A filter-based Raman spectrometer for non-invasive imaging of atmospheric water vapor

The major rationale for the development of the new instrument described here, referred to as a water vapor “Ramanographer,” is to study fundamental processes in the fields of cloud micro-physics, turbulence, and aerosol interactions. Some examples provided in the next paragraph will also underline the need for and the transformative potential of such analytical capability. The physics probed by these studies is still ill-understood and at the forefront of the effort of several groups in the fields of cloud physics, turbulence, radiative transfer through turbid and turbulent environments, and climate change. Several future research investigations can be envisioned and will be enabled by the new capability. Below, we discuss two illustrative examples.

1. Instruments such as the one described here will contribute to the understanding of mixing processes in clouds and especially on the role of turbulence in generating fluctuations of temperature and water vapor concentration that, in turn, result in fluctuations in relative humidity (or supersaturation). Stratiform clouds are estimated to exhibit supersaturation fluctuations on the order of 1%,¹ but observations are sparse and usually quite coarse in time and space due to strong resolution limitations for airborne and remote sensing instruments (see, e.g., Refs. 2 and 3). Yet, relative humidity fluctuations are of direct relevance to aerosol activation and cloud droplet growth/evaporation and may also play a role in new particle formation in the atmosphere.^4,5 The magnitude and degree of correlation of humidity fluctuations with cloud liquid water content fluctuations is an important characteristic of homogeneous vs inhomogeneous mixing of clouds with the surrounding environment.^6,7

2. Aerosols alter the radiative balance of our planet not only by affecting clouds (as discussed earlier) but also by interacting directly with the solar radiation through light scattering and absorption. The aerosol scattering coefficient depends on the concentration of particles, the wavelength of the incident light, the size of particles, their index of refraction, and their shape. Even for a given dry particle mass, its size and, therefore, its light scattering properties can be affected substantially by the relative humidity of the surrounding air, as water is taken up by hygroscopic aerosols.⁸ This effect is detected as an enhanced scattering coefficient, or an increase in size, when the relative humidity increases from low values (e.g., $<$40%) to higher values (e.g., 90%). The changes in size or scattering are often measured with extractive instruments, such as nephelometers or differential mobility analyzers (in tandem configurations: one at dry conditions and another at humidified conditions or simply controlling/modulating the humidity of the aerosol), or by studying single particles levitated in electrodynamic traps and controlled humidity conditions.^9–11 In all these approaches, however, typically the information of possible effects of rapid and local fluctuations in relative humidity—such as those caused by turbulence—on the properties of an ensemble of particles is lost. The effect of humidification on aerosols in a turbulent environment is not well constrained by measurements performed at “homogeneous” humidity conditions as is the case when using tandem extractive instruments, even if the measurements are performed at a relative humidity close to the average humidity of a turbulent environment. The humidity fluctuations, together with hysteresis processes, might result in non-linear effects on the aerosol sizes and scattering. The capability of the Ramanographer can be used in conjunction with three cameras detecting the elastic scattering of the aerosol at different scattering angles to study changes in size and scattering properties of humidified aerosols in turbulent conditions.

The instrument described in this paper utilizes a pair of charge coupled device (CCD) cameras to image a sampling region illuminated by a multi-pass laser setup. The Raman scattering signals are isolated from elastic scattering and optical glare through the use of two pairs of bandpass filters and are used to infer the local concentrations of water vapor. This allows for the non-invasive, two-dimensional mapping of water vapor required by a variety of laboratory experiments, such as those previously described. We will provide details on the fundamental operating principles, construction, calibration, and precision of the instrument.

