Abstract: A method for measuring a position of an object, the method includes probing a sensing mark arranged in a first plane on a substrate to determine the position of the object, a portion of the substrate connecting the sensing mark to the object. An edge of the object can be sufficiently close to an edge of the sensing mark to reduce measurement errors in the position of the object caused by a deformation of the substrate.

Abstract: A method for measuring a position of an object, the method includes probing a sensing mark arranged in a first plane on a substrate to determine the position of the object, a portion of the substrate connecting the sensing mark to the object. An edge of the object can be sufficiently close to an edge of the sensing mark to reduce measurement errors in the position of the object caused by a deformation of the substrate.

Abstract: Disclosed is an apparatus including a mechanical reference frame and a rigid object mechanically coupled to the reference frame by two or more constraints. The stiffnesses of at least two of the constraints are different from one another, and the relative locations and stiffnesses of the constraints cause a designated point on the rigid object to remain stationary with respect to the reference frame during thermal expansion of the rigid object over a range of temperatures.

Abstract: Deformations of a surface of a test object can be measured by attaching mirrors to a surface of a test object, each mirror having a reflective surface with a dimension and a radius of curvature smaller than those of the surface of the test object. Light is directed towards the mirrors and a reference surface, and interference patterns are generated using light reflected from the mirrors and the reference surface. Changes in the surface of the test object are determined based on the interference patterns.

Abstract: Deformations of a surface of a test object can be measured by attaching mirrors to a surface of a test object, each mirror having a reflective surface with a dimension and a radius of curvature smaller than those of the surface of the test object. Light is directed towards the mirrors and a reference surface, and interference patterns are generated using light reflected from the mirrors and the reference surface. Changes in the surface of the test object are determined based on the interference patterns.

Abstract: An instrument for measuring dimensional changes in materials, such as ultra-low thermal expansion materials, contains an optically balanced measuring loop. Both an object beam and a loop beam propagate around the measuring loop. The object beam encounters both opposite side surfaces of the test object and the loop beam encounters remaining components of the measuring loop in common with the object beam. The object and loop beams can be separately compared to reference beams for producing heterodyne signal beams.

Abstract: Thermal expansion characteristics of test materials of ultra-low thermal expansion material are measured with a test beam that is split into a test material-measuring portion and an instrument-measuring portion. Both measuring portions propagate through common portions of a test arm. The test material-measuring portion encounters a test material, but the instrument-measuring portion does not. Thermal expansion characteristics of the test material are measured to high accuracy by manipulating the measures to distinguish displacements associated with the test material from displacements associated with the instrument structure.

Abstract: Rotational motions between a displacement-measuring probe and an optical test surface define a spherical or near spherical datum surface against which measurements of the probe are taken. The probe has a measurement axis that is maintained substantially normal to the optical test surface during the course of measurement.

Abstract: The invention features a phase measurement system for minimizing cyclic errors in a relative phase between exit reference and measurement beams emerging from an interferometer.