Lock-In Role
Rescuing Minuscule Signals from Noise
Rescuing Minuscule Signals from Noise
Electromagnetic energy absorption is a ubiquitous tool for detection and quantitation of matter. Many of us were introduced to spectroscopy using a bench-top Bausch & Lomb Spectronic visible absorption spectrometer. Armed with test tubes containing colored samples, we would insert the reference solution (blank) and adjust percent transmittance (%T) to 100. Placing our sample in the holder, we would read the new %T value, careful to avoid parallax error by hiding the reflected image behind the actual needle. We soon learned it was easier to read the linear %T scale and mathematically calculate absorbance than to interpolate the logarithmic absorbance scale printed on the meter. Spectronic was the Monarch of Measurement. Armed with absorbance, we could quantitate the world. Only later did we read the fine print disclaimers.
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Absorption is an uncomplicated data acquisition method well-suited to introduce the genre of spectroscopy. Light passes through the blank containing none of the species to be measured. The blank is replaced by the sample and a new, smaller amount of light is measured. The difference in energy reaching the detector between the blank and sample is directly related to the amount of absorbing species in the sample. Most samples absorb light at some frequency, so the analysis sample must be quite pure and free of interfering species. Also, the logarithmic value of absorbance is only linear at “infinite dilution” (no sample). However, this shortcoming can be addressed by the proper use of known calibration samples. Additionally, absorption is not generally lauded for its extremely low detection limit. The problem does not lie with the physics of absorption; a single molecule can absorb a single photon. The difficulty is associated with the detector. It is expected to stare into a bright light source and notice when a few photons go missing.
As with all 100% baseline techniques, the noise floor of the absorption detector is associated with both detector and source. The measurement can be transformed into a zero baseline by turning off the source, recording the detector output, turning on the source, again recording output and subtracting the two values. This differential approach removes detector noise. Repeating the on/off process and averaging results reduces source noise. Measuring blank and sample values using this method decreases the overall detection limit of the technique. Since repetitively disrupting power to the light source introduces more noise into the system than this method removes, the light source remains powered and stable while an optical shutter is used to block and unblock light. Often, the shutter takes the form of a rotating slotted wheel known as an optical chopper that pulses the light stream with a 50 percent duty cycle.
A “lock-in amplifier” (LIA) working in concert with the chopper compares on and off values. In this way, small differences between blank and sample can be amplified out of the noise. This temporal model of LIA function is technically accurate. However, the frequency model is more elegant. The frequency spectrum of the source follows an inverse “1/f” envelope displaying a great amount of low-frequency flicker noise associated with drift in source output and noise spikes at the source driving frequency and its harmonics (60 Hz in the U.S.). The chopper modulates measurement frequency from the highest region of source noise (D.C.) to a region of much lower noise (typically kHz). The oscillation circuitry is able to lock onto modulation frequency precisely, thereby reducing noise bandwidth to a few cHz and increasing signal-to-noise (S/N) ratio to a usable level.
Traditional analog filters and oscillators can be used to construct an LIA. However, greater performance can be achieved by digitizing the signal and using digital signal processing (DSP) circuitry such as the Stanford Research Systems Model SR850 DSP LIA. After removing 60 and 120 Hz noise with analog notch filters, the signal passes through a 100-kHz 9th-order elliptical anti-aliasing filter. It is digitized by a 256-kHz, 18-bit analog-to-digital converter and processed by the internal DSP circuitry to obtain the signal at the chopping frequency. SR850 can rescue a 10-nV modulation riding on a noisy source background, resulting in an effective detection limit of a few nano-absorption units. Admittedly more complex than the Spectronic needle, the LIA can find that needle even though it is buried under a very large haystack.
This material originally appeared as a Contributed Editorial in Scientific Computing and Instrumentation 20:02 January 2003, pg. 59.
William L. Weaver is an Associate Professor in the Department of Integrated Science, Business, and Technology at La Salle University in Philadelphia, PA USA. He holds a B.S. Degree with Double Majors in Chemistry and Physics and earned his Ph.D. in Analytical Chemistry with expertise in Ultrafast LASER Spectroscopy. He teaches, writes, and speaks on the application of Systems Thinking to the development of New Products and Innovation.