A measurement method for the Z-direction position of fiber based on depth from focus

Fiber positioning technology is widely used in spectroscopic telescopes. The Z-axis position of the optical fiber tip must be strictly constrained on the focal plane, otherwise the skylight of the celestial body cannot be focused on the optical fiber tip, thus affecting the observation efficiency of the telescope. Taking the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) as an example, 4,000 optical fibers are densely distributed on the focal panel, and the distance between adjacent ones is very small, which means that contact-type instruments cannot be used. Therefore, this article proposes a fiber Z-axis position measurement method based on depth from focus (DFF). First, a new sharpness function based on the maximum edge gradient is proposed according to the edge diffusion distribution of spots in a backlight environment, which can accurately calculate the sharpness value of light spot images at different focus levels. Secondly, in order to improve the measurement speed of DFF, a focus search algorithm based on the blurred spot radius is proposed, which establishes the relationship between the defocus radius of the spot and the focus position. The displacement