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Blog de diseño óptico
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Ocular 10x Apocromático.
Celor Lens.
In the following article we will review the fundamentals of a "Celor Lens". We will calculate one and then introduce these data into Zemax and optimize the system to get the best performance in two different situations. In the first one we will leave the symmetrical system while in the end we will break the symmetry in order to improve the performance. The Celor Lens that we are going to design and optimize corresponds to problem 28 of "Introduction to Lens Desing" by Joseph M. Geary.
The classic design of a "Celor Lens" is shown in Figure 1. It is a symmetrical system where we find the AS between two groups of lenses. Each group consists of a positive and a negative lens, arranged as shown in Figure 1.
In Figure 1 we can also see the conditions that has to design a Celor Lens.
Figure 1. Basic scheme of a Celor Lens and the limitations they have to have.
From the conditions in Figure 1, we can derive the equation we are going to use to calculate the lens radii. Once the quadratic equation is solved, it will give us two results for the power of the negative element (the first element). Next, we find the power of the second lens by replacing the value found in the third equation in Figure 1.
φp refers to the coefficient of the Peztval wavefront, dependent on the powers and refractive indices of the components. In our lenses we are going to leave this value at zero, although we could make a more realistic calculation and set it at 0.03.
Figure 2. Equation from which we calculate the power of the negative lens of the rear group.
Once we find the powers of "a" and "b" through the equation of the total power of two separate lenses, we can find the separation between the lenses. Since the equation in Figure 2 is a quadratic equation, we will have two different solutions. In our case, we keep the positive solutions (they are the ones that give us a negative lens followed by a positive one).
The crystals that we are going to use to design our "Celor Lens" will be the SK4 and BAF4 crystals. Using the equation "the lens builder" we calculate the radii of the lenses.
We have to keep one thing in mind before we go on: the total system will have a total power of 5", but right now it is designed only the rear, so we have to put a power of 10". The f-number of the total system will be 5, but when it comes to calculating the rear system it will be double.
Figure 3. Calculation of powers, radii and separation of the lenses of the previous part.
We already have the necessary data to enter the back in Zemax. Once the radii are entered, we will add a reasonable thickness. We will start optimizing by leaving the lenses as equi-convex lenses, with a total EFL of 10", EPD=1".
In order to optimize we will follow the following steps:
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The first thing we optimize is the EFL (which will have changed with the addition of lens thickness) and color correction. The AS will be on the first surface for now.
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We will reduce the spherical aberration a bit. We will allow all surfaces to be variable, as well as the space between them.
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We will add value to the field little by little. First add 2.5º or 5º and optimize again. When adding field we will see that the value of the comma aberration and astigmatism are big. We will have to optimize them. Once the field is added, we can delay the AS up to a distance of 0.2".
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Once the rear system has been optimized to have an EFL=10", the more or less controlled aberrations and the 5th half field, we add the front system. (In Zemax we can copy the whole rear system, copy it to a previous surface and with the command Ctrl+b we execute the operation "Reverse Lens"). The distance between the front and rear system is going to be 0.4" in total.
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With complete system, we are going to put all the rear system as "slaved" of the front system, the distance between fixed lenses and we are optimizing. Each time we will be adding more field to reach 10 º.
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Once well optimized, we can vary the space between lenses.
Finally, one way to improve the system is to break the symmetry and allow all surfaces to be variable.
Figure 4 shows the results to be beaten.
Figure 4. Results to beat.
Figure 5 shows the results of the "Celor Lens Strict". It is an achromatic system, with a Focal Shift Range 105.53 microns, a RMS Spot Size of 21.402, 124.143 and 103.736 microns for the fields 0º, 14º and 20º respectively.
The field curvature and distortion is less than 0.05 and 0.5 respectively.
Figure 4. Strict "Celor Lens" report.
Figure 6 shows the results of the "Celor Lens Relaxed". It is an achromatic system, with a Focal Shift Range 105.53 microns, a RMS Spot Size of 21.402, 124.143 and 103.736 microns for the fields 0º, 14º and 20º respectively.
With respect to the symmetrical system, there is an improvement in the ray-fan plot, since its scale is much smaller.
Figure 5. Relaxed Celor Lens report.
En ambos casos hemos mejorado los RMS Spot Size propuestos manteniendo el resto de aberraciones compensadas.
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