Spectrometers and Instrumentation

• Signals, background, and noise are key components in understanding signal processing and instrumentation.

Spectrometers

• Spectrometers comprise lamps, filters, monochromators, and detectors.
• Lamps can be incandescent, fluorescent, LEDs, or lasers
• Filters are for absorbance, interference, or holography
• Monochromators can use interferometers
• Detectors use photon transducers like phototubes, PMTs, photodiodes, LDA, CCD, or CMOS
• Thermal transducers like thermocouples, thermistors, or pyroelectrics can be used

Generic Spectrometer

• Contextualizes detector responses within the device using components already discussed
• Includes one addition component

UV/Vis Absorption Spectra

• Generated by comparing two conditions over a range of wavelengths
• Key requirements for spectral measurement include light source, wavelength selection, sample cell, reference blank, and detector detection

Instrumentation for Absorbance

• Light from a continuum source passes through a wavelength selector
• Light interacts with sample or reference
• Detector measures the signal

Choppers

• Choppers aid spectroscopic measurements by facilitating the comparison of two conditions.
• Motorized mirror/chopper arrangements improve absorbance calculations by comparing a sample cell to a reference.
• It is critical the sample and reference cells are matched
• Choppers enable rapid, alternating measurements, useful for scanning wavelengths for spectra.
• Single detectors are more useful because they remove detector bias and reduces cost
• Speed, robustness, accuracy, reproducibility, and cost all improve
• Choppers can monitor background levels in instruments like fluorescence.
• They use dual experiments
• This improves signal levels
• Background light significantly contributes to the total response, which has to get subtracted away
• Background drifts are also useful to monitor

Signal, Background and Noise

• Real-world responses include signal and background elements
• Instrument responses invariably includes fluctuations
• These fluctuations is noise
• The fluctuations can come before the sample

Root Mean Square Noise

• Figure of merit for noise is root mean square noise or N(rms)
• N(rms) is the population standard deviation (σ) of the signal (S).
• Sample standard deviation (s) approximates σ
• N(rms) is approximate to S

Sample Standard Deviation

• Reproducibility of repeated measurements assess precision
• Sample standard deviation characterizes the spread of data in limited samples

Noise

• Peak-to-peak noise (Np-p) can be specified instead of N(rms) and estimated by eye.
• In a normal (Gaussian) distribution, Noise (rms) = 1/4√2 N(p-p) ≈ 0.177 N(p-p) ≈ 1/6 N(p-p)

Signal To Noise Ratio

• Signals get expressed as an average with uncertainty ± N(rms) and/or s
• Signal-to-noise ratio focuses on the ratio of signal to noise (N)
• Expressed as S/N (S/N ratio)
• S/N = S/N(rms) = S/σ ≈ S/s
• Can be estimated from fluctuations in the signal to calculate noise
• The calculations requires an assumptiom

Limit of Detection (LOD) and Limit of Quantification (LOQ)

• The size of the signal, size of the noise, and its relation relates to measurement science
• LOD and LOQ depend on the S/N, if the noise is taken to be the standard deviation of the blank response

S/N and Detection Limits

• High S/N methods are critical for trace analysis.
• In a given method, reducing N as much as possible is key.

Chemical Noise

• Shifts in position of equilibria due to changes in temperature, humidity, pH, or pressure
• Breakdown of sample
• Impurities in solvent

Instrumental Noise

• Shot noise
• Thermal noise
• 1/f noise
• Environmental noise

Shot Noise

• Statistical fluctuations from quantized events happening at a detector
• Shot noise is inescapable and unavoidable
• In general, Nshot is proportional to √S (square root of signal)
• For many measures, Nshot = √S, including photon counting
• Measuring light causes shot noise which effects the baseline
• Shot noise distribution is like Gaussian
• When signal levels are high, the relative contribution of shot noise as compared to signal is insignificant.
• At low signal levels, shot noise has to be taken into account
• Nshot comes from the signal and can't get reduced
• Can reduce signal-to-noise
• The most fundamental noise limit on total noise
• No dependency on frequency

Thermal Noise

• Thermal noise (Ntherm) is "Johnson Noise," and comes from thermal motion of charge carriers
• Ntherm's fluctuations cause voltages through transducers like PMTs and photodiodes
• Thermal noise can get reduced by cooling detectors

Flicker Noise

• Flicker noise is "1/f noise"
• Noise is higher for signals measured at low frequencies
• Flicker noise cannot be reduced, but the effects can be reduced through modulation
• Choppers can modulate what a detector measures
• Helps comparisons between sample and reference response

Environmental Noise

• Environmental noise (Nenv) relies on frequency and from known forces
• Power-line noise is at 60 Hz
• Elevator peaks
• T. Coor, J. Chem. Educ., 1968, 45, A5-40.
• Grounding and shielding circuits can reduce environmental noise

Faraday Cage

• Designs can block long radiofrequency EM radiation
• Metal mesh act as shield
• The conductor should send more signals
• Layering shielding makes a better mesh, one layer won't shield as much

Instrumental Noise Summary

• Shot noise is statistical fluctuations present when quantized events get measured
• Nshot is proportional to √S
• Thermal noise stems from thermal motion in charge carriers
• Cooling helps
• T(thermal) is proportion to √T
• Flicker noise results noise at low frequencies and is fixed through modulation
• Environmental noise stems from grounded, shielded cables and detectors

Combining Noise

• Adding noise types, they combine as the root of the square
• To increase S/N, reduce total noise levels
• Focus on the major source(s)
• Square root of squares is less than regular additive sums

Noise Reduction

• Find any noisy detectors
• B thermal noise will decrease
• The new S/N 80K ≈ 13

S/N Enhancement

• Reducing inherent noise is an ideal goal.
• If not reduces, software can make adjustments

Signal Averaging

• Take multiple spectra to see the center and reduce noise
• STot/NTot = √n (S/N)i
• Multiple scans improve data
• Signal averaging loses no data but takes a lot of time so only do when dat collects fast
• S is proportional to SqrN, can only use signal when S is high

Boxcar Average

• Data gets split into longer time windows
• Take the average within those windows
• Typically done in software
• Data gets lost

Rolling (Moving) Average

• Windows moves over on data point every time
• All the points in the window count the same
• First point may resemble the boxcar average
• The overlapping combines for new averages

Smoothing With a Rolling Average + Information Content

• As you increase the window size, information gets lost
• Separated features appear to blur together

Weighted Rolling Smooth: Savitsky-Golay

• Weight Smoothing works for the roll window, data the center has higher power
• The rest fo data is wieghed aqually in the simple rolling function
• Weigh gives low order of data
• Softwre fits
• Data and number given as well
• SV, -i Si - 2 + 125i + 17S + 12Si+1-3S + 2/35
• i-2 =-5

Savitskyo-Golay Smoothing

• Lets you improve/smoothe at what S/N should be
• Does not lose the highs or lows

Fourier transform

• Remember transformation filters through hreatz can transform through inverse transorm
• Frequency data data data to filter or block
• To create

Fourier Transfer Filtering

• Look at signals that transform filters through heratz and transforms through inverse transform
• Higher frequencies oscillate faster