Water concentration has been measured non-invasively in the past by means of tunable laser absorption spectroscopy. The H₂O molecule has three rotational constants of an asymmetric top rotor, 27.0, 14.4, and 9.4 cm⁻¹,¹² and three fundamental vibration frequencies, ν₁ = 3657.05, ν₂ = 1594.75, and ν₃ = 3755.93 cm⁻¹.¹³ Thornberry et al.¹⁴ developed the “NOAA Water instrument” designed for detection of water vapor in the upper atmosphere, capable of measuring water vapor concentration as low as 0.2 ppm. The instrument utilizes laser absorption spectroscopy at wavelengths corresponding to the fundamental band of the asymmetric stretching mode of water (ν₃). Arroyo and Hanson¹⁵ used an InGaAsP tunable laser diagnostic method to detect water vapor by measuring absorption within the combination band ν₁ + ν₃ near 1.38 μm (7246 cm⁻¹).¹⁶ Combination bands have typically much smaller absorption cross sections than fundamental bands but still orders of magnitude larger than those for Raman scattering. The main advantage of laser absorption spectroscopy is high sensitivity and the ability to measure densities of species on an absolute scale. However, it has multiple disadvantages: (1) both methods mentioned above require tunable lasers and (2) most importantly, they provide information only about water concentration integrated along the laser path, which makes them unsuitable for spatial mapping of water molecules. Water vapor concentrations can also be mapped invasively using readily available probes. This has the advantages of high sampling rates and relative simplicity but has the significant disadvantage of disrupting the sampling volume. Major advantages of the instrument described in this paper are (1) the use of a fixed frequency laser, (2) the ability to use readily available Si detectors with low noise and excellent quantum efficiency, and (3) the ability to measure the number density of water molecules non-invasively over large areas simultaneously with high spatial resolution and to generate maps of water concentration. The latter is a key capability for the study of the effects of turbulence on the water vapor concentration distributions. The disadvantage of Raman scattering is the low cross section, which can be compensated for by the use of higher power lasers, which are readily available in the current market.

All the experiments presented here were performed using the setup shown in Fig. 1. The major components of our apparatus are the following: (1) A Nd:YAG laser (Laser Quantum Gem 532) with continuous wave output at 532 nm and beam divergence less than 0.8 mrad. Spectra were taken with a laser power of 0.5 W and polarization orthogonal to the table. In this setup, both the polarized and depolarized components of the Raman scattered light can reach the detector. A detailed description of the Raman signal in this configuration can be found on page CRS6 in Ref. 17. Due to the very low absorption cross section of atmospheric molecules (on the order of 10⁻²⁷ cm²),¹⁸ a laser power of 0.5 W has a negligible contribution to local heating of the sampling volume. We estimate that for each centimeter of length the laser travels through, the energy absorbed each second is approximately five orders of magnitude lower than the thermal energy at 300 K. This is easily dissipated through the 10⁹ molecular collisions that happen each second in this volume at atmospheric pressure. (2) A series of lenses (L1, L2, L3, and L4) to collect and image photons from the scattering region onto the detector. (3) Two vertically oriented right angle prisms direct the excitation source to pass multiple times through the scattering region. (4) An acrylic chamber houses the scattering region and contains the injection of gases or air fully saturated with water vapor. The chamber was constructed with 0.5 in. wide openings positioned on each side to allow the laser to pass through multiple times unobstructed. (5) A pump to force fully saturated air into the chamber. Relative humidity in the chamber was controlled by varying the flow rate of saturated air until a steady-state humidity level was reached. (6) A long-pass dichroic mirror with center wavelength 638 nm was used to split the Raman signals from N₂ and H₂O. (7) Two 512 × 512 pixel back-illuminated CCD cameras (Andor Ikon-M) with a pixel size of 24 × 24 μm² and a quantum efficiency greater than 90% in the range of 500–700 nm were used to image the sampling volume. The cameras were thermo-electrically cooled to a temperature of 200 K during all experiments. The pixels on the sensor were electronically binned into “superpixels” 16 px wide × 1 px tall. (8) A collection of bandpass filters (F1, F2, F3, F4) allowed for the removal of elastically scattered laser light from our Raman signal of interest. Two “signal” filters (F1, F3) were selected with transmission bands centered on the Q-branch of N₂ and H₂O at 607.7 and 660 nm, respectively. Filters F1 and F3 were manufactured by Alluxa and Thorlabs, respectively. Two “background” filters (F2 and F4) were selected with their transmission bands outside the spectral vicinity of the roto-vibrational Raman bands. Both background filters were manufactured by Thorlabs. We found that filters with center wavelengths at 590 nm for N₂ and 650 nm for H₂O attenuated the Raman signals by over five orders of magnitude. The filters’ transmission is compared to the Raman spectrum for N₂ in Fig. 2. Ideally, the transmission at 532 nm would be identical for all filters. In our experiment, the spectral properties, bandwidths, and transmission were somewhat different due to budget constraints. However, they were sufficiently close for the differences in photon transmission to be negligible when compared to the signal’s noise levels. The spectral bandwidths of the signal filters have little effect on the experiment as long as the transmission region does not include any wavelengths that would be present due to scattering from other molecules or external light sources. The spectral band of the background filters must be outside the roto-vibrational stokes band to avoid transmitting Raman scattering. We found that separating the center wavelengths of the signal and background filters by 10 nm was sufficient based on the bandwidth of our filters. The filters used in this experiment have a full-width at half-maximum of 10 nm. (9) A commercial relative humidity and temperature probe was used to calibrate the system. The probe comprised of a semiconductor type temperature sensor (thermistor) and bulk polymer coated ceramic humidity sensor. The probe was inserted into the acrylic chamber through the top and was positioned directly above the scattering region during all experiments.

