with support lines 102 s as can be seen in fig4 a when the substrate 102 has a concave curvature the flat topped pin 200 contacts the substrate 102 as a location 202 that is less than u2154 of the radius of the substrate i e between the center line 102 c and the support line 102 s when the substrate 102 has a convex curvature as illustrated in fig4 b however the flat topped pin 200 contacts the substrate 102 at a location 204 that is greater than u2154 of the radius of the substrate i e past the support line 102 s the difference between the desired contact location i e at support line 102 s and the actual support location 202 or 204 in this case is approximately the radius of the flat topped pin 200 variation in the location that the substrate 102 is supported changes the gravitational contribution to the substrate shape and thus can add an error to the stoney equation eq 1 calculation of stress for example assume that fig4 a illustrates the substrate during a pre measurement and fig4 b illustrates the substrate during a post measurement and that three flat topped pins with diameters of 8 mm are located on a circle with a diameter of 200 mm and 120 u00b0 apart for a 300 mm wafer the average diameter of the circle of contact will be 192 mm for the pre measurement and 208 mm for the post measurement this 4 change in contact location.