DIC Question

Here you can discuss different microscopic techniques and illumination methods, such as Brightfield, Darkfield, Phase Contrast, DIC, Oblique illumination, etc.
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viktor j nilsson
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Re: DIC Question

#61 Post by viktor j nilsson » Mon May 24, 2021 8:20 pm

Yes, sorry. This question was always off topic here. I'll leave it at that. Go ahead Louise, looking forward to seeing more from this interesting project!

apochronaut
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Re: DIC Question

#62 Post by apochronaut » Mon May 24, 2021 8:44 pm

viktor j nilsson wrote:
Mon May 24, 2021 6:50 pm
apochronaut wrote: Sure, stopping down will close off whatever peripheral aberrations that it does in any specific situation and the tube lens is usually thin and of low curvature and the Raynox DCR-150 is a very wide lens so benefits from it's original aperture and is used reversed, so their negative contributions might be considered somewhat benign but achromats are achromats and despite the slight curvature on these lenses, they still induce chromatism. Can you show me examples where tube lenses have been swapped willy nilly between mfg's and used without other modification and produced better results than the original settup?
Sure.
https://www.closeuphotography.com/tube-lens-test

Here's a test where a Mitutoyo 5x objective was used with a bunch of different tube lenses:

Thorlabs ITL200 Tube Lens
Mitutoyo MT-1 Tube lens
Nikon MXA20696 Tube Lens
Reichert Microscope Tube Lens
Canon 250D Close-up Lens
Century Precision Optics +4 Achromatic Diopter Lens
Century Precision Optics +7 Achromatic Diopter Lens
Cosina MMA Matched Macro Adapter Lens
Raynox +4.8 diopter
Raynox +5.9 diopter
Raynox +8 diopter
Sigma LSA Life Size Attachment Lens

The manufacturer's own tube length (Mitutoyo MT-1) performed quite poorly, and the best was the Thorlabs ITL200, which is actually made by Nikon. Interestingly, the Thorlabs-branded but Nikon-made ITL200 tube lens performs quite a bit better with Nikon and Mitutoyo objectives then the Nikon-branded MXA20696 tube lens that Nikon ships with its CFI and CFI2 microscopes...

I don't know of any equally carefully controlled comparisons with an Olympus UIS2 objective, but I've seen plenty of very clean images taken with Olympus objectives and a Raynox DCR-150 as a tube lens.
Yes. I've seen that and it is very weird. The author seems oblivious to the fact that a few of his test lenses are corrected for specific conditions with built in corrections and therefore are unlikely to be very usefull in his application. It's an apple and orange test. I think there might even be a kumquat in there.
So in Louise's set up she has an achromat guide lens placed somewhere as a tube lens for a ray bundle that begins at infinity, which is located 180mm from what is called the sample plane and focused at that point because it has a 180mm f.l.
That is very much a microscope set up, although in her situation she could alter those parameters if the lens was different, so she could modify the set up so that other tube lenses could work. In this case the term tube lens is being used but it is actually what I would call a telan lens. To me the tube lens is up in the photo tube.
The point was made earlier, ( not by me) that various "tube" lenses can be used with a number of infinity objectives and good to excellent results are possible. Yes, maybe in the photo tube, where things can be modified to suit but I prefaced my question with the term, unmodified, as in putting an Olympus objective in a Nikon stand, or a Nikon objective in a Mitutoyo stand or a Meiji objective in a Reichert stand.

That test uses all modified optics because he changes the location of the lens with each test, so it is a photography test, not a microscopy test. You can't really relate those results very well to an installation where each lens is in a factory set position in a microscope stand.
One thing it does show though, is that there are dramatic differences in tube lenses, so you can't just swap them willy nilly and when they are not corrected properly for a certain application or installed at the wrong distance, that they don't work well.

jmp
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Re: DIC Question

#63 Post by jmp » Wed May 26, 2021 4:38 am

I've been experimenting with Sanderson prisms too, after going over the paper from Rathi et. al. I believe there is an error in the expression that gives the divergence angle:

divergence_function.jpg
divergence_function.jpg (8 KiB) Viewed 457108 times

The problem is that with r and l defined as in their figure (Fig. 1):

prism_schematic.jpg
prism_schematic.jpg (32.13 KiB) Viewed 457108 times

the expression 4r^2 - 3l^2 will yield a negative number for reasonable values of r and l. I bumped into this because I was unable to replicate the linear relationship between the divergence angle and the displacement, of this figure (Fig. 3a):

displacement_vs_divergence.jpg
displacement_vs_divergence.jpg (15.22 KiB) Viewed 457108 times

when evaluating that expression using the measurements given in the paper. However if r is defined as the distance from the center of the prism to the inner pin, and the expression 4r^2 - 3l^2 is replaced with 3l^2 - 4r^2 then I can replicate Fig. 3a.

I wonder if I missed something and I'm wrong, or if someone else caught this too. I stumbled into that when I was trying to get an idea of the dimensions of the prism that I could use to build a slider for an inverted microscope that I wanted to try this with.

jmp
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Re: DIC Question

#64 Post by jmp » Wed May 26, 2021 5:06 am

(Continued)

In the end I built a crude 3D printed slider to accommodate a prism of 70x16x2.38mm:

slider_prototype.jpg
slider_prototype.jpg (55.97 KiB) Viewed 457105 times

It was quite interesting to see how the interference pattern changed as the bending force on the prism increased, when the prism was hold between a pair of crossed polar filters. Here's a snapshot of how it looked after a few turns of the displacement screws:

interference_pattern.jpg
interference_pattern.jpg (23.56 KiB) Viewed 457105 times

So far so good! Thus I gave this a spin in the inverted microscope. One of the upgrades for this microscope was a plasdic kit: a slit slider with a polarizer for the condenser (which I have) and a Nomarski prism for the slider in the back focal plane of the objective (which I unfortunately don't have). Thus I placed the Sanderson prism slider in the back focal plane of the objective and used the slit condenser instead of a second Sanderson prism before the condenser, not ideal but worth a try. Here's the result of the canonical cheek cell comparison using a 10x LWD objective (only edited the white balance, and set the images to grayscale):

cheek_cells_test.jpg
cheek_cells_test.jpg (51.86 KiB) Viewed 457105 times

While the quality of the pictures leaves a lot to be desired, I get the impression that there's a hint of DIC with the Sanderson prism, which is encouraging given how simple this procedure was. The 3D appearance of the oblique image differs from that of the Sanderson prism one.

