Abstract: A projection optical system for forming an image of a pattern in a first plane onto a second plane using exposure light in a wavelength region of shorter than 200 nm. When a projection pattern placed in the first plane and having a dark pattern and a light pattern around the dark pattern is projected onto the second plane, an average illuminance in a area where a projected image of the dark pattern is formed in the second plane is 8 or less, where an illuminance of an image of the light pattern around the dark pattern in the second plane is set to be 100.

Abstract: A position and/or movement sensor for measuring a position or movement of a first object relative to a second object comprises a measuring device including a first member coupled to the first object; a second member coupled to the second object; and one or more first spring elements coupled between the first and second members; one or more stop members for limiting movement of the first member relative to the second member in at least one linear direction and/or about at least one pivot axis; and one or more second spring elements coupled between the first member and the first object. A spring constant of the second spring elements is greater than a spring constant of the first spring elements in at least one linear direction or about at least one pivot axis.

Abstract: An alignment system for a lithographic apparatus has a source of alignment radiation that has a first wavelength and a second wavelength; a detection system that has a first wavelength channel arranged to receive alignment radiation from an alignment mark at the first wavelength and a second wavelength channel arranged to receive alignment radiation from the alignment mark at the second wavelength; and a position determining unit in communication with the detection system. The position determining unit processes information from the first and second wavelength channels in combination to determine a position of the alignment mark based on information from the first wavelength channel, information from the second wavelength channel or combined information from the first and second wavelength channels according to a relative strength of the alignment radiation detected at the first wavelength to alignment radiation detected at the second wavelength. A lithographic apparatus includes the above alignment system.

Abstract: While the alignment beam is focused on a mark on the substrate table, the substrate table is moved substantially perpendicularly to the alignment beam. If the image of the mark moves relative to a reference mark, then the substrate and the alignment beam are not perpendicular. The mark on the substrate table is aligned to a plurality of reference marks. At least two substrate marks are then aligned with a single reference mark. Errors due to the inclination of the alignment beam are eliminated from the expansion and rotation values calculated for the substrate.

Abstract: A lithographic projection apparatus including an interferometer system having a reach extending over a first, measurement station and a second, exposure station. The apparatus stores the position of the mask relative to the mask table initially. A wafer table may be transferred from the first, measurement station to the second, exposure station while fully under the control of the interferometer system. The critical path through the exposure station may then be reduced. The apparatus stores the position of the wafer relative to the wafer table at the measurement station. Subsequent alignment in the exposure station may then be performed in a shorter time as the position of the mask relative to a mask table is known.

Abstract: A scanning exposure apparatus for exposing a substrate (8) to a pattern with an original (1) through a projection optical system (5), while scanning the original and the substrate, includes a first detection system (14c) which detects a first substrate reference mark (18c1, 18c3) corresponding to the substrate through the projection optical system on/at at least one of an optical axis of the projection optical and an off-axis position shifted from the optical axis in a scanning direction, and an alignment system (2, 9) which aligns the original and the substrate on the basis of a detection result of the first detection system.

Abstract: A lithography system and method for cost-effective device manufacture that can employ a continuous lithography mode of operation is disclosed, wherein exposure fields are formed with single pulses of radiation. The system includes a pulsed radiation source (14), an illumination system (24), a mask (M), a projection lens (40) and a workpiece stage (50) that supports a workpiece (W) having an image-bearing surface (WS). A radiation source controller (16) and a workpiece stage position system (60), which includes a metrology device (62), are used to coordinate and control the exposure of the mask with radiation pulses so that adjacent radiation pulses form adjacent exposure fields (EF). Where pulse-to-pulse uniformity from the radiation source is lacking, a pulse stabilization system (18) may be optionally used to attain the desired pulse-to-pulse uniformity in exposure dose.

Abstract: In a method for inspecting positions and types of defects on wafers with circuit patterns in a semiconductor manufacturing process, inspection is made regardless of the types and materials of junctions of circuit patterns of the semiconductor devices, different kinds of defects being distinguished from one another. Further, electrification of the circuit pattern is prevented, and the area to be exposed to an electron beam is controlled evenly and at a desired voltage. During inspection of the positions and types of defects on a wafer using a charged-particle beam from a charged-particle source, an optical beam from an optical source as well as a charged-particle beam are applied to a junction of the circuit pattern of the wafer placed on a wafer holder. Thus, regardless of the types and materials of circuit patterns, a highly sensitive inspection is made according to contrasts in the defects of a captured image.

