KEYWORDS: Modulation, Absorption, Oxygen, Spectroscopy, Vertical cavity surface emitting lasers, Optical amplifiers, Atmospheric optics, Signal detection, Data acquisition, Signal to noise ratio
Wavelength modulation spectroscopy (WMS) with simultaneous detection at high harmonics (up to and
including N = 11) is reported for the first time. A Vertical Cavity Surface Emitting Laser (VCSEL) is used to probe
atmospheric oxygen using a multi-pass optical cell. The laser frequency is modulated at a low modulation index while
synchronous detection is performed simultaneously at all harmonics up to the 11th. These higher harmonic signals allow
for better resolution of congested spectra. Experimental results are used to detect and resolve absorption features in the
A-band region of oxygen. The high harmonic signals are used to distinguish between stronger rotational-vibrational
absorption lines in oxygen and weaker absorption lines formed by low-density isotopic oxygen. This detection method
also allows for the resolution of overlap between these weaker isotopic spectra. Higher harmonic signals resolve
additional structure, which does not appear at direct absorption measurements, or even in lower harmonic signals (N <
3). Since harmonic signal power decreases rapidly with detection order (N), the technique employed clearly shows that
the commonly used signal-to-noise power ratio, while important, is not the only criterion for a good measurement. We
examine the effects of optical pathlength saturation for these weak isotopic lines by measuring the effect of an optically
thick path (at fixed density) on the signal.
We present a novel approach to quantifying and optimizing the amount of information available in radiation
patterns. The technique presented and the results obtained are applicable on a broad scale, including those
in infrared, nanophotonics and other non-intrusive sensing techniques. We investigate the amount of
information lost due to limitations of the detector system. The method, which is based on information
principles developed by Shannon, expands on the many conventional approaches to optimizing performance
of sensors. The fundamental question of how many bits of information can be extracted by any sensor is
addressed. We focus on answering this question for the measurement of the radiation pattern from an
antenna array. The effects of a finite detector size, on the structure of the radiation pattern, are presented,
and we quantify the relationship between loss of structure and loss of information. The work presented may
be extended to a wide range of applications, including remote sensing. While the information content of
antenna array radiation patterns is based on the spatial distribution of photons, the method presented is
general and may be applied to a variety of distributions, such as lineshape functions, important in
spectroscopy, where the information is contained in the frequency distribution of photons.
KEYWORDS: Modulation, Signal to noise ratio, Signal detection, Absorption, Spectroscopy, Interference (communication), Information theory, Sensors, Molecules, Amplifiers
Shannon's information theory is applied to Wavelength Modulation Spectroscopy (WMS) providing quantitative figures
of merit such as the measurement precision and a prediction of the optimal detection harmonic order to be used. The
amount of information, in bits, that can be extracted in any WMS measurement is calculated. The theory is applied to
experimental results we have obtained in WMS experiments in congested spectra with overlapping lines that have highly
disparate absorption cross-sections. A key result is that the complexity of signal structure can play a much more
important role than the conventional signal to noise ratio. We show that there are some parts (where it exhibits turning
points and zero crossings) of the structurally-rich WMS signal that play a larger role in conveying information about the
measurement than other parts of the signal. Practical applications follow immediately. We also show that, for a particular
noise limitation of the apparatus, there is a finite amount of information that can be transmitted (to the detection
equipment) by the probe laser as it samples the probed species. The apparatus is analogous to a Shannon's information
channel. Application of the theory developed to our experimental absorption measurements in the Oxygen A-band shows
why high detection harmonic orders (up to the 7th or 8th) yield the highest resolution. This is in contrast to statements in
the literature, based on conventional signal to noise ratio considerations, that the best results are to be expected with
second harmonic detection.
Wavelength Modulation Spectroscopy (WMS) has been extensively used as a tool for sensitive detection through precise
measurements of the absorption lineshape function of gaseous species. In this paper pathlength saturation in wavelength
modulation spectroscopy is studied. New effects are found when one takes advantage of demodulation at higher
harmonics of the modulation frequency. We show here that modulation spectroscopy is a much more sensitive probe of
these effects. In particular, when synchronous detection is performed at higher harmonics of the modulation frequency,
even very small pathlength saturation effects become clearly visible. The method discussed allows one to probe
lineshape profiles by observing how the signal profile varies with absorption pathlength. In particular, the signal around
line center displays effects of saturation that are characteristic of the lineshape. This method is powerful because,
ultimately, all the information about any measurement is contained in the lineshape profile. Since different lineshape
profiles exhibit different saturation behavior, higher harmonic detection provides a new method to perform sensitive
detection. We have shown effects of saturation on the central lobes of harmonic signals. We also show that there are
definite relationships between the variation of the individual side lobes as well as their relative magnitudes that yield
further information about the lineshape function.
