# Precision Auto-Focusing Apparatus Based on Long-Working-Distance, Wide-Spectrum Microscope
## 2 Materials and Methods  
### System Design  
A high performance microscope instrument forms the core of the CCD splicing equipment device which is used to meet the strict requirements mentioned. A schematic diagram of the focusing system for the microscopic imaging assembly setup is shown in Figure 1, and the main parameters of the microscopic imaging system are shown in Table 1.  
In this work, a two-stage amplification method was used to meet the requirements for magnification and structure-size of the system. The overall magnification of the system is the product of the magnification of the front-end reflective objective and the magnification of the second-stage micro-module. Because the objective lens is a reflective optic, the first stage of magnification does \begin{table}
\begin{tabular}{c c} \hline \hline
**Structural Parameters** & **Specific Value** \\ \hline Working distance & 525 mm \\ System magnification & \(6.5\times 2.5\) (two stage magnification) \\ Numerical aperture & 0.13 \\ Working wavelength & 400–900 nm \\ Obscuration ratio & 4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of microscopic imaging system. Figure 1: Schematic diagram of the focusing system of the mirror-based microscopic imaging assembly setup. not produce chromatic aberration in the image and can simultaneously satisfy the requirements for ultra-long working distance, broad spectral acceptance, and large numerical aperture. The image generated by the first amplification stage is magnified by the secondary microscope module to meet the requirements of compact structure and high magnification. In order to ensure imaging quality when using the secondary module, the image plane of the first-stage of magnification coincides with the object plane of the secondary imaging module; after both stages of amplification, the image of the object is formed on a wide-spectrum CCD. The details of the design theory for a low-obscuration mirror-based objective were obtained in a previous study [14]. Based on the overall size of the microscopic system, we selected the magnification of the objective lens to be 6.5\(\times\) and 0.13 was the numerical aperture (NA) of the objective lens; the obscuration ratio of the system was set to 4%. Zemax simulation results revealed that the effect of obscuration on imaging quality can be neglected. The working distance of the mirror-based objective is 525 mm, which is much greater than the working distance of typical microscope objectives with the same NA. A Zeiss EC Plan Neofluuar objective was selected as the secondary microscope objective; its NA is 0.075. The working distance of the Zeiss EC Plan Neofluuar 2.5\(\times\) objective is 9.5 mm and its magnification is 2.5\(\times\). The secondary microscope module was further combined with a Sony near-infrared camera (EI-30 CE) and tube mirror (VMU-V, Mitutoyo), which magnifies the image twice, and then, the magnified image is imaged on the CCD. The microscope has good imaging performance at wavelengths in the ultraviolet to near infrared range, especially for the 400-1100 nm band, and its transmittance is as much as 80%. The lighting source consists of four high power LED channels, each of which corresponds to a single wavelength, 480, 550, 660 or 850 nm. The light is introduced into the optical system through an optical fiber. The illuminating lens group and the mirror-based objective constitute the light path for Kohler illumination. Figure 2 compares the modulation transfer function (MTF) of the designed mirror-based objective with that of the ideal optical system without obscuration. As shown in Figure 2a, the MTF of the mirror-based objective we designed is close to that of the ideal image when the half-field is smaller than 0.3 mm; due to obscuration effect, the performance of the objective in the middle and low frequency is slightly lower than that of the unobscured objective. Figure 2b shows the MTF of the optical system for larger fields.