We Wish to Measure the Rotational Raman Spectrum of Nitrogen in Room Air

ME770; Fall 2007; Prof. Sanders; Homework #4; Due Oct 31, 2007

We wish to measure the rotational Raman spectrum of nitrogen in room air In particular, we will consider spontaneous anti-Stokes rotational Raman scattering. Here is a previous measurement from Drake et. al.:

We will assume:  532 nm, TEM00 laser is used for excitation (if you are interested in why one might choose 532 nm vs. other wavelengths, see http://homepages.cae.wisc.edu/~ssanders/me_770/homework_assignments/home work_4_wavelength_scaling_raman_spectrometer_considerations.xls)  300 cm-1 coverage (523.5 – 532.0 nm coverage)  1 cm-1 spectral resolution  a grating spectrometer, at least initially  max integration time 5 minutes  max spatial resolution 5 cm  max collection lens / mirror NA = 0.5  max grating size = 5 cm (groove length) x 10 cm  a 2-D Si CCD camera for collection, assumed to be arbitrarily binnable so we can achieve arbitrary pixel size/shape (max 25 mm x 25 mm)  considering the entire anti-Stokes branch, 168 pW are scattered uniformly into 4π Sr for every 1mm of propagation through room air for every 1 W of excitation power (see http://homepages.cae.wisc.edu/~ssanders/me_770/homework_assignments/HW_4 _raman_power_calculations_XA.xls)  11% of the scattered anti-Stokes light will be in the strongest line at room temperature (see http://homepages.cae.wisc.edu/~ssanders/me_770/homework_assignments/HW_4 _raman_power_calculations_XA.xls)  We require a signal-to-noise ratio of at least 20 on this strongest line

 A Rayleigh/Mie/stray rejection filter (perhaps I2 gas cell) is available Your goal will be to design the spectrometer, then indicate what laser power you require.

Finally, try to use Renata’s paper (http://homepages.cae.wisc.edu/~ssanders/me_770/supplemental_material/SHS_OH_fla me_ApplOpt_revision_RJB.doc) to determine whether an interferometric spectrometer would offer better performance