This invention relates to the field of spectroscopy, and in particular to analog electronics for determination of ring-down and ring-up rates in lifetime cavities, also known as ring-down cavities.
Traditional spectroscopic methods are limited in sensitivity to approximately one part per ten thousand (1:104) to one part per hundred thousand (1:105). 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 and Sons, New York, 1984, and Demtroder, Laser Spectroscopy, Springer, Berlin, 1996.
Cavity lifetime spectroscopy, otherwise known as 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 (1:107) to one part per billion (1:109) 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 having an input coupling mirror and an output coupling mirror. Light admitted into the ring-down cavity through. the input coupler circulates back and forth multiple times setting up standing waves having periodic spatial variations. Light exiting through the output coupler is proportional. to the intracavity light intensity.
After the input light source is terminated, 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 of 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 ring-down rate R or the reciprocal of the ring-down decay constant 1/xcfx84 versus the wavelength xcex of the incident light.
In comparison to conventional spectroscopic techniques, CRDS promises to achieve extremely high detection sensitivity because the ring-down rate 1/xcfx84 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.
In conventional absorption measurements, when light passes through a sample of length l, the ratio of the transmitted and incident intensities, It and Io, satisfies Beer""s law:
xcex94I/Io=(Ioxe2x88x92It)/Io=1xe2x88x92excex1l,
where xcex1 is the absorption coefficient of the sample. Any intensity fluctuations will clearly result inuncertainties in the absorption measured. It is possible to define a minimum detectable absorption (MDAL) based on the intensity noise of the system as follows:
MDAL="sgr"I/leff,
where "sgr"I is the root-mean-square (RMS) intensity noise and leff is the effective sample path length (e.g., in a multi-pass absorption measurement cell, the effective sample length can be many times the physical sample path length, since the light beam circulates inside the cell, passing through the sample many times, e.g., up to 500 times or more). Of course, more than one absorption measurement can be taken and the results averaged to reduce the measurement error, however, the fundamental limitation of the system being subject to intensity noise can not be overcome.
In CRDS the measured variable is the decay constant, xcfx84, or the ring-down rate 1/xcfx84, and thus the sensitivity is expressed as:
Sxcfx84="sgr"xcfx84/(leff{square root over (F)}),
where F is the number of measurements taken per unit time and the units are expressed in cmxe2x88x921Hzxe2x88x92xc2xd. Clearly, intensity noise does not figure in this equation. In fact, the ultimate limit of CRDS is the fundamental barrier due to shot-noise inherent in the light beam. Shot-noise results from the discrete nature of photons making up the light beam. The photocurrent produced by a laser beam having power P is i=RP where R is the responsivity of the photodetector. For ideal detection, the photocurrent noise will directly reflect the shot noise of the light. The temporal distribution of shot-noise obeys Poisson statistics and can be expressed as:
"sgr"I,shot-noise={square root over ((2eI))},
where e is the electronic charge (1.602xc3x9710xe2x88x9219C).
Theoretically, if CRDS were only limited by shot-noise, the achievable sensitivity would be in the range of 10xe2x88x9214 cmxe2x88x921Hzxe2x88x92xc2xd 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.
Most experimental CRDS setups have used pulsed laser sources (P CRDS) . However, P CRDS has several practical disadvantages, which preclude shot-noise-limited detection, unless significant effort is made to eliminate them. First, most P CRDS arrangements are limited by the detector noise on the signal, unless special photodetectors such as photomultiplier tubes are used. Unfortunately, photomultiplier tubes can operate only in the ultra-violet to near-infrared wavelength ranges, so that P CRDS in the mid-infrared can be extremely limited. This detection noise is a direct consequence of the limited optical throughput of the high-finesse ring-down cavity. The optical throughput is a function of the ratio of the laser and cavity linewidths. Typical.throughputs for pulsed lasers do not exceed 0.01%. In other words, this problem relates to the excess noise present on the ring-down signals, which makes the signal much more difficult to fit accurately. The greater this excess detector noise, the larger the error in the decay rate fit, and hence the greater the error in the absorption loss measurement.
