Lens simulations (update)

[Stefano]

In a previous topic I asked for some advice on softwares to simulate/design lenses, and I ended up using Winlens 3D by Qioptiq (the free version), which was suggested me by rfcurry. You can watch a tutorial on YouTube to learn how to use it, and it is pretty simple to use. I was able to simulate commercially available lenses as well as designing my own.

 

All lenses shown here were simulated/optimized for infinite conjugate (object at infinity, in my case either at -infinity or - 1 km). Lenses usually perform differently when focuses at infinity or close up.

 

Basics

Here you can see some examples of common lens aberrations (and why a single element, especially if it has spherical surfaces, will make soft images).

 

This is a simple fused silica plano-convex lens (Thorlabs LA4052), with the aperture 1 mm behind the lens and set at f/1.4:

You can clearly see spherical aberration. The external rays are focused closer than the central ray, which will make the image soft.

 

Stopping down to f/4 greatly reduces the aberration:

 

Also, longer focal length lenses generally suffer less from this problem because if the lens' diameter is kept constant, the aperture is narrower (higher f-number). Below Thorlabs LA4380 at f/5:

Off-axis rays may not be focused to a point, and often they are focused closer to the lens (Petzval field curvature). Also, they may suffer from coma (another type of aberration).

 

The same lens, with off-axis rays:

Magnification:

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Achromatic lenses

The refractive index of all materials is not constant with wavelength, but changes slightly (it usually increases for decreasing wavelengths). This means that a lens will split colors exactly how a prism would (in fact lenses can be modelled as a stack of prisms), showing chromatic aberration. To partially solve this, two different types of glass are used, a low index low dispersion crown glass and a high index high dispersion flint glass, so that the chromatic aberrations of the two lenses cancel out, focusing two wavelengths (usually blue and red) in the same plane.

 

This can be done in UV, usually using fused silica as "flint" and CaF₂ as "crown".

 

Andy is interested in Thorlabs UV achromatic doublets, so I decided to simulate them. The shortest one they offer has a focal length of 100 mm (Thorlabs ACA254-100-UV).

 

Here I simulated it at f/5. I used a diameter of 25.4 mm (one inch) which is more than the clear aperture of this lens (18 mm).

The horizontal beam is nicely focused to a point with very little spherical aberration, while the off-axis beams are not as good.

 

Things improve at f/11:

 

Since this is an achromatic lens, I tested its chromatic aberration, and for the UV range I got this (blue: 254 nm, green: 313 nm, red: 365 nm):

 

Apart from a small area near 200 nm, every UV wavelength is focused to a different spot, which surprised me. This is a wider view (300-1100 nm):

 

This lens will focus UV and SWIR in the same spot. The weird UV graph is confirmed by Thorlabs:

 

The longer versions of this lens behave as expected. This is the focus shift for the 150 mm version, between 300 and 500 nm:

 

Edmund Optics sells UV-to-NIR corrected triplets. This is the 90 mm version, at f/5, showing some field curvature:

...and at f/8:

Chromatic aberration (200-1100 nm):

 

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Custom lenses

 

Using two Thorlabs ACA254-100-UV lenses, I made a 63 mm lens with good performance. The distance between the doublets is 9 mm measured from the centers (middle). The aperture is in the middle.

 

Lens at f/3.5:

Chromatic aberration (300-1100 nm):

 

Next, a 142 mm f/7 lens made only with custom elements:

 

Lens at f/7:

 

Chromatic aberration (300-1100 nm):

 

And lastly, a 46 mm f/2 Cooke triplet made only with fused silica elements (no chromatic aberration correction).

 

f/2:

 

Magnification of the on-axis spot:

f/2.8:

 

f/4:

 

Left element: Thorlabs LA4148, middle element: Thorlabs LD4735, right element: Thorlabs LB4096.

Distances (measured between the lens surfaces, in the middle of the lenses):

left-middle: 5 mm

middle-right: 16 mm

aperture 12 mm behind the rightmost surface of the right lens (the exact placing is not strictly important, it could very well be between the middle element and the right element, which it almost is).

[Andy Perrin]

This is very nice! Yeah, I think all lenses (even achromatic) have SOME focal shift. As you saw, Thorlabs tells the truth. But just because there is some focal shift does not mean it will be noticeable or a real problem in practice. 

