Traditional spectroscopic methods are limited in sensitivity to approximately one part per ten thousand (1:10.sup.4) to one part per hundred thousand (1:10.sup.5). The sensitivity limitation arises from instabilities in light source intensity that are translated into noise in the absorption signal. For general information on traditional spectroscopy methods see for example Dereniak and Crowe, Optical Radiation Detectors, John Wiley & Sons, New York, 1984, and Demtroder, Laser Spectroscopy, Springer, Berlin, 1996.
Cavity Ring-Down Spectroscopy (CRDS), a technique first described by O'Keefe and Deacon in an article in Rev. Sci. Instrum. 59(12):2544-2551 (1988), allows one to make absorption measurements with sensitivities on the order of one part per ten million (1:10.sup.7) to one part per billion (1:10.sup.9) or higher. For general information on CRDS see U.S. Pat. No. 5,528,040 by Lehmann, as well as the articles by Romanini and Lehmann in J. Chem. Phys. 102(2):633-642 (1995), Meijer et al. in Chem. Phys. Lett. 217(1-2):112-116 (1994), Zalicki et al. in App. Phys. Lett. 67(1):144-146 (1995), Jongma et al. in Rev. Sci. Instrum. 66(4):2821-2828 (1995), and Zalicki and Zare in J. Chem. Phys. 102(7):2708-2717 (1995).
In a CRDS system, the sample (absorbing material) is placed in a high-finesse stable optical resonator or ring-down cavity. Light admitted into the ring-down cavity circulates back and forth multiple times setting up standing waves having periodic spatial variations. Light exiting the ring-down cavity is proportional to the intracavity light intensity.
The radiant energy stored in the ring-down cavity decreases in time (rings-down). For an empty cavity, the stored energy follows an exponential decay characterized by a ring-down rate that depends only on the reflectivity of the mirrors, the separation between the mirrors and the speed light in the cavity. If a sample is placed in the resonator, the ring-down is accelerated; under suitable conditions, the intracavity energy decays almost perfectly exponentially. An absorption spectrum for the sample is obtained by plotting the reciprocal of the ring-down rate 1/.tau. or of the decay constant .tau. versus the wavelength .lambda. of the incident light.
In comparison to conventional spectroscopic techniques, CRDS promises to achieve extremely high detection sensitivity because the ring-down rate 1/.tau. is not a function of the intensity of the incident light. In other words, intensity fluctuations of the incident light are not related to the ring-down rate in the ring-down cavity and thus do not directly affect the CRDS measurement. Theoretically, if CRDS were only limited by shot-noise inherent in any light beam due to the quantum nature of the photons constituting the light beam, the achievable sensitivity would be in the range of 10.sup.-14 cm.sup.-1 Hz.sup.-1/2 for a CRDS system having a 50 cm long cavity, a 10 mW continuous-wave (CW) laser with a 10 kHz linewidth and mirrors having losses of 50 ppm.
The actual performance of state-of-the-art CRDS in comparison to other conventional methods is illustrated in Table 1.
TABLE 1 ______________________________________ Spectroscopic Typical Scheme MDAL (cm.sup.-1) Cost Complexity ______________________________________ Single-pass absorption 10.sup.-6 low simple Multi-pass absorption 10.sup.-8 moderate simple ICLAS 10.sup.-6 -10.sup.-11 high difficult FM 10.sup.-6 -10.sup.-8 moderate moderate to difficult P CRDS 10.sup.-6 -10.sup.-10 moderate simple CW CRDS 10.sup.-8 -10.sup.-12 low to simple to moderate moderate ______________________________________ ICLAS = intracavity absorption spectroscopy; FM = frequency modulation; P CRDS = pulsed CRDS; CW CRDS = continouswave CRDS
The practical factors limiting sensitivity in P CRDS can be subdivided into three major categories. First, the P CRDS arrangements are limited by optical noise. This noise is due to the limited optical throughput of the ring-down cavity, which is a function of the ratio of the laser and cavity linewidths. In other words, this problem relates to the intensity fluctuations produced during coupling between the laser source and the ring-down cavity. Constant changes in the linewidth ratio affect the signal-to-noise ratio (SNR) at the detector hence producing noise.
