Blog de diseño óptico
Telephoto
Telephoto
Ocular 10x Apocromático.
"Petzval Lens"
In the following article we will look at the fundamental properties of a Petval lens and then design and optimize one. This design corresponds to the exercise of theme 33 of Joseph M. Geary's book.
Figure 1 shows the classic design of a Petzval lens, where we find two positive lenses, the first one a positive achromatic lens and the second one is formed by a separate negative and positive meniscus. In the middle we find the aperture diaphragm.
Figure 1. Basic scheme of a Petzval lens
Figure 2 shows the basic conditions that have to be met in a Peztval lens:
-
The focal length of the first lens must be half of the total focal length.
-
The separation between the lenses is equal to the focal length of the first lens.
-
The second lens must have a focal power equivalent to the total focal.
-
The BFL is equivalent to half the total focal length.
-
The two standards we have to meet without exception is to maintain a ratio of 2 in EFL and BFL and that the AS is always halfway between the two lenses.
Figure 2. Basic conditions of a Petzval Lens
The problem asks us to design a system using LF7 and K7 crystals, with a 5" EFL for a 10º semi-field. The EFL/BLF ratio has to be equal to 2 and the spacing between lenses will initially be 4.4". This space will be modified as soon as it is optimized. It will be designed for the wave lengths F, d and C.
Figure 3 shows the calculations of our Petzval system. To determine the power of the lenses we have used the equations we used in the "Celor Lens". We will assume that the φp=0 (Peztval Power). Part of the difficulty of the problem is that we are "imposed" the front doublet. This doublet will not be modified at any time. We will carry out two versions, a strict one where the conditions exposed in the previous paragraph are fulfilled and another relaxed one with which we will obtain better results.
Figure 4 sets out the objectives to be achieved.
Figure 3. Paraxial calculations of the Petzval lens.
Figure 4. Objectives of the Petzval system.
Figure 5 shows the result of the already optimized strict system. The distortion and field curvature have very small values and the Spot RMS Size is lower than required, especially for the 10º field. The field curvature is less than 0.05 and the distortion is less than 0.5%.
The color correction is not good, as the system is not achromatic and the Ray Fan scale is very high. The performance of the system is poor as can be seen in the MFT.
Figure 5: Inform Peztval Lens estricto.
Figure 6 shows the relaxed system.
In this case the system is achromatic, field curvature and distortion are less than -0.05" and 1% respectively. The RMS Spot Size is lower than required by the problem, being 19.571, 32.517 and 47.264 microns in the fields of 0º, 7º and 10º respectively.
The MTF is quite low, but considering the limitations of the problem and the proposed RMS Spot Size, it is normal.
Figure 6: Inform Peztval Lens relajado.
In the following link I show an own design of a "Petzval Lens Relaxed".
If you found this article interesting, let me know. Below you have how to contact me.
Thank you very much and I'll see you later.