Abstract: In general, in one aspect, the invention features apparatus that include an interferometer including a main assembly having two laterally displaced polarizing beam splitter interfaces, wherein the interfaces are positioned to receive two spatially separated beams and direct them each to make at least two passes to one or more remote objects. Each interface reflects and transmits each beam at least once, and the interferometer is configured to combine the two beams after they make the at least two passes to the one or more remote objects to produce an output beam including information about an optical path length difference between paths traveled by the two beams.

Abstract: Methods and related systems for determining properties of optical systems (e.g., interferometers) and/or optical elements (e.g., lenses and/or lens systems) are described. For example, information related to an optical thickness mismatch of an interferometer can be determined by providing scanning interferometry data. The data typically include obtaining one or more interference signals each corresponding to a different spatial location of a test object. A phase is determined for each of multiple frequencies of each interference signal. The information related to the optical thickness mismatch is determined based on the phase for each of the multiple frequencies of the interference signal(s).

Abstract: A method for determining a spatial property of an object includes obtaining a scanning low coherence interference signal from a measurement object that includes two or more interfaces. The scanning low coherence interference signal includes two or more overlapping low coherence interference signals, each of which results from a respective interface. Based on the low coherence interference signal, a spatial property of at least one of the interfaces is determined. In some cases, the determination is based on a subset of the low coherence interference signal rather than on the entirety of the signal. Alternatively, or in addition, the determination can be based on a template, which may be indicative of an instrument response of the interferometer used to obtain the low coherence interference signal.

Abstract: In general, in one aspect, the invention features assemblies that include a first polarizing beam splitter positioned in the paths of a pair of initial beams, the polarizing beam splitter being configured to combine the pair of initial beams to form an input beam. The assemblies further include an interferometer positioned to receive the input beam and configured to produce an output beam that includes information about an optical path difference between the paths of two component beams derived from the input beam. A second polarizing beam splitter is positioned in the path of the output beam and configured to split the output beam into a pair of secondary output beams that each include information about the optical path difference between the component beam paths.

Abstract: An optical system includes a photolithography system, a low coherence interferometer, and a detector. The photolithography system is configured to illuminate a portion of an object with a light pattern and has a reference surface. The low coherence interferometer has a reference optical path and a measurement optical path. Light that passes along the reference optical path reflects at least once from the reference surface and light that passes along the measurement optical path reflects at least once from the object. The detector is configured to detect a low coherence interference signal including light that has passed along the reference optical path and light that has passed along the measurement optical path. The low coherence interference signal is indicative of a spatial relationship between the reference surface and the object.

Abstract: In general, in one aspect, the invention features a method that includes monitoring a position of a stage along a first measurement axis and a second measurement axis of a multi-axis interferometry system and determining a position of the stage with respect to another degree of freedom based on the monitored positions along the first and second axes and predetermined information about how the measurement axes deviate from being parallel to one another.

Abstract: An optical system includes a photolithography system, a low coherence interferometer, and a detector. The photolithography system is configured to illuminate a portion of an object with a light pattern and has a reference surface. The low coherence interferometer has a reference optical path and a measurement optical path. Light that passes along the reference optical path reflects at least once from the reference surface and light that passes along the measurement optical path reflects at least once from the object. The detector is configured to detect a low coherence interference signal including light that has passed along the reference optical path and light that has passed along the measurement optical path. The low coherence interference signal is indicative of a spatial relationship between the reference surface and the object.

Abstract: A method for determining a spatial property of an object includes obtaining a scanning low coherence interference signal from a measurement object that includes two or more interfaces. The scanning low coherence interference signal includes two or more overlapping low coherence interference signals, each of which results from a respective interface. Based on the low coherence interference signal, a spatial property of at least one of the interfaces is determined. In some cases, the determination is based on a subset of the low coherence interference signal rather than on the entirety of the signal. Alternatively, or in addition, the determination can be based on a template, which may be indicative of an instrument response of the interferometer used to obtain the low coherence interference signal.

Abstract: In one aspect, the invention features a method, including using an interferometer in an interferometry system to produce an output beam comprising a phase related to an optical path difference between a path of a first beam and a path of a second beam, wherein the first beam contacts a measurement object at a first location and the first or second beam contacts the measurement object at a second location, and wherein the first and second locations are different, providing precalibrated information that accounts for contributions to the optical path difference caused by a deviation of the path of the first or second beam from a nominal beam path due to an imperfection of the measurement object at the first location and due to an imperfection of the measurement object at the second location, and determining a position of the measurement object with respect to at least one degree of freedom based on information derived from the output beam and the precalibrated information.

Abstract: In general, in one aspect, the invention features an apparatus including a multi-axis interferometer configured to produce at least three output beams each including interferometric information about a distance between the interferometer and a measurement object along a corresponding measurement axis, wherein at least three of the measurement axes are in a common plane, wherein the output beams each include a component that makes a pass to the measurement object along a common beam path.

