The control unit controls the relative position in an optical axis direction of the projection system and the relative position in a direction perpendicular to an optical axis direction at a third timing after a second timing based on a first distribution of illumination light detected by the detection system at a first timing and a second distribution of illumination light detected by the detection system at the second timing after the first timing, the illumination light detected at the first and second timings having passed through the first and second marks.

Two pairs of alignment targets (one aligned, one misaligned by a bias distance) are formed on different masks to produce a first pair of conjugated interference patterns. Other pairs of alignment targets are also formed on the masks to produce a second pair of conjugated interference patterns that are inverted the first. Misalignment of the dark and light regions of first interference patterns and the second interference patterns in both pairs of conjugated interference patterns is determined when patterns formed using the masks are overlaid. A magnification factor (of the interference pattern misalignment to the target misalignment) is calculated as a ratio of the difference of misalignment of the relatively dark and relatively light regions in the pairs of interference patterns, over twice the bias distance. The interference pattern misalignment is divided by the magnification factor to produce a self-referenced and self-calibrated target misalignment amount, which is then output.

The preset invention provides a method of obtaining an array of a plurality of regions on a substrate, including obtaining, using a prior distribution representing a probability distribution of parameters of a regression model used to estimate the array, a first posterior distribution representing the probability distribution of the parameters, obtaining, using the first posterior distribution as the prior distribution representing the probability distribution of the parameters, a second posterior distribution representing the probability distribution of the parameters, and updating the regression model by deciding the parameters based on the second posterior distribution and obtaining, using the updated regression model, the array of the plurality of regions on a substrate from the second position measurement data.

A method for modeling measurement data over a substrate area relating to a substrate in a lithographic process. The method includes obtaining measurement data relating to the substrate and performing a combined fitting to fit to the measurement data: at least a first interfield model which describes distortion over the substrate and a field distortion model which describes distortion within an exposure field; wherein either: the at least a first interfield model includes a radial basis function model or an elastic energy minimizing spline model; or the method further includes fitting a radial basis function model or an elastic energy minimizing spline model to a distortion residual of the combined fit of a different interfield model and the field distortion model.

Method of measuring a height profile of one or more substrates is provided comprising measuring a first height profile of one or more fields on a substrate using a first sensor arrangement, the first height profile being the sum of a first interfield part and a first intrafield part, measuring a second height profile of one or more further fields on the substrate or on a further substrate using a second sensor arrangement, the second height profile being the sum of a second interfield part and a second intrafield part, determining from the measurements with the first sensor arrangement an average first intrafield part, and determining the height profile of the further fields from the second interfield part and the average first intrafield part thereby correcting the measurements of the second sensor arrangement.

A lithographic apparatus having a substrate table, a projection system, an encoder system, a measurement frame and a measurement system. The substrate table has a holding surface for holding a substrate. The projection system is for projecting an image on the substrate. The encoder system is for providing a signal representative of a position of the substrate table. The measurement system is for measuring a property of the lithographic apparatus. The holding surface is along a plane. The projection system is at a first side of the plane. The measurement frame is arranged to support at least part of the encoder system and at least part of the measurement system at a second side of the plane different from the first side.

The lithography apparatus includes at least two exposure devices and one substrate device. The substrate device includes a substrate stage and a substrate supported by the substrate stage. The at least two exposure devices are disposed in symmetry to each other above the substrate with respect to a direction for scanning exposure and configured to simultaneously create two exposure fields onto the substrate to expose the portions of the substrate within the exposure fields.

A system is disclosed. The system includes a cleaning device and a scanner device. The cleaning device is configured to clean a mask. The scanner device is coupled to the cleaning device and is configured to receive the mask, a reference image and a real-time image that is captured at the mask. The reference image includes at least one first mark image having a plurality of mapping marks on the mask. The real-time image includes at least one second mark image having the plurality of mapping marks on the mask. The scanner device is configured to map the at least one second mark image in the real-time image with the at least one first image in the reference image, when a lithography exposing process is performed. A method is also disclosed herein.

A method for determining one or more optimized values of an operational parameter of a sensor system configured for measuring a property of a substrate. The method includes: determining a quality parameter for a plurality of substrates; determining measurement parameters for the plurality of substrates obtained using the sensor system for a plurality of values of the operational parameter; comparing a substrate to substrate variation of the quality parameter and a substrate to substrate variation of a mapping of the measurement parameters; and determining the one or more optimized values of the operational parameter based on the comparing.

A method including illuminating a product test substrate with radiation from a component, wherein the product test substrate does not have a device pattern etched therein and yields a non-zero sensitivity when illuminated, the non-zero sensitivity representing a change in an optical response characteristic of the product test substrate with respect to a change in a characteristic of the radiation; measuring at least a part of the radiation redirected by the product test substrate to determine a parameter value; and taking an action with respect to the component based on the parameter value.