Typical images recorded with our apparatus are shown in Fig. 3. In this example, the primary spectral features in the range covered by our measurements come from molecular nitrogen. The photograph on the left was taken with signal filter F3 transmitting the Raman signal originating from the Q-branch of N₂. The broadening of the lines toward the top of the image is due to the divergence of the laser beam. This first image contains three distinctively different components: (1) Raman scattered light from N₂ (v = 1 ← v = 0); (2) Rayleigh elastic scattering by air molecules, which was not removed by the signal filter, with identical spatial features as the Raman scattered signal; and (3) laser light scattered on various optical components with spatial characteristics having nothing in common with the Raman or Rayleigh scattering. Next, the photograph in the center was taken with the background filter F4. The background filter removes nearly all Raman scattering, so this image is dominated by two remaining photon sources: (1) remnants of the Rayleigh elastic scattering and (2) light scattered by the optical components. Effectively, this image contains only information about the background light contaminating the Raman signal. Under ideal conditions, this information will be identical to the elastic and optical scattering reaching the sensor in the first image. Therefore, their difference, shown on the very right side in Fig. 3, contains only the Raman signal from molecular nitrogen. Identical reasoning applies for the water vapor images taken with filters F1 and F2. All the analysis presented in this paper is based on these resultant difference images.

Next, we will describe the detailed operational principles of our apparatus. For clarity, we chose to show and analyze information from only a single laser beam passing through the experimental sample. This was achieved by removing the vertically oriented prisms from either side of the vapor chamber. Additionally, we visualize all our results in two dimensions. We plotted the signal in units of number of photo-electrons from a single column of superpixels located in the center of the image vs vertical position. Conversion from images to integrated plots is demonstrated in Fig. 4. The image taken by the camera has been rotated clockwise 90° to better depict this method. The horizontal axes representing the pixel number on the sensor were converted to the vertical positions in physical space within the imaging region. For our setup, each superpixel contains information from a 0.16 mm tall × 2.60 mm wide area in the imaging region. Since the laser beam is approximately cylindrical, the sampling region can actually be described as a volume, with a depth equal to the diameter of the beam, so each superpixel actually represents a region ∼1 mm in depth.

The Raman signal is proportional to the number density of molecules interacting with the laser light. However, the signal also scales with the laser intensity. Therefore, while the concentrations of nitrogen and water molecules in the scattering region are fairly uniform, the water vapor concentrations can be measured by the Ramanographer only where the laser intensity is sufficiently high. This limitation of our current setup implies that the water vapor concentration estimate is possible only where the laser light actually excites the molecules. As seen in Fig. 4, this results in a measurable signal only along the line corresponding to the laser beam. A future improvement could include a better homogenization of the spatial illumination of the measurement volume.

