m . mm c __ EB 1 September 1995 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML OPTICS COMMUNICATIONS ELSEWIER Optics Communications 119 (1995) 352-360 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM Full length article Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer D.S. Mehta, H.C. Kandpal, K. Saxena, J.S. Vaishya, KC. Joshi zyxwvutsrqponmlkjihg Srandards Division, National Physical Laborutory. Dr. K.S. Krishnan Marg, New Delhi 110 012, India Received 24 January 1995; revised version received 27 Much 1995 Abstract The spectra1 changes arising due to interference between two partially correlated beams are investigated experimentally in a Mach-Zehnder interferometer. Two different schemes are used to produce two partially correlated beams. Experimental results obtained from these schemes are compared with the theory. It is shown that the spectral changes in the form of modulations in the superposed spectrum are dependent on the optical path difference of the two beams in the interferometer and can be utilized for determining linear displacements of a few microns. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. Introduction It is well known that interference of two beams with a narrow bandwidth light shows a periodic spatial var- iation of light intensity in the form of interference fringes, while with broad bandwidth light the interfer- ence shows periodic spectral modulations (i.e. modu- lations in the spectra), but in this case no interference fringes are formed [ I 1. The phenomenon of producing spectral modulations (also known as spectral interfer- ence fringes) as manifestations of temporal coherence with spatially coherent light has been given different names, e.g. Edser-Butler fringes [2,3] or channeled spectra [4] etc. The phenomenon of producing such spectral interference fringes has been studied in the framework of optical coherence theory [ 5,6] and it has been shown that the spectral analysis of light in the region of superposition in a two-beam interference experiment could provide information about spectral coherence properties of the light fields. Recently, the spectral interference effect has been studied in connec- tion with coherence-induced spectra1 changes known as the Wolf effect [7,8]. It has been shown 19,101 in the Young double slit interference experiment that the state of coherence of a light field over the plane of the double slit affects the spectrum of light in the region of superposition and can produce a shift in the central frequency for narrow bandwidth light or modulations of spectra in the case of broad bandwidth light. This effect has been verified experimentally ] 11,121. The implications of these spectral interference studies, such as determination of the intensity distribution across a source [ 131 and determination of the angular separa- tion between a pair of sources [ 14,151, have already been shown. A spectral interference law for two partially coherent light beams incident in aMach-Zehnder interferometer has been derived and has been used to illustrate the spectral changes arising due to interference between the two beams [ 161. It has also been shown theoreti- cally that the spectrum of superposed light at some fixed point shows modulations in the spectra depending on the degree of spectral coherence existing between the two beams. It has further been suggested that the real 0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOO30-4018(95)00329-O