[Stefano]

You have a point here. I remember this discussion: 

You said that the more you correct a lens for one portion of the spectrum, the worse it tends to be outside that portion. This is interesting because all modern and vintage lenses are at least achromatic (they bring two wavelengths to the same focus). They have at least two different types of glass. According to what you said, an uncorrected lens (such as my last example here, the fused silica triplet) might have less chromatic aberration in UV and IR than common corrected lenses (corrected for visible light only, that is). I remember seeing less chromatic aberration with my Soligor than with my SvBony lens (which goes against this reasoning), perhaps that's because of the shorter focal length of the Soligor (35 mm vs. 56 mm), or maybe because of other factors. When I take the narrow band photos for TriColour images, I have to refocus everytime by a noticeable amount, but in normal broadband UV photos, chromatic aberration is less visible.

 

I once tried to see how much focus shift there was between 310 nm and full-spectrum light (mainly VIS and NIR), using the SvBony lens.

 

This is a 310 nm image of a glass lens (which is opaque at this wavelength and looks black):

 

Then I took another photo with no filters, without refocusing or changing the aperture:

 

Quite a difference! And then after refocusing:

 

But normal UV photos (with the lens generously stopped down) look much better (this is the same exact lens):

 

 

 

These were taken with very narrow apertures, possibly f/16 and below. If the lens is wide open, chromatic aberration is the least of my concerns:

 

Any lens has some degree of chromatic aberration. Apochromatic lenses are the next step after achromatic lenses, bringing three wavelengths at the same focus, and the very best are superachromatic lenses, which bring four wavelengths into the same focus, and are very expensive and difficult to make. The amount of chromatic aberration can be negligible as you say, in fact that Thorlabs lens (ACA254-100-UV), although not achromatic in UV, still has a very small focus shift there (between 200 nm and 400 nm, the focal length goes from 102.284 mm to 103.945 mm). I doubt you can notice it.

 

Lastly, designing lenses makes you notice all the flaws of the lenses in our eyes. My eyes (and surely yours) have chromatic aberration. If I look at a red and blue LED in the distance (making magenta), I see the red light in focus surrounded by a blue blob, because I cannot focus blue light at infinity. You can notice the same by looking at a screen with blue and red next to each other, for example a checkerboard pattern made with red and blue. Especially from far away, you will not see it clearly.

[Daniel Csati]

Excellent overview! Thanks very much.

I like Winlens a lot. Not many simulation software out there which is so easy to use and is Free. OSLO maybe, but it's definitely not easy to learn.

 

Someone should do the same but with a non-sequential type of simulation. I was looking for so long without luck and ended up buying something.. It was a good investment though :)

 

Here is something from Edmund Optics comparing aspheric, spheric and achromatic doublet lenses. 

https://www.edmundoptics.eu/knowledge-center/application-notes/optics/lens-geometry-performance-comparison/

 

 

[Lou Jost]

This is a fascinating post. However, I think this is not a valid simulation of the Thorlabs UV achromats. As you can see from Thorlabs'  lens diagrams at https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6802 , they are not cemented doublets (which would have identical radii of curvatures on the inner surfaces of the two lens elements, as your diagram seems to show) but rather are air-spaced doublets with four independent radii of curvature. These extra degrees of freedom allow much greater correction of aberrations.

[Stefano]

This was some time ago, but I'm pretty sure I simulated these lenses correcly, as air-spaced doublets. They look close to cemented doublets, if you look at the radii of curvature in your Thorlabs link, you will see that R₂ and R₃ are nearly identical (plus or minus a minus sign), and also the spacing between the lenses is very narrow.

[Lou Jost]

17 minutes ago, Stefano said:

This was some time ago, but I'm pretty sure I simulated these lenses correcly, as air-spaced doublets. They look close to cemented doublets, if you look at the radii of curvature in your Thorlabs link, you will see that R₂ and R₃ are nearly identical (plus or minus a minus sign), and also the spacing between the lenses is very narrow.

Yes, I see you are right; I was going by their lens diagram, but the numbers in their table don't match their diagram and do seem close to your simulation. The one exception is r4, which is positive in the table but which seems to be negative in your simulation. Is that right?

[Stefano]

I think the sign of the radius of curvature refers to the side (left or right) towards which the curvature is "pointing". It is positive if it points to the left, and negative otherwise. A biconvex lens has a positive first radius and a negative second radius, counting from left to right.

 

If you look here at the pdf drawing of the lens, which seems to be accurate, it looks like it does in my simulation.

[Lou Jost]

Yes, you are right about that too. Thanks for your patience in clarifying these points!

[Stefano]

You are welcome!