Raman spectroscopy, similar to most spectroscopic techniques, provides only relative information about the species investigated and must be normalized. We used the signal from the Q-branch of N₂ as a reference to extract the spatial number density distribution of water molecules on an absolute scale. System calibration depends on the assumption that the nitrogen concentration is uniform to within a fraction of a percent. This assumption is justified because there is no large scale N₂ concentration gradient to drive turbulent fluctuations.

A typical Raman signal from water and the background in its vicinity is shown in Fig. 5. The “pure” Raman signal of water after background subtraction spectra is shown in Fig. 6. We extracted the “pure” Raman signals of nitrogen in an identical fashion. These spectra formed the basis of our analysis presented in this paper. To verify the Raman spectrometer’s effectiveness at isolating the Raman signal, we took images of pure oxygen gas using the set of N₂ filters (F3, F4). The results are shown compared to the Raman signal from normal atmospheric air in Fig. 7. Clearly, no nitrogen signal is present after the nitrogen was removed from the scattering region, indicating that the background removal method was successful.

The Raman signal passing through the bandpass filters and detected by the CCD sensors is composed of all rotational lines within the Q-branch (ΔJ = 0, Δv = 1) for N₂ molecules and the within the Q-branch of the ν₁ band for H₂O molecules. For example, the signal from N₂ at the detector measured in units of number of photons, taken at temperature T, is equal to

Here, the “line strength” S_J for the Q-branch is equal to

A contains all fundamental constants, incident laser intensity, collection optics, quantum efficiency of the detectors, and factors accounting for scattering geometry common for all roto-vibrational Raman lines. We would like to point out here that under typical experimental conditions, it is extremely difficult to evaluate A accurately. σ is the cross section common to all rotational transitions within a rigid rotor approximation, n is the number density of molecules, g_J is the nuclear spin factor associated with the rotational quantum number J, and E_J is the energy of rotational state J, ν(v, J) is the frequency of the Raman line corresponding to the vibrational quantum number v and rotational quantum number J, nearly identical for all the lines within the Q-branch, and a₀ is a constant corresponding to trace-scattering. The partition function, Q_r, represents the sum over all rotational states.

The total intensity of the entire Q-branch depends little on temperature as it encompasses all rotational Raman lines. Small changes in the overall intensity of the Q-branch due to a redistribution of populations among initial rotational states can be safely ignored at this scale. We estimate that a change in temperature by 10 K in the vicinity of 300 K contributes to 0.25% variation in Raman signal under the integrated Q-branch for N₂. These changes are due to variations in S_J on roto-vibrational transitions within the Q-branch.

The Raman signal from water vapor can be written in a similar fashion. Under our experimental conditions, A is identical to that for N₂ measurements. All molecular constants and transition frequencies in Eq. (1) for N₂ and H₂O are known, and therefore, the sums can be evaluated. Taking the ratio of two signals cancels the only remaining unknown quantity A and effectively yields the ratio of number densities of H₂O to N₂ molecules,

where α can be calculated or determined experimentally from simultaneous measurements of water vapor concentration by an alternate calibrated instrument and direct comparison to the Raman signals. We opted to use an experimental calibration method rather than a theoretical evaluation of α. This decision was partially motivated by the precision to which the Raman cross sections of water vapor and nitrogen are known. The ratio of their cross sections is currently known only to within 10%,¹⁹ which would limit the precision of the apparatus.

