Anal. Chem. 2005, 77, 6463-6468
Development of Ultra-Low-Noise Spectrophotometry for Analytical Applications Zhi Xu* and David W. Larsen
Department of Chemistry and Biochemistry, University of MissourisSt. Louis, One University Boulevard, St. Louis, Missouri 63121
Methodology and instrumentation that dramatically increase the signal-to-noise ratio of scanning spectrophotometers over present commercial instruments is presented. The increase was accomplished by greatly reducing all important noise components. The random noise from an incoherent light source, which is the dominant noise source for most commercial spectrophotometers, was effectively removed by use of unique noise cancellation circuitry implemented with a dual-beam spectrophotometer configuration. Several other noise sources were also minimized by appropriate instrumental design, so that the observed noise level was attributable to the shot noise of the detectors. Single-wavelength measurements taken with a home-built prototype instrument have achieved a signal-to-noise ratio increase near 100-fold over commercial instruments. A spectrum taken in the visible region with a home-built retrofit detector installed in a commercial instrument showed a 10-fold signal-to-noise ratio increase over the standard commercial instrument. Widespread implementation of the methodology should enable many new types of research activities.
During the past two decades, a range of laser-based (coherent light source) spectroscopic technologies have been developed, capable of reaching the theoretical shot noise limit.1-18 Among them, electronic noise cancellation methodology based on dualdetector optical configuration has demonstrated distinct potential.2-13,15-17 The relatively straightforward technique offers dramatically reduced absorbance baseline noise ranging from 1.0 × 10-6 to 4.2 × 10-8 AU,3-13,17 which corresponds to 20-400 times improvement in LOD over commercial UV/visible/NIR spectrophotometers. Despite its success, scanning applications of the laser-based technology are limited to gas-phase molecules due to the very small wavelength range a laser can scan. As a result, the technology has not been applied to conventional scanning dualbeam spectrophotometers. This paper demonstrates a new spectroscopy technology that extends the principle of noise cancellation to incoherent light sources such as incandescent and discharge lamps that are widely employed in commercial scanning UV/visible/NIR spectrophotometers. The new technology is capable of reducing the spectrophotometric noise to the shot noise level simultaneously over a wide wavelength range so that the sensitivity of absorbance measurements made with scanning spectrophotometers can be dramatically increased.
The role of spectrophotometry in chemistry has a long history. Because of its relatively low cost, ease of use, and general utility, it is the method of choice for a wide range of chemical analyses. The scanning UV/visible/NIR spectrophotometer serves as a single general-purpose instrument for these analyses. The limit of detection (LOD) for absorbance measurements made with current research-grade commercial spectrophotometers is about (5-6) × 10-5 absorbance units (AU), in time drive mode with a 1.0-s time constant. This limit is set by rms noise levels of these instruments, which are generally about (2-3) × 10-5 AU with 1.0-s time constant. This limit has not changed appreciably in several decades. If means can be found to reduce the noise level, the lower limit for absorbance measurements will be correspondingly reduced. This will allow the scope of spectrophotometry to be extended for scanning instruments, such that a range of new applications will be enabled.
