Author Affiliations
1Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China2College of Intelligence Science, National University of Defense Technology, Changsha 410073, China3School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, Chinashow less
Fig. 1. Data transmission flow chart
Fig. 2. Edge ray tracing of Zemax
Fig. 3. Different k values correspond to the measurement surface shape error
Fig. 4. The surface shape errors corresponding to different k values
Fig. 5. Schematic diagram of the influence of image generator positioning error along Z axis
Fig. 6. De-skewed surface shape error caused by the image generator offsetting 0.01 mm along the positive direction of Z axis
Fig. 7. Surface shape error caused by image generator’s offset along the Z axis direction
Fig. 8. Zernike coefficients corresponding to surface shape error
Fig. 9. Size of the surface shape error caused by the offset along the Z axis
Fig. 10. Zernike coefficients corresponding to surface shape error
Fig. 11. Schematic diagram of the change of sampling points when k1 > 0 and k1 < 0
Fig. 12. k1>0, slope and surface shape error caused by detector lens distortion
Fig. 13. Surface shape error caused by lens distortion of detector
Fig. 14. Zernike coefficients corresponding to surface shape error
Fig. 15. In-situ detection system structure
Fig. 16. Change of measurement results with time
Fig. 17. Measurement results of surface shape error and temperature variation with time
direction | maximum surface shape error/nm | | corresponding to Zernike coefficients | PV | RMS | number of terms | number of main items | main types | along the X axis
| 77.2 | 10.1 | | 2、5、8、15 | 5 | 45° primary astigmatism | along the Y axis
| 88.9 | 18.1 | | 3、4、6、7、9 | 4、6 | defocusing and 0° primary astigmatism | along the Z axis
| 152.7 | 30.6 | | 3、4、6、7 | 4、6 | defocusing and 0° primary astigmatism |
|
Table 1. Influence of image generator’s positioning error on the measurement results
direction | maximum surface shape error/nm | | corresponding to Zernike coefficients | PV | RMS | number of terms | number of main items | main types | along the X axis
| 81.8 | 10.8 | | 2、5、8、15 | 5 | 45° primary astigmatism | along the Y axis
| 94.2 | 19.1 | | 3、4、6、7、9 | 4、6 | defocusing and 0° primary astigmatism | along the Z axis
| 161.9 | 32.4 | | 3、4、6、7 | 4、6 | defocusing and 0° primary astigmatism |
|
Table 2. Effect of pinhole diaphragm positioning error on measurement results
| influencing factor | maximum surface
shape error/nm
| | corresponding to Zernike
coefficients
| PV | RMS | number of
terms
| number of
main items
| main
types
| detector lens
distortion
(|k1|=1×10−3)
| pin-cushion distortion | 155.3 | 24.9 | | 3、4、6、11、12、28 | 4、6、11、12 | defocusing, 0° primary astigmatism
and higher-order aberrations
| barrel distortion | 155.3 | 24.9 | | 3、4、6、11、12、28 | 4、6、11、12 | defocusing, 0° primary astigmatism
and higher-order aberrations
|
|
Table 3. Effect of detector lens distortion on measurement results
influencing factor | maximum surface shape error/nm | | corresponding to Zernike coefficients | PV | RMS | number of
terms
| number of
main items
| main types | image generator expansion | 416.9 | 85.3 | | 3、4、5、6、7 | 3、4、5 | defocusing, 45° primary astigmatism,
0° primary astigmatism
| detector expansion | 99.7 | 20.4 | | 3、4、6、7 | 4 | focusing out | support structure expansion | 4.9 | 1.0 | | 3、4、6、7、9 | 4、6 | defocusing and 0°
primary astigmatism
|
|
Table 4. Effect of temperature change on measurement results
measurement serial number | PV/nm | RMS/nm | | measurement serial number | PV/nm | RMS/nm | 1 | 19.2 | 3.1 | | 16 | 46.6 | 9.6 | 2 | 18.4 | 2.9 | | 17 | 46.7 | 9.6 | 3 | 21.7 | 4.0 | | 18 | 47.7 | 10.0 | 4 | 28.3 | 5.4 | | 19 | 49.3 | 10.3 | 5 | 29.7 | 4.8 | | 20 | 44.9 | 9.3 | 6 | 27.7 | 5.2 | | 21 | 42.6 | 8.8 | 7 | 33.7 | 6.6 | | 22 | 45.5 | 9.5 | 8 | 34.4 | 6.6 | | 23 | 43.5 | 8.7 | 9 | 31.3 | 5.9 | | 24 | 41.7 | 7.3 | 10 | 34.3 | 6.6 | | 25 | 41.3 | 6.6 | 11 | 37.4 | 7.1 | | 26 | 50.1 | 9.0 | 12 | 40.5 | 8.1 | | 27 | 60.6 | 10.9 | 13 | 44.5 | 9.3 | | 28 | 45.7 | 9.0 | 14 | 48.2 | 10.0 | | 29 | 37.6 | 6.3 | 15 | 48.1 | 10.1 | | 30 | 39.9 | 7.1 |
|
Table 5. Detection system parameters