Real-time simulation of a scanning fluorescence spectrofluorometer. Students
can set the excitation and emission wavelengths, scan excitation spectra,
emission spectra, or synchronous spectra, change the concentrations of
two fluorescent components, insert and remove the blank and sample cuvettes,
measure the wavelengths of maximum
excitation and emission, Stokes shift, and detection limits,
observe Raleigh and Raman scatter, dark current, photon noise, determine the
frequency of the vibration causing the Raman peak, compare absorption to
fluorescence measurement of
the same solution, optimize measurement of two-component mixture by
selective excitation and synchronous fluorescence methods, generate and plot
analytical curves automatically, and observe the non-linearity and spectral distortion
caused by self-absorption.
Download links: OpenOffice Version, FluorescenceOO.ods Note: to run this spreadsheet, you have to first download the OpenOffice installer (download from OpenOffice),
then install it (by double-clicking on the installer file that you just
downloaded), and then download my spreadsheets from this page.
Once OpenOffice is installed, you can run my spreadsheets just by
double-clicking on them. Note 1:Don't use version 3.1.
There is a bug in OpenOffice 3.1 that causes bad x-axis scaling on
some of my graphs. The problems does not occur in version 3.0 or in the most recent version 3.2. Note 2: Downloading these files with Interent Explorer
will change the file types from ".ods" to ".zip"; you will have to edit
the file names and change the extensions back to ".ods" for them to
work properly. This problem does not occur in Firefox or in Chrome.
This is a simulation of a photodiode-array or rapid-scanning
spectrofluorometer. The simulation displays graphs of the excitation
spectra, emission spectra, and synchronous spectra, as well as
a numerical value for the relative fluorescence emission intensity
(the black box labeled "Intensity").
To change the excitation and emission wavelengths (in nm), adjust the two sliders at the top, labeled "Excitation Wavelength" and "Emission Wavelength". To change the graph scale expansion, use the long vertical slider labeled "Scale xpand". (This effects only the vertical intensity scale of the graphs, not the numerical intensity display).
To view these spectra enlarged, click the tabs at the bottom left of the window, labeled Control, Excitation, Emission, and Synchronous.
The sample solution may contain 1 or 2 fluorescent compounds, A and B,
dissolved in water. You can control the concentrations of these two
components by using the sliders labeled "ppm component A" and "ppm component B". You can also control what is placed in the sample compartment with the "Cuvette control" buttons.
The
transmittance of the sample solution at the excitation wavelength is
also displayed, to aid in comparing fluorescence to absorption
measurement and as an indication of the extend of the self-absorption
or "inner filter" effect.
The synchronous fluorescence spectrum is displayed at the bottom left. The Wavelength Offset control (top right) controls the wavelength difference between the excitation and emission wavelengths in nm.
To inspect the analytical curve with respect to component A
alone (at constant concentration of component B), click the tab at the
bottom of the windows labeled "Analytical curve A". To inspect
the analytical curve with respect to component B alone (at
constant concentration of component A), click the tab at the bottom of
the windows labeled "Analytical curve B".
Operating instructions, WingZ version:
To change the concentrations of the components A and B, click on
the up and down arrows to the left of the concentration
displays(concentration range is zero to 100 ppm in a 1,2, 5, 10
sequence); or you can type in any arbitrary concentration for either
component while the cuvette is removed.
Fluorescence intensity (in arbitrary units) and the absorbance of the
solution at the excitation wavelength are displayed in the black boxes.
Readings are continuous as long as the cuvette is inserted into the
instrument. (The random fluctuations in readings are due to photon
noise).
Clicking "Remove cuvette" simulates removal of the cuvette from the
light path; the intensity read-out displays only the detector's dark
current. Clicking "Insert blank" simulates inserting a cuvette filled
with pure water into the light path; the intensity read-out displays
the light scatter (Rayleigh and Raman) from the water. Clicking "Insert
sample" simulates inserting a cuvette filled with a water solution of
the two components at the specified concentrations. The cuvette must be
removed to type in arbitrary concentrations and then inserted to
measure.
