Abstract: As feature sizes of semiconductor chips shrink there is a need for tighter overlay between layers in a lithography process. This means more advanced and larger overlay corrections may be necessary to ensure that die are properly manufactured into chips, especially in reconstituted substrates where the die can shift in the process of creating the substrate. Systems and methods for correcting these overlay errors in a lithographic process are provided. Additional rotation (theta) and projected image size (mag) corrections can be made to correct overlay errors present in reconstituted substrates by adjusting the stage and the reticle. Furthermore, these adjustments can be made allowing site-by-site or zone-by-zone corrections instead of a one-time adjustment of the reticle chuck as has been done in the past. These corrections can alleviate some of the issues associated with fan-out wafer-level packaging (FOWLP) and fan-out panel-level packaging (FOPLP).

Abstract: In an embodiment, a system includes: an orientation sensor configured to detect an orientation fiducial on a bevel of a wafer; a pedestal configured to rotate the wafer to allow the orientation sensor to detect the orientation fiducial and place the orientation fiducial at a predetermined orientation position; and a defect sensor configured to detect a wafer defect along a surface of the wafer while rotated by the pedestal.

Abstract: A position detecting system has a transport device, a light source, at least one optical element, a reflective member, a drive unit, and a controller. The transport device transports and places an object on a placement table. The light source generates measurement light. The optical element projects the measurement light, as projection light, generated by the light source and receives reflected light. The reflective member is disposed on the transport device. The reflective member reflects the projection light toward the placement table, and reflects the reflected light of the projection light, which is projected toward the placement table, toward the optical element. The drive unit operates the transport device so that the reflective member scans a plurality of linear scanning ranges. The controller calculates positional relationship between the focus ring and the object placed on the placement table based on the reflected light within the plurality of linear scanning ranges.

Abstract: A light beam or other electromagnetic medium is emitted, guided, and received, all within a unitary system frame. The beam retains its characteristics regardless of position or motion of the frame in which it propagates. The beam retains its position in space relative to the detection of motion of the frame. Because the frame and the beam emitted within it are in the same frame of reference, characteristics of their motion are compared to determine parameters including system velocity and planetary velocity which is useful in navigation. Position, orientation, displacement, velocity of an object in motion, and changes in these parameters relative to previous values thereof, are derived from information provided within and directly by the motion of the unitary system itself.

Abstract: A lens shape measurement device, includes: a rotation unit that rotates a lens supported by a stage; a laser displacement meter; a first moving unit that moves the laser displacement meter in a X-direction; a second moving unit that moves the lens in a Y-direction; and a drive controller that controls a drive of the rotation unit, the first moving unit, and the second moving unit in a mirror reflection state in which an incidence angle of the laser beams incident on a measurement target from the laser displacement meter, and a reflection angle of the laser beams reflected by the measurement target are equal to each other with a normal line of the lens passing through the measurement target set as a reference, for each of a plurality of measurement targets set on an edge of the lens in a rotating direction of the lens.

Abstract: Installation of an engine to a support structure includes temporarily attaching first and second alignment structures to the support structure and the engine. One of the alignment structures has a target pattern on its surface. The installation further includes using a machine vision system from the other of the mounting structures to indicate the relative position of the target pattern with respect to a reference. The relative position of the target pattern with respect to the reference provides information about relative position of an engine mounting element (e.g., bolt hole) with respect to a corresponding mounting element (e.g., bolt hole) in the support structure. The relative position of the target pattern with respect to the reference can be used to maneuver the engine in order to align the mounting elements.

Abstract: Embodiments of the invention include a sensor arrangement for inclination determination with respect to at least one axis. The sensor arrangement may include a code element having a code pattern and a line sensor, which is sensitive at least with respect to one wavelength range, having a reception direction orthogonal to its extension direction. In some embodiments the code element and the line sensor are arranged such that the extension direction of the line sensor and an extension direction of the code element are oriented in the same direction. The code element and the line sensor may be rigidly connected at a spacing of at least 1 mm and at most 10 mm such that a location, which is angle-dependent with respect to the reception direction, of a projection of the code pattern onto the line sensor can be determined by means of the line sensor.

Abstract: A beam deflection device including an aluminum disc containing a plurality of lasers, each laser projecting a laser beam substantially along one of the ‘X’, ‘Y’, and ‘Z’ axes of a structural beam to which the device is attached. Wiring is attached to each of the plurality of lasers to provide power and transmit data. Passageways are provided in the solid disc to route the wiring to the exterior. A suction cup on a surface of the device allows it to be attached to the beam by pressing the device against a flat surface area of the beam.