Abstract: In a lithographic projection apparatus, a grating spectral filter is used to filter an EUV projection beam. The grating spectral filter is preferably a blazed, grazing incidence, reflective grating. Cooling channels may be provided in or on the rear of the grating spectral filter. The grating spectral filter may be formed of a material effectively invisible to the desired radiation.

Abstract: A method for marking a semiconductor wafer 302 includes the steps of: providing a reticle 300 including liquid crystal pixels; positioning the semiconductor wafer in proximity to the reticle; directing radiation through a first plurality of the pixels onto a first location on the wafer; changing the relative positions of the semiconductor wafer and the reticle; and directing radiation through a second plurality of the pixels onto a second location on the wafer. The first plurality of pixels can be used to form a first mark and the second plurality of pixels can be used to form a second mark, wherein the second mark is different from the first mark. The marks can be made of a pattern of dots in order to save space. The pixels can be selected to form certain marks by using a computer 304 to turn on or off a transistor that may be associated with each pixel. Also described is a system for marking a semiconductor wafer.

Abstract: The present invention is an adjustment method for a projection optical system which allows measuring the relationship (dependency) of the fluctuation amount of the image formation characteristics of the projection optical system with respect to the change of the installation environment (e.g. barometric pressure) around the projection optical system substantially, without actually changing the installation environment. The illumination light (IL) from the exposure light source (1) illuminates the reticle (9) via the fly eye lenses (2, 4) and the capacitor lens (8) etc., and the pattern image on the reticle (9) is projected onto the wafer (12) via the projection optical system (11) under the illumination light (IL).

Abstract: A lithographic projection system has an illumination system. A plurality of directing elements reflect different sub-beams of an incident projection beam into adjustable, individually controllable directions. By using of re-directing optics any desired spatial intensity distribution of the projection beam can be produced in its cross-sectional plane.

Abstract: An illumination system and exposure apparatus and method involving illuminating a surface over an illumination field (IF) having an arcuate shape. The illumination system comprises a light source (54) for providing a light beam (100), and an optical integrator (56). The optical integrator comprises a first reflective element group (60) having an array of first optical elements (E) each having an arcuate profile corresponding to the arcuate shape of the illumination field. Each of the first optical elements has an eccentric reflecting surface (RSE) comprising an off-axis section of either a spherical surface (S) or an aspherical surface (ASE). The array of first optical elements is designed so as to form a plurality of arcuate light beams (108) capable of forming a plurality of light source images (I).

Abstract: In order to find the positional relation between the reference coordinate system XY which defines the movement of a substrate W and the arrangement coordinate system &agr;&bgr; which corresponds to a plurality of divided areas on the substrate W divided by street lines S&agr; and S&bgr;, the substrate W and an observation field are moved relatively. By allowing position detecting method marks Mk on the substrate W to visit the observation field, the street lines S&agr; and S&bgr; are detected in the observation field during the observation field. According to the results of the detection, an approximate arrangement coordinate system is corrected. The positional relation between the reference coordinate system XY and the arrangement coordinate system &agr;&bgr; is caught with high accuracy enough to allow the observation field to visit the position detection mark (Mk).

Abstract: In a lithographic apparatus, a reference grating 11 mounted on the wafer table WT is illuminated with a measurement beam 20 incident in a direction independent of wafer table tilt. The diffraction orders are detected by detector 30 and used to determine the lateral shift in the wafer table resulting from a non-zero Abbe arm, and hence the Abbe arm, for calibration purposes. The detector 30 may be a detector also used for off-axis alignment of the wafer and wafer table.

Abstract: Systems and methods for reducing colinearity effects in the formation of microdevices are disclosed. A mask with at least one column of microdevice cells is illuminated with pulses of radiation such that only a single column is illuminated. Images of the column are used to form adjacent columnar exposure fields on a workpiece. The columnar exposure fields so formed each have a width much less than that of the full exposure field capable of being formed by the projection lens. One method of the invention includes forming each columnar exposure field with a single pulse of radiation while the workpiece moves continuously relative to a projection lens and mask. Another method includes forming each columnar exposure field with a burst of radiation pulses or a long continuous pulse while stepping the workpiece beneath a projection lens between bursts. By forming columnar exposure fields that contain a single row of devices, a substantial number of error sources that contribute to co-linearity error are eliminated.

