Blog de diseño óptico
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Ocular 10x Apocromático.
60X Microscope Lens
In this article I present my own design of a 60X magnification microscope lens.
In the section of solved exercises we already saw how to build a very simple objective of 10X. One thing we didn't see in that exercise is:
The lateral magnification is related to the length of the tube and the focal length of the lens as follows:
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Lateral magnification = length of the lens tube/focal.
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The numerical aperture and the number f/# are inversely related.
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NA=1/2(f/#)
Just like last time, I'm going to design the microscope backwards. That means that to have an NA of 0.8, the system will have to have a f/# of 0.625. The length of the tube is going to be 160 mm, which tells us that the focal length of the lens is 2.5 mm. The size of the object is 8 mm, so the size of the image will be 0.13 mm (in reality the sample would be 0.13 mm high and we would enlarge it to 8 mm).
Figure 1 shows the system report.
Figure 1. 60X microscope report.
The system consists of 18 surfaces, where there are three doublets. One of the surfaces of the system is conical. The catalogues used in this design are of CDGM, HIKARI, EPPSIR, HOYA, OHARA and SCOTT. As mentioned before, the system has a f/# of 0.625 (equivalent to an NA of 0.8). The focal should be 2.66 mm, but I have allowed it to be 2% higher because I get better result, staying finally at 2.70 mm. The BFL is at 0.537. According to the literature, it should be further away, around 0.8, but the BFL is big enough to be considered good. The total length of the lens is about 20 mm and the diameter of the entrance pupil is 4.37 mm.
The size of the Spot Size RMS is 1.54, 1.331 and 1.236 microns for the fields of 0º, 4º and 8º respectively, being the size of the Airy disk 0.4358 microns. In the graph of the longitudinal aberration we see that the size of the scale is very small, of the order of exponent -3 and that there are at least three zeros for the wavelengths F and C, while there is only one for the line d. The size of the scale is very small, of the order of exponent -3 and that there are at least three zeros for the wavelengths F and C, while there is only one for the line d.
It makes sense that only lines F and C pass twice through zero, as the system is achromatic as can be seen in the "Chromatic Focal Shift" diagram. A noteworthy fact is that the maximum range of focal displacement is only 0.9134 microns.
The MTF indicates that the system at 1200 cycles per mm would have a maximum resolution of 0.47 in the tangential and sagittal plane. In axis the system reaches a resolution of 0.37 in both planes, in the 4º field it reaches a resolution of 0.36 and 0.37 for the tangential and sagittal planes respectively, while for the 8º field the resolution is 0.32 for the tangential plane and 0.36 for the sagittal plane. The system is close to the limit and there is not much room for improvement.
The system collects a lot of light, as the relative illumination does not drop below 90% at any time and the FFT Diffraction Encircled Energy graph is close to the diffraction limit.
The field curvature is less than two microns while the distortion is less than 1%. The lateral color is less than 0.05 microns. In this sense, the field curvature and lateral color are more than compensated for, while the distortion is only slightly below the minimum. Using a grid image you can check the impact of the distortion on the system, which is what you see in the "Grid Distorsion" diagram. Also, I have generated a simulated image with Zemax where it is verified that there is a good quality of image and that this is inverted.
In the graphics of the Ray Fan and OPD, although the graphics themselves do not present a nice drawing of first, when we look at them we see that they have a scale of 10 and 2 waves, which is very good.
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