Abstract: A method for determining the alignment of a pair of vehicle wheels includes the steps of positioning a beam projecting device consecutively on each wheel, in the same angular relationship to the wheel, and projecting a beam to a receptor, which is located in a predetermined angular relationship the other wheel. The projecting device, the receptor or both is utilized to determine the angle between the beams and the angle is related to the alignment of the pair of wheels; the receptor being maintained in the same position for each beam projection.

Abstract: A method and a device for determining a topography under load of the surface of a material, wherein a test piece (40) of the material intended to be determined is subjected to a compression with a determined load between a first and a second clamping surface (7, 27), after which, in a compressed state, at least one representation is made of surface portions of the material that are in contact with at least one of said clamping surfaces (7, 27), and that the representation is evaluated. The compression is controlled in respect of its speed for obtaining said predetermined load, and said at least one representation is made at a chosen point in time or chosen points in time during this process.

Abstract: A vehicle tire changing system is configured with sensors to acquire measurements associated with the relative spatial positions of tire service tools and a vehicle wheel assembly, and dimensions of the vehicle wheel assembly to automate and monitor the movement of an associated tire service tool and optionally, to store or convey the acquired dimensional information for use by other vehicle service systems.

Abstract: The present invention relates to a method for measuring the angular position of a contrasting edge of an object having a luminance transition zone which is substantially rectilinear in a given direction and separates two regions of different luminances. This method comprises the functional steps of: —carrying out, in a transverse direction different from the given direction, an amplitude modulation of the signals delivered by a first and a second optical sensor; and —calculating an output signal (Yout(t)) starting from the signals delivered by the first and the second optical sensors (D1, D2) as a function of the angular position of the luminance transition zone. Device and set of devices for measuring the angular position of a contrasting edge and steering aid system for fixation and tracking a target comprising at least one such contrasting edge.

Abstract: A tracking system includes an emitter array configured to emit radiation around a subject to be tracked in at least one dimension wherein each emitter or group of emitters is modulated to permit identification of a source of the radiation. A receiver is configured to receive the radiation from the emitter array, wherein one of the emitter array and the receiver are located on the subject to be tracked. A processor is configured to interpret changes in radiation and correlate the changes to a device position to output a device position control signal.

Abstract: A scanning probe microscope has a cantilever with a probe facing a sample and a measurement section for measuring a physical quantity occurring between the probe and the sample when the probe scans a surface of the sample, holding the physical quantity constant to measure the surface of the sample. The above microscope further has a probe tilt mechanism, an optical microscope etc. for detecting a position of the probe when the probe is tilted, and a control section for setting the probe in a first tilt posture and second tilt posture, measuring a surface of the sample by the measurement section at each tilt posture, detecting the position of the probe at least at the second tilt posture by the optical microscope etc., and making a measurement location at the second tilt posture match with a measurement location at the first tilt posture for measurement.

Abstract: A method for creating a reference for a first position on a substrate edge. A first reference point is selected relative to a circumference of the substrate edge, and a second reference point is selected relative to a bevel of the substrate edge. A first distance along the circumference of the substrate edge between the first reference point and the first position is identified as a first coordinate, and a second distance along the bevel of the substrate edge between the second reference point and the first position is identified as a second coordinate. The first coordinate and the second coordinate are used as the reference for the first position.

Abstract: A rubbing angle measuring equipment of the invention includes an light source unit, a measuring optical system, an imaging means, and an image evaluation means in which the measuring optical system is adapted such that a light from the light source unit passes by way of an illumination optical system and a polarizer to a rubbed measuring object and further passes by way of an analyzer and a focusing optical system to the imaging means, and the surface of the measuring object is focused to the imaging means, and in which image signals obtained by the imaging means are transmitted to the image evaluation means where signals having an intense periodicity in the image are detected, to measure the rubbing angle of the measuring object in a nondestructive manner, within a short period and at a high accuracy of 0.1° or more.