To change the excitation and emission wavelengths (in nm),
adjust the two sliders at the bottom. To scan a spectrum, click on the
corresponding scan button. To obtain a synchronous spectrum, set the
wavelength offset with the slider on the right and click "Scan both".
Change the y-axis scale of the plots by clicking on one of the seven
small "sensitivity" buttons labeled "10" through "3000", or press
"auto" to allow the computer to automatically adjust the y-axis scale.
Note: the intensity and absorbance displays respond immediately to
changes in concentrations and wavelengths; however, spectra must be
re-scanned after changing the concentrations, wavelengths, or offset.
Pressing "analyt.curve A" runs an analytical curve for
component A and displays a log-log plot of intensity vs concentration
of A from 0.001 to 100 ppm. Pressing "analyt. curve B" does the same
thing for component B. Scanning a spectrum replaces the analytical
curve plot. From this plot it is possible to convert the relative
intensity readings into concentration in ppm.
Instructor's Notes:
This is a simulation of room temperature prompt fluorescence of two
non-interacting fluorophors in aqueous solution with right angle
geometry in a standard cuvette, measured with a corrected dispersive
spectrofluorometer. You can think of the two components as
two analytes or as one analyte (A) and a background or interfering
component (B). Both
components obey Vavilov's law (shapes of the emission spectra of each
component separately are independent of the excitation wavelength, and
vice versa, except for the scatter peaks). The simulation includes
Rayleigh and Raman scatter peaks of the solvent (water); there is only
one Raman band observable, that of the OH stretch of water. (The
Rayleigh peak is fixed in
amplitude but the Raman band height varies with the inverse 4th power
of wavelength). The Raman peak of water is often used to measure the sensitivity and signal-to-noise ratio of fluorescence instruments.
The
simulation includes the self-absorption (inner-filter) effect for both the excitation beam
and the fluorescence emission, and it includes photon noise but not flicker or detector
(dark current) noise. In addition to an intensity display, there is also an absorbance readout,
which gives the absorbance of the sample solution at the excitation wavelength;
this is intended to allow a comparison of fluorescence to absorption measurement
and as an indicator of the presence of self-absorption, but it is
not a full simulation of absorption spectrophotometric measurement (it does not include
stray light or finite spectra bandwidth deviations nor background shifts due to changes in cell transmission).
The simulation has a synchronous scanning mode (constant delta-lambda).
On most computers the scanning speed of the simulated instrument will be faster than typical
real instruments.
There are several parameters that you can change, to modify the
simulation experience
for specific purposes. You can change the spectral characteristics of
the two components. The excitation and the emission spectra are each
modeled as three overlapping Gaussian bands. The
heights, peak wavelengths, and widths of each band are given in the
table at R20..R46. For example, h1ax is the height of the first band of component A's excitation spectrum, and
w3bm is the width of the third band of component B's emission
spectrum, and so forth
(peak wavelengths and widths are in nm; height is in arbitrary units).
You can change the overall signal-to-noise ratio of the instrument
(cell Q17). You can also change
the sequence of concentrations used to construct analytical curves (table in U10..U26 in the WingZ version and the large table starting at U8 in the OpenOffice version).
After making any changes,
I suggest that you Save the simulation under a different file name, so you preserve the original.
Cell definitions and equations (forWingZ version 2.1):
Inputs:
Concentration of A in ppm (cell I12)
Concentration of B in ppm (cell K12)
ex = wavelength of excitation monochromator (cell I8 or excitation slider)
em = wavelength of emission monochromator (cell K8 or emission slider)
of = synchronous offset (cell M8 or offset slider)
epsa = absorption coefficient of component A
epsb = absorption coefficient of component B
snr = signal-to-noise ratio (Cell Q17)
Z1 = 1 if cuvette is inserted; 0 if removed from the instrument.
