Abstract: In general, in one aspect, the invention features a system including a light source, a plurality of interferometers configured to receive light from the light source and to form output light, each interferometer including a first optic and a second optic, the first and second optics configured to be mounted on a first object and a second object, respectively, where first object is moveable with respect to the second object, the first and second optics being configured introduce an optical path length difference (OPD) between two components of the light to form the output light, the OPD being related to the position of the first optic with respect to the second optic.

Abstract: The disclosure features multiple degree-of-freedom interferometers (e.g., non-dispersive interferometers) for monitoring linear and angular (e.g., pitch and/or yaw) displacements of a measurement object with compensation for variations in the optical properties of a gas in the interferometer measurement (and/or reference) beam paths. The disclosure also features interferometry systems that feature an array of interferometers (e.g., including one or more multiple degree-of-freedom interferometer), each configured to provide different information about variations in the optical properties of the gas in the system. Multiple degree-of-freedom interferometers are also referred to as multi-axis interferometers.

Abstract: An optical component has a coating including one or more layers at each reflecting surface. The coating causes the optical component to have polarization eigenstates that are substantially linear and to have the properties of a half-wave plate. The coated optical component can be used in interferometry and microlithography system.

Abstract: In general, in a first aspect, the invention features a lithography system that includes a stage for supporting a wafer, an illumination system including a radiation source and a lens assembly, wherein the illumination system is configured to direct radiation through a mask to produce spatially patterned radiation, and the lens assembly is configured to image the spatially patterned radiation onto the wafer, a first interferometry system configured to monitor a location of the stage within the lithography system as the stage moves relative to the illumination system, a second interferometry system configured to identify an alignment feature on a surface associated with the stage, and an electronic controller coupled to the interferometry systems, wherein the electronic controller is configured to determine information about a location of the stage when the alignment feature is identified.

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. The methods also include monitoring an orientation angle of the measurement object with respect to a rotation axis non-parallel to the three different measurement axes while the measurement object is moving, 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: Apparatus and methods for adjusting the polarizations of the components of an input beam to reduce leakage caused by imperfections in an interferometer are disclosed. The apparatus includes an interferometer positioned to receive an input beam that includes two components having different frequencies and different polarizations, the interferometer including a polarizing beam splitter positioned to spatially separate the input beam into two intermediate beams, the first intermediate beam corresponding to the first component and the second intermediate beam corresponding to the second component, where imperfections in the interferometer cause leakage of one of the components into the intermediate beam corresponding to the other of the components. The apparatus further includes a polarization compensator that includes at least one retardation plate positioned to adjust the polarizations of the components of the input beam to reduce the leakage caused by the imperfections in the interferometer.

Abstract: Disclosed is an apparatus which includes: an interferometer configured to direct broadband spatially coherent test light to a test surface of a test object over a range of illumination angles and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source; and multi-element detector; and one or more optics configured to direct at least a portion of the combined light to the detector so that different elements of the detector correspond to different illumination angles of a region of the test surface illuminated by the test light.

Abstract: In general, in a first aspect, the invention features a method that includes using an interferometry assembly to provide three different output beams, each output beam including an interferometric phase related to an optical path difference between a corresponding first beam and a corresponding second beam, each first beam contacting a measurement object at least once, monitoring the interferometric phases for each of the three different output beams, and deriving information about variations in the optical properties of a gas in the first beam paths from the three monitored phases.

Abstract: Techniques for compensating for geometric effects of beam misalignment in plane mirror interferometers are disclosed.

Abstract: A method for determining a surface profile of an object is described. The method typically includes providing a surface profile (e.g., a height profile) of a test object measured by an interferometric profiler. Information related to field- and object orientation-dependent systematic errors of the interferometric profiler is provided. The surface profile is corrected based on the field- and orientation-dependent errors. Also described is a method for determining the field- and orientation-dependent errors of a profiler.

Abstract: In general, in a first aspect, the invention features methods that include deriving a first beam and a second beam from an input beam and directing the first and second beams along different paths, where the path of the first beam contacts a measurement object, producing an output beam comprising a phase related to an optical path difference between the different beam paths, determining a position of the measurement object with respect to at least one degree of freedom based on information derived from the output beam, monitoring variations in a direction of the input beam, and using the monitored variations in the direction of the input beam to reduce errors in the determined position associated with deviations of the path of the input beam from a nominal input beam path.

Abstract: A two-corner retroreflector that includes a common face positioned to receive two beams and two corners each positioned to receive one of the beams and retro-reflect it back through the common face.

Abstract: Disclosed is an interferometry analysis method that includes comparing information derivable from multiple interferometry signals corresponding to different surface locations of a test object to information corresponding to multiple models of the test object, wherein the multiple models are parameterized by a series of characteristics that relate to one or more under-resolved lateral features of the test object; and outputting information about the under-resolved surface feature based on the comparison.

Abstract: A method including: providing a low coherence scanning interferometry data for at least one spatial location of a sample having multiple interfaces, wherein the data is collected using a low coherence scanning interferometer having an illumination geometry and an illumination frequency spectrum, and wherein the data comprises a low coherence scanning interferometry signal having multiple regions of fringe contrast corresponding to the multiple interfaces; and determining a distance between at least one pair of interfaces based on a distance between the corresponding regions of fringe contrast and information about the illumination geometry.

Abstract: In general, in one aspect, the invention features a method that includes transforming interferometry data acquired for a test sample using a low coherence imaging interferometry system to a frequency domain and, at a plurality of frequencies in the frequency domain, reducing contributions to the transformed interferometry data due to imperfections in the imaging interferometry system thereby producing compensated interferometry data. The errors are reduced based on variations between interferometry data acquired using the low coherence imaging interferometry system for a calibration sample and model interferometry data corresponding to data acquired for the calibration sample using a model interferometry system.

Abstract: Scanning interferometry data for a test object is provided, the data typically 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 define an interference signal for the spatial location, and the intensity values for a common scan position define a data set for that scan position. Scan values are provided for each scan position, in which scan value increments between various scan values can be non-uniform. Information is determined about the test object based on the scanning interferometry data and scan values. The determination includes transforming at least some of the interference signals into a frequency domain with respect to the scan values.

Abstract: Methods and systems are disclosed for analyzing a scanning interferometry signal. A scanning interferometry signal is provided that is produced by a scanning interferometer for a first location of a test object (e.g., a sample having a thin film). A model function of the scanning interferometry signal is provided which is produced by the scanning interferometer. The model function is parametrized by one or more parameter values. The model function is fit to the scanning interferometry signal for each of a series of shifts in scan position between the model function and the scanning interferometry signal by varying the parameter values. Information is determined about the test object (e.g., a surface height or height profile, and/or a thickness or thickness profile for a thin film in the test object) at the first location based on the fitting.

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 interferometer, measuring a location, x2, of the stage along a second measurement axis substantially parallel to the first measurement axis, and determining a location of the alignment mark along a third axis substantially 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 interferometer.

Abstract: A method including: imaging test light emerging from a test object over a range of angles to interfere with reference light on a detector, wherein the test and reference light are derived from a common source; for each of the angles, simultaneously varying an optical path length difference from the source to the detector between interfering portions of the test and reference light at a rate that depends on the angle at which the test light emerges from the test object; and determining an angle-dependence of an optical property of the test object based on the interference between the test and reference light as the optical path length difference is varied for each of the angles.