Abstract: A light detection device for detecting an optical path position of invisible light. The detection device includes a main body and a light guide. The light guide includes a distal end functioning as a light incident portion through which the detected light enters and a light radiation portion from which visible light is emitted. A drive mechanism reciprocates the light guide in an X-direction while vibrating the light guide in a perpendicular Y-direction. The distal end of the light guide rod moves within a light detection area in an XY plane. A visible light-emitting unit radiates visible light from the distal end when the detected light enters the distal end. The visible light-emitting unit includes a photo-detector for detecting the detected light and a light-emitting element for generating the visible light when the photo-detector detects the detected light.

Abstract: An optical pickup unit (OPU) includes a moveable structure that is moved by a voice coil motor component in response to an input signal. The moveable structure includes a pattern that is moved corresponding to the input signal. An encoder reads the pattern to generate an output signal that corresponds to pattern movement as the input signal is applied over a period of time. A controller calculates a calibration factor relating the pattern movement to the input signal.

Abstract: The present invention relates to inspection methods and systems utilized to provide a best means for inspection of a wafer. The methods and systems include wafer-to-reticle alignment, layer-to-layer alignment and wafer surface feature inspection. The wafer-to-reticle alignment is improved by the addition of diagonal lines to existing alignment marks to decrease the intersection size and corresponding area that a desired point can reside. Layer-to-layer alignment is improved in a similar manner by the addition of oblique and/or non-linear line segments to existing overlay targets. Also, providing for wafer surface inspection in a multitude of desired diagonal axes allows for more accurate feature measurement.

Abstract: Methods for measuring the low spatial reflectivity uniformity of a DMD spatial light modulator. These methods are unique since they compensate for the non-uniformities introduced by the tilt angle of the DMD mirrors in addition to the normal system non-uniformities introduced by the illumination source and optics. These methods flatten the image and remove all but the low spatial non-uniformities from the DMD mirrors.

Abstract: A liquid to solid material surface contact angle measurement system operating by way of detecting a transition in the behavior of a liquid sample with the solid material in a changing angular confinement environment along with use of a mathematical algorithm to then determine contact angle. Measurement of the angle at which the tested liquid transitions between apparent wetting and apparent non-wetting behavior, regardless of whether the liquid and solid material are truly classified as wetting or non-wetting, provides a measurement from which disclosed mathematical algorithms can predict the surface wetting characteristics of the liquid on the solid material. Automated performance of the confinement environment measurement and examples are included.

Abstract: A method and apparatus for estimating the adhesion properties of a surface of an article by holding the article so that the surface is facing downwards and placing a droplet of liquid against the surface. The volume of the droplet is incremented until the droplet reaches a critical weight at which some of the liquid drops for the action of the gravity force. The higher is the critical weight, the stronger the mutual adhesion forces between the liquid and the surface. If the characteristics of the liquid are kept constant, it is possible to obtain an immediate evaluation of the adhesiveness of a surface by comparing the measured critical weight with experimental results.

Abstract: A method of determining an angle between a first direction of movement of a print head and a second direction of movement of a print media, comprises: printing an array of markings on said print media, said array of markings extending along said first direction and along said second direction; traversing a sensor device along said first direction, and detecting a signal corresponding to said plurality of markings; identifying a plurality of peaks in said sensor signal as a plurality of data co-ordinates; and obtaining an angle data describing an angle between said plurality of data co-ordinates and a reference data.

Abstract: A gravitational wave generating device is positioned on one side of a material object and a gravitational wave detection device is positioned on the other side of the material object. The intervening material object's texture and internal structure will modify the gravitational wave's polarization, amplitude, speed, frequency, or other characteristics and serve to image the material object's texture and internal structure when the gravitational wave detector on the other side of the material object is connected to a display device. In a preferred embodiment an array of detectors and a gravitational wave lens or lenses can serve to accentuate and concentrate the image of the material object's texture and internal structure. The gravitational waves can also be generated by a celestial background source or sources.

Abstract: A reconfigurable optical method and system for rapidly measuring relative angular alignment of flat surfaces are provided. The method and system can be used to rapidly and simultaneously measure the relative angular alignment of machined flat surfaces of a manufactured part. The system can measure parallelism, perpendicularity or angular alignment of multiple flat surfaces. The system can also be used to set up a range of reference angles to which machined surfaces can be compared.

Abstract: Apparatus and methods for aligning rolls, wherein a first structure, for being associated with a first roll, and a second structure, for being associated with a second roll are provided. A laser is associated with one of the two structures and a target is associated with the other of the two structures. The two structures, the laser and the target are adapted to indicate whether the two rolls exhibit an aligned condition with respect to one another. Also contemplated is a calibration unit for calibrating an alignment device, wherein the unit itself includes two model rolls.

