Human breath analysis via cavity-enhanced optical frequency comb spectroscopy

To date, researchers have identified over 1000 different compounds contained in human breath. These molecules have both endogenous and exogenous origins and provide information about physiological processes occurring in the body as well as environment-related ingestion or absorption of contaminants1,2. While the presence and concentration of many of these molecules are poorly understood, many 'biomarker' molecules have been correlated to specific diseases and metabolic processes. Such correlations can result in non-invasive methods of health screening for a wide variety of medical conditions. In this article we present human breath analysis using an optical-frequency-comb-based trace detection system with excellent performance in all criteria: detection sensitivity, ability to identify and distinguish a large number of biomarkers, and measurement time. We demonstrate a minimum detectable absorption of 8 x 10-10 cm-1, a spectral resolution of 800 MHz, and 200 nm of spectral coverage from 1.5 to 1.7 micron where strong and unique molecular fingerprints exist for many biomarkers. We present a series of breath measurements including stable isotope ratios of CO2, breath concentrations of CO, and the presence of trace concentrations of NH3 in high concentrations of H2O.

These lasers are also used to detect nitric oxide for diagnosing asthma 4 . Finally, both quantum cascade and lead salt lasers have been used to detect ethane which is produced in lipid peroxidation and by some forms of cancer 12,13,14 . While all of these systems provide robust and highly sensitive detections of their analyte molecules, many operate in relatively narrow spectral regions. Others require long times to perform sensitive detections over a large spectral region. Therefore, the number of molecules that can be studied or detected by a single system is rather limited.
Recent approaches to trace detection that use broad bandwidth optical frequency combs have attempted to address this problem by creating parallel detection schemes that in a single shot record large spectral bandwidths 15,16,17,18,19 . Frequency-comb-based systems also take advantage of the high peak intensities of their pulsed output to easily access any spectral region from UV to far infrared via nonlinear conversion 20,21,22 .
Furthermore, the development of mode-locked femtosecond fiber lasers has led to robust frequency comb sources capable of continuous operations without user intervention 23 . In this work we couple the broad spectrum of a mode-locked fiber laser to an optical enhancement cavity to greatly enhance the detection sensitivity of breath samples. High spectral resolution is achieved within the entire 1.5 -1.7 µm spectral region with the use of a virtually imaged phased array (VIPA) detector 24,18 . The relevant spectrum covers many biomarkers, such as ethane 1.68-1.7 µm, acetone 1.67-1.68 µm, methane 1.63-1.69 µm, ethylene 1.62-1.66 µm, carbon dioxide 1.54-1.64 µm, carbon monoxide 1.56-1.6 µm, ammonia 1.5-1.54 µm, methylamine 1.5-1.53 µm.
The cavity-enhanced optical frequency comb spectrometer for breath measurements is shown in Fig. 1. The spectrometer consists of two subsystems; a continuous-flow gas system delivers breath samples, calibration gases, and the reference gas (N 2 ) to the detection chamber, and an optical subsystem records absorption features that are used to determine molecular concentrations. In the scheme of comb-based cavity-enhanced absorption spectroscopy 15,16,17,19 , the intra-cavity absorption signal is enhanced by the cavity multi-pass effect and is recovered by comparing the light transmitted from a high finesse optical cavity with and without absorption present.
Every frequency comb component is coupled to a corresponding cavity resonance mode. For a single tooth of the frequency comb, the electric field E t transmitted from the cavity can be written as the sum 25 , Here, L is the cavity length, R is the mirror reflectivity, n refers to the number of round trips a photon travels inside the cavity, α is the intracavity absorption, and E inc is the incident electric field. The phase term φ n (t) determines the interference of the fields inside the cavity and is written as (2) Here ν(t) is the time-dependent frequency of one of the incident comb teeth and β is the rate at which the incident frequency is swept. The intensity of the beam transmitted from the cavity is given by I(t)=E t (t)E t * (t). The cavity transmission measurements presented here are made with a slow detector that does not resolve the time dependence of I(t). Instead, the integrated cavity transmission is measured. The mirror reflectivity and the cavity length together determine the absorption sensitivity of the instrument and provide a relationship between the change in the transmitted light and the level of intracavity absorption.

