Minimum curvature radius for small concave lens

I’m designing a system with a 7mm diameter (D) lens. This lens tends to optimize to a meniscus shape with a very short curvature radius on the concave surface. I’m now imposing an absolute R> D/2 to avoid hyper-hemispherical conditions, therefore R>3.5mm, but I feel this is still a too weak contraint.
What could be a minimum curvature radius for this surface to be manufacturable?

Thank you

If this is meniscus shape,it’s totally can be designed two diameters,one diamter for concave surface,one diameter for convex surface,I mean, you can decrease the diameter of the concave surface by increasing the planar area of ​​the concave surface.

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A good rule of thumb is 5mm but some shops have tooling to go shorter. Always talk to the shop early in the design process.

In any case, 5mm on a 7mm diameter element is a very fast surface, which makes it difficult to polish and test. You might be better off splitting that into two weaker elements. Doing that will also loosen your tolerances significantly.

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Thank you for the rule of thumb and for the additional hint about power splitting.
I’ve been searching on test-plate lists and stock optics catalogues. It seems test plates easily go below 3mm radii, but I cannot find quite many stock lenses with radii below 3.5mm.

Something else I’m worried about is “diameter to center-thickness” ratio for small lenses. I’m used to stay between 3 and 10, but it seems this rule is completely broken for small lenses such as those used in endoscopes. See for example M_008.zmx from ZEBASE


Does anyone knows if they require dedicated manufacturing equipment?

For us,if the diameter of meniscus lens is 7mm,we can do when R ≥ 4mm,It can be manufactured.
About example M_008.zmx,for us manufacturers,there are too many parameters missing,such as diameter,Arc depth etc.
So it is not convenient to evaluate the feasibility of the optical system for manufacturers.

@Hanter_Xia thanks for this and the previous answer!
As for M_008.zmx example, I’m sorry I cut the column names in the tabular data above the layout!
Here is a better screenshot:


As you can see, lens diameter is about 7.1mm, but center thickness is >20mm, in fact they look more like elongated cylinders than standard lenses.
Regarding “Arc depth”, if you mean “Sagitta” or “Sag”, the deepest concave surface is that of row 13 in the above screenshot and corresponds to a Sag=1.38mm.

@Alberto_Donazzan
Yeah,it just like cylindrical lens,as you said,the thickness is>20mm,so it‘s processing is difficult,But it can be produced,however it should need special tools used for milling and polishing.
I would like to suggest that you reduce the center thickness,but this optical system is suitable for endoscopy,and it may have a great impact on reducing the center thickness.
Here is one point for sharing.
Regarding this achromatic doublet lens,the lens on the left should cancel the platform on the convex surface,which should be unfavorable for processing,even with special tools.
It may be possible to try to use a diamond single point turning machine for production, but the characteristics of the lens material need to be taken into account.

design part-1

Your insight is very helpful.

About the doublet you highlighted, I would say that shape is just for visualization purposes within the optical design sw. In fact, that glass margin is not considered by ray tracing.
I guess in the real world it would make more sense to ignore the flat margin for the left singlet and just cut it to a smaller diameter to make centering, glueing and mounting easier.

Yeah,you are right!
It’s a great honor to have this discussion,It’s meaningful.

From the point of view of production and processing, the concave hemisphere can be processed, and we can guarantee that the surface shape of 90% of the area is no problem. But from a design point of view, the smaller the radius of curvature, the larger the incident angle of marginal rays, and the larger various aberrations, which is unfavorable.

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Alberto,
QED Technologies supplies a 10mm wheel to our customers for our MRF polishing that is able to figure correct 7mm concave RoC parts.

Regards
Brian Charles
Applications Engineer
QED Technologies