Abstract: The invention accurately sets a polarization direction of a polarization element, and prevents deterioration of the usage efficiency of the light and a reduction in image contrast. Field lenses are provided on a projection display device. A polarizer is placed on a flat surface of a field lens. The flat surface of the field lens is provided with a reference shape to place the polarizer at the end thereof. The reference shape may be one or more planes provided on the end of the field lens. In addition, the reference shape may be a straight line drawn on the flat surface of the field lens.

Abstract: An apparatus for measuring rectilinear motion and rotation angle errors of a rectilinearly moving body having a horizontal, parallel two-surface mirror positioned in a horizontal plane and including two reflection mirrors whose reflection surfaces face each other and are spaced by a distance (2)d and a vertical, parallel two-surface mirror positioned in a vertical plane and including two reflection mirrors whose reflection surfaces face each other and are spaced by a distance (2)d, and also has a light source for generating a laser beam, semi-transparent mirrors for splitting the laser beam into two laser beams, optical path changing reflection mirrors for changing a direction of each laser beam, and position sensors for detecting positions of the laser beam reflected from the horizontal, parallel two-surface mirror and the vertical, parallel two-surface mirror, respectively fixed to positions outside of the rectilinearly moving body.

Abstract: A system for visually pointing out locations on a three-dimensional structure such as an airframe of an aircraft includes a laser head that traverses an elongate track erected to pass through or adjacent to the structure. The laser head is traversed and stopped at various positions along the track, and from each position the laser head is calibrated by directing the laser beam onto three or more reference locations on the structure whose nominal coordinates are known in a reference coordinate system such as used in a CAD-CAM definition of the structure. The laser head is operable to determine in its own internal coordinate system the direction of the laser beam to each reference location and the distance to the reference location, and from this information a calibration is determined for relating measurements made by the laser head to the reference coordinate system.

Abstract: The effectiveness of a method for checking for exact alignment of two successive shafts, axles or the like is improved by the fact the no measures with respect to linearization or temperature compensation are necessary any longer by using a light-sensitive array as the light-sensitive sensor. The effects of outside light and reflections can be suppressed. The cross section and the quality of a detected laser beam can be checked especially by visual inspection. Production of the corresponding device for executing this process is facilitated. By using matched beam splitters and reflectors as well as light sources of different colors the number of optoelectronic sensors necessary can be significantly reduced.

Abstract: An angle compensation method compensates for the angle of the light-receiving surface of a photodiode disposed in an inclination detection device. The light-receiving surface is divided into four parts by an a-axis and a b-axis disposed perpendicular to each other and receives light reflected from an object surface that is an X-Y plane. The inclination detection device seeks the inclination of the object surface from changes in the irradiation position of the light reflected onto the photodiode light-receiving surface.

Abstract: Disclosed is a rotation amount detecting system for detecting a rotation amount of a deflection mirror, which is rotatable about an rotation axis, employed in an optical disc drive. The rotation amount detecting system is provided with a light emitting system that emits a light beam to the deflection mirror. The light beam has a line-like cross section extending in a direction perpendicular to the rotation axis. Further, a detecting system is provided to receive the beam reflected by the deflection mirror and determines the rotation amount of the deflection mirror in accordance with the received beam.

Abstract: A device for detecting six components of the relative motion of two bodies during a primarily two-dimensional translatory basic motion is described. The device has a plate which is provided with a two-dimensional, optical grating, and which is equipped with a plurality of vertically arranged devices for distance measuring. A second element which is composed of an arrangement of two or three optical gratings, and a plane surface which is parallel to the gratings is included. The optical gratings permit a detection of the relative displacements in X- and Y- directions parallel to the lower plate via an evaluation of the variations in intensity of the reflected light.

Abstract: A method and apparatus for estimating the adhesion properties of a surface of an article by holding the article so that the surface is facing downwards and placing a droplet of liquid against the surface. The volume of the droplet is incremented until the droplet reaches a critical weight at which some of the liquid drops for the action of the gravity force. The higher is the critical weight, the stronger the mutual adhesion forces between the liquid and the surface. If the characteristics of the liquid are kept constant, it is possible to obtain an immediate evaluation of the adhesiveness of a surface by comparing the measured critical weight with experimental results.

