Accuracy Performance Analysis of a Photosensitive-ink developed checkerboard calibration target

To demonstrate the accuracy of our Photosensitive ink developed calibration target, the Grid Corner locations of calibration target are measured by high accuracy Optical Measurement Machine (OMM). Then the feature (X, Y) locations are analyzed for a better understanding of the performance.

In this report, we have measured checkerboard’s grid corner (x, y) locations in the target as shown in the below:
Ø  Checkerboard grid size:  7.0mm
Ø  Array Size: 37x49
Ø  Pattern Area:  336x252mm
Ø  Development Type:   Photosensitive ink developed on white-coated glass
Ø  OMM machine used:  a Mitutoyo OMM machine with uncertainty Exy = ±(0.6+L/900) um, L is the measured object length in milimeter.(Laboratory temerature 20℃, humidity 49%)
Ø  Test Report (Original data) of this Photosensitive ink developed checkerboard calibration plate ➡ Go Link

Figure 1. Photosensitive Ink developed checkerboard calibration target

Figure 2. Ideal location of Photosensitive Ink developed checkerboard calibration target

Figure 3. Checkerboard corner point detail

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 will be firstly 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. 

After this pre-processing, the accuracy of target plate is analyzed from 3 aspects as follows:

1. Feature Position Accuracy among Entire Pattern Area

The error of every point is analyzed by calculating distance between ideal (x, y) location and actual (x, y) location. The result is shown in Figure 4. 

Figure 4. Positioning error of Photosensitive Ink developed checkerboard calibration target

In order to have a better understanding, the error vectors of all points are also illustrated in Figure 4. Every error vector is pointing from a point’s ideal location to its actual location. In order to have a better visualization, all the vector are enlarged with a scale of 891. As shown in Figure 4, the maximum error vector is marked in red circle. The maximum error of this plate is 6.7um, so it is enlarged to 6mm for a better visualization in below Figure 5. 

Standard deviation of these distance errors is also calculated, 1x standard deviation is 1.1um.

Figure 5. Vector error of all points

2. Feature Spacing Accuracy of Any 2 Points among entire pattern area

In order to quantify the accuracy of this plate among the entire area, the distance errors are analyzed for any 2 point-pairs and illustrated in Figure 6. In this plate, there are 1813X1812/2=1,642,578 pairs of any 2 point-pair distances. 

The minimum and maximum errors are -10.9um and +7.7um. That means for whole plate area, for any two-point pairs the production error is less than [-10.9um, +7.7um]. A negative value means the actual two-neighbor-point distance is less than ideal distance. A positive one means this distance is greater than the ideal value. 

Standard deviation of these 1,642,578 errors is calculated, 1x standard deviation is 2.4um.

Figure 6. Errors of Feature Spacing Accuracy

3. Feature Spacing Accuracy of Any 2 Neighbor Points

In order to evaluate the accuracy of this chessboard plate from a local perspective, the nearest-neighbor distance (ideally 7mm in this plate) error is analyzed and illustrated as Figure 7. In horizontal, there are 37 * (49-1) = 1776 distances; vertically, there are (37-1) * 49= 1764 distances. In this plate, there are 1776+1764 = 3540 pairs of nearest-neighbor (7mm) distances.

The errors of 3540 nearest neighbor distances are analyzed for this plate. The minimum and maximum limited errors are [-2.0um, +2.6um]. That means for arbitrary two-nearest-neighbored-points whose ideal distance is 7mm, the production error is within [-2.0um, +2.6um]. 

Standard deviation of these 3540 errors is also calculated, 1x standard deviation is 0.6um.

Figure 7. Positioning error of Photosensitive Ink developed checkerboard calibration target

Conclusion:
1. From a global perspective, Feature Position Accuracy among Entire Pattern Area is 6.7um.This value shows all points’ positioning error with regards to their ideal position. 

Corresponding standard deviation of 1813 positioning errors is 1.1um.

2. From another global perspective, Feature Spacing Accuracy of Any 2 Points is analyzed to show accuracy performance. The maximum errors of Feature Spacing Accuracy of Any 2 Points among the whole pattern area are within [-10.9um, +7.7um].

Corresponding standard deviation is 2.4um.

3.  From a local perspective, the performance of plate is also analyzed. The accuracy performance of the target is analyzed for any 2 nearest-neighbor points with ideal distance = 7mm. Feature Spacing Accuracy of Any 2 Neighbor Points is [-2.0um, +2.6um]. 

Corresponding standard deviation of nearest neighbor distance error is 0.6um.