Your company has a manual 2D microscope which can measure the coordinates of 2D profiles. You have been asked to develop a least square algorithm in either Matlab or Excel to calculate the centre and radius of circular features.
Describe briefly how measurement uncertainty is evaluated. Given the standard uncertainty of x and y coordinates is 30 μm, calculate the uncertainties associated with the radius and centre coordinates. Describe how to reduce the measurement uncertainties.
To test your algorithm, you can use the following measurement results, the XY coordinates recorded for a ring gauge:

Measurement Results (unit: mm)

X
84.047
73.303
44.041
4.015
-35.996
-65.250
-75.972
-65.241
-35.979
4.025
44.029
73.330
84.006

Y
5.038
45.008
74.326
85.021
74.319
45.003
5.038
-34.997
-64.263
-74.969
-64.241
-34.975
5.006