Abstract: In general, in one aspect, the invention features methods that include interferometrically monitoring a distance between an interferometry assembly and a measurement object along each of three different measurement axes while moving the measurement object relative to the interferometry assembly, determining values of a first parameter and a second parameter for different positions of the measurement object from the monitored distances, wherein for a given position the first parameter is based on the monitored distances of the measurement object along each of the three different measurement axes at the given position, and for a given position the second parameter is based on the monitored distance of the measurement object along each of two of the measurement axes at the given position, and deriving information about a surface figure profile of the measurement object from the first and second parameter values.

Abstract: In general, in one aspect, the invention features methods that include interferometrically monitoring a distance between an interferometry assembly and a measurement object along each of three different measurement axes while moving the measurement object relative to the interferometry assembly, determining values of a parameter for different positions of the measurement object from the monitored distances, wherein for a given position the parameter is based on the distances of the measurement object along each of the three different measurement axes at the given position, and deriving information about a surface figure profile of the measurement object from a frequency transform of at least the parameter values.

Abstract: A method including: (i) directing a beam to an interferometer head using an optical connection, the beam including a first beam component having a first polarization and a first frequency and a second beam component having a second polarization different from the first polarization and a second frequency; (ii) rotating the polarization of the first beam component to the second polarization; (iii) rotating the polarization of the second beam component to the first polarization; and (iv) returning the beam with the rotated polarizations from the interferometer head using the optical connection. For example, the step of directing may include: directing the first beam component into a first fiber of the optical connection; and directing the second beam component into a second fiber of the optical connection. The first beam component may be returned using the second fiber, and the second beam component may be returned using the first fiber.

Abstract: A method includes providing scanning interferometry data for a test object, the data including intensity values for each of multiple scan positions for each of different spatial locations of the test object, the intensity values for each spatial location defining an interference signal for the spatial location, the intensity values for a common scan position defining a data set for that scan position. The method includes providing a scan value for each scan position, wherein increments between the scan values are non-uniform, transforming at least some of the interference signals into a frequency domain with respect to the scan values, and determining information about the test object based on the transformed interference signals.

Abstract: Beam shearing apparatus for introducing a lateral shear between the components of a light beam. The apparatus is an optical assembly having a polarizing interface and input and output facets and two reflecting surfaces one of which is arranged at an angle generally opposite the input facet and the other of which is arranged at an angle generally opposite the output facet.

Abstract: In general, in one aspect, the invention features a method for determining the location of an alignment mark on a stage including measuring a location, x1, of a stage along a first measurement axis using an interferometry system, measuring a location, x2, of the stage along a second measurement axis parallel to the first measurement axis, and determining a location of the alignment mark along a third axis parallel to the first measurement axis based on x1, x2, and a correction term, ?3, calculated from predetermined information including information characterizing imperfections in the interferometry system determined using the interferometry system and the stage.

Abstract: A method including comparing information derivable from a scanning interferometry signal for a first surface location of a test object to information corresponding to multiple models of the test object, wherein the multiple models are parametrized by a series of characteristics for the test object. The information corresponding to the multiple models may include information about at least one amplitude component of a transform of a scanning interferometry signal corresponding to each of the models of the test object.

Abstract: In general, in one aspect, the invention features a method that includes directing a first measurement beam along a first path contacting a measurement object to determine a first interferometric phase related to a position of a measurement object, directing a second measurement beam along a second path contacting the measurement object to determine an second interferometric phase related to the position of the measurement object, and determining a contribution to the first interferometric phase due to perturbations in refractivity along the first path based on the second interferometric phase.

Abstract: In general, in a first aspect, the invention features a method for determining the location of an alignment mark on a stage, which includes directing a measurement beam along a path between an interferometer and a mirror, wherein at least the interferometer or the mirror is mounted on the stage, combining the measurement beam with another beam to produce an output beam comprising information about the location of the stage, measuring from the output beam a location, x1, of the stage along a first measurement axis, measuring a location, x2, of the stage along a second measurement axis substantially parallel to the first measurement axis, calculating a correction term, ?3, from predetermined information characterizing surface variations of the mirror for different spatial frequencies, wherein contributions to the correction term from different spatial frequencies are weighted differently, and determining a location of the alignment mark along a third axis parallel to the first measurement axis based on x1, x2,

Abstract: Spatial filtering of beams in interferometry systems is used to reduce a displacement of the beams from an optical path corresponding to the path of the beams in an optimally-aligned system. By reducing beam displacement from the optical path, the system reduces the magnitude of beam shears and associated non-cyclic errors in linear and angular displacements measured by the interferometry systems.