Two potential polarization configurations for the laser are shown in Fig. 8. In configuration I, the electric field oscillates orthogonal to the observation axis on which the camera is placed. In configuration II, the electric field oscillates parallel to the observation axis. In both configurations, the camera is located along the x-axis, defined to be $θ=π2$⁠. When considering a collection of $N$ randomly oriented molecules being excited by a source in the polarization state p_i with wavenumber ν₀ and irradiance $I$⁠, the intensity of the scattering in the polarization state p_s due to a transition from an initial state with the set of vibrational quantum numbers vⁱ to a final state with the set of quantum numbers v^f can be written as¹⁷ 

Here, $|νvfvi|$ is the frequency corresponding to the transition between vⁱ and v^f; the ± corresponds to anti-Stokes and Stokes transitions, respectively; $Nvi$ is the number of molecules in the initial state; and f (a², γ², δ², θ) is a function of the invariants of the polarizability tensor and the angle from which it is being observed, θ. For all transitions in which Δv = 1, δ² = 0. In configuration I, f is then given by

The value of f in configuration II is

where a is the mean polarizability and γ is the polarizability anisotropy. These are constant and unique to each molecule. Taking a ratio of the intensities in each configuration for any single transition leaves only the ratio of f, as all other terms will cancel,

The values of a² and γ² for N₂ are 3.17 and 0.52, respectively.²⁰ The signal in configuration I is equal to 46.9 times that in configuration II for all transitions in the Q-branch. Since H₂O is almost entirely polarized, the signal in configuration II almost completely vanishes.^21,22 Thus, a setup in configuration I will detect the same Raman signal at a faster exposure time than the one in configuration II. Alternatively, the same exposure time may be used to collect a significantly higher Raman signal. The latter effect is illustrated in the plot of Raman signals in each configuration in Fig. 9.

The calibration process was performed with the setup illustrated in Fig. 1, with only a single laser pass as specified previously (Fig. 4). Saturated air was pumped into the imaging region at various steady state rates. Signal and background images were taken with both cameras set to an exposure time of 6 min. These images were segmented into 2 min sub-exposures, which could be compared with each other to remove cosmic rays. As mentioned previously, the pixels on the camera sensor were binned electronically to form superpixels 16 px wide by 1 px tall. This was done to enhance the signal to noise ratio and reduce uncertainty in the photo-electron counts. Each column of superpixels in the region of interest was then processed individually. The signal in each column was summed over the region immediately surrounding the laser line. The outer limits of this region was taken to be when the N₂ signal had fallen to 25% of the value at its peak. The same region was summed in the corresponding column of the water vapor signal. To match the form of the left side of Eq. (3), a ratio was taken of the signal sums for each column. Our setup restricted us to directly measuring only the average relative humidity value throughout the box, so the data from the entire laser region in each image was aggregated. An arithmetic mean of the ratio values was taken across all of the columns to produce a value that corresponded to the single measured water vapor concentration level. $nH2O$ was calculated using the measurement from the relative humidity and temperature probe. $nN2$ was taken to be a constant value of 78.1% across all images. Figure 10 illustrates the signal changes in the H₂O and N₂ as the H₂O concentration is altered. As expected, the Raman signal for N₂ remains constant with changing H₂O concentrations, while the H₂O Raman signal increases with the concentration.

We measured water vapor to nitrogen integrated signal ratios from a series of spectra across various water concentrations. The ratios produced by the Ramanographer are plotted with the independent measurements taken by the relative humidity and temperature probe in Fig. 11. A total of 21 measurements were taken across the entire range of humidity levels achievable in our laboratory settings. From Fig. 11, it is evident that the two measurements covary with the changing experimental conditions, suggesting good linearity of the Raman ratio with the water vapor molar concentration. Uncertainty in water density measurements obtained from the Raman signals and from the probe used are discussed next.

In order to accurately process our data, the relative humidity and temperature data from the probe were converted to number densities in the form of the volume mixing ratio. The number density of water vapor, $nH2O$⁠, can be calculated as

where RH is the relative humidity in %, P is atmospheric pressure in hPa, and E(T) is a sixth-order polynomial approximation for the temperature dependence as specified in Ref. 23. Uncertainty in the number density propagates as

