIG. 1.

[0042] The method begins by generating an excitation signal 124 that includes a wavelength-scan component and a periodic modulation component, as performed in a generating operation 210. FIG. 3 illustrates components of a tunable-diode-laser spectrometer (TDLS) scan cycle 300, including an example detected signal 302, a laser-drive voltage waveform 304, and a trigger pulse 306 that synchronizes data acquisition.

[0043] As shown in the upper panel of FIG. 3, the detected signal 302 may comprise discrete samples recorded at a raw analog-to-digital converter (ADC) rate. Each point may be oversampled using an internal averaging function of the signal processing microcontroller 102 toHolzer Patel Drennan 8 Attorney Docket: CU2025-063-PCT1reduce electronic noise, yielding a minimum resolvable signal level. This signal represents the intensity of laser radiation after transmission through the open-path cell, including absorption features and background levels.

[0044] The middle panel displays the programmable linear ramp that drives the distributed-feedback (DFB) laser during each scan (e g., based on the excitation signal 124). The ramp may include discrete one-bit DAC steps, spanning a voltage range. This controlled modulation sweeps the output wavelength of the DFB laser across the target analyte absorption line. The high repeatability of this ramp is enabled by a digital-to-analog converter embedded in the radiation source microcontroller 104.

[0045] The lower panel of FIG. 3 shows a trigger pulse 306 produced immediately before each scan. This pulse may be generated by the radiation source microcontroller 104 and may be transmitted to the signal processing microcontroller 102. Upon receipt of the trigger, the receiver records its internal clock time, initializes the ADC, and begins acquisition of the detector waveform. This ensures that all measurements — detector samples, drive-voltage values, and timing information — are synchronized precisely for each scan.

[0046] The signal processing microcontroller 102 may employ a dual-buffer (or an architecture having at least two buffers), direct-memory-access (DMA) architecture that enables continuous, uninterrupted acquisition and processing of high-speed analog data. As such, the signal processing microcontroller 102 may have a first memory buffer 116 and a second memory buffer 118. In this approach, the analog-to-digital converter (ADC) may be configured to sample at a given sampling rate, with DMA transferring each digitized sample directly into memory without processor intervention. The first memory buffer 116 and second memory buffer 118 may function in an alternating manner. That is, while the first memory buffer 116 is being filled with incoming ADC samples, the second memory buffer 118 — containing previously acquired data — may be simultaneously made available to the signal processing microcontroller 102 for signal processing tasks, including background estimation, absorbance computation, harmonic demodulation, and spectral window summation, all of which are described in greater detail below. When the first memory buffer 116 becomes full, a DMA completion interrupt triggers an automatic buffer swap, and DMA begins filling the second memory buffer 118 while the processor transitions to operate on the newly completed first memory buffer 116. This repeated alternation ensures that laser excitation and data capture proceed without gaps, even whileHolzer Patel Drennan 9 Attorney Docket: CU2025-063-PCT1substantial real-time computation, file management, and housekeeping operations (such as temperature and voltage monitoring) are performed on the previously captured dataset. The dual-buffer DMA system therefore enables true concurrency between high-speed data acquisition and computational processing, ensuring reliable, continuous recording and real-time spectral analysis at the full sensor sampling rate. This provides a significant benefit by maintaining uniform laser drive during modulation cycles, which has an impact on temperature control and wavelength stability. If the drive function experiences interruptions, the thermoelectric cooler of the laser may briefly compensate, causing the laser wavelength to shift and potentially introducing "jitter" noise in the measured absorption line position. While processing algorithms can mitigate these effects, consistent buffering is important to minimize such artifacts and facilitate high measurement precision.

[0047] In implementations of the present disclosure, accurate recovery of the harmonic absorbance output, discussed in more detail below, may depend on integrating the absorbance signal over one or more complete periods of the periodic modulation component. Because the harmonic demodulation effectively computes a weighted summation of absorbance samples across a full 360-degree cycle of the sinusoidal modulation, even small timing mismatches between the modulation waveform and the anal og-to-digi tai sampling clock can introduce a residual component at the fundamental modulation frequency. In practical terms, such residuals can be comparable in magnitude to the desired second harmonic signal when the integration window is not aligned with the modulation period to better than approximately one part in 105. To address this, the measurement platform 100 may employ tight synchronization between the signal processing microcontroller 102 and the radiation source microcontroller 104, so that the excitation waveform applied to the radiation source and the acquisition of the detected signal are both referenced to a common timing source.

