Fourier Analysis Of Laser Interferometry For Probing Axisymmetric Spatial Temperatures

Temperature of an object can be known by contact and non-contact measurement.Contact measurement is popular;however,the temperatures measured in the method would be affected more or less by the presence of temperature sensors.In the extreme case that the measured object is very small,the influence is not negligible.In other occasions,such as a steel-making furnace,contact-measurement fails to work.In these situations,non-contact-measurement finds its application.In this thesis,we set up a laser interferometry for probing the axisymmetric temperature field of transparent media,with the aid of high-speed charge-coupled device(CCD)as well as the Fourier transformation.It is well known that the refractive index of air is changed with temperature,which leads to the phase shift of light passing through due to the change of light speed.Here,the Mach-Zehnder interferometer is used to measure the phase shift as well as the temperature field of a candle flame further.So-called wrapped phases are obtained with inverse Fourier transform of the acquired interference fringe pattern in frequency domain,after its noise has been filtered out.After the wrapped phase has been unwrapped,a two-dimensional distribution of phase shift is obtained in the plane of interference fringe.In the condition of spatial symmetry,a three-dimensional distribution of the refractive index of air is resolved with the aid of Abel inverse transform.Provided with the relation of the refractive index to temperature for air,a three-dimensional temperature field of the candle flame is finally obtained.To verify the above method,a set of thermocouples are used to measure the temperature field of the candle flame.By comparing the two obtained temperature fields,we confirm that the fringe Fourier transformation method is effective.It is the most crucial for the phase shift to be determined in the process.In order to filter out the noise as much as possible during extracting the information,several usual filtering methods have been compared and an ideal low-pass filter is found to work well as long as a cosine-shaped edge is coupled to it.The maximal error is achieved in the high-temperature region using an ideal filter,followed by the Gaussian filter.The maximal error of the Butterworth filter is between the results of the cosine-shaped edge filter and the Gaussian filter.The interferogram and its frequency spectrum are in the digital form in the study.In the preparation of filtering out the noise of frequency,shifting the spectrum cannot be moved smoothly but stepwise up to the resolution of CCD image,and accordingly,some deviation has been found in the calculated phase.To eliminate the deviation,an extra picture has to be taken without any flame,and a background interferogram is obtained,where the very deviation exists alone.