(1) Wong, N. C.; Hall, J. L. J. Opt. Soc. Am. B 1985, 2, 1527-1533. (2) Alexander, S. B. J. Lightwave Technol. 1987, LT-5, 523-537. (3) Carlisle, C. B.; Cooper, D. E. Appl. Phys. Lett. 1990, 56, 805-807. (4) Hobbs, P. C. D. Proc. SPIE 1991, 1376, 216-221. (5) Haller, K. L.; Hobbs, P. C. D. Proc. SPIE 1991, 1435, 298-309. (6) Hobbs, P. C. D. Noise Cancelling Circuitry for Optical Systems with Signal Dividing and Combining Means. U.S. Patent 5,134,276, 1992. (7) Xue, Y.; Yeung, E. S. Anal. Chem. 1993, 65, 1988-1993. (8) Rosenzweig, Z.; Yeung, E. S. Appl. Spectrosc. 1993, 47, 2017-2921. (9) Allen, M. G.; Carleton, K. L.; Davis, S. J.; Kessler, W. J.; Otis, C. E.; Palombo, D. A.; Sonnenfroh, D. M. Appl. Opt. 1995, 34, 3240-3249. (10) Zhu, X.; Cassidy, D. T. Appl. Opt. 1995, 34, 8303-8308. (11) Yeung, E. S.; Xue, Y. Noise Suppressing Capillary Separation System. U.S. Patent 5,540,825, 1996. (12) Hobbs, P. C. D. Appl. Opt. 1997, 36, 903-920, (13) Modugno, G.; Corsi, C.; Gabrysch, M.; Marin, E.; Inguscio, M. Appl. Phys. B 1998, 67, 289-296. (14) Chen, W.; Mouret, G.; Boucher, D. Appl. Phys. B 1998, 67, 375-378. (15) Fockenberg, C.; Marr, A. J.; Sears, T. J.; Chang, B. C. J. Mol. Spectrosc. 1998, 187, 119-125. (16) Claps, R.; Englich, F. V.; Leleux, D. P.; Richter, D.; Tittel, F. K.; Curl R. F. Appl. Opt. 2001, 40, 4378-4394. (17) Thanh, N. T. K.; Rees, J. H.; Rosenzweig, Z. Anal. Bioanal. Chem. 2002, 374, 1174-1178. (18) Zondy, J. J.; Vedenyapine, V.; Kaing, T.; Lee, D.; Yelisseyev, A.; Isaenko, L.; Lobanov, S. Appl. Phys. B 2004, 78, 457-463.
* To whom correspondence should be addressed. E-mail:
[email protected]. Fax: (314) 516-5342. 10.1021/ac0510134 CCC: $30.25 Published on Web 09/03/2005
© 2005 American Chemical Society
Analytical Chemistry, Vol. 77, No. 19, October 1, 2005 6463
Figure 1. Schematic of dual-beam spectrophotometer configuration that enables noise cancellation. VS and VR are sample and reference voltage outputs, respectively. VD is the difference voltage output with coherent noise cancellation, in which the small signal can be seen.
NOISE REDUCTION The point of departure for noise reduction is an in-depth assessment of all factors that contribute to spectrophotometric noise. Many sources of random noise have been identified by us, each characterized by its individual variance, σi2. The total variance is of course the sum of all individual variances, Σiσi2. Because there are many noise sources, noise reduction must be implemented iteratively. The variances differ in magnitude, so the largest component must be dealt with first. The dominant factor is identified and minimized. The process continues in this manner, and it ends when no further noise reduction is feasible. For several of our prototype instruments, shot noise from the photodetectors determines the noise level. This noise cannot be eliminated in principle, so that operation in the so-called “shot noise limit” represents a plateau. It is easy to determine that the predominant noise component for commercial scanning spectrophotometers is random fluctuations of the light source. The relative standard deviation for a quartz-tungsten-halogen (QTH) lamp with a stabilized dc power supply is about (2-3) × 10-5 AU in the visible region when the time constant, τ ) 1.0 s, which agrees well with commercial instrument specifications. Since the light source noise is the biggest problem, it must be dealt with first by finding means to minimize its effects. It is found in this study that the random fluctuation noise from the QTH light source can be reduced to below detector shot noise level by use of a new noise cancellation technique. The technique is implemented in a manner consistent with the requirements for a conventional scanning dual-beam spectrophotometer, as shown in Figure 1. The light from a monochromator is divided by a beam splitter into a transmitted beam and a reflected beam. The transmitted beam passes through a sample cell and strikes the sample detector DS, producing a photocurrent IS. The reflected beam strikes a mirror and then passes through a reference cell, after which it strikes the reference detector DR, producing a photocurrent IR. In this study, beam splitting ratio is typically near 50:50 so that IS ≈ IR. The sample photocurrent IS is converted to an output voltage VS, which is proportional to IS, and the reference photocurrent IR is converted to a voltage VR, proportional to IR. The circuitry also converts the photocurrent difference, ID ) IS - IR to an output voltage VD proportional to ID. The three outputs are shown schematically in Figure 1. 6464 Analytical Chemistry, Vol. 77, No. 19, October 1, 2005
Figure 2. Computer simulation of voltage output from the dualbeam spectrophotometer shown in Figure 1, as for example during a wavelength scan. Large coherent noise components in both VS and VR are canceled in VD, allowing the small peak to be seen. Incoherent noises in VS and VR cannot be canceled in VD as shown.