Abstract: An exposure method is provided so that the dividend regions defined on a wafer are successively exposed using pulses of laser light emitted from an excimer laser light source in such a way that each region receives a different level of target exposure levels. And, transmittance of a course energy adjuster, having a number of neutral density filters, is adjusted so that a sub-divided region receiving the least number of exposure pulses can receive a pulse count that exceeds the minimum number of exposure pulses required for optimal exposure. During the process of scanning exposure, transmittance of the coarse energy adjuster is held constant so that, to compensate for variations in the pulse energy, the output power of the excimer laser light source is adjusted according to real-time data output from an integrator sensor.

Abstract: In an off-axis levelling procedure a height map of the substrate is generated at a measurement station. The height map is referenced to a physical reference surface of the substrate table. The physical reference surface may be a surface in which is inset a transmission image sensor. At the exposure station the height of the physical reference surface is measured and related to the focal plane of the projection lens. The height map can then be used to determine the optimum height and/or tilt of substrate table to position the exposure area on the substrate in best focus during exposure. The same principles can be applied to (reflective) masks.

Abstract: The invention relates to a device and a method for detecting, identifying and relocating defects in a material strip of great length. In order to enable defects to be relocated reliably and quickly with relatively little effort, the material strip is checked for defects, and position indicators are applied to the material strip continuously over its length. In the event of a defect being observed, an associated defect position indicator is stored, and during the subsequent relocation of a defect, a current starting position indicator is established, and the material strip is moved over a conveying length which is calculated from the established starting position indicator and the stored defect position indicator.

Abstract: A scanning exposure apparatus and method uses an optical member to change an intensity distribution of exposure light in an illumination region.

Abstract: An exposure apparatus or a device manufacturing method, wherein a focus measuring device measures a best focus position upon projecting and exposing, through a projection optical system, a pattern of an original plate onto a substrate placed on a movable stage, by obtaining predetermined estimating information indicative of a blur degree of an image being observed, when observing a reference mark on the movable stage or the surface of the substrate by the focus measuring device, while changing a relative position between the movable stage and the projection optical system toward an optical axis direction of the projection optical system.

Abstract: A wafer having a plurality of areas is subjected to multiple exposures or a stitching exposure with a plurality of mask patterns being interchanged. A plurality of wafers are sequentially exposed to the plurality of mask patterns, with one wafer being replaced with a next wafer. When the one wafer is replaced with the next wafer, the next wafer is exposed to the mask pattern last used, prior to the replacement. When one mask pattern is interchanged with a next mask pattern, an area of the one wafer, last exposed to the one mask pattern, is first exposed to the next mask pattern.

Abstract: A wafer prealignment apparatus comprising a CCD linear sensor and a wafer prealignment method which facilitate the sensing of wafer presence, improvement in precision of position sensing, and edge sensing adapted to the material of the wafer even of the material is transparent or not. A photodiode (27) is provided in a vicinity of the first pixel from the center shaft of the wafer rotation means of a CCD linear sensor (5) to detect a wafer (1) on the basis of the luminous energy value. The time from the issuance of a measurement command to the sensor (5) to that of an ROG signal for transmitting the detection timing of the sensor (5) is measured to correct the angular error of a measurement position due to the rotation during this measurement. For sensing an edge position of the wafer (1), the scan start point of the sensor (5) is set on the opposite side of the center shaft of the wafer rotation means. When the wafer is transparent a sense signal is binarized to set its change point as the edge position.

Abstract: A movement sequence determining method of obtaining a preferred solution of movement sequence within a predetermined time and an apparatus for realizing it, includes at least an arithmetic step of generating a group including plural movement sequences that can be carried out, out of a group of movement sequence candidates, each indicating a visit order of plural process areas as well as scan directions of local areas in the plural process areas, and selecting a movement sequence in which a movement operation between plural process areas is completed in a shortest time, from the group generated, and a prestep of producing a movement time management table storing movement times, each from a movement start position to a movement end position, in unit lengths between process areas.

