How to Measure Magnification of a Lens System with Liquid Surface

[HomeTinker]

TL;DR Summary

I am trying to solve the issue of the uneven illumination of the imaging surface created by the lens formed from the stop surface of the liquid.

HI

I am currently playing with imaging device that would take pictures of the content of the bottom of the small plastic container. The container is just a tube of 7mm in diameter. When I image an empty tube I get a proper high contrast image of the dust on the bottom of it. However the problem is that I have to take pictures of targets in liquid.

The device has a camera, a lens with 1x magnification (sufficient for the resolution and the target I am trying to image. The problem is the illuminations. I have build a 4f Koehler illumination for the this purpose and it seems to be working fine. When I test the beam of light coming out of it I get mostly parallel beam of light, slightly diverging but not much. When I use that system to image the bottom of the plastic container I get a proper, decent high contrast image of the dust on the bottom of it.

The problem starts when I add liquid into it. The content of the container is no longer evenly illuminated, even though the light outside of it seems to be ok. The effect is that the edges of the container (which is circle) are darker and seems to be slightly out of focus in comparison to the center. The effect is magnified if there is very little liquid added and gradually disappears the more liquid I add (however never getting even close to the picture of the empty container). Clearly the top surface of the water is acting as a lens due to it's meniscus. I tried all sorts of ways to try to mitigate that but with no success and sadly for a good pictures I need even illumination across the entire picture. Small variations I guess would be fine but not more than few percent.

Any ideas how to mitigate this issue in the optical design? How to even measure if this lens made by the water surface is going to be convex or concave?

Any help is very much appreciated.
Many thanks.

 

[sophiecentaur]

Hi. I don't know much about optics but I would imagine that adding liquid into the light path will alter the path length so 'everything' or anything could need re-adjusting. (???)
Perhaps going through the set up procedure with just the tube of liquid first.

 

[berkeman]

Paging @BillTre

 

[berkeman]

Welcome to PF.

I am currently playing with imaging device that would take pictures of the content of the bottom of the small plastic container. The container is just a tube of 7mm in diameter.

Can you post a sketch of the setup, including the position of your illumination sources? Use the "Attach files" link below the Edit window to upload PDF or JPEG files.

 

[HomeTinker]

I have attached the diagram of the illumination. Please let me know if that helps.
To clarify the illumination area is much larger than the diameter of the container. The illumination can access areas outside of the container, however the issue is that the centre of the container liquid is nice and bright but the edges are dark, as if the illumination was not as bright there or the image of the illumination generated by the liquid surface working as lens was too small for the imaging system.
Hence the question - how can I measure, calculate that? Or alternatively what other lens is needed to mitigate the lens generated by the liquid surface....

Many thanks for help

 

[Ibix]

How much control do you have over the depth of the liquid? If the problem is the meniscus, fill the tube to the top so that the meniscus flattens out.

If that isn't practical in "production" use you could at least use it as a test to confirm that the meniscus is your problem.

 

[HomeTinker]

The meniscus it the problem, I tried to check that by gradually adding more liquid to the container and I can see the effect being drastic with small amount of liquid and reducing when I fill the container to the top. Sadly I have no control over the amount of liquid as the system has to be able to work in a range between 50 and 250ul of liquid in the container. The question is how to compensate for that? Will the distance between illumination system and the surface of the liquid make a difference?

 

[sophiecentaur]

I have attached the diagram of the illumination.

I'm sure you could improve on the resolution of the version of your diagram that's been posted.

Or alternatively what other lens is needed to mitigate the lens generated by the liquid surface....

When I have used a microscope I have always used a 'slip' (very thin square of glass) to give a flat upper face to the slide. Perhaps a similar 'flattener' on the top surface of the liquid could work; finding a suitable 'Correcting Lens' could be a problem.

 

[sophiecentaur]

@berkeman that was just an idea! Don't rely on it being "informative". it could be BS for all I know. I am a specialist in bodgery in the things I make.

 

[BillTre]

I tried looking at your diagram, but the printing was too small to make out.

It seems that the direction of light is down, so it is an inverted scope?
If that is true then your drawing appears to show the water container with a non-flat bottom.

If that's the case, it will act as a lens when it has water in it, but not without. Adding more water in the tube could end up reducing the overall difference in OD between neighboring paths.
Most plates made for inverted scopes have flat bottoms to avoid this problem.

The water has a significantly different optical density from that of air, so the light bends.
This might be correctable by flooding the tube's surroundings with water. This might be doable by placing the tube in a water containing petri plate on the microscope stage (depending on how you are doing things). This should remove a lot of the difference in optical densities between paths near the edge, by replaceing air with water.

