In QE measurement by integrating sphere, the spectral irradiance (W/m2) is transformed in to photon irradiance (cps/m2) by dividing the ordinate data by corresponding photon energy at abscissa. The abscissa is also converted to wavenumber scale prior to such transformation, so that the excitation and emission signals could properly be deconvoluted. In this case, we obtain the photon distribution as a function of photon energy in cm-1. The photon distribution for absorption and emission is obtained by taking the difference with reference scattered signal.
Here my understanding is that the total photon count for absorption or emission is the summation of number of photons at each energy. The value of energy is irrelevant (not sure). I am getting difficulty in obtaining the total number of photons for absorption and emission. In literature, the integration is usually taken to get the area under the curve. Also, the abscissa is mostly wavenumber, but sometimes wavelength. My concern is if we take the integration, it also considers the values at abscissa. I tried to integrate same area curve at different wavenumber range (Origin software), which gives different area values. Please suggest if I am making some mathematical mistakes, and also give opinion on how to obtain total photon count and what should be the unit of abscissa for calculations.
Dear Atul,
The product of the intensity and wavelength is proportional to the number of photons within a given wavelength interval. Wavelength is the unit for the abscissa which you should use.
For more detailed information look to the literature, e.g.:
W. R. Ware et al., Relative fluorescence quantum yields using an integrating sphere. The quantum yield of 9,10-diphenylanthracene in cyclohexane. Chemical Physics Letters 39 (3), (1976), 449-453.
J. C. de Mello et al., An Improved Experimental Determination of External Photoluminescence Quantum Efficiency. Advanced Materials 9 (3), (1997), 230-232.
N. C. Greenham, I. D. W. Samuel, G. R. Hayes, R. T. Phillips, Y. A. R.
R. Kessener. S. C. Moratti, A. B. Holmes. R. H. Friend, Measurement of absolute photoluminescence quantum efficiencies in conjugated polymers. Chem. Phys. Lett. 241, (1995), 89-96.
Dear Atul,
The product of the intensity and wavelength is proportional to the number of photons within a given wavelength interval. Wavelength is the unit for the abscissa which you should use.
For more detailed information look to the literature, e.g.:
W. R. Ware et al., Relative fluorescence quantum yields using an integrating sphere. The quantum yield of 9,10-diphenylanthracene in cyclohexane. Chemical Physics Letters 39 (3), (1976), 449-453.
J. C. de Mello et al., An Improved Experimental Determination of External Photoluminescence Quantum Efficiency. Advanced Materials 9 (3), (1997), 230-232.
N. C. Greenham, I. D. W. Samuel, G. R. Hayes, R. T. Phillips, Y. A. R.
R. Kessener. S. C. Moratti, A. B. Holmes. R. H. Friend, Measurement of absolute photoluminescence quantum efficiencies in conjugated polymers. Chem. Phys. Lett. 241, (1995), 89-96.
Since photon energy/frequency/wavenumber are proportional (for light in free space), operations (integrations) over these scales as the abscissa should yield equivalent results.
Wave number (k) and wavelength (l) are inversely proportional, however. Spectral distributions need then be correctly transformed [ using dk = {dk/dl}(l) dl ]. Maybe it would be instructive if you revisit the Planck spectral distribution law as a function of frequency on the one hand and as a function of wavelength on the other. You will find different, seemingly inequivalent power laws as a result of incorporating the derivative {dk/dl} (resp. its equivalent).
If you use a spectrometer, then in principle you should know what the finite spectral interval is connected to. Ideally, it would be either equal energy/frequency/wavenumber intervals or equal wavelength intervals.
Thanks Professor Karola and Professor Kai for helpful replies. I will look the mathematical part one more time in different energy scales. i hope they yield the same values.
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