Excitation band characteristics of component A: (cells R20..R28)
band # 1 2 3
Height: h1ax h2ax h3ax
Position: p1ax p2ax p3ax
Width: w1ax w2ax w3ax
Emission band characteristics of component A: (cells R20..R28)
band # 1 2 3
Height: h1am h2am h3am
Position: p1am p2am p3am
Width: w1am w2am w3am
Excitation band characteristics of component B: (cells R29..R37)
band # 1 2 3
Height: h1bx h2bx h3bx
Position: p1bx p2bx p3bx
Width: w1bx w2bx w3bx
Emission band characteristics of component B: (cells R38..R46)
band # 1 2 3
Height: h1bm h2bm h3bm
Position: p1bm p2bm p3bm
Width: w1bm w2bm w3bm
U10..U26: sequence of component concentrations (ppm) for analytical curves.
Calculated quantities:
Concentration of A in ppb = A = 1000*ppmA
Concentration of B in ppb = B = 1000*ppmB
Wavelength of Raman peak in emission spectrum = raman = ex/(1-ex*0.00034)
Wavelength of Raman peak in excitation spectrum = xraman = em/(1-em*0.00034)
Intensity of Raman peak in emission spectrum = RamInt = 200000000000/ex^4
Intensity of Raman peak in excitation spectrum = xRamInt = 200000000000/em^4
Emission factor, component A
ema = (h1am*exp(-((em-p1am)/w1am)^2)
+h2am*exp(-((em-p2am)/w2am)^2)
+h3am*exp(-((em-p3am)/w3am)^2))
Emission factor, component B
emb = (h1bm*exp(-((em-p1bm)/w1bm)^2)
+h2bm*exp(-((em-p2bm)/w2bm)^2)
+h3bm*exp(-((em-p3bm)/w3bm)^2))
Excitation factor, component A
exa = (h1ax*exp(-((ex-p1ax)/w1ax)^2)
+h2ax*exp(-((ex-p2ax)/w2ax)^2)
+h3ax*exp(-((ex-p3ax)/w3ax)^2))
Excitation factor, component B
exb = (h1bx*exp(-((ex-p1bx)/w1bx)^2)
+h2bx*exp(-((ex-p2bx)/w2bx)^2)
+h3bx*exp(-((ex-p3bx)/w3bx)^2))
Absorbance of sample solution at the excitation wavelength
Aex = epsa*A*(h1ax*exp(-((ex-p1ax)/w1ax)^2)
+h2ax*exp(-((ex-p2ax)/w2ax)^2)
+h3ax*exp(-((ex-p3ax)/w2ax)^2))
+epsb*B*(h1bx*exp(-((ex-p1bx)/w1bx)^2)
+h2bx*exp(-((ex-p2bx)/w2bx)^2)
+h3bx*exp(-((ex-p3bx)/w3bx)^2))
Absorbance of sample solution at the emission wavelength
Aem = epsa*A*(h1ax*exp(-((em-p1ax)/w1ax)^2)
+h2ax*exp(-((em-p2ax)/w2ax)^2)
+h3ax*exp(-((em-p3ax)/w2ax)^2))
+epsb*B*(h1bx*exp(-((em-p1bx)/w1bx)^2)
+h2bx*exp(-((em-p2bx)/w2bx)^2)
+h3bx*exp(-((em-p3bx)/w3bx)^2))
Transmission of sample solution at the excitation wavelength
Tex = 10^(-Aex)
Transmission of sample solution at the emission wavelength
Tem = 10^(-Aem)
Total output intensity (fluorscence + scatter + Raman) (cell M13)
total = Z1*Tex*Tem*((A*ema*exa+B*emb*exb)
+100*exp(-((ex-em)/10)^2)
+RamInt*exp(-((em-raman)/10)^2))
Display outputs:
Absorbance (cell M20)
= Aex + 0.001*(rand()-0.5)
Intensity (cell M12)
=abs(total+(sqrt(total)+2)*(rand())/snr)
Array calculations:
D31..D101: wavelength, 200..600 nm in 6 nm steps
B31..B101: absorbance of solution at wavelength
absorbance = epsa*A*(h1ax*exp(-((wavelength-p1ax)/w1ax)^2)
+h2ax*exp(-((wavelength-p2ax)/w2ax)^2)
+h3ax*exp(-((wavelength-p3ax)/w3ax)^2))
+epsb*B*(h1bx*exp(-((wavelength-p1ax)/w1bx)^2)
+h2bx*exp(-((wavelength-p2ax)/w2bx)^2)
+h3bx*exp(-((wavelength-p3ax)/w3bx)^2))
C31..C101: transmission of solution at wavelength
transmission = 10^(absorbance)
