Accuracy Definition--Feature Position Accuracy among Entire Pattern Area, Feature Spacing Accuracy of Any 2 Neighbor Points, Feature Spacing Accuracy of Any 2 Features points
1 Overview
The general workflow of how we evaluate the accuracy of calibration plate.
A calibration plate has 3 accuracy performance from 3 aspects as shown in below illustration.
2 Example of accuracy analysis from 3 aspects
2.1 Measurement results and preparation
For most measurement results, the measured (x, y) positions may generally have an inclination or eccentricity effect regarding its ideal positions. The original (x, y) results are transformed by a best-fit 2D rigid transformation, which will not change relative position of all points, towards their ideal (x, y) value. After this transformation, the inclination and eccentricity effect of measured value can be eliminated.
| Original/Measured (X, Y) positions | Ideal 2D (X, Y) position | 2D Affined (X, Y) positions | |||||||
| Point Indx | Original X/mm | Original Y/mm | Point Index | Target X/mm | Target Y/mm | 2D Rigid transformed X/mm | 2D Rigid transformedY/mm | ||
| 1 | -0.00069 | 0.00028 | 1 | 0 | 0 | -0.00264 | 0.00011 | ||
| 2 | 14.99929 | 0.00006 | 2 | 15 | 0 | 14.99734 | 0.00088 | ||
| 3 | 30.00429 | 0.00048 | 3 | 30 | 0 | 30.00234 | 0.00229 | ||
| 4 | 0.00106 | 14.99828 | 4 | 0 | 15 | -0.00188 | 14.99811 | ||
| 5 | 15.00132 | 14.99835 | 5 | 15 | 15 | 14.99838 | 14.99917 | ||
| 6 | 30.00636 | 14.99805 | 6 | 30 | 15 | 30.00342 | 14.99986 | ||
| 7 | 0.00280 | 29.99889 | 7 | 0 | 30 | -0.00113 | 29.99872 | ||
| 8 | 15.00330 | 29.99928 | 8 | 15 | 30 | 14.99937 | 30.00010 | ||
| 9 | 30.00874 | 29.99897 | 9 | 30 | 30 | 30.00481 | 30.00078 | ||
2.2 Error analysis for ˇ°Feature Position Accuracy among Entire Pattern Areaˇ±
For all 9 points, the positioning errors are calculated to know the error distribution among the whole plate. And the maximum value of these errors will be Feature Position Accuracy among Entire Pattern Area. Here Point 9 has the maximum deviation from ideal positions, and the Feature Position Accuracy is 4.87um.
| Feature Position Accuracy among Entire Pattern Area |  | ||||
| Ponit Index | Error X | Error Y | Distance vector of a point to its ideal (x, y) location | ||
| 1 | -0.00264 | 0.00011 | 0.00264 | ||
| 2 | -0.00266 | 0.00088 | 0.00280 | ||
| 3 | 0.00234 | 0.00229 | 0.00327 | ||
| 4 | -0.00188 | -0.00189 | 0.00267 | ||
| 5 | -0.00162 | -0.00083 | 0.00182 | ||
| 6 | 0.00342 | -0.00014 | 0.00342 | ||
| 7 | -0.00113 | -0.00128 | 0.00171 | ||
| 8 | -0.00063 | 0.00010 | 0.00064 | ||
| 9 | 0.00481 | 0.00078 | 0.00487 | ||
2.3 Error analysis for ˇ°Feature Spacing Accuracy of Any 2 Neighbor Pointsˇ±
There are totally 12 nearest-neighbor distances in 3X3 grid. Among these 12 distance values, the minimum and maximum value are -2.4um and +5.4um. It means, for the plate the Feature Spacing Accuracy of Any 2 Neighbor Points is [-2.4um, +5.4um].