Here's a larger view, where the pseudo-relief from the Sanderson prism seems to stand out more:
10x_cheek_cells_sanderson_prism.jpg
10x_cheek_cells_sanderson_prism.jpg (99.02 KiB) Viewed 457105 times
Given the results from this experiment, I'll build a second slider to place a second Sanderson prism below the condenser. It was difficult to get enough light (from the 50W halogen) with the slit condenser, it is likely that using a polycarbonate prism instead will significantly aid with the illumination of the sample and perhaps improve the quality of the images. Though I'm not expecting spectacular DIC images out of this setup, I'm doing this mostly to learn and have heaps of fun.

LouiseScot
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Re: DIC Question

#65 Post by LouiseScot » Wed May 26, 2021 12:42 pm

Hi Jmp

I'm glad someone else is having a go! I don't think the equation is wrong - probably a negative solution just indicates relative direction. It's worth going back to the paper by Biss et al. which you can get here: https://af.booksc.org/book/15387605/9162f0
I think the acid test is whether you get a clearly different image with and without the prism. You obviously get birefringence from the polycarbonate under stress and that shows up between the cross polarizers. However, I'm not sure that necessarily translates into actual DIC. From both Rathi and Biss, you need to get destructive interference in the centre of the fringe pattern i.e. a dark band. That's what I'm aiming for at the moment. I've had problems with my prism holders not really working as expected. I've 3D printed them in PLA but they do tend to bend as you tighten the screw(s)! Also the PLA can tend to crush with the pressure of the polycarbonate, under tension. I've remade the 'condenser' prism (Rathi Fig 2b) using masonry nails instead of PLA (which I had originally) for the upper contact points. I've previously been using 2 of the round prism frames for both ends but yesterday printed out an open frame prism holder (I just got some 6mm polycarbonate yesterday). So I'm trying that. Again a problem with bending... A metal frame would be better but I don't have the facilities for making one. However, it might be possible to make the part that tends to bend out of aluminium bar if it proves necessary.
Another thing is imaging the objective's BFP which is likely inside the objective so requires the relay optics to shift it to a point where it can be imaged. Rathi et al. appeared to do all their imaging with a 60x water immersion lens so that would definitely have its BFP inside the Barrel. I've essentially copied the Rathi optical setup but others may work just as well (see Kurvits et al. 2015).

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

jmp
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Re: DIC Question

#66 Post by jmp » Wed May 26, 2021 1:50 pm

To clarify, the problem is not that the angles are negative but that the results that I get from that expression do not agree with the displacement-to-angle relationship depicted in the figure from their paper, unless I make the changes that I mentioned. I might have missed something though, its not my field after all. Thanks for the book reference, that will be useful.

I agree with you in that the results from my test are not actual DIC. The interference pattern that I observed is from a single prism, and as you noted it does not have the destructive interference band in the center (the black line in the figures from Rathi's paper), for that I'd need to have both prisms in the light path. Now that I'm getting a idea of how this works I'll build the slider for the second prism in the next test iteration, and see if I can replicate the interference pattern from that figure in their paper.

I share your thoughts regarding the drawbacks of a 3D printed prism frame, mine also deformed noticeably under the stress from the bent polycarbonate prism once screws where tightened. Its fine for the initial tests but the prism holder will need to be strengthened somehow, probably with a metal frame of some sort, for this to be usable on a regular basis. At that point screws should not directly contact and push on the prism either, like they do now in my crude test frame.

Access to the back focal plane of the objective is not a concern for me at the moment with the microscope that I'm using. Though its a finite 160mm tube length design, it includes the necessary optics to bring the BFP of 10x and 20x objectives to a plane where sliders with the respective phase rings can be inserted. A conjugate plane before the condenser lens is also accessible for a slider that holds a single phase stop that works with both objectives; this is where the slit/polarizer slider from the plasdic kit also sits and where the second Sanderson prism will go in the next test. The setup is handy for learning and tinkering with this, but it won't be usable (if ever) for anything other than 10x/20x, which is fine for my purposes at least for now. By the way, thanks for the reference to the Kurvits paper, its interesting to learn from other designs.

Once I get around to build the second prism I'll share my results here, in case someone else finds them of use.

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Re: DIC Question

#67 Post by Hobbyst46 » Wed May 26, 2021 2:40 pm

Some general literature about 4-point beam bending arrives, for the maximum deflection, at the expression 3L^2-4A^2 (their A is Rathi's r) rather than the other way around. Just guessing that "jmp" is correct and the framed formula divergence_function above is incorrect -
perhaps worth further checking.
Last edited by Hobbyst46 on Wed May 26, 2021 3:23 pm, edited 1 time in total.

LouiseScot
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Re: DIC Question

#68 Post by LouiseScot » Wed May 26, 2021 3:14 pm

Hobbyst46 wrote:
Wed May 26, 2021 2:40 pm
Some general literature about 4-point beam bending arrives, for the maximum deflection, at the expression 3L^2-4A^2 (their A is Rathi's r) rather than the other way around. Just guessing that "jmp" is correct and the framed formula divergence_function above is incorrect -
perhaps worth checking by someone who really knows mechanics !
Hiya

The formula previously comes from Biss et al. But anyway, if X=A-B then -X = (B-A) so if the sign of the result doesn't matter then I don't think it makes much difference arithmetically:)

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#69 Post by LouiseScot » Wed May 26, 2021 6:21 pm

I just took a quick snap of my frame prism between cross-polarizers (illuminated by daylight):


FrameBiRefCrop28pc_190631.jpg
FrameBiRefCrop28pc_190631.jpg (20.55 KiB) Viewed 457053 times

It's reassuring that the birefringence is apparent. You can clearly see the unwanted Saint-Venant effect at the load point but the main fringes are ok. They seem a bit wide to me but I'll have to see how tings vary with increased tension. I just printed a thicker top bar so will try that next (if it still fits ok!)

