A method of measuring overlay uses a plurality of asymmetry measurements from locations (LOI) on a pair of sub-targets (1032, 1034) formed on a substrate (W). For each sub-target, the plurality of asymmetry measurements are fitted to at least one expected relationship (1502, 1504) between asymmetry and overlay, based on a known bias variation deigned into the sub-targets. Continuous bias variation in one example is provided by varying the pitch of top and bottom gratings (P1/P2). Bias variations between the sub-targets of the pair are equal and opposite (P2/P1). Overlay (OV) is calculated based on a relative shift (xs) between the fitted relationships for the two sub-targets. The step of fitting asymmetry measurements to at least one expected relationship includes wholly or partially discounting measurements (1506, 1508, 1510) that deviate from the expected relationship and/or fall outside a particular segment of the fitted relationship.

A method of measuring overlay uses a plurality of asymmetry measurements from locations (LOI) on a pair of sub-targets (1032, 1034) formed on a substrate (W). For each sub-target, the plurality of asymmetry measurements are fitted to at least one expected relationship (1502, 1504) between asymmetry and overlay, based on a known bias variation deigned into the sub-targets. Continuous bias variation in one example is provided by varying the pitch of top and bottom gratings (P1/P2). Bias variations between the sub-targets of the pair are equal and opposite (P2/P1). Overlay (OV) is calculated based on a relative shifht (xs) between the fitted relationships for the two sub-targets. The step of fitting asymmetry measurements to at least one expected relationship includes wholly or partially discounting measurements (1506, 1508, 1510) that deviate from the expected relationship and/or fall outside a particular segment of the fitted relationship.

A detection apparatus detects an orientation reference of an object to be detected which includes an edge including the orientation reference. The apparatus includes a first detection system configured to detect the edge such that the orientation reference is detected, and a second detection system configured to detect, by projecting a pattern to a surface of the object and detecting an image formed by reflected light from the surface, a position of the surface in a direction perpendicular to the surface. After a focusing operation of the first detection system is performed based on the position of the surface detected by the second detection system, the first detection system detects the orientation reference.

A sensor mark including: a substrate having: a deep ultra violet (DUV) radiation absorbing layer including a first material which substantially absorbs DUV radiation; and a protecting layer including a second material, wherein: the DUV radiation absorbing layer has a through hole in it; the protecting layer is positioned, in plan, in the through hole and the protecting layer in the through hole has a patterned region having a plurality of through holes; and the second material is more noble than the first material.

A method of measuring overlay uses a plurality of asymmetry measurements from locations (LOI) on a pair of sub-targets (1032, 1034) formed on a substrate (W). For each sub-target, the plurality of asymmetry measurements are fitted to at least one expected relationship (1502, 1504) between asymmetry and overlay, based on a known bias variation deigned into the sub-targets. Continuous bias variation in one example is provided by varying the pitch of top and bottom gratings (P1/P2). Bias variations between the sub-targets of the pair are equal and opposite (P2/P1). Overlay (OV) is calculated based on a relative shift (xs) between the fitted relationships for the two sub-targets. The step of fitting asymmetry measurements to at least one expected relationship includes wholly or partially discounting measurements (1506, 1508, 1510) that deviate from the expected relationship and/or fall outside a particular segment of the fitted relationship.

Three-dimensional printing methods and systems use a derived geometry and aligns anisotropic inclusions in any orientation at any number of discrete volumetric sections. Structural, thermal, or geometry-based analyses are combined with inclusion alignment computations and print preparation methods and provided to 3D printers to produce composite material parts that meet demanding geometric needs as well as enhanced structural and thermal requirements. In one example, optimal inclusion alignment vectors associated with a section of the object are calculated based on specifications for the object, segmenting a three-dimensional model of the object into layer slices, grouping each section within each layer slice having similar alignment vectors and combining the groupings and generating printing instructions for the object according to the grouped alignment vectors.

According to one embodiment, there is provided an exposure apparatus which projects a pattern of an original onto a substrate by a projection optical system so as to expose the substrate. The exposure apparatus includes a substrate stage, an alignment detecting system, and a controller. The substrate stage holds the substrate on which shot areas each including multiple chip areas are placed. The alignment detecting system detects multiple first alignment marks placed in a peripheral region in a first chip area in the shot area. The controller obtains the first amount of positional deviation for the first chip area according to results of detecting the multiple first alignment marks and controls exposure conditions for the first chip area in the shot area according to the first amount of positional deviation.

Three-dimensional printing methods and systems use a derived geometry and aligns anisotropic inclusions in any orientation at any number of discrete volumetric sections. Structural, thermal, or geometry-based analyses are combined with inclusion alignment computations and print preparation methods and provided to 3D printers to produce composite material parts that meet demanding geometric needs as well as enhanced structural and thermal requirements. In one example, optimal inclusion alignment vectors associated with a section of the object are calculated based on specifications for the object, segmenting a three-dimensional model of the object into layer slices, grouping each section within each layer slice having similar alignment vectors and combining the groupings and generating printing instructions for the object according to the grouped alignment vectors.

Three-dimensional printing methods and systems use a derived geometry and aligns anisotropic inclusions in any orientation at any number of discrete volumetric sections. Structural, thermal, or geometry-based analyses are combined with inclusion alignment computations and print preparation methods and provided to 3D printers to produce composite material parts that meet demanding geometric needs as well as enhanced structural and thermal requirements. In one example, optimal inclusion alignment vectors associated with a section of the object are calculated based on specifications for the object, segmenting a three-dimensional model of the object into layer slices, grouping each section within each layer slice having similar alignment vectors and combining the groupings and generating printing instructions for the object according to the grouped alignment vectors.

A pattern forming method includes: a first step of forming a first pattern to define a first shot arrangement; and a second step of performing an imprint process, thereby forming a second pattern on the imprint material on the first pattern and defining a second shot arrangement. In the second step, the second shot arrangement is defined so as to reduce an overlay error between the first and second shot arrangements by deforming the mold. In the first step, based on information of the estimated second shot arrangement definable on the substrate when the second step is performed after the second pattern formed on the mold is amended by deforming the mold, the first pattern is formed to make an overlay error between the first and second shot arrangements fall within an allowable range.