[0048] To address this limitation, the signal processing microcontroller 102 is configured to transmit a trigger signal — at a regular cadence — to the radiation source microcontroller 104, thereby ensuring that each excitation cycle begins at a deterministic, processor-defined zero point. That is, the signal processing microcontroller 102 generates a digital timing signal and / or trigger pulse that is provided to the radiation source microcontroller 104 before each scan, ensuring that each modulation cycle of the excitation signal begins and ends at precisely defined sample boundaries within the dual -buffer, direct-memory-access (DMA) acquisition architecture.Holzer Patel Drennan 10 Attorney Docket: CU2025-063-PCT1By forcing the radiation source microcontroller — which drives the laser current ramp and superimposed sinusoidal modulation — to remain phase-locked to the sampling clock of the signal processing microcontroller, the system eliminates the need to maintain sub-microsecond alignment between two independent free-running clocks, a requirement that would otherwise exceed the practical clock rates of inexpensive microcontrollers. Instead, each modulation period is delimited by the same microcontroller that acquires the detector waveform, so the harmonic integration window is defined entirely in terms of ADC sample indices rather than absolute time. This architecture allows the summation over a full sinusoidal cycle to cancel the fundamental modulation term to the required precision, thereby enabling accurate second-harmonic absorbance measurements on cost-effective embedded hardware while avoiding spurious residuals that would degrade the calibration-free determination of analyte concentration.

[0049] Both the signal processing microcontroller 102, radiation source microcontroller 104, temperature controller, detector 114, and power-conditioning electronics may reside on a compact, custom-built printed circuit board.

[0050] With returned reference to FIG. 2, the excitation signal may be then used to drive a radiation source so that the source emits radiation following the instantaneous tuning and modulation profile defined by the excitation waveform, corresponding to a driving operation 220. The emitted radiation 128 may be directed through a sample, where it undergoes absorption according to the target analyte’s spectroscopic properties, and a detector measures the transmitted radiation to produce a detected signal, as indicated in a directing operation 230. The detected signal may be represented as a raw signal that is collected and stored in memory using direct memory access as described above. In any regard, the resulting detected signal may be referenced as Sig(t).

[0051] A reference incident intensity may be computed based on the excitation signal, enabling a baseline for quantifying absorption, which is carried out in a computing operation 240. The reference incident intensity may represent the intensity of the detected laser beam in the absence of an absorber. Specifically, the reference laser driving function may be characterized as:7o(t, 0) = C x (S’ x t + B + M x sin(27r / * t + 0) )Equation 1where Io(t, 0) is the detector signal (i.e., “intensity”) in the absence of an absorber in the cell; t is elapsed time from the start of the ramp; S is “slope” of the laser ramp function; B is initialHolzer Patel Drennan 11 Attorney Docket: CU2025-063-PCT1value of the ramp; M is the amplitude of the sine wave modulation added to the ramp; / is the frequency of the sine wave modulation; 0is a phase shift that accounts for timing offset between the start of the sine wave and first data point acquired by the A / D system; and C is a multiplier determined by taking the acquired signal at the start or end of the laser ramp where there is minimal absorption.

[0052] In at least some examples, the reference incident intensity may be at least in part based on the excitation signal and / or reference laser driving function. In this regard, the reference incident intensity may include terms related to the laser driving function, including the slope of the function, the initial value of the ramp, the amplitude of the sine wave modulation, and the frequency of the sine wave modulation. However, other terms may relate to the expected intensity based on the laser drive function, including the constant C, and the phase shift that may account for the timing offset between the start of the sine wave and first data point acquired by the measurement system.

[0053] Using this reference intensity, the detected signal may be converted into an absorbance signal representing the analyte-dependent attenuation of the modulated radiation in a converting operation 250. Specifically, the absorbance signal may be based on the Beer-Lambert Law, which states that the amount of light absorbed by a sample increases predictably with both the concentration of the absorbing species and the distance the light travels through it.Specifically, the Beer-Lambert Law may be represented by the equation:Equation 2where A represents absorbance, Iorepresents the reference intensity, and I represents the measured intensity. In this regard, Equation 2 may be rewritten as:Equation 3where A(t) is the absorbance signal, Io(t,4>) represents the reference intensity signal, phase shifted by a constant ( / >, and Sig(t) is the detected signal as noted above. All are functions of time, t. In a further refinement of Equation 3, the absorbance signal may be written to include terms for the background offset and a normalization constant. The background offset may represent the electronic offset, dark current, or baseline signal. The background offset, B, may be subtractedHolzer Patel Drennan 12 Attorney Docket: CU2025-063-PCT1before logarithmic conversion. The normalization constant, R, may account for laser power, detector gain, optical throughput, modulation depth, line shape, ADC scaling, pressure, temperature, etc., and is the value that is used in calibration in traditional approaches. That is, the term “7ZR” serves as a normalization factor that converts the detected signal to the same units used in parameterizing Io. This ratio ensures that the measured intensity and the reference intensity are directly comparable, allowing for accurate quantification of absorbance and analyte concentration within the sample. By referencing the signal in this manner, the calculation maintains consistency and validity across different measurement conditions.