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#70 Post by jmp » Fri May 28, 2021 3:14 pm

Built the second prism and slider. The interference pattern between crossed polarizers from the two prisms, stacked and aligned on their main prism axes, look like this now:

two_prism_interference_pattern.jpg
two_prism_interference_pattern.jpg (75.59 KiB) Viewed 456984 times

A bit wavy, the 2 screws were not pushing evenly on the prisms, but it approximates the pattern from Fig 3b in the Rathi paper.


For comparison, the interference pattern from a single prims between crossed polarized looks like this:

interference_pattern.jpg
interference_pattern.jpg (38.41 KiB) Viewed 456984 times

So far so good, though I hit a snag with my setup. Until now I didn't pay attention to the orientation of the slider axes in the light path. Turns out that the slider in the back focal plane of the objective is at 45deg in relation to the slider before the condenser. Makes no difference for phase rings, but it does throw off the alignment of the Sanderson prisms in the sliders that I built. As expected with such a difference in the orientation of the prisms a quick test fails to create a DIC effect. Since the condenser can't be rotated in this scope, to align the axes of the sliders I'll need to drill an tap 4 holes to rotate the part of the tube that holds the bfp slider. An unexpected hassle, but not terribly complicated to do. The fun never ends.

Interestingly the plasdic kit for this microscope has a slit slider that sits before the condenser and the slit is at a 45deg from the main axis of the slider, which lines up the slit with the main axis of the wolaston prism slider from that kit at the bfp of the objective. It makes sense to me now. My first test with a single sanderson prism at the bfp of the objective using the slit condenser should have approximated the plasdic effect from the original kit, unfortunately since I don't have the wolaston slider from that kit I can't make a direct comparison.

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Re: DIC Question

#71 Post by LouiseScot » Fri May 28, 2021 5:45 pm

jmp wrote:
Fri May 28, 2021 3:14 pm
Built the second prism and slider. The interference pattern between crossed polarizers from the two prisms, stacked and aligned on their main prism axes, look like this now:


two_prism_interference_pattern.jpg


A bit wavy, the 2 screws were not pushing evenly on the prisms, but it approximates the pattern from Fig 3b in the Rathi paper.


For comparison, the interference pattern from a single prims between crossed polarized looks like this:


interference_pattern.jpg


So far so good, though I hit a snag with my setup. Until now I didn't pay attention to the orientation of the slider axes in the light path. Turns out that the slider in the back focal plane of the objective is at 45deg in relation to the slider before the condenser. Makes no difference for phase rings, but it does throw off the alignment of the Sanderson prisms in the sliders that I built. As expected with such a difference in the orientation of the prisms a quick test fails to create a DIC effect. Since the condenser can't be rotated in this scope, to align the axes of the sliders I'll need to drill an tap 4 holes to rotate the part of the tube that holds the bfp slider. An unexpected hassle, but not terribly complicated to do. The fun never ends.

Interestingly the plasdic kit for this microscope has a slit slider that sits before the condenser and the slit is at a 45deg from the main axis of the slider, which lines up the slit with the main axis of the wolaston prism slider from that kit at the bfp of the objective. It makes sense to me now. My first test with a single sanderson prism at the bfp of the objective using the slit condenser should have approximated the plasdic effect from the original kit, unfortunately since I don't have the wolaston slider from that kit I can't make a direct comparison.
Well done! Looking good! I've still not managed to achieve interference yet :( (Though I've been fiddling about with other things like trying to improve my objective focuser). I've been wondering how Rathi et al. did it with mixes of Sanderson Prisms and Nomarski prisms and with the two different sized Sanderson prisms. Maybe I'm wrong and the relative sizes of the two prisms makes no difference? I was thinking about making a second open frame prism just to check. OTOH if size doesn't matter then my failure is probably an optical one, and to do with getting correct and exact focal lengths. As I understand it, the interference takes place in the objective-side polarizer where the two polarized beams recombine. In Rathi's diagram the BFP is imaged on the objective side prism and the polarizer is adjacent that. My camera imaging lens is actually fl = 240mm but I don't think that would make any difference as it's focussed on infinity. The other possibility is the condenser side prism. I've had to construct a 'condenser'. I've tried to ensure the condenser lens is focused on the prism and the lens is equidistant between the prism and the sample plane. I'm not sure about Rathi's diagram which shows the sample plane 3mm from the the front of the lens and the BFP 3mm behind the front. I previously thought the BFP was located further up the barrel? My Olympus 40x objective has a focal length of 4.5mm and a wd of 0.6mm. I dunno. I have a very similar setup to Rathi's - a 180mm tube lens, and a 208mm fl Lens 1 (rather than Rathi's 200mm). They appear to have used an 80mm diameter lens 2 for some reason (if their reference number is correct). Having written this, it's made me wonder if the condenser prism to condenser lens is critical - Rathi's is 15mm, mine is 40mm. Maybe that's too far?
I'll keep at it!
Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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75RR
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Re: DIC Question

#72 Post by 75RR » Fri May 28, 2021 7:07 pm

.
I think that perhaps the key to all this are the prisms, their orientation, and the degree that they are bent.

Perhaps jmp could provide a birds eye view of his arrangement that provided this result:

Image
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Re: DIC Question

#73 Post by jmp » Fri May 28, 2021 8:53 pm

The contraption that I used to obtain the image of that interference pattern is extremely simple, and it did not involve the microscope or any complex optic setup: literally the prism sliders were directly stacked on top of each other, flanked by cross polarized filters. Just imagine two of these:

Image

one in front of the other. Polarizer #1 is held on the back of slider #1 and polarizer #2 is held in front of slider #2, everything temporarily held together with a couple of rubber bands. A desk lamp with a CFL provided the white light behind polarizer #1, and I held my cellphone camera in front of polarizer #2 to take the picture. Despite the simplicity it the setup was quite didactic for me. It was possible to directly look at how the interference pattern changed in response to changes in the bending force applied by tightening or loosing the screws. I'll document it with a video, and post a picture of my setup.

