Study on spectral distribution and coherence length of light source

When measuring the surface shape of parallel plate glass by phase-shifting interferometry, three groups of interference fringes (front surface and reference mirror, rear surface and reference mirror, front and rear) will occur in the field of view of the interferometer simultaneously, resulting in the failure of the measurement. Therefore, the coherence length of the light source should be smaller than the optical path difference of the front and rear surfaces. The parallel plate thin glass produces in large quantities in the industrial production, which requires that the contrast of interference fringes is greater than 50% in a certain optical path in order to improve the detection efficiency and reduce the complexity of the adjustment. Therefore, the coherence length of light source should not be too short. The classical formula (ΔL = λ ² / Δλ) for calculating the coherence length derived from the light source whose spectral intensity is rectangular distribution. For other distributions, the formula can only describe the relationship between the coherence length and the bandwidth qualitatively, but the cutoff depth and the interference fringe contrast distribution cannot be determined. In this paper, the problem of coherence length and contrast distribution are studied and two new concepts of coherence length equivalent and contrast relative half-height-width are proposed which are used to characterize the coherence of the light source. The coherence length equivalent can quickly calculate the cutoff coherence length. The contrast relative half-height-width represents the length of the optical path when the contrast is 50%, when the cutoff coherence length of different spectral distributions is constant. In this thesis, the interference fringes of several typical light source distributions (Gaussian, Cosine, trapezoidal) are modeled, and the corresponding coherence length equivalents and contrast relative half-height-width are calculated to provide guidance for the selection of light sources and the design of interferometers.