Accuracy Performance Analysis of a chrome on cermaic Halcon12 calibration target

To demonstrate the accuracy of our ceramic calibration plate, the circle center locations of Halcon 12 compatible plate 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 circle center locations (x, y) in the target as shown in the below:
Ø  Neighbor circle distance:  4.0mm
Ø  Array size: 13 rows x 15 columns
Ø  Pattern area:  41.6 horizontal x 58 vertical mm
Ø  Development type:   chrome pattern on ceramic plate
Ø  OMM machine used:  a Mitutoyo OMM machine with uncertainty Exy = ±(0.6+L/900) um.
Ø  Test Report(Original data) of this chrome on cermaic Halcon calibration plate ➡ Go Link

Figure 1. Chrome on ceramic Halcon12 calibration target

Figure 2. Ideal Circle center locations of chrome on ceramic Halcon12 calibration target

For most measurement results, the measured (x, y) positions may generally have a inclination or eccentricity effect regarding its ideal positions. The original (x, y) results will firstly be 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 3. 

Figure 3. Positioning error of chrome on ceramic Halcon12 calibration target

In order to have a better understanding, the error vectors of all points are also presented 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 vectors are enlarged with a scale of 1835. As shown in Figure 4, the maximum error is marked in red circle. The maximum error of this plate is 1.6um, so it is enlarged to 3mm for a better visualization in below figure.

Standard deviation of these 13X15=195 errors is calculated, 1x standard deviation is 0.34um.

Figure 4. 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 5. In this plate, there are 195X194/2=18,915 pairs of any 2 point-pair distances. 

The minimum and maximum errors are -2.1um and +3.0um. That means for whole plate area, for any two-point pairs the production error is less than [-2.1um, +3.0um]. 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 18,915 errors is calculated, 1x standard deviation is 0.7um.

Figure 5. Errors of Feature Spacing Accuracy

3. Feature Spacing Accuracy of Any 2 Neighbor Points

In order to quantify the accuracy of this circle dot array plate (Halcon 12 compatible pattern) in a short scope/local view, the nearest-neighbor distance (4mm in this plate) error is analyzed and illustrated as Figure 5. There are 530 pairs of nearest-neighbor (4mm) distances.

Generally, 530 nearest neighbor distances are counted for this 13x15 plate. The minimum and maximum limited errors are [-1.0um, 0.9um]. That means for arbitrary two-nearest-neighbored-points whose ideal distance is 7mm, the production error is in between [-1.0um, 0.9um].

Standard deviation of these 530 errors is also calculated, 1x standard deviation is 0.36um.

Figure 6. Positioning error of chrome on ceramic Halcon12 calibration target

Conclusion:
1. From a global perspective, Feature Position Accuracy among Entire Pattern Area is 1.6um.This value shows all points’ positioning error with regards to their ideal position. 

Corresponding standard deviation of these 13X15=195 positioning errors is 0.34um.

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 [-2.1um, +3.0um].

Corresponding standard deviation is 0.7um.

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 = 4mm. Feature Spacing Accuracy of Any 2 Neighbor Points is [-1.0um, +0.9um]. 

Corresponding standard deviation of nearest neighbor distance error is 0.36um.