A method of applying a measurement correction includes determining an orthogonal subspace used to characterize the measurement as a plot of data. A first axis of the orthogonal subspace corresponds to constructive interference output from an interferometer of the metrology system plus a first error variable and a second axis of the orthogonal subspace corresponds to destructive interference output from the interferometer of the metrology system plus a second error variable. The method also includes determining a slope of the plot of data and determining a fitted line to the plot of data in the orthogonal subspace based on the slope.

A method for determining a center of a radiation spot irradiated on a surface by a sensor, the sensor including a radiation source and a detector. The method includes: emitting, with the radiation source, a first emitted radiation beam onto the surface to create the radiation spot on the surface, wherein at least a part of a target arranged at the surface is irradiated by the radiation spot; receiving, with the detector, a first reflected radiation beam at least including radiation from the radiation spot reflected by the target; detecting the presence of the target based on the first reflected radiation beam; determining a first measured position of the target based on the first reflected radiation beam; and determining a center of the radiation spot as projected on the surface in at least a first direction based on the first measured position of the target.

Described are computer-based methods and apparatuses, including computer program products, for aligning a wafer for fabrication. A first image of a first portion of a wafer is received from a first image capturing device. A second image of a second portion of the wafer is received from a second image capturing device, wherein an image capturing device transform defines a first relationship between the first image capturing device and the second image capturing device. A first fiducial pattern in the first image and a second fiducial pattern in the second image are identified, based on the image capturing device transform, a fiducial transform that defines, based on a specification for the wafer, a second relationship between the first fiducial pattern and the second fiducial pattern, and a threshold value configured to identify low contrast fiducial patterns on wafers. An alignment of the wafer is determined based on the identified first and second fiducial patterns.

A lithographic apparatus includes an alignment sensor including a self-referencing interferometer for reading the position of a mark including a periodic structure. An illumination optical system focuses radiation of different colors and polarizations into a spot which scans said structure. Multiple position-dependent signals are detected in a detection optical system and processed to obtain multiple candidate position measurements. Each mark includes sub-structures of a size smaller than a resolution of the optical system. Each mark is formed with a positional offset between the sub-structures and larger structures that is a combination of both known and unknown components. A measured position of at least one mark is calculated using signals from a pair of marks, together with information on differences between the known offsets, in order to correct for said unknown component of said positional offset.

The present invention provides a measurement apparatus that includes a movable stage and measures a position of a mark on the stage, comprising an imaging device including a plurality of pixels arranged at a pitch and imaging the mark, a driving device changing a relative position between the stage and the imaging device, a measurement device measuring the relative position, and a processor obtaining the position of the mark based on a plurality of images respectively obtained by the imaging device at a plurality of relative positions between the stage and the imaging device that are different from each other and associated with the pitch, wherein the processor is configured to obtain, based on a deviation with respect to one of the plurality of relative positions, a target relative position with respect to another of the plurality of relative positions.

A method and device for enhancing alignment performance of a lithographic device can provide an optimal alignment light source type to perform alignment according to product features. Overlay performance of the product can be improved, wafer reject can be reduced, and production efficiency can be enhanced.

A system comprises a topography measurement system configured to determine a respective height for each of a plurality of locations on a substrate; and a processor configured to: determine a height map for the substrate based on the determined heights for the plurality of locations; and determine at least one alignment parameter for the substrate by comparing the height map and a reference height map, wherein the reference height map comprises or represents heights for a plurality of locations on a reference substrate portion.

A position detection apparatus configured to detect a pattern including a plurality of pattern elements formed on an object includes a control unit configured to detect the pattern by performing pattern matching between a template including a plurality of feature points and the plurality of pattern elements. While, performing pattern matching, the control unit changes positions of the plurality of feature points such that a correlation between an image and the template is within a predetermined allowable range.

Disclosed is a method of obtaining data describing an object structure. The method comprising the steps of: (a) illuminating the object structure with illuminating radiation; (b) modulating the phase of the illuminating radiation after scattering by the object structure, the modulation comprising applying a first phase factor dependent upon at least one controllable parameter and an aberration function having a form of a subadditive function of a vector norm; (c) capturing a plurality of intensity patterns, wherein each intensity pattern corresponds to a unique value of the at least one controllable parameter; and (d) reconstructing the data describing the object structure based on the plurality of intensity patterns. Also disclosed are corresponding inspection and lithographic apparatuses, a method of manufacturing devices and a computer program.

A method of applying a measurement correction includes determining an orthogonal subspace used to characterize a first principal component of the measurement and a second principal component of the measurement, and rotating the orthogonal subspace by a first angle such that the first principle component rotates to become a first factor vector and the second principle component rotates to become a second factor vector. An asymmetry vector is generated by rotating the second factor vector by a second angle, where the asymmetry vector and the first factor vector define a non-orthogonal subspace. An asymmetry contribution is determined in the measurement based on the projection of the measurement onto the first factor vector in the non-orthogonal subspace. The method also includes subtracting the asymmetry contribution from the measurement.