The probe used for calibration had an uncertainty of ±1 K across the entire temperature range being analyzed and ±1%RH below 90%RH. At or above 90%RH, the uncertainty increases to ±3%RH due to material properties of the probe. These values were closely monitored throughout the exposure time and were found to fluctuate less than 1 K and 1%RH across the entire 6 min period. In the vicinity of 300 K and 1000 hPa, the value of $nH2O$ as determined by the probe carries uncertainty of ∼7% for the entire range of humidity levels in our experiment. A single-parameter least squares regression according to Eqs. (10) and (11) was applied to calculate a value for α in Eq. (3). Standard uncertainty propagation methods were applied throughout the calculations,

This method resulted in a value for α of 3.65 ± 0.65 (17.8%). The regression is plotted along with the experimental data in Fig. 12. At the scale of 3.5 × 10¹⁷ cm⁻³, we can determine the number density on an absolute scale with accuracy of 7.1 × 10¹⁶ (20%). This uncertainty decreases slightly at higher water vapor concentrations. It should be noted that a large portion of this uncertainty originates from the probe that was used, and higher precision may be achieved with calibration against a more precise physical measurement method. Relative changes in water vapor concentration can be known more precisely, as no conversion to an absolute scale is required. This precision is independent of α and is based only on the square root of the number of photo-electrons detected within the summation range. Thus, the relative changes in number density can be determined with uncertainty less than 10%.

The precision of this instrument in its current state is comparable with other Raman-based water vapor detection methods. The LIDAR system described by Whiteman et al.²⁴ was found to have accuracy between 10% and 20%, depending on the altitude being observed, when deriving water vapor mixing ratios. More recent measurements from the WAVES 2006 Campaign²⁵ have similar uncertainties of 20% below 7 km in altitude. The uncertainty of the Ramanographer can easily be improved in future applications with higher power lasers or larger collection optics.

Spatial and temporal resolutions can be exchanged depending on needs, but an ideal instrument investigating turbulent environments would follow the kinetic energy dissipation rate. Balancing the kinetic energy dissipation rate with the required uncertainty levels yields an optimal temporal and spatial resolution. With the 0.5 W laser, we estimate the spatial and temporal resolutions of 23.8 mm³ and 0.62 s, respectively. This would yield similar uncertainty values and enable the study of turbulent interactions on the proper scale. Calibration should be performed at spatial and temporal scales that allow for homogenization of the sampling region. This can be achieved by lengthening the timescale and shrinking the spatial resolution.

We have described in this paper the technique for measuring water vapor concentrations in air using the integrated Raman signal of the Q-branch of nitrogen and water vapor in the atmosphere. We have developed a non-dispersive Raman imaging spectrograph capable of monitoring water vapor concentrations with high spatial resolution. This instrument has the advantage of generating two-dimensional maps of concentrations without the requirement of invasive measurement. Our results were independently verified by a high-end commercial bulk polymer-coated ceramic hygrometer with a precision of 1%RH. The Raman non-invasive, in situ measurement provides large maps of water vapor concentrations with a spatial resolution of 0.4 mm³ and a relative precision of at least 10% at water vapor densities of 3.5 × 10¹⁷ cm⁻³ and better at higher concentrations. The typical observation time was 6 min. The primary limiting factor in achieving better temporal resolution was the relatively low laser power and small collection optics used. Additionally, spatial resolution could, in theory, be exchanged for higher temporal resolution, but the ideal system follows the kinetic energy dissipation rate. Our analysis suggests that high sensitivity in water vapor concentration—sufficient to study atmospheric turbulent processes with a spatial and temporal resolution of 10 mm³ and 0.25 s, respectively (as discussed in Sec. I)—can be achieved with commercially available lasers with a power of about 30 W. Local heating at 30 W increases by two orders of magnitude but is still negligible. This power is several orders of magnitude lower than the typical peak power of lasers used in Raman LIDARs.²⁶ 

Financial support from the National Science Foundation (Grant No. ATM1625598) is gratefully acknowledged. We thank Dr. Tyler Capek for fruitful discussions and help in the laboratory. T.K. would like to acknowledge the Elizabeth and Richard Henes Center for Quantum Phenomena for supporting him with a research summer fellowship.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.