[0054] Using these terms and concepts, Equation 3 may be rewritten as:Equation 3'

[0055] In conventional WMS, harmonic demodulation is performed directly on the intensity -based detector signal, resulting in a 2f (or higher-order) output whose amplitude contains unknown variables tied to laser power, optical coupling efficiency, detector responsivity, and other instrument-dependent factors. Because these terms remain embedded in the intensity signal, traditional systems require periodic empirical calibration to relate the demodulated harmonic signal to a known absorbance or known analyte concentration. This practice is widespread in the WMS literature, where the Beer-Lambert calculation is typically bypassed for computational ease, and the harmonic extraction is performed on the raw or baseline-subtracted detector waveform rather than on a properly normalized absorbance signal.

[0056] By contrast, the present disclosure departs from this conventional paradigm by explicitly computing Beer-Lambert absorbance on a point-by-point basis prior to harmonic demodulation, thereby removing all instrument-dependent constants or variables and reducing remaining offsets to additive terms that cancel during integration over full modulation cycles. This absorbance-domain step is often skipped in traditional WMS implementations, even though it is essential for achieving calibration-free behavior. Consequently, the harmonic absorbance output produced by the methods disclosed herein represents a true second-harmonic of absorbance, rather than a second-harmonic of just the detector signal, the value of which will depend on the variables described above and requires calibration in traditional approaches. In turn, the disclosed examples herein that are absorbance-based enable calibration-independentHolzer Patel Drennan 13 Attorney Docket: CU2025-063-PCT1determination of analyte concentration and improve both accuracy and robustness relative to traditional signal-based WMS approaches.

[0057] The absorbance signal may be demodulated at a harmonic of the periodic modulation component to obtain a harmonic absorbance output that corresponds to the harmonic representation of the signal, which directly corresponds to the absorbance of the target analyte within the sample, completing a demodulating operation 260. Of note, this demodulation is of the absorbance signal determined above in Equation 3'. The demodulation may include applying a function to the absorbance signal. Specifically, the demodulation may include applying an equation at least in part based on the Beer-Lambert Law of absorbance and a modified second harmonic sinusoidal reference function. Specifically, one example of the equation is described as:(sin(47r * t -I- 0 4- 0' ) )dtEquation 4where, 2 / represents a sum of discrete points over a full “2 ” cycle of the sinusoidal excitation function corresponding to the product of the transformed detected signal from Equation 3’ and a corresponding stepwise representation of the sinusoidal component of the excitation signal. The constant, < / >', explicitly accounts for the wavelength response of the laser that is shifted in time relative to the excitation function, ( / >. Importantly, (f)' and ( / > are not necessarily dependent on one another, as they relate to different aspects of laser excitation by injection current and thermal response by resistive heating and external cooling. In contrast to conventional WMS techniques that perform harmonic demodulation directly on detected signals using a single phase shift that represents the sum <f> + (f> the new approaches described herein first transform the detected signal into an absorbance signal using a phase shift ', and then apply a harmonic reference waveform to the absorbance with a phase shift ( / ) I / >'. Although this difference is subtle, the results are transformative; the harmonic absorbance output corresponds to a derivative (e.g., second harmonic) of absorbance rather than a derivative of signal. This absorbance-domain demodulation formulation, exemplified in Equation 4, is distinct from traditional WMS-2f techniques and provides a calibration-independent metric that is insensitive to multiplicative instrument variations.Holzer Patel Drennan 14 Attorney Docket: CU2025-063-PCT1

[0058] Notably lacking from Equation 4 is a constant “C” that precedes the summation (or integral), which in traditional WMS approaches represents a “calibration factor” that converts a detected signal into an observable quantity, such as the concentration of the target analyte in the sample. This is because demodulation of the absorbance signal includes integrating over an integer number of modulation cycles, where ln(R), represented in the term A(t,<f>), is constant. Furthermore, sin(t) has a zero mean as a sinusoidal signal. In turn, after integration, these constant values that are unchanged over the modulation cycles cancel from the equation, thus resulting in a calibration-free approach. That is, this approach is calibration-free because Beer-Lambert normalization removes all multiplicative instrument effects before harmonic demodulation, and the remaining additive constants are orthogonal to the 2f reference and cancel upon integration. The only remaining dependence of the 2f value is on the known amplitude of the sinusoidal modulation, as with traditional second-harmonic demodulation methods; this quantity, called the “modulation amplitude,” is prescribed by the excitation function, and is predetermined to optimize the sensitivity of the 2f signal as a function of pressure or line-shape.

