Fig. 1. (a) Measuring result of the shallow scratch on the super-smooth optics; (b) geometrical features of the shallow scratch.

Fig. 2. (a) Schematic of dark-field imaging; (b) dark-field images captured (the grayscales of the shallow scratch have been artificially enhanced to be observed conveniently).

Fig. 3. Results of separating the image with different gray thresholds. (a) Dark-field image including the shallow scratch; (b) the result with T1′=60; (c) the result with T2′=45.

Fig. 4. (a), (c), (e) Partial histogram of background, shallow scratch, and common scratch; (b), (d), (f) grayscale distribution.

Fig. 5. Flow chart of the ASMD.

Fig. 6. (a) Image of optical surface gotten by the dark-field detection method; (b)–(d) results of the ASMD; (e) result of gray stretching; (f) result of ASMD in region A; (g) result of ASMD in region B.

Fig. 7. (a) Dark-field image without using the ASMD; (b) the positions of scratches contained in (a) are marked by SDES; (c) the dark-field image after using the ASMD; (d) the positions of scratches contained in (c). The 6×6 images are located on different optical surfaces. We just stitch them to conveniently calculate the total length of scratches. (e) Depth of shallow scratches. Depths above 10 nm can be detected effectively, while some shallow scratches (near 5 nm) cannot be detected.