 

[Gleb1964]

I think picture is illustrated 4f Köhler illumination described here 4f Koehler transmission illumination

 

[HomeTinker]

Apologies for the poor quality of the image, seems like upload to the forum downscaled it. I tried to increase the font to make it more readable:

To summarise, yes this is in essence inverted microscope. The illumination is from the top, camera is located below and focusing on the bottom of the container. The bottom of the container is mostly flat, as much as plastic moulding allows. The lensing effect seems to be done by the top surface of the liquid. To be fair I am not even sure if that surface is working as concave or convex lens at this point.

Sadly I cannot immerse the container in any other liquid due to environmental constrains. I somehow need to illuminate the edges of the bottom of the container.

 

[HomeTinker]

4f Koehler transmission illumination I think picture is illustrated 4f Köhler illumination described

Yes that is pretty much what I am using here for illumination and I can prove that the beam of light is mostly parallel when it comes out from the illumination system. Then the light seems to be bent when it goes from air to liquid inside the container.

 

[BillTre]

Much better picture.

Do you have to use water?
Maybe an oil of something instead, with less of a meniscus.

Is this some kind of biological prep?

Could you flood the tube and put a coverslip on top with no bubbles? This would make an optically good surface.

 

[HomeTinker]

I really wish it was that simple.
Liquid is water based with some medium for microbiology and cannot be changed.
Sadly it cannot be filled in to the top and covered either for handling.
The working volume is about 3/4 of the height of the container.

The solution has to be down to optics, corrective lens I am afraid.
Not sure how to calculate what is needed.

 

[berkeman]

Liquid is water based with some medium for microbiology and cannot be changed.
Sadly it cannot be filled in to the top and covered either for handling.
The working volume is about 3/4 of the height of the container.

The solution has to be down to optics, corrective lens I am afraid.

Or post-processing of the image. Have you looked at Fourier transform options for post-processing?

 

[Drakkith]

You might be able to do something like a flat-field correction. It is commonly used in photography and astro-photography to correct for uneven illumination/brightness. Do you have any image processing software? Send me a PM and I'll try to figure out something with you.

 

[sophiecentaur]

Sadly it cannot be filled in to the top and covered either for handling.

It may be that there's not a 'simple' solution. A major change in design may be needed.

A suitable correcting lens would be difficult to make. Hard enough to correct if the air / water interface were spherical but very hard for this situation with a very non-spherical shape to correct..
Use a shorter tube?
Use a wider tube with a ring to obscure the curved part of the surface?
Cover the water with a thin layer of oil?

Other workers are sure to come across this problem. Some more reading round, perhaps.

 

[HomeTinker]

Many thanks for the answers, I assume post processing may help to certain degree but I think there must also be some additional update to the optics.
I am looking to use something like this:
https://en.wikipedia.org/wiki/Meniscus_corrector

But how do I calculate the curvature I need?

 

[Drakkith]

I am looking to use something like this:
https://en.wikipedia.org/wiki/Meniscus_corrector

A meniscus corrector corrects for spherical aberration, not uneven illumination. It acts as a slightly negative lens and will possibly make the problem worse. Though I am not an optical engineer, so I can't say for certain.

 

[Gleb1964]

While been an optical engineer, there is not a good description of the problem to see the exact "trade of" of the optical design.
The perihelial of field seems to be vignetted close to the tube walls, the involved factors are meniscus shape of the liquid surface, the depth of the liquid, the inner diameter of tube and the length of the tube walls, preventing the illumination light cone to be accepted by the microscope lens.
The meniscus lens can change the cross section of illumination beam, it does produce the non-zero angular magnification, the spherical aberration is a secondary and not significant factor there, but I don't see directly where it should be placed.

 

[sophiecentaur]

A meniscus corrector corrects for spherical aberration,

Afaics, the name "meniscus" is only used because the lens 'looks a bit like one'. It's designed for spherical lenses, which the meniscus on top of the liquid is not.

Just a thought: the meniscus could be corrected a bit by altering the inner surface of the tube with a suitable paint / varnish or even some soap.

 

[Gleb1964]

Think about reverting the optical layout. You have an imaging system, collecting light, so the illumination should match your collection system. If you want even background illumination, the illumination system is supposed to fill the acceptance cone of the imaging lens at every point of the illuminated field. I can assume that the imaging system is telecentric at the object space (where you have a sample). That means that the aperture stop is located at infinity or far enough, to consider that acceptance light cones are parallel at the sample field. Propagating the acceptance light cones backwards, they should hit the light source. But the light cones at the margin of the field would find the walls of the cuvette, where the part of the cone would expire internal reflection, changing its direction somewhere else, missing the source.

 

[sophiecentaur]

It is commonly used in photography and astro-photography to correct for uneven illumination/brightness.

