Möbius Band Interferometer and Its Application to Fourier Spectroscopy

In Fourier spectroscopy a tilting of the wavefront while the interferogram is being recorded gives rise to false structure in the computed spectrum. It is desirable to automatically tilt compensate the interferometer. One of the compensation schemes is to form a Mobius band through the interferometer. This paper discusses details of the construction of a Mcibius interferometer and test results of its compensation property. This interferometer is also fully corrected against polarization defects which exist generally in the three dimensional interferometer configuration. When the ordinary Michelson interferometer is used in Fourier Spectroscopy, a false interferogram is frequently obtained due to a misalignment of the movable mirror from its proper orientation, a tilt. Automatic compensation of this tilt can be achieved using several optical devices [I-31. The Mobius band interferometer to be described in the present paper has a property of compensating for this tilt as well as for polarization effect [4]. Figure 1 is a schematic of the interferometer optics. The mirror pairs, 5-7 and 6-8, form the retroreflecting system. The orientation of both beams can be adjusted so that they come normal to either sides of the mova(*) This work was supported by the Laboratory Directors Fund, AFCRL. (**) Present address : National Standards Laboratory. Chippendale, N. S. W., Australia. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1967219 C 2 9 2 J. L. PRITCHARD, H. SAKAI, W. H. STEEL AND G. A. VANASSE ble double surface mirror 9. Both beams are twisted 180° with respect to each other on the face of this mirror, completing the Mobius band through the interferometer. Tilt Compensation. When the mirror is tilted from the proper orientation, a displacement at a point on the mirror surface from its original position becomes complimentary to that at the opposite point about the center of the mirror surface. Thus a tilting of the wavefront from one face of mirror 9 is accompanied by an identical tilt of the wavefront on the opposite face of mirror 9 when both beams are twisted 180° ; this results in perfect tilt compensation. When the twist is other than 1800, the compensation becomes less perfect. Both wavefronts make the same amount of polar angle displacement from the original, but their azimuth angles are now different. Figure 2 shows the resultant angular displacement y between the wavefronts for a tilt 6 when the relative twist of the two beams is 1800 f 0. From the spherical triangle defined by 6 and 8, the angle y is obtained as cos y (cos 6)' + (sin 6)' cos 6 . (1) Since we may assume small angles, the resultant angular displacement cp is given by