Analysis of slit function errors in single-shot coherent anti-Stokes Raman spectroscopy (CARS) in practical combustors

Abstract

The temperature determined by a single-shot coherent anti-Stokes Raman spectroscopy (CARS) system is directly related to the half width at half maximum of the instrument slit function. Therefore, an accurate knowledge of the instrument slit function is necessary to determine temperature with CARS. However, in turbulent systems, the input slits of the spectrometer may be removed in order to guarantee signal throughput and establish the necessary dynamic range. In this case, the physical input slits of the spectrometer are replaced with apparent slits created by focussing the input beams near the entrance plane of the spectrometer. The slit function will then depend on the physical relationship among all of the optical components, the probe volume, and the dispersive performance of the spectrometer and detector, as well as the optical path through density and temperature gradients which may not be invariant in a turbulent system. The presence of high temperatures and turbulence levels can effect the size of the CARS signal origin and the optical path, and as a result, the slit function is not invariant. Ignoring these changes can result in large root mean square temperatures (decreased precision) as well as mean temperature errors. The variability of the slit width can be accounted for on a shot-to-shot basis by using a two parameter (HWHM of the slit function and temperature) fitting routine. For temperatures greater than 1200 K there is convergence on a best curve implying both a temperature and a slit width. This method can be used alone or in concert with various weighting schemes to improve the precision. There are two major advantages gained by allowing the slit function to vary in a CARS system: (a) it allows an increase in the precision; (b) it allows temperatures to be calculated without the assumption that the slit function does not change with temperature or turbulence or position within the flame. In fact, it allows the temperature to be determined with almost no previous knowledge of the slit function except the general shape. These two advantages combine to significantly simplify the study of turbulent combusting systems with CARS and to improve the precision, both point-to-point and shot-to-shot, of CARS.