Effect of Slit Width on Signal-to-Noise-Ratio in Emission Spectroscopy

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[Background] [Cell definitions and equations] [Student assignment handout]

Simulation of a typical signal-to-noise optimization problem of measuring an atomic emission line superimposed on a continuum background emission (e.g. flame or plasma background emission). This simulation allows students to explore the effect of the the slit width of the spectrometer. The bar graph shows how the contribution of the three primary noise sources (flicker, photon, and detector) changes as the spectrometer slit width is changed. Students attempt to find the slit with that gives best signal-to-noise ratio. Note: flicker in continuum background emission is commonly compensated by using a wavelength modulation system.

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Other related simulations:
Effect of Slit Width on Signal-to-Noise Ratio in Absorption Spectroscopy
Signal and Photon SNR of Atomic Emission Spectrometer
Wavelength Modulation System

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Background

What is slit width? Slit width is the width (usually expressed in mm) of the entrance and exit slits of a monochromator. The slits are rectangular apertures through with light enters into and exits from the monochromator. Their purpose is to control the spectral resolution of the monochromator, that it, its ability to separate close wavelengths. In the diagram below, B is the entrance slit and F is the exit slit.

From
http://en.wikipedia.org/wiki/Image:Czerny-turner.png

Optical diagram of a common monochromator design; from Wikipedia

Light is focused onto the entrance slit B, is focused by concave mirror C onto the grating D, which disperses the light according to wavelength. Concave mirror E then focuses the light onto the exit slit F, forming a spectrum across the exit slit. Only the particular wavelength that falls directly on the exit slit passes through it and is detected. (In the diagram above, the light from three different atomic lines enters the monochromator at A, corresponding to the red, green, and blue colors, but only the green wavelength passes through and are detected at G). Adjusting the rotating angle of the grating changes the wavelength that passes through the exit slit. In a standard monochromator design, the entrance and exit slits have equal width. The wider the slit widths, the larger the range of wavelengths that passes through the monochromator. Most research-grade instruments have user-controllable slit widths. In general, smaller (narrower) slit widths yield greater spectral resolution but cut down the amount of light that is transmitted through the monochromator.

In an atomic emission spectrometer, a monochromator is used to limit the wavelength range of the light measured by the detector, to allow the analyte atomic line to be resolved from potential spectral interferences. In the most common arrangement, the light from the flame, plasma, arc, or spark is focused onto the entrance slit and the photodetector is placed immediately after the exit slit.

What is the optimum slit width for emission spectroscopy? This is a compromise between two extremes. If the slit width is too small, then the light intensity received by the detector will be too small and the signal-to-noise ratio will be poor, because of photon noise and detector noise, leasing to poor measurement precision. If the slit width is too large, two problems result: (1) the spectral discrimination between atomic lines is poor, increasing the possibility of a spectral interference (a common type of additive interference), and (2) the signal-to-noise ratio may decrease because of the increase in continuum background emission.

All atomizers (flames, plasmas, arcs, or sparks) generate a certain amount of background emission, on top of which is superimposed the atomic line emission of the analyte and other elements. Some of this background emission is structured (band emission from small molecules and molecular fragments from the flame gases, combustion products or from the solvent) and some is continuous (like white light), from blackbody emission from hot particles in the atomizer and from ion-recombination emission. The measured intensity of both types of background increases with slit width. The measured intensity of the continuous (white light) emission increases with the square of slit width because two separate factors are operating. First, the total slit area increases in proportion to the slit width, which increases the spacial fraction of the light source intensity that enters the monochromator (assuming that the image of the light source formed on the entrance slit by the entrance optics is larger than the width of the slit, which is almost always the case in normal instruments). Second, the spectral bandpass of the monochromator increases in proportion to the slit width, which increases the spectral fraction of the background emission that enters the monochromator - in other words, more photons of different colors get through. These two factors operate independently, with the result that the measured intensity of the continuum background increases with the square of the slit width.