Second, CRDS is limited by the quality of the laser beam transverse profile. Ideally, only a single mode-the fundamental TEM.sub.00 mode-should be excited in the ring-down cavity. Excitation of higher order modes causes a multi-mode excitation condition which imposes a sinusoidal modulation on the ring-down signal beam exiting the ring-down cavity. This causes slow detectors to register a noise band superimposed on the decay signal. In other words, because each mode has slightly different optical losses in the ring-down cavity, the modulation or mode beating will produce a superposition of exponentially decaying signal beams, each having a slightly different decay constant .tau..
Hence, trying to determine the decay constant .tau. for one particular mode, i.e., the fundamental mode, becomes difficult.
Third, the repetition rate of most pulsed laser systems is limited to 100 Hz, so that extensive averaging to improve sensitivity cannot be performed. Moreover, pulsed lasers tend to be bulky and expensive, and therefore impractical for commercial versions of P CRDS.
In addressing the first problem of P CRDS, CW CRDS uses a narrow line-width CW laser with external modulation to limit the optical noise by achieving high overlap between the laser linewidth and the ring-down cavity linewidth. The second problem of mode beating is limited by optically filtering the CW laser beam profile to almost pure TEM.sub.00. The third problem of is addressed by using repetition rates in excess of 1 kHz and up to 10 kHz thus permitting averaging operations.
The above improvements introduced in CW CRDS systems to overcome the problems associated with P CRDS have resulted in some improvements in the ability to perform spectral scans in realtime. Still, CW CRDS with direct detection as presently implemented does not allow to reach the true shot-noise limit because of the decaying signal which, no matter how large at the beginning, always decays to zero and hence always hits the detector noise floor. To date, the highest sensitivities obtained for P CRDS and CW CRDS do not approach the theoretical shot-noise limit. The best arrangements for P CRDS reported so far have sensitivities of about 8.times.10.sup.-10 cm.sup.-1 Hz.sup.-1/2. The best results obtained for CW CRDS are in the range of 8.times.10.sup.-13 cm.sup.-1 Hz.sup.-1/2 using a 10 mW laser. These figures are still far short of the theoretical limits. In fact, in a shot-noise limited CW CRDS system the expected sensitivity is about 1.times.10.sup.-14 cm.sup.-1 Hz.sup.-1/2, i.e., almost two orders of magnitude better than state of the art.
In terms of SNR, a ring-down decay signal is ultimately limited by the fluctuations in photon number that occur for a constant power level. For a power level of 1 mW, the shot-noise-limited SNR is 1.8.times.10.sup.6 :1, while for 1 .mu.W the SNR is 5.6.times.10.sup.4 :1. These figures are not achieved by state-of-the-art CRDS.
In striving to achieve higher signal sensitivity and work around noise sources other spectroscopy techniques have resorted to methods such as heterodyning. For example, in U.S. Pat. Nos. 4,817,101 and 4,905,244 Wyeth et al. teach a heterodyne laser spectroscopy system for improved measurement precision. Jun Ye et al. in "Ultrasensitive Detection in Atomic and Molecular Physics: Demonstration in Molecular Overtone Spectroscopy", Journal of the Optical Society of America B, Vol. 15, No. 1, January 1998, pp. 6-15 teach a heterodyne technique building on spectroscopic techniques employing frequency modulation (FM) detection. In U.S. Pat. No. 4,193,690 Marc Levenson et al. teach a heterodyne detection for coherent Raman signals. Additional references include: Marc Levenson et al. "Polarization-Selective Optical Heterodyne Detection for Dramatically Improved Sensitivity in Laser Spectroscopy", Applied Physics, 19, pp. 1-17, 1979; Gary Eesley et al. "Optically Heterodyned Raman Spectroscopy", IEEE Journal of Quantum Electronics, QE-14, pp. 45-48, 1978; and Jun Ye "Ultrasensitive High-Resolution Laser Spectroscopy and its Application to Optical Frequency Standards", PhD Thesis, University of Colorado at Boulder, Apr. 22, 1997.
Unfortunately, the above adaptations of heterodyning are not well-designed to measure exponentially decaying waveforms. In particular, these techniques do not work well for signal detection in CRDS.