[0059] As such, 2 / represents the second derivative of absorbance, rather than the second derivative of signal in Equation 4. This approach accomplishes two objectives. Firstly, this approach makes the calculation simple, such that it can efficiently be performed on small, low-cost microprocessors. In addition, the result is independent of variations that affect the magnitude of the signal, such as condensation on mirrors, degradation of the laser, variations in laser power, or detector efficiency. Accordingly, the result is “calibration free” so long as one knows the modulation amplitude, the spectral parameters of the target analyte, and can verify a ratio of direct absorption to the second harmonic signal within the analyte sample.

[0060] An additional outcome of using this approach is that if the raw data of the detected signal can be stored on an appropriate medium, the direct absorption spectrum can be determined with very high accuracy with post-acquisition processing of the raw data using a simple function that requires one more constant determined in the laboratory. This constant may represent the attenuation of the amplitude of the sinusoidal modulation applied to the laser in “wavelength” space. In other words, the temporal variation and amplitude of the wavelength modulation of the semiconductor diode laser output are phase-shifted and attenuated, respectively, relative to the laser power output.Holzer Patel Drennan 15 Attorney Docket: CU2025-063-PCT1

[0061] With further reference to FIG. 5, an illustration 500 of the results of the method 200 of FIG. 2 is shown. Both a direct absorption spectrum 502 and a 2f spectrum 504 may be derived from the same raw data vectors (e.g., the detected signal). In traditional second-harmonic WMS, the two spectra (the direct absorption spectrum 502 and the 2f spectrum 504) are obtained separately at two different modulation amplitudes. Specifically, the direct absorption spectrum 502 is obtained with no sinusoidal modulation in a separate time interval from the 2f spectrum 504, which is obtained with a pre-set modulation. A calibration matrix is then developed that allows for the conversion of the 2f spectrum 504 to the concentration of the target analyte. Some approaches include a method referred to as “2f / lf,” where the second harmonic (2f) is divided by the first harmonic (If) to “normalize” the 2f signal by the laser power (i.e., / o). While in practice this method may provide accurate results, it suffers from the drawback that the DFB laser's behavior differs with different sinusoidal modulation amplitudes and frequencies due to its thermal properties.

[0062] In practical applications of traditional WMS — including both conventional 2f demodulation and the commonly used 2f / lf normalization approach — the achievable concentration accuracy is typically limited to approximately 5-10%, due largely to disparities between modulation amplitudes used for the direct-absorption and 2f scans and to the thermal response characteristics of distributed-feedback (DFB) lasers, which cause thewavelength-modulation amplitude to differ from the imposed emission-intensity modulation.

[0063] Because these traditional WMS approaches obtain the direct absorption spectrum and the 2f spectrum in separate scans, empirical calibration matrices must be constructed to relate the demodulated harmonic signal to analyte concentration, and inaccuracies in these matrices further degrade performance.

[0064] In contrast, by deriving both the direct absorption spectrum and the 2f spectrum from the same raw data vectors and by converting to Beer-Lambert absorbance prior to harmonic demodulation, the present approach described herein eliminates the dependence on separate calibration measurements and reduces the influence of DFB wavelength lag. As a result, implementations of the present disclosure have been shown to achieve significantly improved accuracy on the order of 1-2%, representing a substantial performance enhancement over traditional techniques while simultaneously simplifying system operation.Holzer Patel Drennan 16 Attorney Docket: CU2025-063-PCT1

[0065] FIG. 6 illustrates an example plot 600 of raw data vectors 602 and an example of a calculated 2f spectrum 604. Traditional methods simply average the raw data vector, then apply the Beer-Lambert Law to derive a “direct absorption” curve, yielding two lobes and a depression in the middle. A 2f signal has two lobes because, as the laser wavelength oscillates back and forth across an absorption line, absorption increases on one side of the line and decreases on the other — and the second harmonic records those two opposite changes separately.