If unsuspected and uncorrected, the background emission would result in an analytical error, if the background emission intensity is greater in the samples that in the standards. This might happen if some of the background arises from matrix constituents present in the sample that are not present in the standards. For example, if you are trying to measure lithium is blood serum by flame emission, the sodium present in the samples will produce a certain amount of continuum background emission that spreads out over a wide wavelength range, including the wavelength of the lithium emission line. Unless the standards also have exactly the same amount of salt as the sample, that background emission will generate a positive analytical error (that is, the measured lithium concentration will be too high). The standard way to correct this is to scan over the lithium line and measure the height of the lithium peak relative to the background. But even if the systematic error due to the background emission is eliminated, there remains the random noise caused by the background: photon noise andflicker noise. Photo noise of the background is proportional to the square root of the background intensity. and flicker noise is directly proportional to the background intensity. Flicker noise is caused by the turbulence in the flame or plasma. ( Wavelength modulation can compensate for the continuum background emission automatically and continuously, and it can eliminate most of the flicker noise, if the modulation frequency is high enough, but it can not eliminate the photon noise).

The result of all this is that there is actually a slit width that yields a optimum (maximum) signal-to-noise ratio. That is the point of this simulation.

Inputs:

W, slit width, (cell B6), selected by pop-up menu.
A, analyte radiance (cell C6)		
B, background radiance (cell D6)			
AFF, analyte flicker factor,  (cell E6)		
BFF, background flicker factor (cell F6)		
DN, detector noise (cell G6)	

Calculated quantities:

            signal   photon noise   flicker noise
Analyte     =A*W     =sqrt(A*W)    =AFF*A*W
Background  =B*W*W   =sqrt(B*W*W)  =BFF*B*W*W

Total noise (cell F9) = sqrt((analyte photon noise)^2
                        +(background photon noise)^2
                        +(analyte flicker noise)^2
                        +(background flicker noise)^2
                        +(detector noise)^2)		
signal/noise (cell G9) = (analyte signal)/(total noise)		
signal/background (cell H9) = (analyte signal)/background signal)

The bar graphs shows the total (analyte plus background) photon noise,
the total flicker noise, and the detector noise.

Student assignment:

This worksheet simulates the classical signal-to-noise ratio optimization problem of measuring of an atomic emission line superimposed on a continuum background emission (e.g. flame or plasma background emission). The table in boldface type at the top shows the factors you can change. You can change the slit width by using the pop-up menu under slit width at the top left of the window. The table below that gives the analyte and background signals, the breakdown of the individual noise contributions from analyte and background shot and flicker noise, the total noise, signal to noise ratio (ratio of analyte signal to total noise) and the signal-to-background ratio (ratio of analyte signal to background signal).

The bar graph compares the amplitudes of the photon, flicker, and detector noises. The line plot is a simulated signal tracing such as might be recorded on a flame or plasma emission system with continuous solution introduction, showing the blank signal and noise (background only), the analyte signal and noise (analyte signal plus background) followed by another measurement of the blank. This simulation considers only random noise errors; it assumes that some method of background
correction has already been applied to correct the systematic error caused by the background intensity at the analyte wavelength (for example, wavelength modulation).

1. Start with analyte radiance = background radiance = 10000, analyte and background flicker factors = .01, and detector noise = 20. Vary the slit width from 0.01 to 3 mm. Make a plot of the analyte signal and the background signal vs. slit width. Explain.

2. Why does the SNR improve in going from 0.01 to 0.03 mm?

3. Why does the SNR decrease in going from 1 to 3 mm? (Hint: look at the breakdown of the flicker noise).

4. At what slit width is the SNR optimum?

5. Make a plot of the total photon, flicker, and detector noise (as estimated from the bar graph) vs. slit width.

(c) 1991, 2015. This page is part of Interactive Computer Models for Analytical Chemistry Instruction, created and maintained by Prof. Tom O'Haver , Professor Emeritus, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu. Number of unique visits since May 17, 2008: