fig2 is a diagram showing an apparatus used with a solder bump measuring method of this invention . this measuring apparatus generally indicated by reference numeral 100 has an operation stage 105 on which a work is placed and measured , a control unit 120 , an operation panel 130 , a printer 140 for outputting measurement results , a monitor tv for monitoring a measurement area of the operation stage 105 , and the like . fig3 is a block diagram showing the control system of the measuring apparatus 100 shown in fig2 . a table frame on which a work 1 is placed is mounted on an anti - vibration base 210 . the table frame has a θ stage 212 for controlling an angle around the work vertical axis ( z axis ), an x stage 214 for controlling a motion in a guide axis ( x axis ) in the plane perpendicular to the vertical axis , a y stage 214 for controlling a motion in a guide axis ( y axis ) perpendicular to the x axis , and a β inclination stage 218 and an α inclination stage 220 respectively for controlling inclination of the surface of a work positioning mechanism ( work table ) 230 . each control axis is controlled by outputs from an axis controller / driver apparatus 240 . an optical microsensor 250 is mounted on a z axis driver mechanism 270 and is used for controlling the optical microsensor in the z axis relative to the work table 230 . this optical microsensor 250 can be retracted away from a measuring position of the work table 230 by a retracting mechanism 272 so that the work 1 can be easily placed on or dismounted from the operation stage . a motion amount in the z axis is measured by a digital micrometer 274 . an optical camera 252 is mounted at the side of the optical microsensor 250 , and the state of the measuring area can be monitored by a crt 150 . the optical microsensor 250 is controlled by a controller 260 , and the measured data is a / d converted and supplied via a digital input / output interface 264 to a computing apparatus , for example , a personal computer 266 . the measurement results are supplied via a digital input / output interface 280 to a computing apparatus , for example , a master personal computer 110 . the measurement results are displayed on the personal computer 110 and printed out from a printer 140 . the measurement results of solder bumps are judged in accordance with coordinate data of each bump position and correction amount data of each control axis , by using an operation switch 284 . fig4 shows the structure of the optical micro head 250 which has a semiconductor laser 252 and a light receiving element 255 . a laser beam radiated from the semiconductor laser 252 passes through a lens 253 and applied to a bump 10 as a laser beam lb . the laser beam reflected at the surface of the bump 10 passes through a lens 254 and is received by the light receiving element 255 . the light receiving element 255 measures the height position of the bump surface in accordance with a position where the reflected light is received , by using the principle of triangulation , and also detects the amount of reflected light . the x axis of the table is aligned with the optical axis of the laser beam lb . fig5 shows scan paths along which the bump 10 is scanned with the laser beam lb . the surface area including the apex of the bump 10 is measured by three paths . three paths are used for obtaining a correct value while considering the position displacement of each bump . three paths are only illustrative and a plurality of paths may be set depending upon the measurement conditions . fig6 shows an example of the measurement results wherein the abscissa represents the x axis and the ordinate represents a detected level . a first curve c 1 indicates a level of reflected and received light , and a second curve c 2 indicates a change in height of the bump . a reference value tl of the level of the reflected and received light c 1 is preset . an x axis position where the received light becomes larger than the reference value tl and an x axis position where the received light becomes smaller than the reference value are detected . the value of the height signal c 2 at the middle coordinate position x 10 is used as the height of the apex of the bump . fig7 a and 7b illustrate a relationship between the surface 8 of the substrate 2 and the height position of the bump 10 . the laser beam lb scans the surface 8 of the substrate 2 and the bump 10 to detect the height positions of the surface 8 and bump 10 . the substrate is not always absolutely flat , since it may have a swell or the like . therefore , as shown in fig8 a regression plane p 1 of the surface 8 of the substrate 8 and a regression plane p 2 of the apexes of bumps are calculated . an absolute height h 1 from the regression plane p 1 and a relative height h 2 from the regression plane p 2 are then obtained . there is not always a constant relationship between the size and shape of the substrate of a work to be measured and the position of each solder bump on the substrate , because a work precision of the substrate has a limit . therefore , after the work is placed on the table , the mount posture of the work is aligned before measurement . the regression plane means a virtual plane which minimizes the distances to bumps . this is the same concept as a regression line . it is more effective from the viewpoint of process to evaluate the bump height from the distance to the regression plane than using the absolute bump height . fig9 shows a positioning device for positioning an lsi carrier as a work on the work table 230 which moves in x and y directions . a work 1 is of a square shape . a right angle block 232 conformal to the work 1 is mounted on the table 230 . the block 232 has reference stoppers 233 . the work 1 is pushed against the stoppers 233 by a pushing pin 234 which moves toward the stoppers 233 . the table 230 has a suction device 235 which uses a negative pressure to suck the bottom of the work 1 . there are some errors of the outer dimension of the lsi substrate and bump positions because of substrate scribe errors , shrinkage of substrate material , or the like . for this reason , a process of detecting the position of a first bump 10 - 1 of the work 1 is executed as illustrated in fig1 . the controller knows in advance the position , as designed , of the first bump 10 - 1 relative to the substrate of the