# Design of a High-Performance Digital Slit-Lamp Microscope with Five-Switched Zoom
## 3 Design Results  
The layout of the non-coaxial DSLM optical system consisted of 11 lens elements with spherical surfaces. Lenses with spherical surfaces and in the least number were employed in the design to reduce cost and assembly difficulty. As shown in Figure 3a, the elements E1 and E2 comprise the front objective; E3 and E4 comprise the Galilean telescope; and E5, E6, and E7 comprise the photographic lens. In the design, the beam splitter is replaced with a parallel plate. The structures of the Galilean telescope, as illustrated in Figure 3a,b, in which the eyepiece is before the objective lens, can provide magnifications of 6\(\times\) and 10\(\times\). The magnifications of 25\(\times\) and 40\(\times\) can be provided as shown in Figure 3d,e, where the objective is before the eyepiece lens. It can be seen in Figure 3c that the Galilean telescope can be removed from the light path, and the magnification of this system is 16\(\times\). The designed lens prescription is provided in Table 2.  
Figure 3: Layout of the non-coaxial DSLM optical system. The magnifications of the system are (**a**) 6\(\times\), (**b**) 10\(\times\), (**c**) 16\(\times\), (**d**) 25\(\times\), and (**e**) 40\(\times\). BS: Beam Splitter. In the actual optical system, its point image becomes a speckle because of diffraction of light and aberrations. In Zemax, the characteristics of imaging faculae can be observed through spot diagrams, which are representations of the imaging quality. Figure 4 shows the spot diagrams for the different magnifications of 6\(\times\), 10\(\times\), 16\(\times\), 25\(\times\), and 40\(\times\). Three representative wavelengths of 486 nm, 588 nm, and 656 nm were analyzed, which are indicated by different colors. As we all know, the spatial resolution of traditional microscopy is limited by the diffraction limit, and the minimum resolvable detail can be scaled by the radius of the Airy disc [25]. At magnifications of 6\(\times\), 10\(\times\), 16\(\times\), 25\(\times\), and 40\(\times\), the radii of the Airy disc (dark circle) were 5.018 \(\upmu\)m, 5.017 \(\upmu\)m, 5.018 \(\upmu\)m, 5.014 \(\upmu\)m, and 7.164 \(\upmu\)m, respectively. In Figure 4a-c, it can be seen that the spots of the 6\(\times\), 10\(\times\), and 16\(\times\) magnifications at different fields are almost within the Airy disc. In the systems with high magnification (25\(\times\) and 40\(\times\)), as shown in Figure 4d,e, the spot size at 656 nm is slightly larger than the Airy disc due to the chromatic focal shift. The maximum root-mean-square (RMS) radii of diffuse spots were 2.834 \(\upmu\)m, 3.463 \(\upmu\)m, 3.590 \(\upmu\)m, 3.658 \(\upmu\)m, and 5.459 \(\upmu\)m for the magnifications of 6\(\times\), 10\(\times\), 16\(\times\), 25\(\times\), and 40\(\times\), respectively. On the whole, all the spots are well within the Airy disk, which indicates that quasi-diffraction-limited performance was achieved for all the wavelengths, all the fields, and all the magnifications in the designed system. The modulation transfer function (MTF) can comprehensively reflect the imaging quality of an optical system and is one of the most important evaluation methods for optical design [26]. In this study, since the pixel size of the sensor is \(\sigma=2.2\)\(\upmu\)m, the Nyquist sampling spatial frequency of the CCD can be calculated as \(N\)s = 1/2\(\sigma\) = 227 lp/mm. In the full-color image plane, the cut-off frequency of the system was set to \(N\)s/2 = 113.5 lp/mm. Figure 5a-e shows the polychromatic diffraction MTF curves for each configuration with different magnifications and across the entire fields. The MTFs for all fields at 115 lp/mm are greater than 0.3 (for magnification of 6\(\times\)), 0.2 (for magnifications of 10\(\times\), 16\(\times\) and 25\(\times\)), or 0.15 (for magnification of 40\(\times\)).