[0066] Once the absorbance signal has been computed by forming the logarithmic ratio of the reference incident intensity to the detected signal, the resulting absorbance waveform provides a quantitative measure of the attenuation imposed by the target analyte. Because the disclosed method removes instrument-dependent factors before demodulation, the subsequent harmonic absorbance output is directly proportional to the true absorbance of the sample. Using this proportional relationship, the concentration of the analyte can be determined by comparing the harmonic absorbance output to a synthetic or modeled harmonic spectrum generated from known spectroscopic parameters of the target analyte, such as line strength, pressure-broadened line shape, and temperature. In effect, the harmonic absorbance output serves as a calibration-free observable whose amplitude scales with analyte concentration along the optical path. By applying Beer-Lambert physics, which relates absorbance to the product of concentration, path length, and line-shape function, the system’s signal processor computes the analyte concentration without requiring empirical reference measurements. This enables accurate and repeatable retrievals of concentration even under varying environmental or instrument conditions, provided that pressure, temperature, and optical path length are known or measured.

[0067] FIG. 7 illustrates an example of strong water vapor absorption 700, demonstrating the approaches described herein, in which a direct absorption signal 704 can be derived from a simple transformation of the laser excitation function, as given in Equation 1. FIG. 7 shows 12,000 raw samples, 602 in a single scan of the laser, along with a traditional method of computing a “direct spectrum” from these points using an average over a single cycle, in this case, an 18-point averaging (or smoothing) function corresponding to a full sinusoidal period. Note that the true absorbance is significantly larger than the value one would calculate from this average by about a factor of two (representing the combined absorbance of the two lobes of the blue curve).Holzer Patel Drennan 17 Attorney Docket: CU2025-063-PCT1

[0068] In FIG. 8, the 12,000 points are converted into absorbance 804 using Equation 3. A 1-cycle average smoothing 804 of these raw points is also illustrated. By phase-shifting Equation 1 and applying a factor “Atf less than 1 to the sinusoidal term to account for attenuation of the wavelength range exhibited by the laser relative to the modulation amplitude applied to the input current (e.g., output intensity), the following equation can be used to transform from intensity to wavelength:(t, 0 + 0') = (S x t + B + M x Att x sin(27r f * t + 0 -I- 0') )Equation 5

[0069] Using the second phase introduced in Equation 4 (i.e., ’) and an empirically determined attenuation factor, Alt, a plot 900 of A(t, (p) versus ft, 0 -I- 0') is shown in FIG. 9 for the results in FIG. 8. A first curve 902 and a second curve 904 are depicted in FIG. 9, with the first curve 902 representing the average of values and the second curve 904 representing the maximum value observed in a given range of wavelengths, both plotted versus wavelength (x-axis). Because individual points are discreet measurements of absorbance as wavelength is rapidly scanned, the peak absorption will not be captured in every scan. However, the ratio of the maximum value to the average is a strict function of the parameters of the measurement (e.g., scan rate, number of points in a sinusoidal cycle, line shape), which can be related to the fundamental absorption properties of the molecule with high accuracy.

[0070] In turn, highly accurate concentrations can be derived from single scans using a lookup table of values relating the 2f spectrum obtained from Equation 4 to the peak absorbance measured using Equation 5 wavelength transformation.

[0071] The approaches described herein provide substantial advantages, particularly for atmospheric science, where high-accuracy, high-frequency measurements of trace gases are essential for understanding boundary-layer processes, cloud-aerosol interactions, pollutant transport, and upper-tropospheric humidity dynamics. The ability to performcalibration-independent TDL spectroscopy using lightweight, low-power electronics enables deployment on platforms that were previously impractical for precision spectroscopic instruments. As noted in the present disclosure, the measurement platform can be directly integrated with aerial vehicles such as drones, unmanned aerial systems (UAS), and weather balloons, allowing the compact spectrometer — along with its signal-processing microcontroller, radiati on- source controller, and synchronized excitation waveform generation — to operate as aHolzer Patel Drennan 18 Attorney Docket: CU2025-063-PCT1fully self-contained atmospheric probe. By coupling the system to such mobile airborne platforms, researchers can obtain continuous, high-resolution gas-phase measurements in regions of the atmosphere that are otherwise difficult or expensive to sample using conventional aircraft-borne instruments. Because the disclosed architecture maintains accuracy without empirical calibration and is robust to optical contamination, laser drift, and power fluctuations, it supports autonomous long-duration flight, rapid vertical profiling, and spatial mapping of atmospheric structure, thereby expanding the scientific utility of emerging drone and balloon-based observational networks.