Second, P CRDS is limited by the quality of the mode-matching between the laser beam transverse profile and the ring-down cavity modes. Ideally, only a single transverse and longitudinal cavity modexe2x80x94the fundamental TEM00 modexe2x80x94is excited in the ring-down cavity. However, because most pulsed laser linewidths tend to be large, multiple longitudinal modes can be excited if the ring-down cavity length is sufficiently large. Moreover, because it is difficult to accurately match the transverse profile of pulsed laser beams to the ring-down cavity mode geometry, multiple transverse modes become excited. Excitation of higher order modes, each having a distinct resonance frequency, can impose a sinusoidal beating which is superposed on the ring-down signal intensity exiting the ring-down cavity, unless all modes are perfectly collected onto a perfectly uniform detector. Physically, such detection is very difficult to implement. In addition, because each cavity transverse mode samples a different portion of the mirrors forming the cavity, each of the modes will experience slightly different reflection and diffraction losses in the cavity. Thus, multiple-mode excitation will also produce a superposition of exponentially decaying signals, each having a slightly different decay constant xcfx84. Hence, trying to determine the decay constant xcfx84 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 TEM00. The third problem is addressed by using repetition rates in excess of 1 kHz and up to 10 kHz thus permitting averaging operations. More information about these solutions can be found in D. Romanini et al. xe2x80x9cCW Cavity Ring-down Spectroscopyxe2x80x9d, Chem. Phys. Lett., 264, p. 31 (1997); D. Romanini et al. xe2x80x9cCavity Ring-down Spectroscopy with an External Cavity Diode Laserxe2x80x9d, Chem . Phys. Lett., 270, p. 538 (1997); B. A. Paldus et al. xe2x80x9cLaser Diode Cavity Ring-down Spectroscopy Using an Acousto-optic Modulatorxe2x80x9d, J. Appl. Phys., 82, p. 3199, (1997); and U.S. Pat. No. 5,528,040 to K. K. Lehmann.
Unfortunately, the above improvements introduced in CW CRDS systems to overcome the problems associated with P CRDS have not resulted in significant improvements in the ability to perform spectral scans in real-time and, most importantly, have not managed to significantly improve the sensitivity of the CRDS technique. To date, the highest sensitivities obtained for P CRDS and CW CRDS do not approach the theoretical shot-noise limit. The best arrangements reported so far have sensitivities of about 8xc3x9710xe2x88x9210 cmxe2x88x921Hzxe2x88x92xc2xd and 2xc3x9710xe2x88x9210 cmxe2x88x921Hzxe2x88x92xc2xd respectively. These figures are still far short of the theoretical limits.
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 1.8xc3x97106:1, while for 1 xcexcW the SNR is 5.6xc3x97104:1. These figures are not achieved by state-of-the-art CRDS.
At this point, it should be noted that most CRDS arrangements, with the exception of a boxcar integrator arrangement (see D. Romanini et al., J. Chem. Phys., 102, p. 633 (1995)), as well as most other spectroscopy schemes utilize digital detection electronics. For example, U.S. Pat. No. 5,821,533 to Bingham et al. teaches immediate conversion of an exponentially decaying signal obtained in Ionizing Radiation Spectroscopy to a digital signal. In CRDS the exponentially decaying signal beam or ring-down beam from which the absorption data is derived is first sent to a photodetector which generates a corresponding current or voltage signal. The latter is digitized by a digitizer and passed on to digital processing electronics for determining the decay rate xcfx84 from which the absorption is determined. In this arrangement the technical noise of the photodetector and the detection electronics limit detection sensitivity. In fact, in this type of direct detection the ring-down signal decays into the noise of the detection electronics, which causes the electronic noise to become the limiting noise source.
