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: 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: 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.

Abstract: An interferometric method including: generating a variable frequency source beam; from the source beam, generating a collimated beam propagating at an angle ? relative to an optical axis; introducing the collimated beam into an interferometer that includes a reference object and a measurement object, wherein at least a portion of the collimated beam interacts with the reference object to generate a reference beam, at least a portion of the collimated beam interacts with the measurement object to generate a return measurement beam, and the reference beam and the return measurement beam are combined to generate a combined beam; causing the angle ? to have a first value and at a later time a second value that is different from the first value; and causing the variable frequency F to have a first value that corresponds to the first value of the angle ? and at the later time to have a second value that corresponds to the first value of the angle ?.

Abstract: Methods and systems for determining information about the incident angle of a beam are disclosed, the method including directing a beam having an s-polarized component and a p-polarized component to reflect from an interface at a non-normal angle, where the non-normal reflection introduces for each component a phase change upon reflection that is different for each component, and measuring an optical interference signal related to the phase change between the components of the reflected beam.

Abstract: An interferometry system includes an interferometer to split an input beam into a measurement beam and at least one other beam. The interferometer directs the measurement beam along a measurement path that includes at least two passes to a measurement object, and overlaps the measurement beam with the other beam after the measurement beam completes the at least two passes. The path of the measurement beam is sheared during the first and second passes when the measurement object moves along a direction orthogonal to a portion of the measurement path that contacts the measurement object. The interferometry system includes optics to redirect the measurement beam after the first pass and before the second pass so that shear imparted during the second pass cancels shear imparted during the first pass.

Abstract: A wavefront interferometry system including: a wavefront interferometer that during operation combines a reference beam from a reference object and a measurement beam from a measurement object to generate a combined beam; and a processor system programmed to processes the combined beam to concurrently generate therefrom a control signal and information about the difference in wavefront profiles of the reference and measurement objects, wherein the control signal controls a system parameter so as to maintain an optical path length difference between a spot on the reference object and a corresponding spot on the measurement object at a constant value mod 2?.

Abstract: A method of operating a wavefront interferometry system that generates an array of interference signals that contains information about relative wavefronts of measurement and reference beams, the method involving: from the array of interference signals, computing a first array of phase measurements for a first time and a second array of phase measurements for a second time; computing a difference of the first and second arrays of phase measurements to determine an array of rates of phase changes; and from the array of rates of phase changes, computing an array of atmospheric turbulence effect values which is a measure of atmospheric turbulence effects in the wavefront interferometry system.

Abstract: In general, in one aspect, the invention features an interferometer assembly for use in a lithography tool used for fabricating integrated circuits on a wafer, wherein the lithography tool includes a support structure and a stage for positioning the wafer relative to the support structure, the interferometer assembly including an interferometer configured to direct a measurement beam between the stage and the support structure and combine the measurement beam with another beam to form an output beam which includes a phase related to a position of the stage relative to the support structure, wherein the interferometer is mechanically secured to the lithography tool through an interferometer surface selected to cause the phase of the output beam to be insensitive to thermal changes of the interferometer over a range of temperatures.

Abstract: An interferometric system including: an interferometer that directs a measurement beam at an object point to produce a return measurement beam, focuses the return measurement beam to an image point in an image plane, and mixes the return measurement beam with a reference beam at the image point to form a mixed beam; a beam combining layer located at the image plane which is responsive to the mixed beam and produces an optical beam therefrom, wherein the layer comprises a thin film with an array of transmissive openings formed therein and further comprises a fluorescent material associated with each of the openings of the array of openings; a detector that is responsive to the optical beam from the beam combining layer; and an imaging system that directs the optical beam from the beam combining layer onto the detector.

Abstract: In certain aspects, the invention features interferometry systems that include an input assembly positioned to receive a beam emitted from a light source comprising a first component beam and a second component beam, the input assembly being configured to change a dimension of one of the component beams relative to the dimension of the other component beam, an interferometer positioned to receive the component beams propagating from the input assembly, the interferometer being configured to direct the component beams along different paths and to produce an output beam by directing the component beams along a common path, wherein the output beam comprises information about an optical path difference between the different component beam paths, and an output assembly positioned in the path of the output beam and configured to change a dimension of the component beam that contacts the measurement object.

Abstract: An external cavity structure including: a light source for generating a light beam; a dispersive system which in combination with the light source defines a cavity, the dispersive system for directing a selected wavelength of the light beam back into the light source, the dispersive system including a grating for selecting said wavelength of the light beam; and a beam-conditioner positioned within the cavity along a light path between the light source and the dispersive system, the beam conditioner including a beam deflecting element for changing the direction of propagation of the light beam as that light beam that travels between the light source and the dispersive system.

Abstract: An interference signal S(t) is provided from interference between two beams directed along different paths. The signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time. An error signal is provided to reduce errors in an estimate of {tilde over (L)}(t). The error signal is derived at least in part based on one or more collective properties of a distribution of multi-dimensional values. At least one of the multi-dimensional values in the distribution is generated from a plurality of samples of the signal S(t) (e.g., samples of the signal captured at different times).

Abstract: In general, in one aspect, the invention features interferometry systems that include an interferometer configured to direct a first beam and a second beam derived from common light source along different paths and to combine the two beams to form an output beam including information related to an optical path difference between the different paths, wherein the path of the first beam contacts a measurement object. The interferometry systems also include an afocal system positioned in the path of the first beam and configured to increase a dimension of the first beam as it propagates from the interferometer towards the measurement object and reduces the dimension of the first beam as it returns from the measurement object propagating towards the interferometer.

Abstract: Apparatus and methods for in situ and ex situ measurements of spatial profiles of the modulus of the complex amplitude and intensity of flare generated by an optical system. The in situ and ex situ measurements comprise interferometric and non-interferometric measurements that use an array of diffraction sites simultaneously located in an object plane of the optical system to increase signals related to measured properties of flare in a conjugate image plane. The diffraction sites generate diffracted beams with randomized relative phases. In general, the interferometric profile measurements employ phase-shifting point-diffraction interferometry to generate a topographical interference signal and the non-interferometric measurements are based on flare related signals other than topographic interference signals.