Absorption and emission spectroscopy measurements have been extensively and effectively utilized in the probing and monitoring of gases. As in any real experimental situation, the measurement of absorption or emission profiles results in a loss of information due to practical limitations, such as a finite precision of the detector. Also, it is now accepted that there is a relationship between information loss and thermodynamics. Hence, the question "How much information, in bits, is lost when making a practical spectroscopic measurement and how much heat is generated in the process?" arises. Shannon's information theoretical concepts are used to quantify the information lost due to the finite precision in wavelength measurement, of a detector used in a spectroscopic measurement. The heat generated in such a detector is also studied. The relationship between the heat generated and information lost as a result of the finite precision of a practical detector is investigated.
Wavelength Modulation Spectroscopy (WMS) utilizes low frequency modulation of the probe, followed by synchronous detection at the modulation frequency or at one of the harmonics. WMS provides a particularly useful tool for resolving highly disparate overlapping lines, because the high-order derivative-like structure of higher harmonics results in an enhancement of features, not possible with conventional ("direct") absorption spectroscopy. An important question, not yet systematically addressed in the literature is, "Given that in any measurement seeking to resolve overlapping spectra there is always a minimum harmonic detection order, how does one determine this order?" To address this issue, a Rayleigh-like criterion is defined and used to determine when two lines are barely resolved. Shannon's information theoretical principles are then used to calculate the information obtained when overlapping spectra are barely resolved at a particular harmonic. The results obtained allow one to predict the minimal harmonic detection order that should be used to resolve overlapping lines.
An information theoretic approach to maximizing the efficacy of optical sensing devices is presented. The principles used and the results obtained are applicable on a wide range of scales, including those in nano photonics sensing and detection. A key factor which is investigated is the aspect of extraction of the maximum amount of information in any given environment. The method used, which is based on information principles developed by Shannon, augments the many conventional approaches to optimizing performance of sensors. The fundamental issue of how many bits of information can be extracted by a sensor is addressed. The radiation pattern from a radiating or receiving sensor-array provides a spatial probability density function, which carries all the information about the system. Various such arrays are treated and the significance of the structure of the radiation pattern is examined. The technique is extended to the well-known concept of the lineshape profile of radiative atomic and molecular transitions, which is a probability density function in the frequency domain. Extensions of this work have applications in nanotechnology.
A quantitative analysis of Wavelength Modulation Spectroscopy (WMS) signals at various harmonic detection orders for use in precision, non-intrusive measurements is performed. A theoretical analysis of fitting of WMS signals is developed. The detailed structures of WMS signals at various harmonic detection orders are studied and analyzed, using statistical measures. It is shown that the variance of errors increases with mesmatches in linewidth in a particular (Nth order) harmonic signal. However, this rate of increase in variance is characteristic of the harmonic detection order used, thereby demonstrating the advantage in measurements at different harmonics. It is shown that for a constant error in estimation of linewidth of a profile, the variance of errors can be higher for higher detection orders. Therefore, mismatches in fits are more prominent at some optimal detection order. The methods developed can be used to examine subtle effects such as Dicke narrowing in certain molecular spectra. These small perturbations of lineshape profile reveal details of the molecular collision kinetics, and hence yield precise measurements that are difficult to achieve by other techniques.
KEYWORDS: Modulation, Spectroscopy, Absorption, Distortion, Signal detection, Molecules, Sensors, Information theory, Frequency modulation, Thermodynamics
Modulation Spectroscopy is a sensitive, convenient, versatile and cost-effective method for monitoring gaseous species and for obtaining quantitative information about molecular collision dynamics through precise measurements of the absorption lineshape function. Even slight perturbations in the lineprofile can be measured precisely, and because these perturbations are directly linked to changes in physical conditions of the sampled target, one obtains very precise non-intrusive measurements of these parameters. Over the last few years, we have extended this technique to the regime of higher harmonic detection and demonstrated that, in many cases, one obtains a higher precision by using an optimal harmonic detection order higher than the commonly used second harmonic. Experimental and theoretical results have been presented. In this paper we use the principles of Information Theory developed by Shannon to describe the information content in modulation spectroscopic signals. A simple argument is used to show that information that may otherwise be lost because of distortion can be recovered by derivative like techniques, such as those used in low frequency modulation spectroscopy. Experimental results obtained for the resolution of overlapping lines of disparate strength are discussed.
