Expressions have been derived and calculations have been made which show that combined effects lead to asymmetric interferograms and reduction in power at zero path difference. Criteria are given for estimating maximum allowable mirror misalignment

Goorvitch, D.

Kunz, L. W.

English

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Deoember 1974	 B74-10246 
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Ames Research Center 
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Combined Effects of a Converging Beam of Light and 
Mirror Misalignment in Michelson Interferometry 
.
In work with a Michelson interferometer, it is de-
sirable to obtain maximum modulation of the fringes 
with respect to mirror position. However, there are 
two conditions when modulation is degraded: (1) the 
incident beam of light is convergent and (2) the 
mirrors on the interferometer are misaligned. Prior 
work has shown that each condition separately leads 
to symmetric interferograms with modulations less 
than 100%, but the effect produced when both con-
ditions exist simultaneously has not been reported.
optic axis to the intersection with M1. 
Expressions have been derived and calculations 
have been made which show that the combined effects 
lead to asymmetric interferograms and a reduction in 
the power at zero path difference. The maximum am-
plitude of the asymmetric part of the interferogram 
depends on a2/(f/)2. The quadratic dependence on 
a reflects the symmetry of the problem with respect 
to the sign of a. The dependence on / number is due 
to the fact that for a smaller / number a larger area 
of the misaligned mirror is used by the converging 
beam. There is then a greater path difference between 
the edges of the beam. 
Criteria are given for estimating the maximum al-
lowable mirror misalignment for a given / number 
and wave number. 
Reference: 
Kunz, L. W., and Goorvitch, D.: Combined Effects 
of a Converging Beam of Light and Mirror Misalign-
ment in Michelson Interferometry. Applied Optics, 
vol. 13, no. 5, p. 1077, 1974. 
The geometry of the problem for the combined 
effects of a converging beam of light at half-angle e 
and mirror misalignment a is shown in the diagram. 
M1 is the fixed mirror, M2 is the image of the moving 
mirror misaligned by an angle a from the position M2' 
parallel to M1. The distance from M1 to the focus is 
D. the distance of M 2 from the position of zero path 
difference is d, the polar coordinates of the intersec-
tion of the incoming ray of light with M2' are p and 
, and r is the distance of the incoming ray from the 
S
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Government nor any person acting on behalf of the United States
Note: 
No additional documentation is available. Specific 
questions, however, may be directed to: 
Technology Utilization Officer 
Ames Research Center 
Moffett Field, California 94035 
Reference: B74-10246 
Source: Louis W. Kunz and David Goorvitch
Ames Research Center 
(ARC-10889) 
Category 03 
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
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Combined effects of a converging beam of light and mirror misalignment in Michelson interferometry

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