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Research on interferometric equivalent wavelength of broadband light sources

Broadband sources have been suggested for use in the interferometric measurement for which cannot easily generate interference fringes with good contrast unless the optical path difference (OPD) is very small. This leads to another problem: how to get the equivalent wavelength of a broadband light source. For a monochromatic source, the OPD between adjacent fringes is one wavelength; but for a broadband light source which has a variety of wavelengths of light, we need to know which wavelength the OPD between adjacent fringes is equal to. The distribution of the Power Spectral Density (PSD) of the broadband source has a great influence on the value of the equivalent wavelength. For a symmetrical PSD, the equivalent wavelength is its center value; for a non-symmetrical PSD, the equivalent wavelength is not a fixed value which is related to the fringe order. For high-precision interferometry, the equivalent wavelength of such a source must be calculated precisely. In this paper, a formula for the equivalent wavelength of a non-symmetrical PSD of a broadband source is deduced. Because of the complexity of the formula, the relationship between optical path difference and equivalent wavelength is not very intuitive so that a lot of simulation calculations have been done. According to those simulation calculations: the equivalent wavelength of the zero-order fringe is the centroid wavelength of the broadband spectrum; within a range of OPD and with the increase of the fringe order, if the peak wavelength of the spectrum is greater than the centroid wavelength, the equivalent wavelength will increase; if the peak wavelength is less than the centroid wavelength, the equivalent wavelength will decrease; the narrower the spectral bandwidth is, the less obvious the change is.