E31..E101: excitation spectrum (including Rayleigh and Raman scatter)
excitation = Tem*transmission*(A*((h1ax*exp(-((wavelength-p1ax)/w1ax)^2)
+h2ax*exp(-((wavelength-p2ax)/w2ax)^2)
+h3ax*exp(-((wavelength-p3ax)/w3ax)^2))*ema)
+B*((h1bx*exp(-((wavelength-p1bx)/w1bx)^2)
+h2bx*exp(-((wavelength-p2bx)/w2bx)^2)
+h3bx*exp(-((wavelength-p3bx)/w3bx)^2))*emb)
+100*exp(-((wavelength-em)/10)^2)
+xRamInt*exp(-((wavelength-xraman)/10)^2))
G31..G101: excitation spectrum with photon noise
ex+noise = $Z$1*(abs(excitation+(sqrt(excitation)+2)*(rand())/snr))
I31..I101: emission spectrum (including Rayleigh and Raman scatter)
emission = Tex*transmission*(A*(exa*(h1am*exp(-((wavelength-p1am)/w1am)^2)
+h2am*exp(-((wavelength-p2am)/w2am)^2)
+h3am*exp(-((wavelength-p3am)/w3am)^2)))
+B*(exb*(h1bm*exp(-((wavelength-p1bm)/w1bm)^2)
+h2bm*exp(-((wavelength-p2bm)/w2bm)^2)
+h3bm*exp(-((wavelength-p3bm)/w3bm)^2)))
+100*exp(-((wavelength-ex)/10)^2)
+RamInt*exp(-((wavelength-raman)/10)^2))
K31..K101: emission spectrum with photon noise
em+noise = $Z$1*(abs(emission+(sqrt(emission)+2)*(rand())/snr))
Transmission at offset wavelength (wavelength+offset)
A31..A101: Toff
Toff = 10^(-epsa*A*(h1ax*exp(-((wavelength-p1ax+of)/w1ax)^2)
+h2ax*exp(-((wavelength-p2ax+of)/w2ax)^2)
+h3ax*exp(-((wavelength-p3ax+of)/w3ax)^2))
+epsb*B*(h1bx*exp(-((wavelength-p1ax+of)/w1bx)^2)
+h2bx*exp(-((wavelength-p2ax+of)/w2bx)^2)
+h3bx*exp(-((wavelength-p3ax+of)/w3bx)^2)))
M31..M101: synchronous spectrum (including Rayleigh and Raman scatter)
synch = Toff*transmission*(A*((h1ax*exp(-((wavelength-p1ax)/w1ax)^2)
+h2ax*exp(-((wavelength-p2ax)/w2ax)^2)
+h3ax*exp(-((wavelength-p3ax)/w3ax)^2))
*(h1am*exp(-((wavelength-p1am+of)/w1am)^2)
+h2am*exp(-((wavelength-p2am+of)/w2am)^2)
+h3am*exp(-((wavelength-p3am+of)/w3am)^2)))
+B*((h1bx*exp(-((wavelength-p1bx)/w1bx)^2)
+h2bx*exp(-((wavelength-p2bx)/w2bx)^2)
+h3bx*exp(-((wavelength-p3bx)/w3bx)^2))
*(h1bm*exp(-((wavelength-p1bm+of)/w1bm)^2)
+h2bm*exp(-((wavelength-p2bm+of)/w2bm)^2)
+h3bm*exp(-((wavelength-p3bm+of)/w3bm)^2)))
+100*exp(-((of)/10)^2)
+RamInt*exp(-((wavelength+of-(wavelength/(1-wavelength*0.00034)))/10)^2))
O31..O101: synchronous spectrum with photon noise
synch+noise = $Z$1*(abs(synch+(sqrt(synch)+2)*(rand()/snr)))
Graphs:
Excitation spectrum: excitation+noise vs excitation wavelength
Emission spectrum: emission+noise vs emission wavelength
Synchronous spectrum: sync+noise vs excitation wavelength
Analytical curves: Intensity vs concentration of A or B in ppm
Student assignment, WingZ version:
Simulation of Scanning Fluorescence Spectrometer
This is a simulation of a scanning spectrofluorometer. The simulation displays excitation spectra, emission spectra, and synchronous spectra, relative fluorescence intensity, and absorbance at the excitation wavelength. Operating instructions are contained in the scrolling text field in the upper right of the screen. Answer the following questions on a separate sheet to turn in. Please do not make repeated print-outs of this spreadsheet.
