[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.
Excel version: EffectOfSlitWidthOnSNR.xls
OpenOffice version: EffectOfSlitWidthOnSNR.ods
OpenOffice installer: OpenOffice.org
WingZ version: EffectOfSlitWidthOnSNR.wkz
Wingz player application installer, for windows PCs or Macintosh
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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.
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.
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)
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
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.