[0072] FIG. 10 illustrates an example schematic of a computing device 1000 suitable for implementing aspects of the disclosed technology, including the calibration-independent method using the signal processing microcontroller 102 and / or radiation source microcontroller 104 as described above. For example, the signal processing microcontroller 102 and / or radiation source microcontroller 104 may comprise aspects of the computing device 1000 described herein. The computing device 1000 includes one or more processor unit(s) 1002, memory 1004, a display 1022, and other interfaces 1038 (e.g., buttons). The memory 1004 generally includes both volatile memory (e.g., RAM) and non-volatile memory (e.g., flash memory). An operating system 1010, such as the Microsoft Windows® operating system, the Apple macOS operating system, or the Linux operating system, resides in the memory 1004 and is executed by the processor unit(s) 1002, although it should be understood that other operating systems may be employed. The computing device 1000 may include one or more communication interfaces 1036 for communication with other devices.

[0073] One or more applications 1050 are loaded in the memory 1004 and executed on the operating system 1010 by the processor unit(s) 1002. Applications 1050 may receive input from various input local devices such as a microphone, input device 1035 (e.g., keypad, mouse, stylus, touchpadjoystick, instrument mounted input, or the like). Additionally, the applications 1050 may receive input from one or more remote devices such as remotely located smart devices by communicating with such devices over a wired or wireless network using more communication transceivers 1030 and an antenna 1032 to provide network connectivity (e.g., a mobile phone network, Wi-Fi®, Bluetooth®). The computing device 1000 may also include various other components, such as a positioning system (e.g., a global positioning satellite transceiver), one or more accelerometers, one or more cameras, an audio interface (e.g., the microphone, an audioHolzer Patel Drennan 19 Attorney Docket: CU2025-063-PCT1amplifier and speaker and / or audio jack), and storage devices 1028. Other configurations may also be employed.

[0074] The computing device 1000 further includes a power supply 1016, which is powered by one or more batteries or other power sources, and which provides power to other components of the computing device 1000. The power supply 1016 may also be connected to an external power source (not shown) that overrides or recharges the built-in batteries or other power sources.

[0075] In an example implementation, the computing device 1000 comprises hardware and / or software embodied by instructions stored in the memory 1004 and / or the storage devices 1028 and processed by the processor unit(s) 1002. The memory 1004 may be the memory of a host device or of an accessory that couples to the host. Additionally or alternatively, the computing device 1000 may comprise one or more field programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), or other hardware / software / firmware capable of providing the functionality described herein.

[0076] The computing device 1000 may include a variety of tangible processor-readable storage media and intangible processor-readable communication signals. Tangible processor-readable storage can be embodied by any available media that can be accessed by the computing device 1000 and includes both volatile and nonvolatile storage media, removable and nonremovable storage media. Tangible processor-readable storage media excludes intangible communications signals and includes volatile and nonvolatile, removable and non-removable storage media implemented in any method or technology for storage of information such as processor-readable instructions, data structures, program modules or other data. Tangible processor-readable storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CDROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other tangible medium which can be used to store the desired information and which can be accessed by the computing device 1000. In contrast to tangible processor-readable storage media, intangible processor-readable communication signals may embody processor-readable instructions, data structures, program modules or other data resident in a modulated data signal, such as a carrier wave or other signal transport mechanism. The term "modulated data signal" means an intangible communications signal that has one or more of its characteristics setHolzer Patel Drennan 20 Attorney Docket: CU2025-063-PCT1or changed in such a manner as to encode information in the signal. By way of example, and not limitation, intangible communication signals include signals traveling through wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared, and other wireless media.

[0077] Some implementations may comprise an article of manufacture. An article of manufacture may comprise a tangible storage medium to store logic. Examples of a storage medium may include one or more types of processor-readable storage media capable of storing electronic data, including volatile memory or non-volatile memory, removable or non-removable memory, erasable or non-erasable memory, writeable or re-writeable memory, and so forth. Examples of the logic may include various software elements, such as software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, operation segments, methods, procedures, software interfaces, application program interfaces (API), instruction sets, computing code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. In one implementation, for example, an article of manufacture may store executable computer program instructions that, when executed by a computer, cause the computer to perform methods and / or operations in accordance with the described implementations. The executable computer program instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, and the like. The executable computer program instructions may be implemented according to a predefined computer language, manner or syntax, for instructing a computer to perform a certain operation segment. The instructions may be implemented using any suitable high-level, low-level, object-oriented, visual, compiled and / or interpreted programming language.