Abstract: An exposure apparatus includes a first transferring passage and a second transferring passage arranged at two different levels between a load/unload position and an exposure position, a first table and a second table one positioned in the load/unload position while the other positioned in the exposure position, a hoist mechanism which elevates one of the first and second tables to the first transferring passages, and lowers the other of the second and first tables to the second transferring passage, and a conveyor mechanism which transfers the first and second tables respectively to the load/unload position and the exposure position. Each of the first and second tables has a stage plate on which a work is placed, and a light-transmissible plate to which a mask is previously mounted.

Abstract: A method, apparatus, control system and computer program product are provided for controllably positioning the solar concentrator. The method, apparatus, control system and computer program product determine the respective errors generated by more and different error sources than prior techniques, including error sources selected from the group consisting of a gravitational residue error, an elevation transfer function error and an error attributable to atmospheric refraction. Based upon the respective errors, the method, apparatus, control system and computer program product determine an elevation command and an azimuth command to compensate for the vertical error and the horizontal error between the centerline of the solar concentrator and the sun reference vector such that the solar concentrator can be more precisely positioned, thereby improving the efficiency with which the solar concentrator collects solar energy.

Abstract: The exposure apparatus comprises a projection optical system that has an image field capable of exposing a shot area in a scanning exposure apparatus in one shot. This allows a 1 in 1 exposure, with the shot area being the maximum exposable range of the scanning exposure apparatus. In addition, the main control unit changes the control factor of the exposure system contributing to the throughput, in accordance with the minimum line width of the pattern. The control factor is changed so that the state (or the value) moves into a state where more priority is put on throughput, only when reduction in exposure accuracy is allowed. This makes it possible to improve the throughput while maintaining the exposure accuracy, compared with the case when the exposure system is controlled based on the same value at all times.

Abstract: An illumination optical system for illuminating a mask using light from a light source includes a shape varying mechanism for continuously making a shape of an effective light source variable, wherein the shape varying mechanism includes a first stop plate that has a first aperture part for allowing the light to pass through the first aperture part, and a second stop plate that has second aperture part for allowing the light that has passed through the first stop plate through the second aperture part.

Abstract: To provide a winding appearance inspection device of a tape capable of gathering a line speed in an inspection process, as well as capable of inspecting a winding appearance of the tape wound on a roll body core, even in a reel having a flange formed in a roll body core (a roll body core). Winding appearance inspection device 10 serves as a device that evaluates the winding appearance of the tape such as film T or the like wound on roll body core H, comprising light projector 12 that irradiates a light along winding surface S of the tape such as film T or the like that at least partially passes near the roll body core H, and receiver 13 that receives the light.

Abstract: In a method of detecting a position of a position detection grating mark formed with a small step structure on a surface of a flat object, an illumination light beam is irradiated on the grating mark at a predetermined incident angle. The illumination light beam includes a plurality of coherent beams having n (n≧3) different wavelengths &lgr;1, &lgr;2, &lgr;3, . . . , &lgr;n. The n wavelengths are set to approximately satisfy the following relation within a range of about ±10%: (1/&lgr;1−1/&lgr;2)−(1/&lgr;2−1/&lgr;3)= . . . =(1/&lgr;n−1−1/&lgr;n) where the wavelengths have a condition &lgr;1<&lgr;2<&lgr;3 . . . <&lgr;n. Photoelectric detection of a change in light amount of a diffracted light component generated from the grating mark in a specific direction is performed upon irradiation of the illumination light beam having the n wavelength components.

Abstract: A tension control device for a printing press having an adjustment roller, with a web of the press passing from a supply roll of the web to the adjustment roller. Means are provided for measuring the tension on opposed sides of the web passing downstream from the adjustment roller, and means are provided responsive to the measuring means for automatically approximately equalizing the tension of the web by adjustment of the adjustment roller on one end only of the adjustment roller.

Abstract: An object is held on a stage of an equipment, the stage is rotated in order to acquire a detection signal corresponding to a position of an outer peripheral edge of the object, a displacement of the object with respect to an alignment reference position is obtained based on this detection signal, and the stage is subjected to movement control so as to eliminate this displacement, thereby aligning the object.

Abstract: In an apparatus for determining the exposure conditions, a developed pattern is converted into an optical information formed by exposing a plurality of different positions of a substrate at different exposure amounts and focus values to light at a predetermined pattern and developing the pattern thereby to determine the combination of the optimum exposure amount and the optimum focus value from the optical information.