1. Set A=1 ppm and B=0. Determine the wavelengths of maximum excitation and emission for component A. What is its Stokes shift?
2. Does Vavilov's Law* seem to hold for compound A, that is, is the shape of the emission spectra independent of the excitation wavelength, and vice versa, except for the scatter peaks?
3. Is there any sign of Rayleigh or Raman scatter? How could you distinguish these from genuine fluorescence?
4. Check the blank (click on "Insert Blank"). Increase the sensitivity setting as necessary. Is there any sign of dark current or background fluorescence? What are the main features of the excitation and emission spectra of the blank. Estimate the spectral bandpass of the monochromators.
5. Does the wavelength separation between the Rayleigh and Raman scatter peaks in the emission spectrum vary with excitation wavelength? What is the frequency, in cm-1, of the vibration causing the Raman peak? What vibration is most likely the cause?
6. Find the combination of excitation and emission wavelength that gives the best precision of measurement of low concentrations of component A. Estimate the detection limit of component A in ppm. Is the detection limit lower by fluorescence or by absorption measurement? By approximately what factor?
7. Over most of the concentration range, what is the source of noise in the intensity readings and in the spectra? How could you prove this?
8. Is there evidence of non-linearity in the relationship between concentration and intensity at high concentrations? What is the most likely source of the non-linearity?
9. Vary the wavelength offset and observe the synchronous spectrum. What offset gives the largest peak height? Explain the effect of Rayleigh and Raman scatter on the synchronous spectrum. Note: this is a constant wavelength synchronous spectrum.
10. Set A=0 and B=1 ppm. Determine the wavelengths of maximum excitation and emission for component B. What is its Stokes shift? Can mixtures of these two components be determined by fluorescence measurement?
*
Vavilov's Law states that the shape of the fluorescence emission
spectrum of a single fluorophor is independent of the excitation
wavelength, and vice versa. This holds only for the fluorescence
peaks, not Raman or scatter peaks.
Frequently-Asked Questions
1. Question:Why is fluorescence intensity measured in "arbitrary units"? Answer:
Nothing more is needed for the common applications of fluorescence
spectroscopy: for quantitative applications, a calibration curve can be
prepared and used on the same instrument employing any set of intensity
units equally well, and for qualitative applications, the shape of a
spectrum is the same no matter what intensity units are used.
Calibrating a fluorescence spectrophotometer to read in absolute
physical units (watts, for example) would add to the cost and would not
result in any real advantage for most applications. Most fluorescence
spectrophotometers simply measure the detector signal, which
is proportional to the fluorescence intensity. The magnitude of
that signal at a given analyte concentration is somewhat arbitrary,
depending upon the choice of detector and its operating conditions, as
well as the intensity of the light source and the characteristics of
the monochromator and the rest of the optics. See "Signal-to-Noise Ratio and Detection Limit of Fluorescence Spectroscopy" for a detailed analysis of the factors influencing the detector signal.
