Simulation of Fluorescence Spectroscopy
Version 2.0, May 2000. Click to see a larger view.
[Operating instructions] [Instructor's Notes] [Cell definitions and equations] [Student assignment handout]
[Operating instructions] [Instructor's Notes] [Cell definitions and equations] [Student assignment handout]
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-linearily and spectral distortion caused by self-absorption.
Version 2.0: May, 2000. New controls for changing solutions concentrations; blank solution button; automated analytical curve plots for either component. This version can be operated using only the mouse-activitated on-screen controls; no keyboard entry is required (useful when used in a lecture-demonstration environment with a computer video projection system in a darkened room, where it is often difficult to use the keyboard). Version 2.1, June, 2000: Corrections to inner-filter calculations (Intensity display now agrees with spectra plots at high concentrations).
Download links:
Version 1: Fluorescence.wkz;
New version 2.1: fluor2.wkz;
Having trouble getting this to work? Download the complete system of modules for
PC or Mac
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Note: This is a computationally intensive simulation and will work best on machines of at least 400 MHz Pentium class and better.
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 wavlengths (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.
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 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 also change the sequence of concentrations used to construct analytical curves (table in U10..U26) and the overall signal-to-noise ratio of the instrument (cell Q17). After making any changes, I suggest that you Save the simulation under a different file name, so you preserve the original.
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: This is a simulation of a scanning fluorescence 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? 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?