In view of the above problems, it would be desirable to develop a CRDS scheme which permits one to approach the theoretical sensitivity limit of CRDS measurements. Specifically, it would be very desirable to provide a detection system for both P CRDS and CW CRDS whose primary limiting factor in determining the decay rate xcfx84 is the shot-noise present in the exponentially decaying ring-down beam.
In light of the above, it is a primary object of the present invention to provide a shot-noise limited detection system for determining the decay rate xcfx84 of an exponentially decaying ring-down beam or an exponentially building ring-up beam issuing from a lifetime or ring-down cavity. The detection system should be adaptable to CW CRDS as well as P CRDS schemes.
It is another object of the invention to provide a fast detection system for enabling large frequency scan rates. Furthermore, the system should provide for reliable isolation of the portion of the exponentially decaying signal or exponentially growing signal from which the decay rate or build-up rate is to be computed.
Yet another object of the invention is to ensure that the detection system is compatible with other noise. reducing measures used in CRDS.
The above objects and advantages, as well as numerous additional improvements attained by the detection. system and method of the invention are pointed out below.
The objects and advantages of the invention are achieved by an analog detection system which determines a ring-down rate or decay rate 1/xcfx84 of an exponentially decaying ring-down beam issuing from a ring-down cavity during a ring-down phase. Alternatively, the analog detection system determines a build-up rate of an exponentially growing beam issuing from the cavity during a ring-up phase. The analog system can be employed in P CRDS and CW CRDS arrangements. The analog system has a photodetector for receiving the ring-down beam or ring-up beam and generating from it an exponentially decaying analog signal or an exponentially growing analog signal respectively. The analog signal is fed to a converter which converts it to a linear analog signal. The system is further provided with an analog signal processing circuit for determining the slope of the linear analog signal. The decay rate or ring-up rate is derived by the analog circuit from the slope of the analog signal by using the fact that the slope is generally proportional to the decay rate or the ring-up rate, respectively. For calculation purposes, the analog signal processing circuit can convert the decay rate or ring-up rate to a decay or ring-up rate voltage. An additional element is provided for converting the voltage to a figure indicating the absorption loss of the ring-down cavity.
For detection of the ring-down beam the detection system is equipped with a control element which activates the system during the ring-down phase of the ring-down cavity. In other words, the control element ensures that the detection system performs the above-described operations on the ring-down beam while the cavity is in the ring-down phase. In addition, the analog detection system can have a triggering mechanism for performing its operation during a certain portion of the exponentially decaying analog signal.
For detection of the ring-up beam the detection system is turned on. during the ring-up phase or when the light intensity is building up within the ring-down cavity. The wave form detected during the build-up phase is the reverse of the decay wave-form.
The ring-down cavity is pumped by a pump beam derived from a pump laser. In the P CRDS scheme the laser is a pulsed laser and in the CW CRDS scheme the laser is a continuous-wave laser. In order to determine the absorption spectrum of an absorptive sample placed in the ring-down cavity, the laser is further provided with a frequency adjustment element for altering the frequency of the pump beam. The absorptive sample will alter the decay rate of the ring-down beam or the ring-up rate of the ring-up beam by an amount dependent on the frequency of the pump beam.
In the CW CRDS system a chopping mechanism is provided for interrupting the pump beam during the ring-down phase. In this arrangement the control element activates the detection system during the time when the pump beam is interrupted.
In one embodiment of the invention the pump beam has a certain polarization. For example, the pump beam admitted to the ring-down cavity is of the s-polarization. In this arrangement the p-polarization can be used for performing adjustments, e.g., controlling the length of the ring-down cavity.
An analog detection method for determining the decay rate of an exponentially decaying ring-down beam or the ring-up rate of an exponentially growing ring-up beam in accordance with the invention can be employed in any CRDS in conjunction with other noise reducing measures. Further details on the detection system and method are found below in the description with reference to the attached drawing figures.
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