It's common to use 'greys'. These are shots of a flat grey background which are then subtracted / added to (or is it multiplied by?) the wanted image to give an aesthetically pleasing look.

 

[HomeTinker]

Many thanks for some good replies. To put things into context please see that image below taken from the side of the container showing how the liquid bends inside.

The illumination is from the top and imaging is below.
The system is telecentric, the center of illumination is at the center of the container, imaging lens and the camera.

And here are example images with 200 ul (showing the issue) and 400ul of liquid which is the container filled up to the top.

All parameters of the system are this same other then the level of liquid in the container.

Question to Gleb1964:
Are you saying that essentially I see the "shadow" of the container walls and there is no way I can get the light into this areas? Apologies if I misunderstood your comments.

Many thanks for help.

 

[Drakkith]

Interesting. It looks to me like the meniscus is, essentially, a negative lens. The surface forms small angles near the center and larger angles as we move outwards, meaning the light is entering close to normal and hardly refracting at all near the center but being very sharply refracted near the edges. That should explain why the illumination is so uneven. The 400 ml sample has a much shallower meniscus and is roughly twice as far away from the bottom, which would help even out the illumination.

I'd guess that placing a positive lens somewhere before the meniscus-surface would counteract the effect somewhat. I'm unsure if it can be eliminated entirely.

I also wonder if a diffuse light source instead of a collimated source would help. Though that might affect the quality of the dust particles in the image.

Again, just my non-professional thoughts.

 

[HomeTinker]

That is what I am thinking, there should be a way to minimise the effect optically (I am sure completely removing it may be difficult). The question is, how to calculate the lens needed.

I also tried the version with just the LED and the diffusor before making it Koehler and the issue was still present (I would say even more prominent).

But here is what I cannot understand.
If the liquid surface is bending that way, the light rays from the illumination system should be bent outwards towards the sides of the container when they cross from air to water via the liquid surface. If anything that should make the opposite effect than what is on the pictures.

Any ideas what am I missing here?

 

[Drakkith]

If the liquid surface is bending that way, the light rays from the illumination system should be bent outwards towards the sides of the container when they cross from air to water via the liquid surface. If anything that should make the opposite effect than what is on the pictures.

The light near the center is less strongly refracted than light entering the water on the outer band of the meniscus. The center 10% is barely refracted at all, and so is barely dimmed. But the outer 10% is refracted entirely out of the container through the glass (I don't know the exact percentage, that's just an example). The light that actually makes it to the outer 10% of the sample came from somewhere in the middle band of the meniscus, not from the outer radius.

Also note that the center of the meniscus is much closer to the bottom of the sample than the outer portions. So light entering from the center of the meniscus has less distance in which to diverge than light entering from the outer bands of the meniscus. It simply can't spread out as much before hitting the bottom of the sample.

 

[Gleb1964]

What if you place a plano-covex lens at the bottom of container, flat side towards bottom and observe the cuvette through the convex side of the lens? The aim of such lens is to form sort of Galilean telescopic system in combination with the negative water meniscus. In that case the illumination system woud function as it should.

 

[HomeTinker]

Surely if I did that the image of the elements on the bottom of the container that I am trying to take will be distorted, right?

By the way - is there any software that could be used to model this?

 

[berkeman]

Surely if I did that the image of the elements on the bottom of the container that I am trying to take will be distorted, right?

Which comment are you replying to? And I'm pretty sure that neither of them like to be called Shirley.

 

[Drakkith]

What if you place a plano-covex lens at the bottom of container, flat side towards bottom and observe the cuvette through the convex side of the lens? The aim of such lens is to form sort of Galilean telescopic system in combination with the negative water meniscus. In that case the illumination system woud function as it should.

The problem is that by the time the light passes through the bottom of the sample much of it has already been lost. Plus that will require modification of the camera end of the system since you have introduced a positive lens into it.

 

[HomeTinker]

Which comment are you replying to? And I'm pretty sure that neither of them like to be called Shirley.

Apologies, that was a reply to the idea of adding plano-convex lens on the bottom of the container.

 

[HomeTinker]

The problem is that by the time the light passes through the bottom of the sample much of it has already been lost. Plus that will require modification of the camera end of the system since you have introduced a positive lens into it.

Modification of the camera lens is possible, there is a complete freedom on that side. What I cannot do is to interfere with the container itself or it's content.

 

[Drakkith]

Modification of the camera lens is possible, there is a complete freedom on that side. What I cannot do is to interfere with the container itself or it's content.

Like I said, I think you will have already lost too much light by the time it reaches the new lens, but you could always try it. I'd recommend reaching out to an optical engineer and getting their professional opinion on the matter.