KEYWORDS: Signal detection, Absorption, Modulation, Semiconductor lasers, Distortion, Oxygen, Spectroscopy, Frequency modulation, Signal to noise ratio, Fermium
Recent developments in the use of diode lasers as ultra sensitive sensors are presented. Particular emphasis is placed on higher harmonic detection using the wavelength modulation technique. Experimental results are presented illustrating that this method, which uses a compact, portable apparatus, yields measurements with very high precision. Theoretical analyses of these experimental results are also provided. Novel ways of extracting detailed information of the probed sample are described. These include measurements of fine features, as well as simultaneous measurements of multiple overlapping lines. Such fine features allow one to accurately probe the collision dynamics of gaseous samples yielding values of temperature, density, and pressure. The method described here utilizes several novel features of higher harmonic detection. These features include a set of self-consistent measurements, by employing coherent detection up to the eighth harmonic order. The highest harmonic detection order achievable with this technique is limited by the bandwidth of the synchronous phase-sensitive demodulation apparatus and the noise figure for the detection system. Applications in basic science, in pollution monitoring and detection, and in industrial environments are briefly discussed.
We discuss the utility of wavelet transform methods in signal processing in general, and in particular, demonstrate the technique in optoacoustic applications. In several optoacoustic experiments with different samples, we have successfully enhanced the signal to noise ratios. Wavelet transforms optimize resolution by utilizing a tailored, variable time-window in different frequency regions. The technique's great advantage lies in the fact that the wavelet transform adds some redundancy to the original signal, and some desired features can be enhanced in the transformed space. In addition, proper choice of the basis set allows a sparse representation of the signal. Therefore, even when some components are suppressed in the transformed space, the signal itself can maintain its fidelity. This technique has great potential in biomedical optoacoustics, such as medical image processing and signal denoising. We use the wavelet transform technique to resolve acoustic echoes in the time-dilation space. White noise was removed by the wavelet shrinkage method. This processing was used to analyze several experimental results. These include optoacoustic measurements in solid samples as well as in biological tissues.
Wavelength modulation spectroscopy using semiconductor lasers is a sensitive tool for identifying species and measuring concentrations, velocities, and temperature in gaseous media. One advantage of modulation spectroscopy is that detection is carried out at frequencies far from the base-band noise, improving the signal-to-noise ratio. An additional benefit of performing wavelength modulation spectroscopy is that it allows for detection at harmonics of the modulation frequency. When a sinusoidal modulation is imposed, the harmonic detection signals resemble the frequency derivatives of the absorption profile, where the derivative order corresponds to the harmonic detection order. For this reason, the higher harmonic signals can be exploited to obtain more sensitive measurements of spectroscopic parameters, such as lineshape profile, absorption cross-section, temperature, and concentration. Wavelength modulation of semiconductor lasers, such as Fabry-Perot, vertical cavity, and external-cavity lasers, is discussed along with the advantages and disadvantages associated with each laser source. Applications of wavelength modulation spectroscopy are explored and it is shown that the higher harmonic detection signals exhibit structure and magnitude variations that are extremely useful in many spectroscopic applications.
Wavelength modulation spectroscopy was employed to investigate water vapor absorption lines in the 1.462 micrometer wavelength region using an external-cavity diode laser. These measurements were necessary in the development of a lidar (light detection and ranging) instrument for differential absorption measurement of the concentration and movement of water vapor in the Earth's atmosphere. Differential absorption measurements require that the laser frequency remain stable throughout the duration of the measurement. To ensure this stability, the laser output wavelength is monitored and a feedback control loop set up to minimize laser line drift. Three lines were investigated in the 1.462 micrometer region. The first-harmonic spectroscopic signal of the strongest of these lines was used as an error signal for the stabilization feedback loop. The derivative-like nature of harmonic signals provides a zero crossing for odd harmonics which can be used to determine the polarity of the requisite feedback voltage and compensate the laser wavelength accordingly. The feedback control loop utilized the virtual instrument capabilities of Labview and locking to within plus or minus 5.2 MHz was achieved using this method.
Theoretical and experimental results are presented to show that the etaloning problem in wavelength modulation experiments can be overcome by using harmonic detection that is greater than the commonly used second. The conditions under which such an advantage is obtained are discussed. Since the fringes due to parasitic Fabry-Perot etalons often place a limit to the ultimate sensitivity of such experiments, the method discussed has applications wherever sensitivity has to be increased. The method of higher harmonic detection is an alternative to synchronous mechanical jittering of an offending optical element that has been used in the past to average out the fringes.
Theoretical and experimental results related to wavelength modulation absorption spectroscopy using single-mode diode lasers are presented. This method uses a phase-sensitive detection technique, and the implications of detection at harmonics greater than the commonly used second-harmonic are discussed. It is shown that several advantages accrue with such higher-harmonic detection. Applications of the method in increasing sensitivity to measurements of density and temperature fluctuations; in increasing wavelength resolution of modulation and pressure broadened congested spectra; and in applications for accurate characterization of absorption lines of molecular spectra, are discussed. It is shown that wing structure of absorption lines can be obtained with much more accuracy using higher harmonic detection than either direct absorption or the commonly used second harmonic detection technique. Experimental results obtained are compared to the predictions of the theory developed.
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