I have not taken a picture of the interference pattern at the back focal plane of the objective yet. I briefly looked at it though, using the Bertrand lens built in the magnification changer of the trinocular, when I later mounted both sliders in the microscope. What I saw at the bfp of the objective was a different pattern, more like a crosshatch, which I suspect originates from the 45deg rotation between the slider mounts in the microscope. I saw a similar crosshatch pattern when I rotated one of the prisms by approximately 45deg in the contraption that I described at the beginning, which would confirm my suspicion. I didn't snap a picture of this but I'll do so and post it here later.

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Re: DIC Question

#74 Post by LouiseScot » Tue Jun 01, 2021 4:01 pm

Just a quick update.. I've managed to reproduce the interference patterns using new open-frame holders although my bands were not so narrow or so symmetric. My dark band always tends to be in the bottom half of the prisms. That may be related to my use of 6mm bars rather than 3mm ones - I don't know. I'll remake my open frame prisms with 3mm polycarbonate when I get a minute. Anyway, I've read Rathi's paper several times but find myself confused by what they've said. In their fig 3A they've plotted a graph showing the linear relationship between screw displacement and divergence. At about 0.9mm displacement they get 500 urad divergence. But.. when it comes to DIC imaging with the prisms they are talking about 65 urad and 14 urad. They say they matched the divergences to their Nomarski prisms. But if that's correct then their screw displacements must be tiny, if not negligible? Am I reading their data wrong? If not, I think it's going to be difficult to duplicate. Also, they say they get the interference bars when 'configured for imaging' but I with little screw displacement I can get background colours but not really the bands as such. I'll try it again with the 3mm polycarbonate in the open frames. Presumably, the 3mm polycarbonate will need greater tension, but smaller displacement, in order to produce the interference bands - and Rathi's polycarbonate was actually used 3/32" = ~2.4mm. 2.5mm would be the nearest though I've only seen 2 or 3mm.

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#75 Post by jmp » Thu Jun 03, 2021 4:00 am

Some images of the setup I've been using for testing.

The individual parts:
20210602_205101.jpg
20210602_205101.jpg (49.29 KiB) Viewed 456605 times
left to wright, top to bottom: filter tray with a polarizer, sanderson prism slider #1 (for the back focal plane), rubber bands, analyzer, sanderson prism slider #2 (between light source and condenser). Both prisms are made from ~2.4mm thick polycarbonate.

Test setup with only one slider between polarizers:
20210602_202343.jpg
20210602_202343.jpg (42.73 KiB) Viewed 456605 times
Interference pattern from one slider:
20210602_202637.jpg
20210602_202637.jpg (44.83 KiB) Viewed 456605 times
Test setup with both sliders between polarizers:
20210602_203020.jpg
20210602_203020.jpg (44.82 KiB) Viewed 456605 times
Interference pattern from two sliders with prisms lined up:
20210602_203231.jpg
20210602_203231.jpg (33.31 KiB) Viewed 456605 times
Change of the interference pattern as the bending force of one of the prisms is adjusted:



The movement of the whole contraption does not help, but on careful inspection the video reveals that the space between the interference lines decreases when the bending force is increased (I tightened the crews pushing on opposite sides of the prism).

I've also modified the microscope that I'm using, and now both sliders have the same orientation. I can now see the interference pattern from the two sliders, like the one above and the one in Rathi's paper, on the back focal plane of the objective using a Bertrand lens. No DIC effect though. For that to happen I would need to adjust the prisms to yield specific divergence angles, unfortunately I don't know at this point what the angles should be for my setup. As Louise mentions, Rathi's paper aimed at 65 and 14 urads for the 60x objective that they used. That sounds to me like a good starting point for trial and error, but that could take a long time of basically blind guessing. I'd prefer to study more on the subject and determine if it would be possible to calculate the approximate divergence angles that I should aim for with my setup.

As Louise pointed out, the angles mentioned in Rathi's paper are small, and translate to very small displacements of the screw that was used for bending the prisms. With my current setup it would be difficult to measure the displacement with the required precision. I also still have an issue with the expression that relates bending displacement with divergence angles, since substitution of the variables with the values given in the paper does not match what they report in their figure (and I'm not referring to the sign of the angles). The underlying cause of this likely something trivial (perhaps a silly mistake on my end) not a flaw in the paper. Though now I need to get the numbers to match, if I'm to understand this and be able to move on to the next tests.

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Re: DIC Question

#76 Post by 75RR » Thu Jun 03, 2021 4:53 am

.
Nice work - thanks for the detailed steps!
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Re: DIC Question

#77 Post by LouiseScot » Fri Jun 04, 2021 6:27 pm

jmp wrote:
Thu Jun 03, 2021 4:00 am
Some images of the setup I've been using for testing.

The individual parts:

20210602_205101.jpg

left to wright, top to bottom: filter tray with a polarizer, sanderson prism slider #1 (for the back focal plane), rubber bands, analyzer, sanderson prism slider #2 (between light source and condenser). Both prisms are made from ~2.4mm thick polycarbonate.

Test setup with only one slider between polarizers:

20210602_202343.jpg

Interference pattern from one slider:

20210602_202637.jpg

Test setup with both sliders between polarizers:

20210602_203020.jpg

Interference pattern from two sliders with prisms lined up:

20210602_203231.jpg

Change of the interference pattern as the bending force of one of the prisms is adjusted:



The movement of the whole contraption does not help, but on careful inspection the video reveals that the space between the interference lines decreases when the bending force is increased (I tightened the crews pushing on opposite sides of the prism).

I've also modified the microscope that I'm using, and now both sliders have the same orientation. I can now see the interference pattern from the two sliders, like the one above and the one in Rathi's paper, on the back focal plane of the objective using a Bertrand lens. No DIC effect though. For that to happen I would need to adjust the prisms to yield specific divergence angles, unfortunately I don't know at this point what the angles should be for my setup. As Louise mentions, Rathi's paper aimed at 65 and 14 urads for the 60x objective that they used. That sounds to me like a good starting point for trial and error, but that could take a long time of basically blind guessing. I'd prefer to study more on the subject and determine if it would be possible to calculate the approximate divergence angles that I should aim for with my setup.