Noise cancellation is accomplished by current subtraction, and the results appear in the voltage output VD. Since ID ) IS - IR, any noise that is common in both IS and IR will tend to cancel in ID and in the output VD. For a typical dual-beam spectrophotometer with optical configuration similar to that depicted in Figure 1, the light source fluctuation noise collected by the two detectors is always in-phase for frequency components lower than 1 MHz, so that the noise will be canceled to some extent in the output VD. Outputs VS and VR contain large amounts of source fluctuation noise, such that the small signal in VS is not readily seen. However, since the light source fluctuation noise is canceled in the differential output VD, the small signal can be easily seen as shown. This noise cancellation approach is illustrated more clearly in Figure 2 by a simulation of the three voltage outputs from the dual-beam spectrophotometer. The top trace shows VS, which contains a large coherent noise component to represent light source noise, a smaller noncoherent noise component to represent other noise sources, and the analytical signal. The bottom trace shows VR, which contains the same large coherent noise component as in VS and a smaller noncoherent noise component. The middle trace shows VD, in which the large coherent noise component is canceled, allowing the small signal (e.g., an absorbance peak) to be clearly seen. The noise in the middle trace arises from noncoherent noise components in both VS and VR, which is not canceled. The noise cancellation circuitry used in this study is shown schematically in Figure 3. Photocurrents IS and IR from photodiodes DS and DR are fed to the summing point, as shown. The photocurrent difference at the summing point (IS - IR) is converted by current to voltage amplifier AD to output voltage VD. Also, current to voltage conversion amplifiers (AS and AR) are used to convert photocurrents IS and IR to output voltages VS and VR, respectively. For noise cancellation as explained below, one needs to have VD ≈ 0. Note that as IS f IR, VD ) 0 so that the light source fluctuation noise is completely eliminated in VD. With a 50:50 beam splitter, VD will be small and fine adjustment can be made by partially blocking the stronger beam. With this simple approach,
Figure 3. Schematic of electronic circuitry used for light source noise cancellation in dual-beam spectrophotometer with photodiode detectors. The current adjust module (dashed line connections) is an optional component used to supply additional current IS′ to supplement IS, allowing current balance to be achieved.
the current subtraction is done directly and continuously at the summing point by the photocurrents themselves without any intermediate electronic processing. Alternatively, fine adjustment for the VD ≈ 0 condition can be accomplished using a current adjust module, connected (dashed lines) as shown. The module provides a small adjustable current IS′, which is proportional to IS, back to the summing point. Thus, by varying IS′, the total current at the summing point can be electronically adjusted to near zero; i.e., IR + IS + IS′ ) 0. This configuration allows for almost pure current mode subtraction and gives excellent cancellation results in practice. In this study, over 100-fold noise cancellation can be easily obtained by concurrent application of the two cancellation approaches. Implementation to Absorbance Measurement. To obtain the absorbance spectrum of a dilute solution, one needs to measure two sets of voltages VD and VR. The first set, designated VD0 and VR0, is taken as a function of wavelength (λ), time (t), or both, with both cells containing pure solvent. The second set, designated VD1 and VR1, is obtained with the dilute solution in the sample cell and the pure solvent in the reference cell. Because VS/VR ) 1 + VD/VR, it is easily shown that the absorbance spectrum can then be obtained as
A(λ,t) ) -log
[
]
1 + VD1(λ,t)/VR1(λ,t)
1 + VD0(λ,t)/VR0(λ,t)
(1)
in which the source fluctuation noise is effectively canceled. See ref 19 for further details. For time drive mode measurements, the wavelength dependence in eq 1 is removed and the methodology requires the output voltages to be balanced only once, before measurement of the first set of voltages VD0 and VR0. In practice, it is not required that VD0 ) 0, but only that VD0 be sufficiently small compared to VR0. For example, noise cancellation by a factor of 1000 can be obtained with VD0/VR0 ) 0.001, allowing a voltage imbalance of 0.1%. Attaining such voltage balance does not require precise or difficult adjustment. (19) Larsen, D. W.; Xu, Z.; Garver, W. Ultrasensitive Spectrophotometer. U.S. Patent 6,741,348, 2004.
