Why are Localized Fringes Curved in a Michelson Interferometer Experiment?

[spadille]

hi everyone,
can anyone explain why localised fringes are curved in michelson interferometer experiment with a monochromatic light used, when the mirrors are held not exactly perpendicular to each other and there is wedge formation.

 

[jtbell]

In general, the interference pattern of a Michelson interferometer consists of concentric circles, and the viewing screen shows only a small part of the pattern. When the mirrors are exactly perpendicular, the center of the circles is at the center of the screen. When the mirrors are not perpendicular, the center of the circles is beyond the edges of the screen.

[added] Actually, this is only an approximate description, which is pretty good when the mirrors are nearly perpendicular. For a more complete description see here for example:

http://www.phy.davidson.edu/stuhome/cabell_f/diffractionfinal/pages/Michelson.htm

 

[Andy Resnick]

Hang on there- the fringes are concentric circles (etc...) if the wavefront entering the device is diverging/converging. It's possible to have linear fringes (flat wavefront, mirrors tilted with respect to each other) or all kinds of oddball shapes which reflect the aberrations/Zernike polynomials present in the wavefront:

http://en.wikipedia.org/wiki/File:Zernike_polynomials2.png

Evaluating these types of fringes are important in terms of lens testing/assembly.

 

[spadille]

thanx Andy and jtbell..

 

[JJThompson]

Your source it too close to the beam splitter. You said “localized fringes” so you must be using an extended source. You must be viewing the fringes through a telescope or other imaging arrangement to view the image which is located on the surface of the beam splitter (Born and Wolf, 6th edition, p301).

When viewed through a lens, an extend source produces the same fringe pattern as a point source. (Imagine the extended source being imaged with pin-hole lens on an image plane. Only one ray from each point of the source reaches the image plane, except those destructively interfered in the interferometer.)

Straight fringes are produced by plane-wave light as produced by a laser or a point source located a long way away. If you focused your laser beam, the image will be located at the focal point. To get plane wave light the image (or light source) has to be a long way away.

You could look at http://www.colorado.edu/physics/phys5430/phys5430_sp01/PDF%20files/Michelson%20Interferometer.pdf, p5.7. For non curved fringes rp would tend to infinity which would happen if ds were very large.