As Louise pointed out, the angles mentioned in Rathi's paper are small, and translate to very small displacements of the screw that was used for bending the prisms. With my current setup it would be difficult to measure the displacement with the required precision. I also still have an issue with the expression that relates bending displacement with divergence angles, since substitution of the variables with the values given in the paper does not match what they report in their figure (and I'm not referring to the sign of the angles). The underlying cause of this likely something trivial (perhaps a silly mistake on my end) not a flaw in the paper. Though now I need to get the numbers to match, if I'm to understand this and be able to move on to the next tests.

Hi again

I didn't get a forum notification for some reason so apologies for slow response. Anyway, thanks for your post jmp. I've setup one of my open frames to take a micrometer head. That should allow me to measure approximately the delta y value directly (albeit in a stepwise manner outside of the optics). With some care I should be able to create a dataset / plot of delta y against turns of the loading screw. I might also possibly be able to rig something equivalent to Rathi's expensive Thorlabs PDP90A just using a camera sensor and some image processing - and maybe some optics - well, I'll have a go! I'll have to have a think about how it might be done. At the moment I'm using a 40x/0.65 objective. Presumably that would need greater divergence angles compared to the 60x/1.2 that Rathi used? I'll try out the micrometer over the weekend and hopefully get some useful data. If I could also measure deflections with a laser that would be great - but I'm not holding my breath on that one!
I believe the divergence angle equation is correct - it's used in other papers. I'm not 100% sure of the units though - I'll do some research to check it out. I did do a quick calculation based on my 3mm thick polycarbonate, an r of 14mm and an l of 94mm which gave a divergence angle of about 0.00264 x delta y . Annoyingly Rathi didn't quote actual delta y values, only screw displacement which which they say 'scales approximately linearly' to the bending of the bar. My micrometer should measure delta y directly though only to an accuracy of about 10um, maybe to 5um. I should still be in the right ball park, hopefully, at least for larger bending moments. It's all good fun!

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#78 Post by jmp » Fri Jun 04, 2021 9:13 pm

Louise, I agree with you, the divergence angle equation is not the problem. I am clearly plugging in the wrong values for the variables in my attempt to replicate their angle vs screw displacement plot, yet I've not been able to put my finger on what exactly I'm doing wrong... it should have been pretty straightforward. Though with your last comment you gave me a clue:
Annoyingly Rathi didn't quote actual delta y values, only screw displacement
Perhaps that's it. I've been using the screw displacement as the delta-y values, that might be why I can't replicate their figure.

I was also giving it a thought about how to go about measuring screw displacement and prism bending. It occurred to me that I can just measure the prism bending under the stereoscope. I have an old MBS-10 which I can use to get pretty accurate measurements of the displacement using the ocular micrometer, and/or use ImageJ/Hayear/Toupview to do the measuring directly from photos of the sliders taken under the stereoscope. As in your case, taking the measurements will be more involved but not too much of a hassle (in particular if just using the ocular micrometer). I'll post the measurements that I get here if/when I get them.

With measurements of the displacement it should be possible to configure the prisms for specific divergence angles (using the given equation). My guess is that the error in setting the angle will not be that bad, even with my current crude setup. The biggest problem for me will be to determine what divergence angles would work with my 10x and 20x objectives. The original plastdic kit for this microscope consists of only one wollaston prism that is used with both objectives. Given that, my impression is that there's a good chance of a large tolerance around the divergence angle that I'll need to replicate. I would just need to figure out what that angle is.
It's all good fun!
I couldn't agree more, this little project is heaps of fun!

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Re: DIC Question

#79 Post by LouiseScot » Fri Jun 04, 2021 9:25 pm

jmp wrote:
Fri Jun 04, 2021 9:13 pm
Louise, I agree with you, the divergence angle equation is not the problem. I am clearly plugging in the wrong values for the variables in my attempt to replicate their angle vs screw displacement plot, yet I've not been able to put my finger on what exactly I'm doing wrong... it should have been pretty straightforward. Though with your last comment you gave me a clue:
Annoyingly Rathi didn't quote actual delta y values, only screw displacement
Perhaps that's it. I've been using the screw displacement as the delta-y values, that might be why I can't replicate their figure.

I was also giving it a thought about how to go about measuring screw displacement and prism bending. It occurred to me that I can just measure the prism bending under the stereoscope. I have an old MBS-10 which I can use to get pretty accurate measurements of the displacement using the ocular micrometer, and/or use ImageJ/Hayear/Toupview to do the measuring directly from photos of the sliders taken under the stereoscope. As in your case, taking the measurements will be more involved but not too much of a hassle (in particular if just using the ocular micrometer). I'll post the measurements that I get here if/when I get them.

With measurements of the displacement it should be possible to configure the prisms for specific divergence angles (using the given equation). My guess is that the error in setting the angle will not be that bad, even with my current crude setup. The biggest problem for me will be to determine what divergence angles would work with my 10x and 20x objectives. The original plastdic kit for this microscope consists of only one wollaston prism that is used with both objectives. Given that, my impression is that there's a good chance of a large tolerance around the divergence angle that I'll need to replicate. I would just need to figure out what that angle is.
It's all good fun!
I couldn't agree more, this little project is heaps of fun!
Yeah, screw displacement doesn't equal delta y but is linearly related to it. I'll do some micrometer measurements tomorrow and see if I can work out some relationship. Yeah, you should be able to take some measurements photographically also.

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#80 Post by viktor j nilsson » Fri Jun 04, 2021 10:15 pm

I haven't read up on the Sanderson prism theory, and skimmed parts of this thread, so I may be missing something obvious here, but do you really need to measure and replicate the exact same divergence angles as those used in the paper?

In regular DIC, the following criteria needs to be met to achieve proper DIC:

Image
where:
fc: condenser focal length
alphaQ: condenser prism wedge angle
fob: objective focal length
alpha: objective prism wedge angle

In other words, it's not the shear angle itself that is critical, but rather the product of shear angle and the focal length of its corresponding lens.

