A tool calibration apparatus for a robot manipulator having a tool is disclosed. The tool calibration apparatus comprises a base, an X-axis measurement device, a Y-axis measurement device and a Z-axis measurement device. Each of the X-axis measurement device, the Y-axis measurement device and the Z-axis measurement device comprises a measuring plate and a sensor. The measuring plates of the X-axis measurement device, the Y-axis measurement device and the Z-axis measurement device move in a direction along the X-axis, Y-axis, and Z-axis, respectively. The sensors of the X-axis measurement device, the Y-axis measurement device and the Z-axis measurement device measure a displacement of the corresponding measuring plate. According to the displacements, information of a tool center point of the tool is acquired so as to calibrate the tool center point.

Methods and apparatus for substrate position calibration for substrate supports in substrate processing systems are provided herein. In some embodiments, a method for positioning a substrate on a substrate support includes: obtaining a plurality of backside pressure values corresponding to a plurality of different substrate positions on a substrate support by repeatedly placing a substrate in a position on the substrate support, and vacuum chucking the substrate to the substrate support and measuring a backside pressure; and analyzing the plurality of backside pressure values to determine a calibrated substrate position.

A process for the determination of the cross-sectional area and volume of an object including the steps of a. Providing a container having a closed bottom, an open top, a side wall, a tap at a reference height, b. Providing a flowable medium having a surface in the container, c. Providing at least one measuring means for measuring a height of the surface of the flowable medium in the container relative to the reference height, d. Providing an object having a vertical Z-axis relative to the X,Y plane of the surface and positioning the object in the container, the object being at least partly submerged in the flowable medium, e. Providing calculating means for calculating the cross-sectional area and/or volume of the object in the X,Y plane relative to a position on the Z-axis, f. Opening the tap in the container to allow the flowable medium to flow out of the container, g. Measuring the height of the surface of the flowable medium relative to the reference height as a function of time (h(t)) during the outflow of the flowable medium, h. Calculating the cross-sectional area of the object (A.sub.o) as a function of the height relative to the reference height based on the determined height of the surface as a function of time (h(t)) during the outflow of the flowable medium in step f). A device for measuring the cross-sectional area and volume of an object.

A process for the determination of the cross-sectional area and volume of an object including the steps of a. Providing a container having a closed bottom, an open top, a side wall, a tap at a reference height, b. Providing a flowable medium having a surface in the container, c. Providing at least one measuring means for measuring a height of the surface of the flowable medium in the container relative to the reference height, d. Providing an object having a vertical Z-axis relative to the X,Y plane of the surface and positioning the object in the container, the object being at least partly submerged in the flowable medium, e. Providing calculating means for calculating the cross-sectional area and/or volume of the object in the X,Y plane relative to a position on the Z-axis, f. Opening the tap in the container to allow the flowable medium to flow out of the container, g. Measuring the height of the surface of the flowable medium relative to the reference height as a function of time (h(t)) during the outflow of the flowable medium, h. Calculating the cross-sectional area of the object (A.sub.o) as a function of the height relative to the reference height based on the determined height of the surface as a function of time (h(t)) during the outflow of the flowable medium in step f). A device for measuring the cross-sectional area and volume of an object.

Systems and methods of the present disclosure relate to identifying geometric features of a conduit. A method includes controlling a flow into or out of a conduit to induce pressure waves in the conduit; measuring, with a pressure transducer, pressure responses in the conduit due to contact of the pressure waves with a geometric feature of the conduit; and identifying the geometric feature, based on the pressure responses.

Systems and methods of the present disclosure relate to identifying geometric features of a conduit. A method includes controlling a flow into or out of a conduit to induce pressure waves in the conduit; measuring, with a pressure transducer, pressure responses in the conduit due to contact of the pressure waves with a geometric feature of the conduit; and identifying the geometric feature, based on the pressure responses.