Lens design #1

[Stefano]

Do we need a dedicated lens design section?

 

Here's a lens I designed using WinLens3D Basic. The optical layout was inspired by Llewellyn Optics's 6 mm M12 lens available on MaxMax site. Link: https://maxmax.com/uv-lenses/lenses

 

Here's the design posted on the site:

 

My lens uses Thorlabs elements, all made of fused silica (the lens is not corrected for chromatic aberration), and (barely) covers an APS-C sensor (judging from the ray tracing graphs below I'm guessing the corners would look dark). The software gives an image distance of 31.7 mm (I'm guessing this is the distance between the rear element and the sensor).

 

Here's the optical layout:

 

Below the ray tracing drawings. Maximum ray angle of 35°, object points set at linear height, but are not projected linearly by the lens, they are "squished" at the edges, thus there's probably barrel distorsion.

 

f/1.4:

 

f/2:

 

f/2.8:

 

f/4:

 

f/5.6:

 

f/8:

I would say the lens is kind of usable from f/2.8, and should be quite sharp from f/5.6. Probably the biggest challenge in building it is fitting an iris in that tight space.

 

As for the focal length, I don't know where to read it. I could work it out from the aperture, but at this point I'm not sure about what the software is doing. Here's some information:

 

I posted large images, hope it isn't too confusing. I can re-upload them if necessary.

 

 

[photoni]

@Stefano  The focal distance of a lens is measured by focusing at infinity and measuring the distance from the center (usually where the aperture is) and the film plane.

(Remember that focal distance divided by lens diameter = f)
If you need help I can give you the address of a friend from Padova who has designed lenses

[dabateman]

Well just the elements uncoated from Thorlabs, no tax or shipping is $418.12

Getting all the elements with 245-400nm AR coatings is $513.60, no tax, no shipping.

Then you need the housing, aperture and helicoid. 

I can see this still being an expensive lens.

 

The aperture isn't too hard actually,  you can get something like this: 

https://www.ebay.com/itm/273449402272?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=2W7zKMt9Qv-&sssrc=2349624&ssuid=RxqKLNPYQr-&var=&widget_ver=artemis&media=COPY

 

[Stefano]

8 hours ago, photoni said:

@Stefano  The focal distance of a lens is measured by focusing at infinity and measuring the distance from the center (usually where the aperture is) and the film plane.

(Remember that focal distance divided by lens diameter = f)
If you need help I can give you the address of a friend from Padova who has designed lenses

For some extreme retrofocus lenses the distance between the aperture and the sensor is much greater than the effective focal length. It is probably better to calculate the equivalent focal length from the field of view. Give me the address if you want. Thanks.

[Stefano]

7 hours ago, dabateman said:

Well just the elements uncoated from Thorlabs, no tax or shipping is $418.12

Getting all the elements with 245-400nm AR coatings is $513.60, no tax, no shipping.

Then you need the housing, aperture and helicoid. 

I can see this still being an expensive lens.

 

The aperture isn't too hard actually,  you can get something like this: 

https://www.ebay.com/itm/273449402272?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=2W7zKMt9Qv-&sssrc=2349624&ssuid=RxqKLNPYQr-&var=&widget_ver=artemis&media=COPY

 

Yes, it's not a cheap lens, but perhaps somewhat cheaper than other options.

 

You would need two separate tubes to mount the lenses, separated by the aperture. Using an M42 aperture with adapters could barely be possible, otherwise you would need an aperture like the one you linked.

[Andrea B.]

However, $400-500 for a UV lens is inexpensive relative to $7000 for a UV-Rayfact !! 

 

How would one correct for chromatic aberration? Just curious.

[Stefano]

You need lenses made of at least two different materials, such as fused silica and calcium fluoride. Their different refractive indices and dispersion characteristics allows to basically produce two opposite chromatic aberrations that cancel out, bringing two wavelengths at the same focus.

 

Using lenses made all of the same material, such as in this case, makes chromatic aberration unavoidable, provided the material has a continuously decreasing refractive index as the wavelength increases, which is the case for most if not all materials as far as I know.

 

At shorter wavelengths, the lenses have a higher refractive index, bending light more and decreasing the focal length. For common singlet lenses with common focal lengths (like 50 mm), the shift from UV to IR is often several millimeters.

[Andrea B.]

You need lenses made of at least two different materials, such as fused silica and calcium fluoride. Their different refractive indices and dispersion characteristics allows to basically produce two opposite chromatic aberrations that cancel out, bringing two wavelengths at the same focus.

 

Ah, got it! Thanks.

[lukaszgryglicki]

But this corrects for two wavelengths, right? AM I understanding correctly? How about so-called APO lenses?

Can I assume that using 3 types of materials allows correcting for 3 wavelengths - or maybe coatings?

One mor equestions - why calcium fluoride not magnesium fluoride? The latter is less water soluble I think and its metal is less electro positive (Mg vs. Ca).

I wonder about BeF2 but berillium is rather very expensive... but then berillium alone is stable in air, magnesioum barely and calcium is not (I mean metals not their fluoride salts).

 

[Stefano]

Yes, it corrects for two wavelengths. Although the curves are more complex than that, a non-corrected lens has an approximately linear focus shift with wavelength, while a normal achromatic lens has a curve that look like a parabola: the focal length is longer in UV, shortest often in green light and then longer again in IR, thus red and blue are focuses together, and often also UV and IR. Even though there's still some chromatic aberration left (green light is focused in a different plane in respect to red and blue), the residual focus shift is less than an uncorrected lens.

 

It is possibile to build apochromatic lenses, which bring three wavelengths to the same focus (the curve looks like a cubic), and the most extreme correction is superachromatic (four wavelengths at the same focus). These lenses use many different types of glass.

 

Calcium fluoride has a very low but non-zero water solubility (0.016 g/L at 20 °C, from Wikipedia), and although it is a cristalline material, to my understanding it should have no birefringence as the crystal unit cell is cubic (and thus symmetrical). Magnesium fluoride is actually more soluble (0.13 g/L), and it is slightly birefringent which is something you don't want in a lens. Lithium Fluoride (LiF), which is the deepest UV-transmitting material existing, is even more water-soluble than magnesium fluoride (1.27 g/L at 18 °C). It is transparent to at least 110 nm, maybe even 100 nm.

 

There are other UV windows that can be made into a lens, such as sapphire.

 

The problem in UV is that there aren't many available materials and some are delicate, water soluble or birefringent. Also, the refractive indices of fused silica and calcium fluoride are very similar, they aren't as different between each other as common crown and flint glasses, and this makes correcting for chromatic aberration more difficult, especially at shorter focal lengths. That's probably one of the reasons why UV-dedicated lenses such as the UV-Nikkor have long focal lengths, in the 60-105 mm range. Fused silica and calcium fluoride aren't different enough from each other to build a corrected wide-angle lens.

 

MaxMax has designed a 75 mm f/4 lens, and a 25 mm f/4 C-mount lens which is apochromatic and transmits UV below 200 nm. It uses fused silica, calcium fluoride, magnesium fluoride and sapphire elements.

https://maxmax.com/uv-lenses