Wouldn't the same basic principle apply for the Sanderson prisms as well? So, unless your objective and condenser lenses have the exact same focal lengths as the ones used in the paper, you still need to find a set of shear angles that satisfies the equation above. To me it seems like you could decide to fix one prism (the one that is hardest to adjust) at a reasonable shear angle and then tweak the other (by trial and error) until you get true DIC (which is easiest to see by observing the BFP).

Or am I missing something?

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Re: DIC Question

#81 Post by LouiseScot » Fri Jun 04, 2021 10:54 pm

viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
I haven't read up on the Sanderson prism theory, and skimmed parts of this thread, so I may be missing something obvious here, but do you really need to measure and replicate the exact same divergence angles as those used in the paper?

In regular DIC, the following criteria needs to be met to achieve proper DIC:

Image
where:
fc: condenser focal length
alphaQ: condenser prism wedge angle
fob: objective focal length
alpha: objective prism wedge angle

In other words, it's not the shear angle itself that is critical, but rather the product of shear angle and the focal length of its corresponding lens.

Wouldn't the same basic principle apply for the Sanderson prisms as well? So, unless your objective and condenser lenses have the exact same focal lengths as the ones used in the paper, you still need to find a set of shear angles that satisfies the equation above. To me it seems like you could decide to fix one prism (the one that is hardest to adjust) at a reasonable shear angle and then tweak the other (by trial and error) until you get true DIC (which is easiest to see by observing the BFP).

Or am I missing something?
Yes, I think the correct and useable divergence angle will indeed need to be tweaked acoording to the optics used. The Sanderson Prism angle is given by the formula quoted in the Rathi, Biss and Sanderson's papers. In this case it is a function of the photoelastic bending moment of the prism, as well as the dimensions of the prism and position of the supports etc., and what it's made of i.e. polycarbonate. I'm not trying to just replicate the divergence angles that Rathi used. But I have to find ones that will work with my objective and my diy condenser though they will likely be in the same ballpark i.e. likely <100urad. To do that, we need to work out the relationship between the change in prism deflection for a given turn of the screw, as it were. But Rathi quote beam divergences of ~14urad and 65urad, using their 60x/1.20 objective and a prism-condenser fl of 15mm (which I've tried to replicate), and they are difficult to arrive at by blindly turning the bending screws without knowing the exact relationship. Rathi et al. were able to measure deflections and compare with their Nomarski prisms. Unless I can figure out how to measure the divergence and/or the screw/divergence relationship, it will be difficult to get anywhere with this project. Unless I get lucky ha ha. I could buy a Thorlabs PDP90A lateral effect position detector to measure divergence but they are expensive (getting on for £400 in the UK). If anyone knows of where to get a cheap equivalent... :)

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#82 Post by viktor j nilsson » Fri Jun 04, 2021 11:29 pm

I actually think you can get pretty close to 65urad simply by looking at the interference bands between crossed polarizers (as in figure 3 in Rathi et al). High and low-magnification prisms are easy to tell apart, as in this figure from Olympus' DIC primer:
Image
It should be pretty obvious when you are getting close.

I am also quite confident that it is a lot more important to satisfy the equivalence in the equation I posted above, and get the prisms positioned as close as possible to the the BFPs, than it is to get the divergence angle exactly right.

The BFP position seems the trickiest. There's a lot of moving parts when you use Rathi's approach of using additional lenses to project an image of the prism on the objective BFP. If I were to do this, I would start with a low-magnification objective where the BFP is located outside the objective.

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Re: DIC Question

#83 Post by LouiseScot » Fri Jun 04, 2021 11:55 pm

viktor j nilsson wrote:
Fri Jun 04, 2021 11:29 pm
I actually think you can get pretty close to 65urad simply by looking at the interference bands between crossed polarizers (as in figure 3 in Rathi et al). High and low-magnification prisms are easy to tell apart, as in this figure from Olympus' DIC primer:
Image
It should be pretty obvious when you are getting close.

I am also quite confident that it is a lot more important to satisfy the equivalence in the equation I posted above, and get the prisms positioned as close as possible to the the BFPs, than it is to get the divergence angle exactly right.

The BFP position seems the trickiest. There's a lot of moving parts when you use Rathi's approach of using additional lenses to project an image of the prism on the objective BFP. If I were to do this, I would start with a low-magnification objective where the BFP is located outside the objective.
I'm sure you're right but I don't have any practical experience of visible light Normarski DIC / prisms so find it hard to relate to the interference diagrams. Obviously I can get similar banding but maybe not quite the same. For example, I've not been able to replicate quite the same patterns (I think I said before) - my dark bands have not been in the centre of the prism but towards the bottom edge. That may just be to do with the amount of tension I've been applying. From their fig 3b scale bar it appears that their diagrams represent images that are ~30mm square? Not sure how they did that. There open frame prism is only 20mm in height. Maybe I missed something there... I wish they'd printed bigger versions! Anyway, I'll endeavour to do some quantitative measurements and images of interference patterns tomorrow or Sunday. I'm sure when/if I can replicate everything it will come into focus for me, so to speak!

