shearing interferometer

The testing device consists of a high-quality optical glass, like N-BK7, with extremely flat optical surfaces that are usually at a slight angle to each other. When a plane wave is incident at an angle of 45°, which gives maximum sensitivity, it is reflected two times. The two reflections are laterally separated due to the finite thickness of the plate and by the wedge. This separation is referred to as the shear and has given the instrument its name. The shear can also be produced by gratings.

Parallel-sided shear plates are sometimes used, but the interpretation of the interference fringes of wedged plates is relatively easy and straightforward. Wedged shear plates produce a graded path difference between the front and back surface reflections; as a consequence, a parallel beam of light produces a linear fringe pattern within the overlap.

With a plane wavefront incident, the overlap of the two reflected beams shows interference fringes with a spacing of $d\_f\; =\; \backslash frac\{\backslash lambda\}\{2\; n\; \backslash theta\}$, where $d\_f$ is the spacing perpendicular to shear, $\backslash lambda$ is the wavelength of the beam, n the refractive index, and $\backslash theta$ 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: $R\; =\; -\backslash frac\{s\; \backslash cdot\; d\_f\}\{\backslash lambda\; \backslash tan\; \backslash gamma\}$, with $s$ the shear distance, $d\_f$ the fringe distance, $\backslash lambda$ the wavelength and $\backslash gamma$ 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 $R\; =\; -\backslash frac\{s\; \backslash cdot\; k\_f\}\{\backslash lambda\; \backslash sin\; \backslash gamma\}$, where $k\_f$ is the fringe spacing normal to the fringes. {{Cite journal|url = https://www.osapublishing.org/ao/abstract.cfm?uri=ao-16-10-2753|title = Laser Beam Divergence Utilizing a Shearing Interferometer|last = Riley|first = M|date = 1977|journal = Applied Optics|doi = 10.1364/AO.16.002753|pmid = 20174226|volume=16| issue=10 |pages=2753–6|bibcode =1977ApOpt..16.2753R|url-access = subscription}}

Image:Shear-plate sideview with English text.png

• 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.

{{Reflist}}

• [http://www.optik.uni-erlangen.de/odem/index.php?lang=e&type=10&topic=shear University of Erlangen — Optical Design and Microptics] {{Webarchive|url=https://web.archive.org/web/20160222144055/http://www.optik.uni-erlangen.de/odem/index.php?lang=e&type=10&topic=shear |date=2016-02-22 }}

Category:Interferometers