Fig. 1. Diagram of LAMOST auto-focusing camera system structure

Fig. 2. A part of the LAMOST spectrometer calibration lamp spectrum

Fig. 3. (a) Normal spots; (b) Pixel depth distribution curve about normal spots in the Y direction; (c) Spots of slightly defocus; (d) Pixel depth distribution curve about spots of slightly defocus in the Y direction; (e) Spots of excessively defocus; (f) Pixel depth distribution curve about normal spots in the Y direction

Fig. 4. Flow chart of spots information acquisition

Fig. 5. (a) Fitting comparison of normal spots in the Y direction; (b) Fitting comparison of slghtly defocus spots in the Y direction; (c) Fitting comparison of excessively defocus spots in the Y direction

Fig. 6. (a) FWHM distribution of all spots under the normal condition; (b) FWHM distribution of all spots in the defocus

Fig. 7. Relational graph of X-RSS, Y-RSS and Δf

Fig. 8. Diagram of defocus function model

Fig. 9. Comparison diagram of normalized image definition evaluation curve

Fig. 10. Results of defocus diagnosis

Table 1. R² of three types of spots under the different terms of four functional models

Table 2. FWHM values of three types of spots under four functional models

Table 3. The number of spots identified by spectra at different defocus amount

Table 4. The comparison of image definition function evaluation criterion