Spectrometer characterization
A mode-locked Er +3 fiber laser provides 100 nm spectrum from 1.5 to 1.6 µm with 40 mW of average power. For spectral measurements between 1.5 and 1.6 µm, the output of the laser is coupled directly into the optical enhancement cavity. For spectral measurements from 1.6 to 1.7 µm, we exploit the high peak intensity of the modelocked laser output by using a Raman shifting amplifier to shift the spectrum and provide 300 mW of power (Fig. 2a). A simple flipper mirror is used for rapid switching between the two laser configurations. The laser is mode-matched into the cavity constructed from two mirrors with a 2 m radius of curvature and a peak reflectivity of R  The minimum detectable absorption for the spectrometer is determined by comparing consecutive sets of images taken while the detection cavity contains only nitrogen. The differential intensity noise from these sets of images is then converted to absorption noise at a particular wavelength using the mirror reflectivity ( Fig. 2b) and the integral of equation (1). Figure 3 shows the residual absorption noise at 1.6 µm as a function of the number of camera frames averaged. The contribution from the camera dark counts is also shown. The residual absorption noise is primarily due to laser intensity noise, cavity-laser coupling noise, and residual interference fringes generated within thin optical elements, such as the glass cover of the InGaAs diode array. The results show that after 2000 averages taken within 30 s, the minimum detectable absorption is 8 x 10 -10 cm -1 per detection channel.

Breath measurements
The relevant molecules studied for breath analysis are CO, CO 2 , H 2 O, CH 4 , and NH 3 , with more than 8000 known spectral features between 1.5 µm and 1. Our protocol for breath measurements of CO 2 stable isotopes and CO concentration requires the test subject to first take one deep breath. Next, the subject inhales normally and the breath is held for five seconds. Finally, the first half of the breath is released into the air before the second half of the breath is exhaled into the 1 liter Tedlar sample bag shown in Fig. 1. The use of only the second half of the breath sample increases the concentration of alveolar breath that is measured.
The first set of our breath measurements involves the analysis of stable isotopes.
Here we focus on measurements of CO 2 isotopes, but other isotopes such as H 2 O and CH 4 also exist in measurable quantities within our spectral region. Two spectral windows centred at 1.59 µm and 1.63 µm contain spectroscopic features of three isotopes of CO 2 , all of roughly equal absorption strengths. Figure 4 shows the breath spectrum of a healthy graduate student in the window centred at 1.63 µm and illustrates a unique feature of broadband detection. The two zoomed-in panels (a) and (b) both contain a number of spectral features for each of the three isotopes. By measuring many absorption lines and computing a concentration for each line, the overall accuracy of the isotope ratio measurement is enhanced by the square root of the number of lines measured. To calculate the isotope ratios from the spectrum shown in Fig. 4c, a modest selection of 5 lines is chosen for each isotope. Typically, isotope measurements are expressed in parts per thousand such that δ = (R sample -R standard )/R standard x 1000, where R standard is the natural abundance of the isotope and R sample is the abundance found in the breath sample. Using this analysis we find that δ 18 O = -9.1 ± 4.2 and δ 13 C = -28.8 ± 4.1.
The δ 13 C ratio is currently the only breath biomarker that is used widespread for clinical diagnosis. However, the ability to measure other stable isotopes of CO 2 (Fig. 6). Furthermore, if techniques are implemented to remove water vapor from the breath sample prior to measurement, such as flowing the breath sample through a cold (0 °C) glass tube, a much lower detection limit for NH 3 can be achieved.