Cheers
Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#84 Post by jmp » Sat Jun 05, 2021 6:29 pm

viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
I haven't read up on the Sanderson prism theory, and skimmed parts of this thread, so I may be missing something obvious here, but do you really need to measure and replicate the exact same divergence angles as those used in the paper?
Replicating the divergence angles from the paper is, in my case, just part of my learning process. A matter of having a positive control... if I can't replicate it then I'm likely doing something wrong. Given that this is not my field, details that might be obvious to some are not so to me.
viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
In regular DIC, the following criteria needs to be met to achieve proper DIC:

Image
where:
fc: condenser focal length
alphaQ: condenser prism wedge angle
fob: objective focal length
alpha: objective prism wedge angle

In other words, it's not the shear angle itself that is critical, but rather the product of shear angle and the focal length of its corresponding lens.
That's exactly where I wanted to go next, you've given me a great starting point!
viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
Wouldn't the same basic principle apply for the Sanderson prisms as well?
With the little I know, I would say yes.
viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
So, unless your objective and condenser lenses have the exact same focal lengths as the ones used in the paper, you still need to find a set of shear angles that satisfies the equation above. To me it seems like you could decide to fix one prism (the one that is hardest to adjust) at a reasonable shear angle and then tweak the other (by trial and error) until you get true DIC (which is easiest to see by observing the BFP).
The key part in what you say is defining what the 'reasonable shear angle' would be. My only reference were the angles given in Rathi's paper, until I read your second post:
viktor j nilsson wrote:
Fri Jun 04, 2021 11:29 pm
I actually think you can get pretty close to 65urad simply by looking at the interference bands between crossed polarizers (as in figure 3 in Rathi et al). High and low-magnification prisms are easy to tell apart, as in this figure from Olympus' DIC primer:
Image
It should be pretty obvious when you are getting close.

I am also quite confident that it is a lot more important to satisfy the equivalence in the equation I posted above, and get the prisms positioned as close as possible to the the BFPs, than it is to get the divergence angle exactly right.

The BFP position seems the trickiest. There's a lot of moving parts when you use Rathi's approach of using additional lenses to project an image of the prism on the objective BFP. If I were to do this, I would start with a low-magnification objective where the BFP is located outside the objective.

Those images of the expected interference bands for the different magnification objectives was what I needed. That gives me a reference frame to came up with the range of angles to try. Not only that, but as you said, to try this empirically... just by directly comparing the interference patterns! Thus, I ran a few tests, mostly untightening the screws to reduce the bending force (and shear angles) and I think I got to true DIC on the 10x. This is how the canonical check cells look (with my apologies for the bad quality of the images):

comparison.jpg
comparison.jpg (54.95 KiB) Viewed 456474 times

Not going to win a photography contest that but as you said, the difference should be pretty obvious. Indeed the difference between bright-field and DIC was striking when looking through the oculars. The effect was also clearly different from oblique.

These are (ugly) images of the back focal plane when only one of the prisms and when both prisms are inserted in the light path:
bfp_interference_comparison.jpg
bfp_interference_comparison.jpg (35.54 KiB) Viewed 456474 times
I'm not seeing the dark interference band in the center as in the Olympus figure, which is puzzling to me. There must be some level of interference: without the prism at the bfp the image of the sample is almost the same as that from bright-field, with the prism inserted at the bfp the image looks like DIC (in both cases, polarizers and the prism below the condenser are left untouched).



I think your intuition about how much leeway one would get in terms of tolerances is likely right if I really got DIC under my test conditions.
viktor j nilsson wrote:
Fri Jun 04, 2021 10:15 pm
Or am I missing something?
No, you were definitely spot on. Many thanks for your comments!

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Re: DIC Question

#85 Post by viktor j nilsson » Sun Jun 06, 2021 10:02 pm

Glad you found it useful! You are clearly doing good progress. Looking forward to seeing further updates.

One thing that I started thinking about is if the Sanderson prisms are stable over time, or if the shearing characteristics will change over time due to fatigue. Have you read anything about this?

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Re: DIC Question

#86 Post by LouiseScot » Mon Jun 07, 2021 7:17 pm

viktor j nilsson wrote:
Sun Jun 06, 2021 10:02 pm

One thing that I started thinking about is if the Sanderson prisms are stable over time, or if the shearing characteristics will change over time due to fatigue. Have you read anything about this?
Hi Viktor

I'm not sure though I think it should be. It's obviously dependent on the bending moment which, in turn, depends on the pressure exerted by the screw(s). That could drift somewhat over time. But once everything is set up it shouldn't be too difficult to recheck and tweak. Also, if the stressed polycarbonate prism optical properties do change over time, it's very cheap and easy to make new ones.

Louise
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#87 Post by Hobbyst46 » Tue Jun 08, 2021 3:17 pm

LouiseScot wrote:
Mon Jun 07, 2021 7:17 pm
viktor j nilsson wrote:
Sun Jun 06, 2021 10:02 pm

One thing that I started thinking about is if the Sanderson prisms are stable over time, or if the shearing characteristics will change over time due to fatigue. Have you read anything about this?
Hi Viktor

I'm not sure though I think it should be. It's obviously dependent on the bending moment which, in turn, depends on the pressure exerted by the screw(s). That could drift somewhat over time. But once everything is set up it shouldn't be too difficult to recheck and tweak. Also, if the stressed polycarbonate prism optical properties do change over time, it's very cheap and easy to make new ones.

Louise
There is a fairly extensive research over the fatigue of polycarbonate (PC) over time, for example in the University of Eindhoven (NL).
However, the conditions of measurement were fairly remote from the conditions relevant to your (admirable) efforts on the DIC - if I am not wrong.
Those tests were done under pressures of ~50 MPa or temperatures of 120C or more. I dare a cheeky guess here - really amateurish !
IF the dimensions of the PC bar are 70x16mm, and the deflection angle is 65uR, then deltaY = 70mm x sin(65uR) = 0.0045mm
So, Strain = deltaY/16mm = 0.00028.

Now, from Fig 2a in the article:
PREDICTING THE LONG-TERM FAILURE OF POLYCARBONATE: A CONSTITUTIVE APPROACH
E.T.J. KLOMPEN, T.A.P. ENGELS, R.P.M. JANSSEN, L.E. GOVAERT, H.E.H. MEIJER
Dutch Polymer Institute (DPI), Materials Technology (Mate), Eindhoven University of Technology, Eindhoven, The Netherlands


It seems that for low Strains, Strain = 0.001xStress. Hence, the stress on "our" PC bar is 0.00028x1000 = 0.28 MPa. Or about 2.8 bar.

From Fig 4 of the same article, stresses of 50 MPa cause failure within the order of at least 10000 seconds. Or 2.8 hours. BUT, at stresses below 45 MPa, the lifetime becomes a million or more seconds, and seems to be independent of the stress. So, a million seconds times 50/0.28 = 6 years.

