We consider the Michelson set-up adjusted for the observation of fringes of equal thickness at the air wedge located between two mirrors. Usually the interferometer is illuminated by a point source at the focus of an objective lens, but here it is only replaced by a single mode fiber. The input ray is divided in two when it arrives on the semireflecting face of the beam splitter. The ray is individually reflected on the plane mirrors 1 and 2, returns and falls into the screen together. We can treat the two beams reflected from the two mirrors of the Michelson interferometer as one point source at distance h reflected from two layers with wedge inclination l and wedge gap d (Fig.2):

where q is the incident angle, l is the wavelength of the light source, and m is the fringe order. From d =d0 +x tana and cos q =

(d0 is the distance from the original point of the rectangular coordinate system on mirror 1' to the mirror 2, x,y is the rectangular coordinate values of the fringe location on the mirror 1') , we obtain the distribution of the fringe position:

In our experience, when the path-difference between two beams is small in a Michelson interferometer without a compensator plate a hyperbolic fringe appears. With the direction of the fringes movement toward four directions, the hyperbolic fringes bring multi-information and excellent sensitivity.

We can see if d0 is small and a is big enough, we obtain the hyperbolic curves[5].

In the computer simulation it's reasonable to try the original value m0 :

m0 @ 2 d0 / l , m0 is an integer,

and then the x-axis coordinate value x0 of the center point of the fringe pattern is given as:

x0=

From the value x0, we correct the value of fringe order m0 again:

m0 =2 (d0+ x0 tan a )/ l .

By repeating these steps, we can obtain the numerical solution of the center point of the fringes of a Michelson interferometer.

In the case where we don't use the compensation plate, the beam which passed through the beam splitter twice will shift a lateral displacement l:

l=t sin b [ 1 - ]

where,

b is the incident angle to the beam splitter,

t is the thickness of the beam splitter,

N is the refractive index.

Although there is the vibration problem of the fiber head but will not affect our measurement. From the above discussions we know the fringes are very sensitive to the relative motion of the two mirrors, but the slight movement of the light source will bring no influence on the fringes pattern. Here we only need to tilt the mirrors at each other to overlap the two beams to obtain the fringes. We can't avoid the hyperbolic fringes appearing if we adopt a Michelson interferometer without a compensation plate. The hyperbolic fringes yield at the same time that the two optical paths of two beams are very close, and the span of the fringes is big enough to distinguish.

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