With measurement of VD1 and VR1, one anticipates VR1 ≈ VR0, but because of solute absorption, one will observe VD1 < VD0. For measurement of very small absorbances where cancellation is crucial, VD1 will be only very slightly less than VD0. Thus, the degree of noise cancellation will remain essentially unchanged, and it will be possible to detect the small absorption of light by the dilute solution in the measured value of VD1. As the solution to be analyzed becomes more concentrated, the decrease in VD1 becomes more pronounced, and the degree of noise cancellation is reduced. However, as the absorbance increases, less noise cancellation is required, so that the technique can be used to measure absorbance over the entire concentration range. Implementation of noise cancellation was the necessary first step toward obtaining shot noise limited operation. However, even after effective removal of the large light source fluctuation noise, other noise sources greater than the shot noise limit were still present. Baseline drift was also much more noticeable in the absence of light source fluctuations. Thus, to realize the full potential for noise cancellation, many other factors had to be addressed. In general, factors that affect the two signals differentially in the dual-beam configuration will cause problems. Thermal drift can affect optics, electronics, cells, and liquids. It is advantageous to isolate the light source from the rest of the apparatus, to use good insulation, and to ensure that internal thermal equilibrium is rapidly attained. Airborne dust particles in the beams are easily seen as baseline noise and they must be eliminated. Particulates suspended in the liquids are also easily seen, so that liquids must be carefully filtered before measurement. Bubbles and dissolved gases are also potential sources of noise. A full discussion of the methods used by us is given elsewhere.19 EXPERIMENTAL SECTION Spectrophotometer. The commercial instrument used in this study was a computer-controlled Perkin-Elmer Lambda-14 doublebeam spectrophotometer, with a 30-W QTH lamp as its light source in the visible to near-infrared region. The 2-nm slit width was used in all time drive mode measurements, while 4 nm was used for all scanning measurements. The baseline noise of the instrument is found to be independent of the slit width, consistent with our finding that the spectrophotometer baseline noise is dominated by the random fluctuation of light source. Prototype Units. Two home-built devices were used in this study, a single wavelength unit and a retrofit module for scanning applications. Figure 4 shows the optical layout of the singlewavelength unit. In brief, the light source is a 30-W QTH lamp powered by a stabilized dc power supply. After passing two broadband optical filters, the polychromatic light from the QTH lamp is introduced into the optical system via an optical fiber. The monochromatic light at 633 nm was obtained using interference filters from Melles Griot, 03 FIL 024 (fwhm ) 10 nm) and 03 FIL 006 (fwhm ) 10 nm). No difference in cancellation behavior was found with use of either filter. A 50:50 dielectric beam splitter from Edmund Optics (43-359) is used in this study, and light collection is accomplished with two silicon diodes from Hamamatsu (S13371010BQ). A home-built optical attenuator is used in the reference path for obtaining fine optical balance. Great care is taken to Analytical Chemistry, Vol. 77, No. 19, October 1, 2005
6465
Figure 4. Optical layout of the single-wavelength prototype instrument. More details can be found in ref 19.
