Effect of Slit Width on Signal-to-Noise-Ratio

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[Cell definitions and equations] [Student assignment handout]

Simulation of a "classical" 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.

Download links: EffectOfSlitWidthOnSNR.hqx; EffectOfSlitWidthOnSNR.wkz
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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.

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.