Abstract: A system is provided for positioning a substrate having a surface required to be characterized with a contact angle measurement. The system includes a stage which supports the substrate and a dispenser assembly having a dispensing tip through which a liquid droplet having a preselected volume is dispensed onto the surface of the substrate. A first actuating mechanism moves the stage in response to first actuation signals and a second actuating mechanism which changes the vertical spacing between the dispensing tip and the surface of the substrate and dispenses the liquid droplet from the dispenser assembly in response to second actuation signals. A controller is connected to the actuating mechanisms and delivers the first and second actuation signals to the first and second actuating mechanisms, respectively, so as to place the liquid droplet at a predetermined location on the surface of the substrate for performing the contact angle measurement.

Abstract: A sensing device, for installation in a wafer probe tester for sorting wafers according to the quality thereof, includes a main body for mounting on the wafer probe tester, an upper member and a lower member extending from the main body to define an open area therebetween for insertion of any one of different sized wafers, a plurality of light emitting devices spaced apart at fixed intervals and installed on the upper member, a plurality of light receiving devices spaced apart at respective locations opposed to the light emitting devices across the open area and installed on the lower member, and a control circuit, connected to the light emitting devices and the light receiving devices, for detecting a flat zone of any one of the different sized wafers inserted into the open area. The different sized wafers include 4 inch, 5 inch and 6 inch wafers.

Abstract: A method for monitoring surface roughness by applying a controlled amount of liquid onto a specimen surface to form a liquid protrusion. The diameter or area of the a liquid protrusion is measured and correlated to surface roughness. In an alternative embodiment, the contact angle between the specimen surface and the liquid protrusion is measured. Surface roughness is computed from the contact angle measurement and several known physical constants of the liquid and specimen surface.

Abstract: In an apparatus and method for measuring in-plane distribution of surface free energy, a target substrate is immersed in a liquid, and a parameter representing a state of meniscus to be formed at an intersection area of a target surface with a surface of the liquid is measured along the surface of the liquid. This measurement is performed by descending or ascending the substrate, thereby measuring the parameter throughout the entire surface of the target surface, and then, the in-plane distribution of the surface free energy of the target surface is calculated.

Abstract: A system for calibrating production throttle bodies in which a throttle body (18) is mounted in a fixture (16) and light is transmitted by a light source (12) through the throttle body main bore (20) onto a translucent screen (22). A camera (14) senses the light regions (34) and transmits the information to a controller (26), which calculates the angular position of the throttle valve (32).

Abstract: In an etch monitor system, a method and apparatus for adjusting the angle of incidence to normal between a laser beam and a reflective surface, such as a silicon wafer, includes a rotatable mirror having a pinhole formed therethrough, the rotatable mirror moveably mounted to be positioned in a first location within a light path and a second location out of said light path. When the rotatable mirror is located in the light path, the pinhole allows a beam of the laser beam to pass from a laser source to the reflective surface. If the beam is normal to the reflective surface, the beam is directed back toward the laser source through the pinhole. If the beam is not normal to the reflective surface, the beam is reflected by the rotatable mirror to a target, allowing observation on a lit spot of the target to enable normalization by making appropriate adjustments.

Abstract: A device and method for determining the center and orientation of a circular workpiece such as a semiconductor wafer. A beam of light from a light emitting diode is nearly collimated by a collimation lens before being reflected by a conical mirror. After reflecting from the conical mirror, the beam is reflected by a frustoconical mirror down to a flat annular mirror positioned below a semiconductor workpiece. That portion of the beam not intercepted by the workpiece is reflected back to the frustoconical mirror by the flat mirror. The return beam is then reflected by the conical mirror and passes through the collimating lens and forms a ring of light on a quadrature photodiode array. Light striking the quadrature photodiode array is converted into an electrical voltage or signal proportional to the amount of light striking each photodiode.

Abstract: A split-field pupil plane determination apparatus (10) having a wedge assembly (16) with a first glass wedge (18) and a second glass wedge (20) positioned to divide a laser beam (12) into a first laser beam half (22) and a second laser beam half (24) which diverge away from the wedge assembly (16). A wire mask (26) is positioned immediately after the wedge assembly (16) in the path of the laser beam halves (22, 24) such that a shadow thereof is cast as a first shadow half (30) and a second shadow half (32) at the input to a relay telescope (14). The relay telescope (14) causes the laser beam halves (22, 24) to converge such that the first shadow half (30) of the wire mask (26) is aligned with the second shadow half (32) at any subsequent pupil plane (34).

