Shearing interferometer

The shearing interferometer is a simple means to observe interference and to use this phenomenon to test the collimation of light beams, especially from laser sources which have a coherence length which is usually significantly longer than the thickness of the shear plate (see graphics) so that the basic condition for interference is fulfilled.

The shearing interferometer is a simple means to observe interference and to use this phenomenon to test the collimation of light beams, especially from laser sources which have a coherence length which is usually significantly longer than the thickness of the shear plate (see graphics) so that the basic condition for interference is fulfilled. With a plane wavefront incident, the overlap of the two reflected beams shows interference fringes with a spacing of d_f = \frac{\lambda}{2 n \theta} , where d_f is the spacing perpendicular to shear, \lambda is the wavelength of the beam, n the refractive index, and \theta the wedge angle. This equation makes the simplification that the distance from the wedged shear plate to the observation plane is small relative to the wavefront radius of curvature at the observation plane. The fringes are equally spaced and will be exactly perpendicular to the wedge orientation and parallel to a usually present wire cursor aligned along the beam axis in the shearing interferometer. The orientation of the fringes varies when the beam is not perfectly collimated. In the case of a noncollimated beam incident on a wedged shear plate, the path difference between the two reflected wavefronts is increased or decreased from the case of perfect collimation depending on the sign of the curvature. The pattern is then rotated and the beam's wavefront radius of curvature R can be calculated: R = -\frac{s \cdot d_f}{\lambda \tan \gamma} , with s the shear distance, d_f the fringe distance, \lambda the wavelength and \gamma the angular deviation of the fringe alignment from that of perfect collimation. If the spacing normal to the fringes is used instead, this equation becomes R = -\frac{s \cdot k_f}{\lambda \sin \gamma} , where k_f is the fringe spacing normal to the fringes.

See also

List of types of interferometers Air-wedge shearing interferometer Spectral phase interferometry for direct electric-field reconstruction, a type of spectral shearing interferometry, which is similar in concept to the one in the present article, except that the shearing is performed in the frequency domain instead of laterally.

References

University of Erlangen — Optical Design and Microptics

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