Abstract: An apparatus for sensing mis-alignment between an aircraft inertial reference frame and a reference frame of an attached sensor is disclosed. The apparatus includes a first laser mounted on the sensor and in the center of and normal to a first measuring surface; and, a second laser also mounted on the sensor perpendicular to the first laser and in the center of and normal to a second measuring surface. A first reflector is mounted to and aligned with the inertial reference frame of the aircraft and is disposed for reflecting a beam of light from the first laser, whereby misalignment in roll and yaw between the sensor and the aircraft is reflected on the first measuring surface.

Abstract: A pod for transporting a cassette of semiconductor wafers that is equipped with a cover latch indicator is described. The pod is constructed by a base, a cover, a latch means and an indicator means. The base is used to support the cassette positioned thereon, while the cover removably carries on the base for protectively covering the cassette to prevent contamination of the wafers. The latch means is carried on the base for latching the cover onto the base. The latch means may be actuatable from a latched position in which the cover is latched onto the base to a released position allowing removal of the cover from the base. The indicator means is coupled with the latch means for providing a visual indication of the condition of the latch means.

Abstract: A method of detecting a relative positional deviation between first and second objects by use of a first alignment mark provided on the first object and a second alignment mark provided on the second object, wherein the first alignment mark includes a first grating lens and a second grating lens having a mirror image of the first grating lens, and the alignment mark includes a third grating lens and a fourth grating lens having a mirror image of the third grating lens. The incidence position information of first light coming via the first grating lens and the third grating lens and incident upon a first predetermined plane, and the incidence position of second light coming via the second grating lens and the fourth grating lens and incident upon a second predetermined plane, are detected, on the basis of which the relative positional deviation between the first and second objects in a predetermined direction is detected.

Abstract: An apparatus for exposing a light sensitive surface (e.g., a printed circuit board) to light. An optical processor subsystem, which includes a reflector and an integrator-collimator assembly, processes light from a light source to produce a uniform and collimated light beam having a mean angle of incidence relative to the light sensitive surface of less than or equal to 2° and having illumination uniformity that departs by less than ±10% from a mean value. An optical light shaper subsystem transforms the uniform and collimated light beam into a uniform and collimated light strip. A displacement mechanism provides relative movement between the light strip and the light sensitive surface. A speed matching mechanism matches the speed of relative displacement to the brightness of the light strip and to the sensitivity of the light sensitive surface. The light source remains stationary in one construction and moves relative to the light sensitive panel in another construction.

Abstract: Several optical heads are mounted on a common carriage adapted to scan a photosensitive printing plate. Each head is equipped with a laser source, a modulator and projection optics and can project a segment containing a plurality of pixels. The optical track of beams in each head is folded several times in such a way as to reduce the width of the head as well as its height. When the carriage moves from one edge of the plate to the other edge a swath of pixels is projected. Each head includes means to adjust the width, location, orientation and intensity of the segment it generates. Each head is accurately positioned on the carriage so that at least two abutting swaths are projected during each sweep of the carriage to produce a wider swath.

Abstract: A method and apparatus for imaging material. A section of a medium is photographed with a first camera having a first field of view. The medium is advanced along a feed direction and the section is photographed with a second camera having a second field of view. At least one of the first field of view and the second field of view is shifted from a nominal location by one or more reflective surfaces. An actual advance of the medium is compared with an intended advance of the medium and it is determined whether at least one of a media advance error and a dimensional change in the media exists in response to the comparing step.

Abstract: A system for monitoring wafer surface topography during a lithographic process is described that includes projection optics that illuminate a portion of the wafer surface. The system further includes at least one off-axis wafer surface gauge that monitors wafer surface height relative to the projection optics as well as at least one backplane gauge that monitors wafer position relative to a backplane. The system also includes a filter that translates time-domain measurements of off-axis wafer surface gauge and the backplane gauge into space-domain measurements. A coordinate transformer is included that transforms the space-domain measurements into a single coordinate system. A computational element that combines the space-domain measurements with a focus set-point to determine correction data is also included together with a delay line for storing the correction data until the wafer has moved a predetermined distance.

Abstract: In a method of detecting a position of a position detection grating mark formed with a small step structure on a surface of a flat object, an illumination light beam is irradiated on the grating mark at a predetermined incident angle. The illumination light beam includes a plurality of coherent beams having n (n≧3) different wavelengths &lgr;1, &lgr;2, &lgr;3, . . . , &lgr;n.