Abstract: A table holding a substrate thereon is placed on a focusing and levelling stage through three fulcrums, and a calculator receives as inputs the coordinates values of the table measured by an interferometer, the amount of positional deviation between the surface of a wafer and a predetermined fiducial plane at each of a plurality of measuring points on the substrate which is measured by a multipoint AF sensor, and a weight coefficient given to be to the amount of positional deviation at each of the plurality of measuring points, thereby calculating the residual deviation at each of the three fulcrums. A controller adopts the PID control system and controls the amounts of displacement of the three fulcrums on the basis of the residual deviation calculated by the calculator, the integrated value of this residual deviation and the differentiated value of this residual deviation.

Abstract: An apparatus for optically detecting the offset of the pick up of a component having an irregular shape relative to a pick-up device so as to calculate the amount of offset for accurately positioning the component. The system uses an optical measuring system that is capable of making the calculations from certain forms of regular shapes. The component has different sections with different shapes one of which is regular and the apparatus is constructed so as to insure that the proper area of the component will be measured.

Abstract: A method and apparatus for finding wafer index marks and centers. A wafer having a flat or notch along its edge is placed on a rotatable platform so that a portion of the wafer's edge is positioned within a sensor assembly. The wafer is rotated, and the sensor reads the distance from the center of rotation to the edge of the wafer. This distance is measured at several angles of the wafer and the data is stored in a digital computer as a series of datapoints including an angle and a distance. A computer-implemented process calculates various geometries concerning the wafer including the location of the index mark and the center of the wafer.

Abstract: First and second plates (10 and 12), each having a reflective surface (14) opposite the reflective surface on the other plate, are aligned substantially parallel to each other by first separating the second plate (12) from the first one. A beam of collimated light (24) is then directed at the first plate (10) so the beam is reflected along a path lying in the field of view of a light detector (26). The second plate (12) is then positioned relative to the first plate (10) so that the beam (24) is reflected from the second plate onto the first plate for reflection therefrom onto the second plate so as to undergo at least one reverberation before being reflected from the second plate into the light detector so as to appear at substantially the same point before the plates were separated.

Abstract: This invention relates to a process for measurement of the relative positions of the center-lines of an aperture and of a cylindrical outline of a sample.The process includes the following steps:introducing a calibrated rod into said aperture;performing measurements to define at least a pair of segments representative of the mid-points of the cylindrical outline and of a calibrated rod respectively.The measurements are performed utilizing a light beam which is scanned parallel to the beam in a direction perpendicular to the center-line of the cylindrical outline. This enables measurement of the coaxiality and/or of the concentricity of the center-line of the outline and of the aperture.

Abstract: A two-axis inclinometer having an inclination-sensitive ray-deflecting device is described, via which a geometrical figure having at least one angle is projected onto a linear array. In addition to providing high resolution, a large measurement range is also opened up by the special arrangement and configuration of the geometrical figure. X-, Y- and overlapping inclinations can be determined simultaneously using the described inclinometer.

Abstract: A method and apparatus for determining the contact angle of a droplet of test liquid on a substrate surface. The apparatus includes a test article support plate, a pipette for depositing a droplet of test liquid onto a substrate surface of the test article, and a lamp for projecting an image of the deposited droplet onto a projection screen with a base line of the image positioned on a horizontal axis line of the screen. The screen further has a protractor scale calibrated to read twice the normal angular value, and a rotatable reference line which upon positioning through a contact point of the droplet with the substrate surface and an apex point of the droplet farthest removed from the substrate surface directly indicates the value of the contact angle of the on the protractor scale.

Abstract: A wafer center detecting method comprises steps of giving turn to a wafer held by a holder, optically detecting two points at which the true rim line of the wafer crosses the fictitious rim line thereof obtained when the center of the wafer is in accord with the rotation center of the holder, and measuring an angle formed by these two intersecting points relative to a reference point, obtaining from the angle formed by the two intersecting points a direction in which the center of the wafer is shifted from the rotation center of the holder, obtaining a central angle formed by the two intersecting points relative to the rotation center of the holder, and obtaining, on the basis of the central angle and a previously-measured wafer radius, the extent to which the center of the wafer is shifted from the rotation center of the holder.