ensure the thermal stability of the instrument. More details can be found elsewhere.19 To demonstrate noise cancellation in wavelength scanning mode, a small noise cancellation detection module was built to serve as a retrofit detector for the Perkin-Elmer Lambda-14 spectrophotometer. The detector module was small enough to fit neatly inside the sample compartment and still leave room for the sample and reference cells. The retrofit device collects lights from the original sample and reference paths of the instrument, and the cancellation signal (VD) and the reference signal (VR) were recorded by a computer. Solutions. Laser dye grade Nile Blue was purchased from Exciton. Its two solutions, 5 × 10-10 and 2 × 10-9 M, were prepared using optical grade methanol from Fisher Scientific. In all experiments involving solvent and solutions, suspended particulates were removed using 0.45-µm PTFE filters from Fisher Scientific. RESULTS AND DISCUSSION Single-Wavelength Baseline Measurement. To directly illustrate the magnitude of the noise reduction, Figure 5 shows a comparison of noise levels from the Perkin-Elmer Lambda-14 spectrophotometer and from the single-wavelength prototype instrument illustrated by Figure 4. Two absorbance baselines taken at 633 nm in the visible region are shown. The top trace shows the output from the Lambda-14 operating in the time drive mode with a time constant of τ ) 0.5 s. The baseline absorbance is given as a function of time, and the rms noise level is ∼2.5 × 10-5 AU. The bottom trace shows the corresponding output from the single-wavelength prototype spectrophotometers employing identical time constant. Its noise level is greatly reduced compared to the commercial unit. The rms noise level of the prototype is ∼3.0 × 10-7 AU, comparable to the detector shot noise. This corresponds to a noise reduction factor greater than 80. The 80-fold noise reduction is attributable solely to the intrinsic characteristics of the prototype, which uses (a) a standard dual-beam optical configuration, (b) inexpensive silicon photodiode detectors, (c) unique but relatively simple and inexpensive electronic circuitry, and (d) no data manipulation. To date, the lowest rms noise level obtained with our latest prototype is 8.2 × 10-8 AU, corresponding to over 200-fold reduction in spectrophotometer baseline noise. It should be emphasized that, for the prototype instrument, the results shown in Figure 5 (bottom) cannot be obtained by employing only source noise cancellation. The other noise sources 6466 Analytical Chemistry, Vol. 77, No. 19, October 1, 2005
Figure 5. Absorbance baselines at 633 nm obtained with a PerkinElmer Lambda-14 spectrophotometer (top) and with a home-built prototype instrument (bottom). Both baselines were obtained under the same experimental conditions, using a time constant of 0.5 s.
mentioned in the Noise Reduction and Experimental Sections must also be addressed.19 Single-Wavelength Solution Measurement. The power of the noise reduction methodology is further demonstrated in Figure 6, which shows comparative absorbance measurements of a solution of Nile Blue in methanol at 633 nm. The concentration of the solution is ∼5 × 10-10 M. Results obtained with the PerkinElmer Lambda-14 spectrophotometer are shown in the top trace in Figure 6. For the commercial unit, the time drive mode was used and three separate measurements were made. First, the baseline absorbance was measured with pure solvent in both cells. Next, the solution absorbance was measured with the solution in the sample cell, and finally, the baseline absorbance was measured again to check for baseline drift. The results are shown in regions A (left), B, and A (right), respectively. The time constant was 1.0 s, and baseline rms noise is ∼2 × 10-5 AU. Clearly, the baseline random noise prevents the instrument from meaningful signal detection at this absorbance level and below. Results obtained with the single-wavelength prototype instrument are shown in the bottom trace in Figure 6. Similarly, the three separate measurements were taken and corresponding absorbance for each measurement was calculated using eq 1. The solution absorbance is the difference between the solution value (region B) and the baseline value (region A), which is ∼5 × 10-5 AU, with excellent signal-to-noise ratio. The time constant was 0.25 s, and the baseline rms noise is 4.25 × 10-7 AU. Considering the difference in time constant, τ ) 1.0 s for the Lambda-14 instrument and τ ) 0.25 s for the prototype, this result indicates a near 100-fold reduction in baseline noise and correspondingly,
Figure 6. Absorbance of 5 ×10-10 M Nile Blue in methanol at 633 nm. Results are from the Perkin-Elmer Lambda-14 spectrophotometer (top) and from a home-built prototype instrument (bottom) configured on the basis of noise cancellation methodology. Pure solvent baselines are shown in A regions, and solution results are shown in B regions.
