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Ocular 10x Apocromático.
Microscope objective.
In the following article we will see the properties of a microscope lens, we will see how to make a paraxial design, calculating the power and separation between lenses to later convert those paraxial lenses into achromatic doubles. Once the calculations are done, we will introduce them in Zemax and optimize the system.
The microscope objective that we are going to design corresponds to problem 20 (Mid-Term Exam) of the book "Introduction to Lens Desing" by Joseph M. Geary.
In it, we are asked to design the objective of a microscope with a magnification of 10X and an NA of 0.25. The length of the microscope tube will be 170mm. The crystals that we are going to use are models BK7 and SF2.
In Figure 1 we see the problem statement and the data we need to find out. The construction of the objective will be done "upside down", that is, we will start from the final image towards the object. As everything has been calculated paraxially, as soon as we add thicknesses we will have a mismatch and we will have to readjust. Then we'll have to optimize.
The steps to calculate all we need are:
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Through the value of the numerical aperture we can find the value of "U3". Next, we find the value of "U1" through the lateral increase.
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The next step is to simplify the system to a single lens, and see what the resulting angle will be when doing the paraxial ray tracing from the object.
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As our system has two lenses, we divide that angle between two: the entry and exit angle. We can calculate the power of the lenses through the equations of paraxial tracing.
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To calculate the distance between the lenses, what we are going to do is calculate the distance at which the ray of the first lens would cross the optical axis. We divide that distance by two and this will be the distance between lenses.
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We calculate the total power of the system.
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Acromatize the two lenses.
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Introduce the lenses in Zemax. We optimize them separately and finally we put the whole system together, to be optimized again until we reach an optimal result.
Figure 1. Basic scheme of the microscope lens.
Figure 2 shows the results directly from the system. Summarizing the proposed paraxial system:
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The focal length of the first lens is 16.1904 mm and 38.0952 mm for the second lens.
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The total seal of the system is 13.6039 mm, a f/1.88 and the distance between the lenses is 8.94 mm.
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Using the BK7 and SF2 lenses, and keeping the previously found focal points, we obtain two achromatic lenses.
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The wavelengths F, d and C must be configured in Zemax. For the field we are going to put a 1º.
Figure 2 shows all the necessary data that we introduce in Zemax.
Figure 2. Calculations for the preliminary design of the microscope lens.
From the calculations in Figure 3 we began to design the system. Figure 3 shows the results of the updated system.
Figure 3. System report.
The system is Limited Difracted on the shaft. The performance of the system is very good, as can be seen in the MTF, as the spatial frequency in cycles per mm is practically reduced at the same time as the OTF module. The Maximum Focal Shift is 16.18 microns.
The distortion is below 2%, the field curvature is less than 0.05 mm, the RMS Spot Size is 1.640 and 1.857 microns for the field of 0º and 1º respectively. The ray-fan shows us that the system has well compensated aberrations. The lateral color is limited difracted as can be seen in Figure 3. The relative illumination is 90% in both fields.
With this, I conclude the design of this problem.
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