| Feature Spacing Accuracy of Any 2 Neighbor Points (For 3X3 grid, there are 12 nearest-neighbor distances) |  | |||||
| Distance Index | Name | Actual 2-point distance values | Ideal 2-point distance values | Error (Actual-Ideal) | ||
| 1 | DISTANCE (1,2) | 14.99998 | 15.00000 | 0.0000 | ||
| 2 | DISTANCE (1,4) | 14.99800 | 15.00000 | -0.0020 | ||
| 3 | DISTANCE (2,3) | 15.00500 | 15.00000 | 0.0050 | ||
| 4 | DISTANCE (2,5) | 14.99829 | 15.00000 | -0.0017 | ||
| 5 | DISTANCE (3,6) | 14.99757 | 15.00000 | -0.0024 | ||
| 6 | DISTANCE (4, 5) | 15.00026 | 15.00000 | 0.0003 | ||
| 7 | DISTANCE (4, 7) | 15.00061 | 15.00000 | 0.0006 | ||
| 8 | DISTANCE (5, 6) | 15.00504 | 15.00000 | 0.0050 | ||
| 9 | DISTANCE (5,8) | 15.00093 | 15.00000 | 0.0009 | ||
| 10 | DISTANCE (6, 9) | 15.00092 | 15.00000 | 0.0009 | ||
| 11 | DISTANCE (7,8) | 15.00050 | 15.00000 | 0.0005 | ||
| 12 | DISTANCE (8, 9) | 15.00544 | 15.00000 | 0.0054 | ||
2.4 Error analysis for ˇ°Feature Spacing Accuracy of Any 2 Feature Pointsˇ±
| Index | Distance name | Actual 2-point distance values | Ideal 2-point distance values | Distance Error of Any 2 Features points |  The figure's point location does not match the left side point locations, but it shows the sorting rule of any 2-point distances among 9 points | |
| 1 | Distance (P1, P2) | 14.99998 | 15.00000 | -0.00002 | ||
| 2 | Distance (P1, P3) | 30.00498 | 30.00000 | 0.00498 | ||
| 3 | Distance (P1, P4) | 14.99800 | 15.00000 | -0.00200 | ||
| 4 | Distance (P1, P5) | 21.21326 | 21.21320 | 0.00006 | ||
| 5 | Distance (P1, P6) | 33.54633 | 33.54102 | 0.00531 | ||
| 6 | Distance (P1, P7) | 29.99861 | 30.00000 | -0.00139 | ||
| 7 | Distance (P1, P8) | 33.54191 | 33.54102 | 0.00089 | ||
| 8 | Distance (P1, P9) | 42.43215 | 42.42641 | 0.00574 | ||
| 9 | Distance (P2, P3) | 15.00500 | 15.00000 | 0.00500 | ||
| 10 | Distance (P2, P4) | 21.21069 | 21.21320 | -0.00251 | ||
| 11 | Distance (P2, P5) | 14.99829 | 15.00000 | -0.00171 | ||
| 12 | Distance (P2, P6) | 21.21678 | 21.21320 | 0.00358 | ||
| 13 | Distance (P2, P7) | 33.53840 | 33.54102 | -0.00262 | ||
| 14 | Distance (P2, P8) | 29.99922 | 30.00000 | -0.00078 | ||
| 15 | Distance (P2, P9) | 33.54427 | 33.54102 | 0.00325 | ||
| 16 | Distance (P3, P4) | 33.54292 | 33.54102 | 0.00191 | ||
| 17 | Distance (P3, P5) | 21.21380 | 21.21320 | 0.00059 | ||
| 18 | Distance (P3, P6) | 14.99757 | 15.00000 | -0.00243 | ||
| 19 | Distance (P3, P7) | 42.42634 | 42.42641 | -0.00007 | ||
| 20 | Distance (P3, P8) | 33.54039 | 33.54102 | -0.00063 | ||
| 21 | Distance (P3, P9) | 29.99849 | 30.00000 | -0.00151 | ||
| 22 | Distance (P4, P5) | 15.00026 | 15.00000 | 0.00026 | ||
| 23 | Distance (P4, P6) | 30.00530 | 30.00000 | 0.00530 | ||
| 24 | Distance (P4, P7) | 15.00061 | 15.00000 | 0.00061 | ||
| 25 | Distance (P4, P8) | 21.21549 | 21.21320 | 0.00229 | ||
| 26 | Distance (P4, P9) | 33.54820 | 33.54102 | 0.00718 | ||
| 27 | Distance (P5, P6) | 15.00504 | 15.00000 | 0.00504 | ||
| 28 | Distance (P5, P7) | 21.21254 | 21.21320 | -0.00066 | ||
| 29 | Distance (P5, P8) | 15.00093 | 15.00000 | 0.00093 | ||
| 30 | Distance (P5, P9) | 21.21889 | 21.21320 | 0.00569 | ||
| 31 | Distance (P6, P7) | 33.54458 | 33.54102 | 0.00356 | ||
| 32 | Distance (P6, P8) | 21.21624 | 21.21320 | 0.00303 | ||
| 33 | Distance (P6, P9) | 15.00092 | 15.00000 | 0.00092 | ||
| 34 | Distance (P7, P8) | 15.00050 | 15.00000 | 0.00050 | ||
| 35 | Distance (P7, P9) | 30.00594 | 30.00000 | 0.00594 | ||
| 36 | Distance (P8, P9) | 15.00544 | 15.00000 | 0.00544 |