work 1 . therefore , first , the coordinates of the x axis of the table are aligned with the design coordinates of the first bump 10 - 1 , and a first scan s - 1 is performed for measurement while moving the table in the y direction . with this scan s - 1 , a curve indicating a change in the amount of reflected and received light of the first bump 10 - 1 , such as the curve c 1 shown in fig6 can be obtained . the center position of the light amount of this curve is obtained , this position being assumed as the center ( origin ) of the first bump 10 - 1 . if the received light amount does not exceed the reference value , the x axis coordinates are shifted by a distance d 1 to execute a second scan s - 2 to detect the temporary origin and determine the y axis coordinates . next , after the y axis coordinates are fixed , a scan s - 3 is performed in the x axis direction to determine the position of the first bump 10 - 1 from the center of the received light amount . if the received light amount does not exceed the reference value at the x axis coordinates , the y axis coordinates are shifted by a distance d 2 to execute a scan s - 4 to perform similar operations as above . the coordinate values obtained in the above manner are used as a temporary origin k 1 . a first row of bumps including the temporary origin k 1 is scanned ( s - 10 ), and the apex positions of bumps are obtained which show a received light amount in excess of the reference value . an average value of shift amounts between the x axis coordinates of apex positions and the designed x axis coordinates is calculated ( refer to fig1 ). next , a similar scan ( s - 11 ) is performed for the bump row remotest from the above bump row to thereby calculate an average value of shift amounts in the x axis coordinates . in accordance with shift amounts , a correction value of a distance from the end of the work substrate to the first bump in the x axis direction is determined to correct the x axis coordinates of the origin . similar scans are executed in the y axis direction to calculate the shift amounts of the y axis coordinates and correct the y axis coordinates of the origin . if the work is mounted being rotated about the center axis and a scan is performed by shifting the scan position by a designed value , then the peak values of the received light amount on the scan line change in a predetermined direction and a shift occurs between the peak position and the design position ( refer to fig1 a ). in accordance with this change , a correction value for the work rotation angle θ is calculated to rotate the θ stage and correct its position ( refer to fig1 b ). while a scan for the θ correction is executed in the x axis direction , the heights at positions 8 - 1 , 8 - 2 , 8 - 3 , . . . on the work substrate are ( refer to fig1 ). in accordance with the change in the heights , a regression line l - 1 is calculated and a correction value a for an inclination angle from the reference line ( horizontal line ) in the x axis direction is calculated to correct the a inclination stage 220 . similarly , a correction value β for an inclination angle in the y axis direction is calculated to correct the β inclination stage 218 . after the above alignment processes are completed , all bumps are scanned to measure the apex heights as already described with fig5 . with precise alignment , a measuring laser beam can be scanned highly precisely at high speed . therefore , the bump heights can be measured highly precisely at high speed . fig1 shows a regression plane pl - 1 formed by the measured apex positions of bumps 10 . a shift of each bump apex position is calculated from this regression plane pl - 1 and the judgement results are displayed on the display 112 . fig1 is a graph showing the measurement results displayed on the screen . the abscissa represents a difference between each bump apex and the regression plane , and the ordinate represents the number of bumps . this work has 5200 bumps , the standard deviation is 0 . 5 μm , and 3δ is + 1 . 95 . if a target value is set to +/− 2 μm , the work is judged good from the standard deviation , and is transported to the next process . the work may be judged good to transport it to the next process , if all bumps are in a range of predetermined reference values . fig1 shows examples of various displays displayed on the screen 112 of the measuring apparatus . an operation screen 300 has a display area 302 for a present operation mode and the like , an area 304 for displaying a relative height occurrence frequency distribution graph , an area 306 for displaying judgement results , and an area 308 for displaying the detailed results for each lsi as a work . ( a ) present operation mode ( alignment , apex measurement , base measurement , judgement calculation , second time individual measurement ). ( c ) coordinates of defective bump of inspected lsi with graphics and values . for the display of the position of a defective bump , for example , the position of a defective bump 10 - n of the work 1 is displayed with graphics . the relative height occurrence frequency distribution graph 304 is shown in fig1 . the judgement results are displayed in the area 306 by ok or ng . for the detailed results for each lsi in the area 308 , the alignment results are displayed by values of x , y , z , θ , α , and β , and also a bump average height , standard deviation of relative heights , received light average amount , and base shrinkage ratios in x and y directions are displayed . a position shift graph screen 310 shows a distribution of a shift amount of an apex position from a design value for each bump . a height three - dimensional distribution graph screen 320 shows a 3d graph of relative heights of respective bumps and a two - dimensional distribution graph in different colors . a defective lsi information graph screen 330 shows a judgement mode of a defective lsi after full automatic operation ( in units of magazine ). an inspection condition setting screen 340 is used for setting inspection parameters such as judgement threshold values . with this invention , for example , an operation speed of 32 mm / sec , optical micro head frequency of 16 khz , measurement resolution in the horizontal direction of 2 to 3 μm , and measurement resolution in the height direction ( z direction ) of 0 . 05 μm , can be realized .