2. Question: Why not measure absorbance or transmission, as in absorption spectroscopy? Answer: This
is due to the different optical configuration of absorption and
fluorescence measurement. In absorption spectrometry, the light beam
that passes through the sample is measured directly by a detector
placed a 180º angle from the incident beam, which allows the incident
beam intensity to be measured simply by replacing the sample with a
"blank". In fluorescence spectrometry, the light beam that passes
through the sample is not measured at all; rather,
the fluorescence emission is measured, usually at a 90º angle
from the incident beam. Therefore, absorbance or transmission
can not be measured in a fluorescence spectrometer because the
detector does not measure the incident beam. Even if you tried to move
the detector around to 180º to measure the incident beam, it
wouldn't work very well because the light intensity of the incident
beam can be as much as 1013 times brighter
than the fluorescence intensity, and no detector in common use can
measure intensities over that wide a range. (Note: some
instruments do sample a small portion of the incident bean and measure
it with a second (lower sensitivity) detector, then calculate the ratio
of the fluorescence intensity to the incident intensity. Even
this ratio, however, is not comparable between instruments, in the same
way that absorbances can be compared
3. Question: How does fluorescence intensity vary with concentration? Answer: Fluorescence
intensity is directly proportional to concentration (i.e. the
calibration curve is linear), as long as the absorbance of the analyte
at the excitation wavelengths is very low, say, less than about 0.004
(99% T). If the absorbance is greater than this, then the
excitation intensity is reduced by the absorption, and
the calibration curve becomes non-linear (concave down). The
effect is exacerbated if the analyte also absorbs at the emission
wavelength.
4. Question: Why is fluorescence measured at a 90º angle to the incident (excitation) beam? Answer: There
is nothing magic about 90º. The fluorescence can't be
measured at a 180º, because the transmitted beam would completely swamp
the fluorescence. The choice of 90º is a matter of convenience,
especially when conventional square cross-section cuvettes are
used.
5. Question: What are the relative detection limits of absorption and fluorescence measurement? Answer: This depends largely on thefluorescence quantum efficiency
of the analyte (the ratio of the number of photons emitted as
fluorescence to the number absorbed). For a highly fluorescent molecule
such as quinine, which has a
quantum efficiency of 0.5, fluorescence has a better (lower)
theoretical detection limit than absorption by a factor of roughly 103 using comparable instrumentation, as you can demonstrate by comparing AbsorptionSNR.ods to FluorescenceSNR.ods.
But most fluorescent molecules have quantum efficiencies lower than
0.5, so the advantage of fluorescence is not so large on average. But
by the same token, any molecule with a quantum efficiency higher than
0.0005 is likely to be at least marginally better by fluorescence, at
least in terms of theoretical detection limit.
6. Question: How can a fluorescent peak can be distinguish from an Raman peak? Answer: Vary
the excitation wavelength slightly. If the peak shifts in wavelength
and its wavelength is longer than the excitation wavelength, it's a
Raman peak; if it changes its intensity but not its wavelength, it's a fluorescent peak.
7. Question: Why choose a fluorescence measurement over absorption? After all, any molecule that fluoresces must also absorb. Answer: The
choice depends on the fluorescence characteristics of the analyte and
the matrix that it is present in. If the analyte exhibits fluorescence
at excitation and emission wavelengths within the range of your
instrument, then it is a candidate for fluorescence measurement, if its
quantum efficiency is high enough. But a further requirement is that
the fluorescence emissions of other chemical components in the sample
not interfere, either because they are very weak or because the
excitation or emission wavelengths of those components can be
successfully resolved from that of the analyte. Each case has to
be evaluated individually. Usually a fluorescence measurement is chosen
over an absorption measurement when the analyte is strongly fluorescent
and the other components in the sample have absorption that interfere
with an absorption measurement but do not exhibit strong fluorescence
emission that would interfere with a fluorescence measurement. (c) 1992, 2009, 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.
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