Blog de diseño óptico
Telephoto
Telephoto
Ocular 10x Apocromático.
Telephoto objective.
We are asked to design a telephoto lens with an EFL of 10", f/5.5, achromatic and a ratio of 0.8. It has to be designed for spectral lines F, d and C, using K3 and F3 crystals. The field angle will be 10º. Figure 1 shows the preliminary design of the system.
The main characteristics of a tele-objective are that the main image plane is found in front of the lenses, which gives us a relatively large focal while the system is compacted.
In these systems a K number is specified, known as the "Telephoto ratio". In this design will be 0.8 but can be higher. This number is important because it intervenes in the calculations.
In this design we have to take into account that:
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The total length is KxEFL of the system.
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The BFL is half the focal length. This way the system will be compacted.
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The main image plane is in front of the system.
Figure 1. Basic scheme of the telephoto lens.
Figure 2 shows the results of the telephoto lens calculations according to the requirements of the problem.
The system overview is:
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The focal length of the first lens is 6 mm and the focal length of the second lens is -7.5 mm.
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The BLF is 5 mm.
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Figure 2 shows the calculation of achromatic lenses based on the initially calculated powers.
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The separation between the lenses will initially be 3", placing the AS halfway between the two lenses.
In Figure 3 we can see the target spot size. In this case, we will first achieve the spot size of the strict system, that is, keeping the BLF to be the exact half of the EFL and the distance between the lenses will be 3". In the non-strict system, we will have a margin in both the BFL and the distance between lenses of ±3%.
Figure 2. Preliminary system calculations.
Figure 3. Rms Spot Size target.
Figure 4 shows the system optimized to the required degrees, keeping the total distance of the system very close to 8" and improving the spot size beyond those required, especially in the fields 0º and 5º.
Figure 4. Strictly optimized system.
In Figure 4 we see that the size of the Spot Size RMS is smaller than what we are asked. However, the system has serious performance problems. The system does not have the color corrected, the astigmatism is very high, around 21.5 waves, the spherical aberration and coma are also high, 8.5 and 7.4 waves respectively. The field curvature is also relatively high, as the units are in inches and as you can see in the Ray Fan, there is a lateral color problem.
The reason for this poor performance is attributed to the limitations imposed on us, only use two elements, the crystals are predetermined and the system must meet a series of very restrictive parameters.
Figure 5 shows the system where we relaxed the design conditions by about ±3%. in terms of distances between lenses and the BFL.
Figure 5. Optimized relaxed system.
By relaxing the conditions we can see how the distortion has been reduced by five, as well as the field curvature is reduced by half. The size of the RMS Spot Size is much smaller in the second system, almost 4 times smaller in the relaxed system than in the strict system. The color remains uncorrected.
Astigmatism has been reduced by 3, and now has a value of 8.1 waves, as well as spherical aberration and coma, which now have a value of 5.8 and -1.2 waves respectively.
In both systems the Spot Size RMS proposed by the problem has been surpassed and I conclude this article.
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