Disclosed is a bandwidth calculation system for determining a desired wavelength bandwidth for a measurement beam in a mark detection system, the bandwidth calculation system comprising a processing unit configured to determine the desired wavelength bandwidth based on mark geometry information, e.g. comprising mark depth information representing a depth of a mark. In an embodiment the desired wavelength bandwidth is based on a period and/or a variance parameter of a mark detection error function. The invention further relates to a mark detection system, a position measurement system and a lithographic apparatus comprising the bandwidth calculation system, as well as a method for determining a desired wavelength bandwidth.

A measurement apparatus including an illumination system configured to illuminate a target with light including light of a first wavelength and light of a second wavelength, a wavefront changing unit configured to change a wavefront aberration in light from the target, and a control unit configured to control the wavefront changing unit, wherein the wavefront changing unit includes a first region where the light of the first wavelength enters, and a second region where the light of the second wavelength enters, and the control unit controls the wavefront changing unit such that a first correction wavefront for correcting a first wavefront aberration in the light of the first wavelength is generated in the first region, and a second correction wavefront for correcting a second wavefront aberration in the light of the second wavelength is generated in the second region.

A method for detecting a mark using a detection apparatus including a detection unit includes performing a first movement process that moves the detection unit to a first position, performing a second movement process that moves the detection unit to a second position, detecting the mark after the first movement process and the second movement process, and correcting a measurement value of the detected mark using first information about a movement of the detection unit in the first movement process and second information about a movement of the detection unit in the second movement process.

An exposure apparatus for transferring a pattern of a reticle onto a wafer is provided. The exposure apparatus includes an illumination module, a reticle stage, a projection module, a wafer stage, and a control unit. The control unit is configured to calculate an alignment setting of the reticle. The wafer includes a first layer and a second layer disposed on the first layer. The first layer includes a first alignment parameter. The second layer includes a second alignment parameter. The control unit obtains a first weighting factor predetermined according to a property of the first layer, and a second weighting factor predetermined according to a property of the second layer. The alignment setting of the reticle is calculated according to the first alignment parameter, the first weighting factor, the second alignment parameter, and the second weighting factor.

A method of determining a set of metrology point locations, the set including a subset of potential metrology point locations on a substrate, the method including: determining a relation between noise distributions associated with a plurality of the potential metrology point locations using existing knowledge; and using the determined relation and a model associated with the substrate to determine the set.

The invention provides a position sensor (300) which comprises an optical system (305,306) configured to provide measurement radiation (304) to a substrate (307). The optical system is arranged to receive at least a portion of radiation (309) diffracted by a mark (308) provided on the substrate. A processor (313) is applied to derive at least one position-sensitive signal (312) from the received radiation. The measurement radiation comprises at least a first and a second selected radiation wavelength. The selection of the at least first and second radiation wavelengths is based on a position error swing-curve model.

A method, involving determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.

A method to determine a performance indicator indicative of alignment performance of a processed substrate. The method includes obtaining measurement data including a plurality of measured position values of alignment marks on the substrate and calculating a positional deviation between each measured position value and a respective expected position value. These positional deviations are used to determine a directional derivative between the alignment marks, and the directional derivatives are used to determine at least one directional derivative performance indicator.

The present invention provides a processing system that includes a first apparatus and a second apparatus, and processes a substrate, wherein the first apparatus includes a first measurement unit configured to detect a first structure and a second structure different from the first structure provided on the substrate, and measure a relative position between the first structure and the second structure, and the second apparatus includes an obtainment unit configured to obtain the relative position measured by the first measurement unit, a second measurement unit configured to detect the second structure and measure a position of the second structure, and a control unit configured to obtain a position of the first structure based on the relative position obtained by the obtainment unit and the position of the second structure measured by the second measurement unit.

A method of determining an optimal operational parameter setting of a metrology system is described. Free-form substrate shape measurements are performed. A model is applied, transforming the measured warp to modeled warp scaling values. Substrates are clamped to a chuck, causing substrate deformation. Alignment marks of the substrates are measured using an alignment system with four alignment measurement colors. Scaling values thus obtained are corrected with the modeled warp scaling values to determine corrected scaling values. An optimal alignment measurement color is determined, based on the corrected scaling values. Optionally, scaling values are selected that were measured using the optimal alignment measurement color and a substrate grid is determined using the selected scaling values. A substrate may be exposed using the determined substrate grid to correct exposure of the substrate.