An interferometer apparatus comprises an adjustable birefringent device configured to receive an input radiation and produce corresponding replicas having reciprocally orthogonal polarizations and delayed from each other by an adjustable time delay. The birefringent device also introduces an additional time delay between the replicas. The interferometer apparatus also comprises a compensation optical device optically coupled to the adjustable birefringent device and configured to have a respective structural thickness and respective ordinary and extraordinary refractive indexes to introduce a compensation time delay between the replicas having a sign opposite to a sign of the additional time delay.

A displacement detection apparatus can reduce a measurement error even when a diffraction grating is displaced and/or tilted to a direction other than the measurement direction. A displacement detection apparatus includes a light source which emits light, a luminous flux-splitting section, a diffraction grating, a diffracted light-reflecting section, a correcting lens, a luminous flux-coupling section, and a light-receiving section. The diffracted light-reflecting section reflects a first luminous flux and a second luminous flux so as to be perpendicular to one of measuring planes of the diffraction grating and be parallel to each other. The correcting lens is arranged between the diffracted light-reflecting section and the diffraction grating.

A position measurement system includes an interferometer to determine a position of an object. The interferometer is arranged to generate a first, second and third signals representative of the position by irradiating respective first, second and third areas of a reflective surface of the object. Along a line, the first and second areas are at a first distance relative to each other, the second and third areas are at a second distance relative to each other, and the first and third areas are at a third distance relative to each other. The interferometer is arranged to provide a rotation signal representative of a rotation of the object along an axis based on the first, second and third signals. The axis is parallel to the reflective surface and perpendicular to the line.

An atomic interferometer and methods for measuring phase shifts in interference fringes using the same. The atomic interferometer has a laser beam traversing an ensemble of atoms along a first path and an optical components train with at least one alignment-insensitive beam routing element configured to reflect the laser beam along a second path that is anti-parallel with respect to the first laser beam path. Any excursion from parallelism of the second beam path with respect to the first is rigorously independent of variation of the first laser beam path in yaw parallel to an underlying plane.

A method, an interferometer, and a signal processing device, each for determining an input phase and/or an input amplitude of an input light field, are disclosed. Here, an input light field is divided into a first light field and a second light field by amplitude splitting. The first light field and the second light field are propagated such that the propagated second light field is defocused relative to the propagated first light field. The propagated first light field is superimposed on the propagated light field and caused to interfere.

A method, an interferometer, and a signal processing device, each for determining an input phase and/or an input amplitude of an input light field, are disclosed. Here, an input light field is divided into a first light field and a second light field by amplitude splitting. The first light field and the second light field are propagated such that the propagated second light field is defocused relative to the propagated first light field. The propagated first light field is superimposed on the propagated light field and caused to interfere.

A laser heterodyne interferometric straightness measurement apparatus and method with six DOFs determination includes a part for determining the straightness and its position based on laser heterodyne interferometry and a part for error determination and compensation. The optical path for determination of four DOFs errors including three common beam-splitters, a polarizing beam-splitter, a planar mirror, a convex lens, a position-sensitive detector and two quadrant detectors is added in the optical configuration of the part for determining the straightness and its position based on laser heterodyne interferometry.

The present invention provides a measurement apparatus for measuring a position of an object, comprising a reflecting portion provided on the object and having a surface on which reflectors configured to retroreflect light are arrayed, an optical system configured to cause first light to be incident on the surface, receive second light as reflected light of the first light, cause third light generated from the second light to be incident on the surface, and receive fourth light as reflected light of the third light, and a processor configured to determine the position of the object based on a detection result of the forth light, wherein the optical system is configured such that a displacement between optical paths of the first light and the second light is corrected by a displacement between optical paths of the third light and the fourth light.

In a method for characterizing the surface shape, the following steps are carried out iteratively: (A) calculating a first figure based on first measurements; (B) subtracting the first figure from first measured values, to determine a first test set-up error; (C) using the first test set-up error for calculating a corrected first figure,; (D) subtracting the corrected first figure from second measured values, to determine a second test set-up error; (E) using the second test set-up error for calculating a corrected second figure; (F) using the corrected second figure for correcting the first test set-up error by subtracting the corrected second figure from the first measured values, to determine a corrected first test set-up error; (G) using the corrected first test set-up error for calculating a first figure corrected once again; and (H) comparing the result with a convergence criterion and optionally repeating steps (A) to (H).

In a method for characterizing the surface shape, the following steps are carried out iteratively: (A) calculating a first figure based on first measurements; (B) subtracting the first figure from first measured values, to determine a first test set-up error; (C) using the first test set-up error for calculating a corrected first figure,; (D) subtracting the corrected first figure from second measured values, to determine a second test set-up error; (E) using the second test set-up error for calculating a corrected second figure; (F) using the corrected second figure for correcting the first test set-up error by subtracting the corrected second figure from the first measured values, to determine a corrected first test set-up error; (G) using the corrected first test set-up error for calculating a first figure corrected once again; and (H) comparing the result with a convergence criterion and optionally repeating steps (A) to (H).