a near 100-fold increase in signal-to-noise ratio. The two baseline measurements in the bottom graph show a small amount of baseline drift. This drift is also observable in the B region. Such drift is thermal in nature and will always be a potential problem in measurements of very low absorbance. Wavelength Scan Measurement. The full power of noise cancellation is in its application to obtaining spectra over a wide range of wavelength. Two spectra of the 2 × 10-9 M Nile Blue solution were taken, the first using the Lambda-14 spectrophotometer with its built-in detectors and the second with the homebuilt module fitted into the sample compartment. For both measurements, the slit width was 4 nm and scan speed was 30 nm/min. The results are shown in Figure 7. The top trace was obtained with the built-in detection configuration of the Lambda-14 and the bottom trace with the retrofit module. The substantially increased signal-to-noise ratio, ∼10-fold, has been achieved across the entire wavelength region from 500 to 700 nm. We see also in Figure 7 that the signal-to-noise ratio increase is less than that obtained in Figure 6. This is largely attributable to problems associated with scanning that are not present for single-wavelength measurements. There are two major culprits for scanning measurements. First, eq 1 must be applied at every wavelength sampled across the entire wavelength range of the spectrum. This means that IS and IR should remain balanced within 1% or better across the entire wavelength region scanned. This desired high degree of current balance can be upset by the wavelength-dependent beam splitting ratio of the instrument.
Figure 7. Spectra of 2 ×10-9 M of Nile Blue in methanol. Results are from the Perkin-Elmer Lambda-14 spectrophotometer (top) and from a home-built prototype instrument (bottom) configured on the basis of noise cancellation methodology.
Therefore, the cancellation is degraded in wavelength regions where the balance is insufficient. Second, limitations in the wavelength reproducibility of the monochromator will cause further degradation in the effectiveness of noise cancellation. It can be seen from eq 1 that
A(λ,t) ) -log[1 + VD1(λ,t)/VR1(λ,t)] + log[1 + VD0(λ,t)/VR0(λ,t)] (2)
in which the absorbance at any wavelength requires all four voltage measurements to be made at exactly the same wavelength. For scanning applications, the noise cancellation method can reach its full potential only if the absorbance error produced by wavelength irreproducibility (monochromator jitter) is lower than the corresponding shot noise. CONCLUDING REMARKS It has been demonstrated that, for the first time, the random fluctuation noise from an incoherent light source such as QTH lamps can be reduced to below detector shot noise level in transmission spectroscopic measurements using a standard dualbeam optical configuration coupled with the unique electronic cancellation circuitry. The single-wavelength prototype instrument has achieved a near 100-fold improvement in signal-to-noise ratio over a commercial spectrophotometer in solution-phase measurements. A 10-fold increase in signal-to-noise ratio has been obtained in scanning measurements in the wavelength range from Analytical Chemistry, Vol. 77, No. 19, October 1, 2005
6467
500 to 700 nm using a home-built detector unit retrofitted to the Lambda-14 spectrophotometer. Further improvements in noise reduction under scanning conditions are expected when two important technical problems, reducing the wavelength dependence of the beam splitter and increasing the monochromator reproducibility, are addressed. With further improvements, noise reduction results comparable to those obtained with the singlewavelength measurements in Figure 6 will be possible for scanning measurements.
6468
Analytical Chemistry, Vol. 77, No. 19, October 1, 2005
ACKNOWLEDGMENT The authors gratefully acknowledge a grant from the Office of Research, University of MissourisSt. Louis.
Received for review June 8, 2005. Accepted August 2, 2005. AC0510134