[0078] Clause 1. A method for calibration-independent determination of absorbance of a target analyte in a sample, comprising: generating an excitation signal including a wavelength scan component and a period modulation component; driving a radiation source using the excitation signal to generate emitted radiation according to the excitation signal; directing the emitted radiation through the sample and detecting transmitted radiation to produce a detected signal; computing a reference incident intensity corresponding to the excitation signal; converting the detected signal to an absorbance signal based on the reference incident intensity;Holzer Patel Drennan 21 Attorney Docket: CU2025-063-PCT1and demodulating the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output corresponding to the absorbance of the target analyte in the sample.

[0079] Clause 2. The method of clause 1, wherein the converting comprises applying a logarithmic ratio of the reference incident intensity to the detected signal.

[0080] Clause 3. The method of any one of clauses 1-2, wherein the converting the detected signal to the absorbance signal further comprises subtracting a detector background level prior to applying the logarithmic ratio.

[0081] Clause 4. The method of any one of clauses 1-3, wherein the harmonic absorbance output is integrated over a complete period of the period modulation component.

[0082] Clause 5. The method of any one of clauses 1-4, wherein the wavelength scan component spans an absorption feature of the target analyte in the sample.

[0083] Clause 6. The method of any one of clauses 1-5, wherein the harmonic absorbance output is directly proportional to a concentration of the target analyte in the sample.

[0084] Clause 7. The method of any one of clauses 1-6, wherein determining a concentration comprises comparing the harmonic absorbance output to a synthetic harmonic spectrum generated from known spectral parameters.

[0085] Clause 8. The method of any one of clauses 1-7, wherein the converting the detected signal to absorbance occurs prior to the demodulation of the absorbance signal, such that instrument-dependent constants are removed during demodulation.

[0086] Clause 9. The method of any one of clauses 1-8, wherein the computing the reference incident intensity comprises generating a model of the excitation signal, including a ramp over the wavelength scan and a sinusoidal modulation component corresponding to the excitation signal.

[0087] Clause 10. The method of any one of clauses 1-9, wherein the demodulating employs a reference waveform including a phase term compensating laser source variables.

[0088] Clause 11. The method of clause 1, wherein both direct absorption and harmonic absorption spectra are obtained from a common scan of the detected signal.

[0089] Clause 12. The method of any one of clauses 1-11, further comprising: storing the detected signal as one or more raw data vectors in a memory; and after demodulating the absorbance signal at the harmonic of the periodic modulation component, generating a directHolzer Patel Drennan 22 Attorney Docket: CU2025-063-PCT1absorption spectrum from the one or more raw data vectors using a modulation-attenuation constant that characterizes attenuation of a sinusoidal modulation amplitude in wavelength space arising from thermal lag of a distributed-feedback laser.

[0090] Clause 13. The method of any one of clauses 1-14, wherein demodulating the absorbance signal at the harmonic of the periodic modulation component comprises generating a second-harmonic absorbance signal that corresponds to a second derivative of absorbance with respect to wavelength.

[0091] Clause 14. An apparatus for determining a concentration of a target analyte in a sample, comprising: a radiation source configured to generate emitted radiation based on an excitation signal comprising a wavelength-scan component and a periodic modulation component, a radiation path through which the emitted radiation is directed through the sample; a detector configured to detect radiation transmitted through the sample to generate a detected signal representing transmitted intensity of the emitted radiation through the sample; and a signal processor configured to: compute a reference incident intensity corresponding to the excitation signal, convert the detected signal into an absorbance signal by forming a logarithmic ratio of the reference incident intensity to the detected signal, demodulate the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output, and determine the concentration of the target analyte based on the harmonic absorbance output, which is directly proportional to absorbance.

[0092] Clause 15. The apparatus of clause 14, further comprising: a radiation source controller, discrete from the signal processor, the radiation source controller operative to control the radiation source to generate the emitted radiation based on the excitation signal.

[0093] Clause 16. The apparatus of any one of clauses 1-15, wherein the signal processor is further operative to acquire the detected signal from the detector for direct memory access writing of the detected signal to a memory.

[0094] Clause 17. The apparatus of any one of clauses 1-16, wherein the signal processor comprises a plurality of write buffers for the direct memory access writing, wherein at least one write buffer is used for direct write access to the memory while data written by at least another write buffer is processed from the memory.Holzer Patel Drennan 23 Attorney Docket: CU2025-063-PCT1

[0095] Clause 18. The apparatus of any one of clauses 1-15, wherein the signal processor is further operative to communicate a trigger signal to the radiation source controller to initiate the generation of the excitation signal, the trigger signal being provided at a regular cadence.

[0096] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any technologies or of what may be claimed, but rather as descriptions of features specific to particular implementations of the particular described technology. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a sub-combination.

[0097] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0098] Thus, particular implementations of the subject matter have been described. Other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.