So, for the benefit and interest of some or many of us, please create the DIC, and forget about its future lifetime ;)

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Re: DIC Question

#88 Post by LouiseScot » Thu Jun 10, 2021 1:00 pm

Time for an update!
I still seem to be struggling to get my fringes the same as jmps :( I'm not sure what I'm doing wrong, or not doing right.
Here is a pic of the open frame I'm using:
Holder1.jpg
Holder1.jpg (21.56 KiB) Viewed 456318 times
It's just 3D printed with some grooves to support the polycarbonate. I've gone with jmp's method of using two set screws (M5) as using a thumbscrew just seems to cause the frame itself to bend. I've used 6mm Aluminium rod for the lower supports. The prism is 110 x 20mm with l = 94mm and r = 15.7mm (pretty much l/6). I have two prisms the same (A and B).

This are the sort of fringes I get with Prism A:
PrismA-1_0160.jpg
PrismA-1_0160.jpg (22.48 KiB) Viewed 456318 times
PrismA-2_0161.jpg
PrismA-2_0161.jpg (21.97 KiB) Viewed 456318 times
PrismA-3_0162.jpg
PrismA-3_0162.jpg (21.13 KiB) Viewed 456318 times
and with B:
PrismB-1_0163.jpg
PrismB-1_0163.jpg (24.61 KiB) Viewed 456318 times
ctd in second post...
A Nikon CF plan 20x; A Swift 380T; A DIY infinity corrected focus rail system with a 40x/0.65 Olympus Plan, a 10x/0.30 Amscope Plan Fluor, and a 20x/0.75 Nikon Plan Apo

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Re: DIC Question

#89 Post by LouiseScot » Thu Jun 10, 2021 1:25 pm

from previous:

Another prism B:
A+B-1_0165.JPG
A+B-1_0165.JPG (25.16 KiB) Viewed 456318 times
Prism A+B:
A+B-1_0165.JPG
A+B-1_0165.JPG (25.16 KiB) Viewed 456318 times

I can't seem to get the fringes symmetric or centred like jmps has and like the actual prisms show :(

I've used 3mm polycarbonate but that shouldn't make a huge difference? Lighting for the above images was with a cfl lamp.

Plus I've measured the max delta y bending using a micrometer at 1.40mm which seems huge?? But with little tension I just get wide bands. putting delta Y as 1.4 in the equation gives a deflection of 0.00075 which I presume is millirads with other dimensions in mm. So that would be 750 urads which is off of Rathi's graph's scale! If I try and tighten the screws any further a) it gets difficult to do and b) tends to cause crushing and deformation.

FWIW the polycarbonate sheet I'm using is 'Palsun' which I think is French. The open diameter of the polarizers is about 35mm (They are Hoya 40.5 mm linear polarizers)

Any ideas anyone? I'm sure I shouldn't need to bend the prisms so much especially when Rathi is talking about less than 100urads?

Thanks for any analysis and ideas

Louise
Attachments
PrismB-2_0164.jpg
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Re: DIC Question

#90 Post by jmp » Thu Jun 10, 2021 8:39 pm

Hi Louise,

Note that for a single prism the interference pattern that I obtain within crossed polarizers is asymmetric, without a dark fringe band in the center:

Image

The interference pattern from above is similar to the one at the top part of the ones that you showed from a single prism:

Image

In your case the banding is much more compact due to the large bending force that you are applying. If I increase the bending force on my prism the pattern starts resembling the one that you've shown. With considerable bending I obtain a dark fringe band, but its not located in the middle of the prism, instead it appears near one edge of the prism and starts migrating towards the center as more bending force is applied (and as that happens bands start to get narrower and closer). I've not been able to move that band towards the center, the frames for my prisms start to deform, the screws start to damage the edge of the prism, etc; I've gone as far as having it between 1/4 and 1/3 of the center. Though the trend would indicate that with not much more force the dark fringe band will eventually be centered.

Another observation is that given the way in which the screws push on the edge of the prism, in my setup, there is a tendency of the prism to rotate along its longer axis (up an out of the slider on the side where the screws make contact with the prism); think twisting the prism in opposite directions from the extremes on the longer axis. As a result the bands start to appear less defined, fuzzy, as if out of focus. Pressing the prism back so that it lays flat causes the bands to appear well defined. I wonder if some of that twisting might be happening in your setup?

Up to this point I'd say that we are both pretty much doing the same and obtaining similar results.

What is different is that to observe a symmetric interference pattern like this:

Image

I have two prisms placed within the crossed polarizers; not one, two. Have you tried that yet? It is not what is described in the papers. It wasn't clear to me at the time if that was the interference pattern that was expected from a single prism, or from both, so I tried both ways.

Very little bending force is applied to each of the prisms in this configuration. The separation and width of the fringes is easy to change with small adjustments to screws, from one or both prisms. The interference pattern looks exactly like the one from Rathi's paper but, again, its from 2 prisms, not from one as in their Paper. According to the information here the expected interference pattern from a single Nomarsky or Wollaston prism between crossed polarizers should be symmetric with a dark fringe in the center too. Clearly not what I'm doing here.

In my tests with the microscope I've also used the prisms adjusted so that when both are within crossed polars the dark fringe band is in the center. There is interference and it has a marked effect in the image contrast, but it does not seem to be true DIC... yet.

I need to study and think more about this (to busy with work at the time though). For the moment, given how easy it is to obtain the 'expected' interference pattern from 2 prisms, I wonder if it would be worth to change my setup to use 2 prisms on each slider (in spite of doubling the amount of polycarbonate in the light path) and just do some more empirical tests.

While at this, thanks to the information that Viktor shared (DIC fundaments from Olympus linked above), I learned that for Nomarksy prisms the interference pattern is projected outside the prism and not located within the prism itself, as is the case with Wollaston prisms. Because of this Nomarsky prisms can sit outside the rim of the objective, while the interference fringes appear on the back focal plane of the objective, inside the objective itself. If this were to be the case for Sanderson prisms that would be a huge advantage too; adapting existing microscopes would perhaps be easier without the need of extra optics to project the back focal plane elsewhere as in Rathi's paper.

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