Abstract: A parameter calculation unit statistically calculates the estimations and their certainty of a predetermined number of parameters, which uniquely specify any position on an object, for each of a plurality of measured sample sets on the basis of position information of marks composing the sample set. A valid value calculation unit calculates statistically valid values of the predetermined number of parameters on the basis of groups of the estimations and their certainty of the predetermined number of parameters for the respective sample sets. Furthermore, an evaluation unit statistically evaluates if the number of marks composing a sample set can be reduced. If it is determined that the number of marks can be reduced, the parameter calculation unit calculates values of the predetermined number of parameters by using a new sample set having reduced number of marks.

Abstract: Electromagnetic energy is emitted from an illumination source of a lithography device. A portion of the emitted electromagnetic energy passes through an illumination optics module. The illumination optics module includes a one-dimensional optical transform element having a pupil plane. An aperture device having an adjustable aperture is located proximate to the pupil plane so that a portion of the electromagnetic energy received by the one-dimensional optical transform element passes through the aperture of the aperture device. The angular distribution of the electromagnetic energy passing through the illumination optics module is adjusted as a function of illumination field position using the aperture device, thereby improving line width control in the lithography device.

Abstract: In an exposure apparatus, a main controller calculates the thickness of a light transmitting protective member that protects a pattern surface of a mask, based on detection signals of a first and second reflection beams of a detection beam irradiated from an irradiation system, reflected off the front and back surfaces of the protective member, and received by a photodetection system. This makes exposure that takes into account the variation in the image forming state of the image pattern depending on the calculated thickness of the protective member possible. Accordingly, exposure with high precision is possible, without the difference in thickness of the protective member protecting the pattern surface of the mask affecting the exposure. In addition, when the incident angle of the detection beam is optimized, setting a detection offset in the photodetection system, or resetting the origin will not be necessary.

Abstract: An exposure method for exposing a pattern formed on a reticle onto an object includes a flatness measurement step for measuring the flatness of the object and storing the information obtained, a position measurement step for measuring positions at plural points on the object, and a changing step for changing at least one of the position and tilt of the object on the basis of the information obtained by the flatness measurement step, and information on the position obtained by the position measurement step.

Abstract: A virtual gauging system for use in a lithographic process is described that includes means for gauging a region at a surface of a wafer when the region is located away from an axis of illumination producing wafer surface data, while other portions of the wafer are being illuminated. The system also includes means for converting the wafer surface data into wafer correction data and means for adjusting a separation distance between an exposure lens and the region at the surface of the wafer based on the correction data when the region is located at the axis of illumination. The means for gauging includes at least two wafer surface gauges located on opposite sides of an illumination slot.

Abstract: A scanning exposure apparatus and method for synchronously moving a mask and a substrate with respect to an exposing radiation flux to project an image of a mask pattern on the mask onto the substrate, includes an alignment sensor detecting the initial rotational angle of the mask relative to the substrate, a mask position detector, a substrate position detector, a calculation unit processing the position signals of the mask and the substrate in accordance with the projection ratio of the projection optical system and the initial rotational angle of the mask relative to the substrate to derive a positional deviation of the mask stage relative to the substrate stage, and a controller controlling the mask stage movement and the substrate stage movement to eliminate the positional deviation.

Abstract: Various options for improving throughput in an e-beam lithography apparatus are described. A slider lens moves in synchronism with the scanning motion of the electron beam.

Abstract: A method of detecting focus information about an image projecting optical system includes performing mark projection through the optical system, and, based on illumination lights having different chief ray incidence directions, the mark projection is carried out so that mark images formed by the illumination lights, respectively, are superposed one upon another approximately upon an imaging plane, and detecting focus information about the optical system on the basis of information related to a deviation between the mark images superposed.

Abstract: An apparatus for adjusting curvature of a disc head slider having a bearing surface is provided. The apparatus includes a light source and an apparatus for controlling the light source. The light source is adapted to produce a light beam capable of altering material stresses in a working surface of the slider. The apparatus for controlling the light source is adapted for obtaining a measure of first and second curvature characteristics of the bearing surface and for scanning the light beam across the working surface in a pattern to alter the material stresses in the working surface such that the first and second curvature characteristics move to within predetermined specifications. The pattern is based on the measures of the first and second curvature characteristics and estimates of responses in the first and second curvature characteristics to the pattern.