Discussion
The measurements presented in the previous section provide only a modest glimpse of the capabilities of our cavity-enhanced optical-frequency-comb spectrometer. The large number of biomarkers that can be measured by the system coupled with sub-minute measurement times enable a cost effective way to accelerate research in breath analysis and to provide reliable clinical instrumentations. Fortunately, frequency comb technology is progressing very rapidly with ever improved spectral coverage, power output, and ease of use. Commercial mode-locked fiber lasers are available today with all operations performed by the laser completely automated.
Furthermore, since such lasers are based on technology created for the telecommunications industry, they are reliable for years of uninterrupted operations.
Similarly, the detection cavity is highly resistant to contamination, demonstrating no degradation in finesse after hundreds of hours of continuous flow of gas and breath samples.
Frequency comb technology is currently being extended for convenient operation in the 3 µm spectral region that promises to increase the detection sensitivity for biomarkers by a factor of 10 to 10 3 compared to our current system. Also, new designs of high-finesse prism cavities promise to expand the spectral coverage of optical cavities from 200 nm to several microns, greatly increasing the number of biomarkers that can be measured by a single system 26 . Although future developments of frequency comb-based systems promise to make further dramatic advances, we note that our current system can already be used for large scale clinical trials to gather statistics necessary to institute new, non-invasive, health screening tests. GHz, resolved by the 800 MHz resolution of our system. A modified Voigt fit that includes the resolution of the spectrometer is performed to find the g(ν) and relate α(ν)

Methods
to n. By finding the value of the instrument resolution that provides the best fit to the experimentally recorded lineshape, an instrument resolution of 800 MHz has been experimentally verified.
To calibrate the spectrometer we use three gas mixtures containing a total of four trace gases. These mixtures consist of 10 ppm CO 2 , 1 ppm CH 4  A flow diagram of the spectral recovery process is presented in Fig. 7. A pair of 256 x 320 pixel images, one reference and the other contains absorption, is converted into a 25 nm absorption spectrum. The first step in this process is to locate the nearly vertical fringes produced by the VIPA spectrometer within the picture frame. This is typically done using the reference image. Fringes are identified by an algorithm that starts at the peak of each fringe at the middle of the frame (i.e. row 128) and 'walks' along each fringe upward and downward, locating the peak of each fringe on the frame.
Next, the intensity of each fringe is converted into a column vector, creating a fringe array containing all of the frequency resolved cavity transmission information. 13 As a first-order correction for laser intensity drift between acquisitions of the absorption and reference frames, an area of low absorption in the absorption fringe array is compared to the reference fringe array, and the absorption fringe intensity is equalized to the reference fringe intensity. The absorption fringe array is then subtracted from the reference fringe array, before being divided by the reference fringe array. The result is a differentially measured and normalized fringe array that contains the relative intensity information.
The etalon FSR is determined using the pattern of absorption peaks from the subtracted fringe array. All unique information about molecular absorptions is contained within this interval. The etalon used in our system has a FSR = 50 GHz.
Once this interval is determined, the subtracted fringe array is unwrapped into a one dimensional spectrum of relative intensity versus wavelength. The generalized grating equation for the VIPA can be used to obtain a high precision mapping of position on the subtracted fringe array to wavelength 23 . A low pass filter is then employed to remove noise from the picture at spatial frequencies higher than the resolution of the spectrometer. Also, for sharply peaked spectra, a background subtraction routine is used to remove higher order intensity fluctuations between the reference and absorption frames due to laser noise, laser/cavity coupling noise, or pointing instability. Finally, the relative intensity information is converted into quantitative absorption strengths using the integral of equation (1). with the gas handling system for breath analysis. Fig. 2 a) The spectrum generated by the mode-locked fiber laser from 1.5 to 1.6 µm (red) and the amplified, Raman shifted, spectrum from 1.6 to 1.7 µm (blue). b) The measured reflectivity of the cavity mirrors as a function of wavelength. c) The measured absorption spectrum of the air in our laboratory from 1.5 µm to 1.7 µm.