Error-sensitive factors analysis and verification for optical element in-situ measurement device based on phase measuring deflectometry

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

Table 1. Influence of image generator’s positioning error on the measurement results

Table 1. Influence of image generator’s positioning error on the measurement results

direction	maximum surface shape error/nm		corresponding to Zernike coefficients
direction	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 2. Effect of pinhole diaphragm positioning error on measurement results

Table 2. Effect of pinhole diaphragm positioning error on measurement results

direction	maximum surface shape error/nm		corresponding to Zernike coefficients
direction	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 3. Effect of detector lens distortion on measurement results

Table 3. Effect of detector lens distortion on measurement results

	influencing factor	maximum surface shape error/nm		corresponding to Zernike coefficients
	influencing factor	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
detector lens distortion (\|k₁\|=1×10⁻³)	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 4. Effect of temperature change on measurement results

Table 4. Effect of temperature change on measurement results

influencing factor	maximum surface shape error/nm		corresponding to Zernike coefficients
influencing factor	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 5. Detection system parameters