Disclosed is a substrate, associated patterning device and a method for measuring a position of the substrate. The method comprises performing an alignment scan of an alignment mark to obtain simultaneously: a first measurement signal detected in a first measurement channel and a second measurement signal detected in a second measurement channel. The first and second measurement signals are processed by subtracting a first direction component of the first measurement signal from a first direction component of the second measurement signal to obtain a first processed signal, the first direction components relating to said first direction. The position of an alignment mark is determined with respect to the first direction from the first processed signal.

A method for calibrating the alignment of a wafer is provided. A plurality of alignment position deviation (APD) simulation results are obtained form a plurality of mark profiles. An alignment analysis is performed on a mark region of the wafer with a light beam. A measured APD of the mark region of the wafer is obtained in response to the light beam. The measured APD is compared with the APD simulation results to obtain alignment calibration data. An exposure process is performed on the wafer with a mask according to the alignment calibration data.

A detection apparatus including a plurality of detection systems arranged spaced apart from each other so as to detect, of a plurality of marks provided on an object held by a stage, marks different from each other, and a processing unit configured to perform a first process of obtaining a first detection value by detecting the plurality of marks by one or more detection systems in a first state in which the stage is arranged at a first rotation angle, and a second process of obtaining a second detection value by detecting the plurality of marks by two or more detection systems in a second state in which the stage is arranged at a second rotation angle, and obtain a difference between the first detection value and the second detection value for each of the plurality of marks.

A calibration system includes a plate, a fixed alignment mark, and a variable diffraction grating. The plate is adjacent to a wafer alignment mark disposed on a wafer. The fixed alignment mark is disposed on the plate and is configured to act as a reference mark for an initial calibration of the calibration system. The variable diffraction grating is disposed on the plate and includes a plurality of unit cells configured to form a plurality of variable alignment marks. The variable diffraction grating is configured to calibrate a shift-between-orders of one of the variable alignment marks and the fixed alignment mark.

The present invention provides a measurement apparatus for measuring a position of a first pattern and a position of a second pattern provided in a target object, the apparatus including an image capturing unit including a plurality of pixels which detect light from the first pattern and light from the second pattern, and configured to form an image capturing region used to capture the first pattern and the second pattern by the plurality of pixels, and a control unit configured to adjust the image capturing unit such that a relative ratio of an intensity of a detection signal of the first pattern generated based on an output from a first image capturing region and an intensity of a detection signal of the second pattern generated based on an output from a second image capturing region falls within an allowable range.

Disclosed is a method of metrology such as alignment metrology. The method comprises obtaining pupil plane measurement dataset at a pupil plane relating to scattered radiation resultant from a measurement of a structure. The method comprises determining a measurement value or correction therefor using the pupil plane measurement dataset and a sensor term relating to sensor optics used to perform said measurement.

In a dark-field metrology method using a small target, a characteristic of an image of the target, obtained using a single diffraction order, is determined by fitting a combination fit function to the measured image. The combination fit function includes terms selected to represent aspects of the physical sensor and the target. Some coefficients of the combination fit function are determined based on parameters of the measurement process and/or target. In an embodiment the combination fit function includes jinc functions representing the point spread function of a pupil stop in the imaging system.

A calibration system includes a plate, a fixed alignment mark, and a variable diffraction grating. The plate is adjacent to a wafer alignment mark disposed on a wafer. The fixed alignment mark is disposed on the plate and is configured to act as a reference mark for an initial calibration of the calibration system. The variable diffraction grating is disposed on the plate and includes a plurality of unit cells configured to form a plurality of variable alignment marks. The variable diffraction grating is configured to calibrate a shift-between-orders of one of the variable alignment marks and the fixed alignment mark.

Disclosed is a method for determining a stage position or correction therefor in a lithographic process. The method comprises obtaining transmission data describing the transmission of alignment radiation onto the substrate; obtaining position data relating to a stage position of said stage and/or a sensor position of said sensor. A weighting is determined for the position data based on said transmission data. The position based on said transmission data, position data and weighting.

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.