MÖBIUS BAND INTERFEROMETER AND ITS APPLICATION TO FOURIER SPECTROSCOPY

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Submitted on 1 Jan 1967

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MÖBIUS BAND INTERFEROMETER AND ITS

APPLICATION TO FOURIER SPECTROSCOPY

J. Pritchard, H. Sakai, W. Steel, G. Vanasse

To cite this version:

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MOBIUS

BAND

INTERFEROMETER

AND ITS APPLICATION TO FOURIER SPECTROSCOPY

(*)

J. L. PRITCHARD

Idealab, Inc., Franklin, Massachusetts, U. S. A.

and

H. SAKAI, W. H. STEEL (**) and G. A. VANASSE Optical Physics Laboratory

Air Force Cambridge Research Laboratories (0. A.

R.)

L. G. Hanscom Field, Bedford, Mass., U. S. A.

Rksume. - En spectroscopie de Fourier une rotation du plan d'onde pendant l'enregistrement de l'interfkrogramme donne naissance a une structure erronnke dans le spectre. I1 est souhaitable de rkaliser un interfkrometre automatiquement compensk de l'effet d'une rotation. Un prockdk de compensation consiste a tordre le faisceau dans l'interfkrombtre comme un ruban de Mobius. Cet article dkcrit les details de construction d'un interferometre de Mobius et les rksultats d'essais sur la qualitk de la compensation. Cet interfkrombtre est aussi entierement protege contre les defauts dus a la polarisation qui existent en gknkral dans les configurations d'interfkrometres a trois dimensions.

Abstract. - 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 t o 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 t o 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.

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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 accom- panied 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

y = 6 0 . (2)

Polarization Compensation. - The state of polarization through the interferometer is characterized

polarization effects, the matrix for each arm A , and A, must be connected with an identity relation

A , = A,. (3) Each matrix consists of a product of three matrices :

where T and R represent the transmission and reflec- tion matrices at the beam splitter. Since both matrices are diagonal, the matrix B, the polarization matrix in each arm, is required to be diagonal ; besides the condition

Generally the interferometer in the three-dimensional configuration does not satisfy these two conditions, even if it satisfies eqn. (5). When in such an interferometer, the direction at any part of the beam in each arm is either normal or parallel to the plane of incidence, those two conditions can be satisfied and the interferometer is fully compensated for polarization effects. The contrast in the fringe system obtained in such an interferometer becomes independent of the state of polarization of the incident radiation. The Mobius interferometer of figure 1 is designed according to the polarization compensation condition.

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C 2

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94 J. L. PRITCHARD, H. SAKAI, W. H. STEEL AND G. A. VANASSE of the optics is minimized after it is once set in align-

ment. The interferometer and its housing is shown in figure 3.

The mirror pairs (retroreflectors) 5-7 and 6-8, are aligned using an autocollimator to within a few seconds of arc. The pair is mounted on a base plate and aligned as a unit. The pair, 5-7, is designed to give a lateral shift and the pair 6-8 to produce a rotation about the line joining its center. These adjustments are necessary to introduce the correct twist in the beams.

The double surface center mirror 9 is made of Pyrex. Both surfaces are parallel within 2 minutes of arc. On one surface of mirror 9 are engraved marks t o check the relative twist of the beams. These are shown in figure 4 including mirror dimensions.

The driving assembly is shown in figure 5. The motor is magnetic and its motion is servoed with a solid-state control unit. Thus it can be manually operated or automatically sweeped with a wide range of length of stroke (+ .500 cm at maximum) and speed. The mirror and its mount are attached on the carriage which slides on the V-shape grooves through super-accurate ball bearings. This type of mechanical assembly with carefully lapped V-shape grooves and good ball bearings can, according to our expe- rience, maintain a tilt error of less than a second of arc. But for the present purpose, such high accuracy is not necessary. The one used in this interferometer has a tilt measured to be about 7 seconds of arc from one end of the stroke to the other.

All optical surfaces are set mechanically to be close to their proper orientation. Then the mirror pair, either 1-2 or 3-4, is adjusted to obtain circular Hai- dinger fringes. This is quite similar to aligning a regular Michelson interferometer. The twist of the beam is then adjusted looking a t the fiduciary marks engraved on the central mirror 9. Figure 6 is a photo- graph of these marks.

With this accuracy in the beam twist, the interferometer achieved excellent tilt compensation. Figure 7 shows the Fizeau fringes obtained at various path differences. To observe these fringes, the interferometer was slightly misaligned. No noticeable change is seen in the spacing of these fringes, which indicates two wavefronts having the same inclination throughout the entire path difference. Thus the interferometer illuminated with a narrow spectral line is expected to give the circular Haidinger fringes of good visibility throughout the entire path difference. This is seen in the set of fringe photographs taken with a green mercury line of 5 461

A

(Fig. 8). The result

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SC 2

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96 J. L. PRITCHARD, H. SAKAI, P i . H. STEEL AND G. A. VANASSE

radiation. The test was performed using the green mercury line. The measured visibility, unpolarized or polarized, was the same within the experimental error. The visibility itself in the vicinity of zero path difference was found rather poor, probably due to a strong scattering observed from the beam splitter. Also it was noticed that the transmission of the radiation through the interferometer is strongly polarization dependent because of the beam splitter and compensator. With respect to the plane of incidence to the interferometer, the parallel component is observed to be three times more intense than the perpendicular component.

Future usage of this interferometer in Fourier spectroscopy is planned in the near infrared region. At this moment, no spectra have been analysed with this instrument. Since the technique to be used is standard in this measurement, we do not wish to cover this subject any further. Figure 9 shows the interferogram of a tungsten incandescent lamp obtained using

a silicon photoconductive diode detector I N 2175 in the vicinity of zero path difference, as an example. The interferogram shows good symmetry obtained adjusting the compensator orientation.

Conclusion. - The Mobius interferometer described in this paper is found rather easy to align, even though it is slightly more complicated than the ordinary Michelson interferometer. The complexity in the alignment due to the twist adjustment is definitely not great enough to cancel the gain achieved in the tilt compensation. Small error in the twist of the beams is not effective at all, as eqn. (2) indicates. That is to say that with careful machining the interferometer is easy to align, and that it is very practical to use. The polarization effect, which may reduce the contrast without proper compensation against it, is negligible in this interferometer of rather complex structure.

Bibliographie

111 PECK (E. R.), J. Opt. SOC. Amer., 1948, 38, 66, 1015. [2] SCOTT (L. B.), U. S. Patent, 2, 841, 049.

[3] CONNES (P.), Lecture given at AFCRL, 1965. [4] STEEL (W. F.), Optica Acta, 1964, 11, 211.

INTERVENTION