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Ocular 10x Apocromático.
90X Microscope Lens
In this link we can see another design different from a 60X lens, where many fewer elements are used, but without as much quality as this one. The article I write again so that the reader has all the information on this page.
In this article I present my own design a 90X magnification microscope lens, with a numerical aperture of 0.8 and immersed in air.
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/#)
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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 0.088 mm (in reality the sample would be 0.088 mm high and we would enlarge it to 8 mm).
Figure 1 shows the system report.
Figure 1. 90X microscope report.
The system consists of 25 surfaces. All surfaces are spherical. 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 point of the system is 1.80 mm but should be 1.77 mm. The difference is minimal and acceptable. The BFL is at 0.847. 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 31.92 mm and the diameter of the entrance pupil is 2.89 mm.
The system is optimized for five spectral lines, ranging from 0.47 to 0.65 microns.
The size of the Spot Size RMS is 0.435, 0.483 and 0.690 microns for the fields of 0º, 4º and 8º respectively, being the size of the Airy disk radius of 0.4246 microns. The system is practically "limited diffracted".
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 two zeros for the wavelengths of the spectrum used.
The system is achromatic for lengths of 0.64 and 0.55. It is close to being apochromatic, as can be seen in the "Chromatic Focal Shift". A noteworthy fact is that the maximum range of focal displacement is only 0.5226 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 0.45 in both planes, in the 4º field it reaches a resolution of 0.44 and 0.45 for the tangential and sagittal planes respectively, while for the 8º field the resolution is 0.39 for the tangential plane and 0.44 for the sagittal plane. The system is very close to the diffraction limit.
The system picks up a lot of light, the relative illumination does not drop below 90% at any time and the FFT Diffraction Encircled Energy graph is close to the diffraction limit. In this last graph it can be verified that the irradiance stays above all in the first ring.
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 Ray Fan and OPD graphics they have a scale of 5 and 0.5 waves, which is very good. The curves present in the graphs indicate that the aberrations of the system are well corrected, the highest being astigmatism with a value of 0.256 waves.
In Figure 2 we perform a study of the tolerance of the system, where I show the limitations imposed and the results obtained.
Figure 2. Report of tolerances relative to the 90X microscope.
These results could be considered good, as the change is very little, 0.007412. The biggest problem that the system can have is the decentralization in the closest surfaces to the object.
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