Systems and methods for unwrapping a phase map are disclosed. Such systems and methods may include receiving a wrapped phase map associated with an interferometric measurement of a sample including patterned features; removing a tilt from the wrapped phase map; generating a background; detecting features in the wrapped phase, the features in the wrapped phase map corresponding to least some of the patterned features of the sample; replacing phases of the features with the background at corresponding locations in the wrapped phase map; unwrapping the modified wrapped phase map using a global phase-unwrapping; applying local phase-unwrapping to restore the phases of the features; and reapplying the tilt to generate an output unwrapped phase map.

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).

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 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.

An interferometer includes a light source, a beam splitter, a reference reflector, a measuring reflector, a detection unit, and at least two transparent plane-parallel plates. The beam splitter splits a beam of rays into at least one measuring beam and at least one reference beam. Until being recombined, the measuring beam propagates in a measuring arm, and the reference beam propagates in a reference arm. The reference beam falls at least three times on the reference reflector located in the reference arm. The measuring reflector is disposed in the measuring arm and is joined to an object to be measured, which is movable along a measuring direction relative to the reference reflector. The measuring beam falls at least three times on the measuring reflector. At least one distance signal with regard to the position of the object to be measured is ascertainable from the interfering measuring and reference beams via the detection unit. The plane-parallel plates are disposed parallel to each other in the beam path between the light source and the detection unit. At least the measuring reflector is movable relative to the plane-parallel plates along the measuring direction. The plane-parallel plates each include a plurality of optical elements that exert such an optical effect on the measuring beam and the reference beam that they propagate parallel to each other in the direction of the measuring reflector and reference reflector, respectively.

A light detecting module that detects interference light that has exited an exit end surface of an optical fiber in an OCT instrument includes: a ball lens including an incident surface entered by the interference light that has exited the exit end surface, and an exit surface exited by the interference light that has entered the incident surface; and a photodiode including a detecting surface entered by the interference light that has exited the exit surface. The interference light obliquely enters the incident surface with respect to a perpendicular line at an incident position of the interference light. The interference light obliquely exits the exit surface with respect to a perpendicular line at an exit position of the interference light. The interference light obliquely enters the detecting surface with respect to a perpendicular line at an incident position of the interference light.

A device for interferential distance measurement between two objects that are situated in a movable manner with respect to each other along at least one shifting direction includes at least one light source as well as at least one splitting element, which splits a beam of rays emitted by the light source at a splitting location into at least two partial beams that propagate onward at different angles. The device furthermore includes at least one deflecting element that effects a deflection of the incident partial beams in the direction of a merging location, where the split partial beams are superimposed in an interfering manner and the optical paths of the partial beams of rays between the splitting location and the merging location being arranged such that the traversed optical path lengths of the partial beams between the splitting location and the merging location are identical in the event of a change of distance between the two objects. Furthermore, at least one detector system is provided for detecting distance-dependent signals from the superimposed pair of interfering partial beams.

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 conversion unit converts a first electrical signal to a first distance value indicating a distance from an interferometer to a measurement target. An inclination value calculation unit calculates an inclination value based on the first distance value. A first distance value correction unit corrects the first distance value based on the inclination value. A second distance value correction unit calculates a second distance value indicating a distance from the optical interference range sensor to the measurement target based on the first distance value that has been corrected by the first distance value correction unit. If the number of times that the first electrical signal is detected is smaller than a second threshold, the first distance value correction unit corrects the first distance value based on an inclination value that precedes the inclination value associated with the first distance value in a storage unit.