[0099] A number of implementations of the described technology have been described. Nevertheless, it will be understood that various modifications can be made without departing from the spirit and scope of the recited claims.Holzer Patel Drennan 24 Attorney Docket: CU2025-063-PCT1Holzer Patel Drennan 25 Attorney Docket: CU2025-063-PCT1

Claims

What is claimed is:

1. A method for calibration-independent determination of absorbance of a target analyte in a sample, comprising:generating an excitation signal including a wavelength scan component and a period modulation component;driving a radiation source using the excitation signal to generate emitted radiation according to the excitation signal;directing the emitted radiation through the sample and detecting transmitted radiation to produce a detected signal;computing a reference incident intensity corresponding to the excitation signal; converting the detected signal to an absorbance signal based on the reference incident intensity; anddemodulating the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output corresponding to the absorbance of the target analyte in the sample.

2. The method of claim 1, wherein the converting comprises applying a logarithmic ratio of the reference incident intensity to the detected signal.

3. The method of claim 2, wherein the converting the detected signal to the absorbance signal further comprises subtracting a detector background level prior to applying the logarithmic ratio.

4. The method of claim 3, wherein the harmonic absorbance output is integrated over a complete period of the period modulation component.

5. The method of claim 1, wherein the wavelength scan component spans an absorption feature of the target analyte in the sample.

6. The method of claim 1, wherein the harmonic absorbance output is directly proportional to a concentration of the target analyte in the sample.Holzer Patel Drennan 26 Attorney Docket: CU2025-063-PCT17. The method of claim 6, wherein determining a concentration comprises comparing the harmonic absorbance output to a synthetic harmonic spectrum generated from known spectral parameters.

8. The method of claim 1, wherein the converting the detected signal to absorbance occurs prior to the demodulation of the absorbance signal, such that instrument-dependent constants are removed during demodulation.

9. The method of claim 1, wherein the computing the reference incident intensity comprises generating a model of the excitation signal, including a ramp over the wavelength scan and a sinusoidal modulation component corresponding to the excitation signal.

10. The method of claim 1, wherein the demodulating employs a reference waveform including a phase term compensating laser source variables.

11. The method of claim 1, wherein both direct absorption and harmonic absorption spectra are obtained from a common scan of the detected signal.

12. The method of claim 1, further comprising:storing the detected signal as one or more raw data vectors in a memory; andafter demodulating the absorbance signal at the harmonic of the periodic modulation component, generating a direct absorption spectrum from the one or more raw data vectors using a modulation-attenuation constant that characterizes attenuation of a sinusoidal modulation amplitude in wavelength space arising from wavelength lag of a distributed-feedback laser.

13. The method of claim 1, wherein demodulating the absorbance signal at the harmonic of the periodic modulation component comprises generating a second-harmonic absorbance signal that corresponds to a second derivative of absorbance with respect to wavelength.

14. An apparatus for determining a concentration of a target analyte in a sample, comprising:Holzer Patel Drennan 27 Attorney Docket: CU2025-063-PCT1a radiation source configured to generate emitted radiation based on an excitation signal comprising a wavelength-scan component and a periodic modulation component,a radiation path through which the emitted radiation is directed through the sample; a detector configured to detect radiation transmitted through the sample to generate a detected signal representing transmitted intensity of the emitted radiation through the sample; anda signal processor configured to:compute a reference incident intensity corresponding to the excitation signal, convert the detected signal into an absorbance signal by forming a logarithmic ratio of the reference incident intensity to the detected signal,demodulate the absorbance signal at a harmonic of the periodic modulation component to obtain a harmonic absorbance output, anddetermine the concentration of the target analyte based on the harmonic absorbance output, which is directly proportional to absorbance.

15. The apparatus of claim 14, further comprising:a radiation source controller, discrete from the signal processor, the radiation source controller operative to control the radiation source to generate the emitted radiation based on the excitation signal.

16. The apparatus of claim 15, wherein the signal processor is further operative to acquire the detected signal from the detector for direct memory access writing of the detected signal to a memory.

17. The apparatus of claim 16, wherein the signal processor comprises a plurality of write buffers for the direct memory access writing, wherein at least one write buffer is used for direct write access to the memory while data written by at least another write buffer is processed from the memory.Holzer Patel Drennan 28 Attorney Docket: CU2025-063-PCT118. The apparatus of claim 15, wherein the signal processor is further operative to communicate a trigger signal to the radiation source controller to initiate the generation of the excitation signal, the trigger signal being provided at a regular cadence.Holzer Patel Drennan 29 Attorney Docket: CU2025-063-PCT1

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