A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

Unpolarizedlight

BigWarp has lots of options for how to export the result, and it’s definitely possible to make sure the output is not cropped. Maybe if you attach an example I can understand better?

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When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle.  Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

In your case, changing the Resolution technically doesn’t matter - but only because the two images have the same resolution. For your use case, you probably want to export the moving image at the same resolution that it started at

The figure below shows the trace of the field vector Ex = E0exp(i(kz - ωt)), Ey = E0exp(i(kz - ωt + φ)) in a plane perpendicular to the z-axis when looking towards the source.  (E0x = E0y = E0)

The extraordinary ray violates both Snell’s Law and the Law of Reflection.  It is not necessarily confined to the plane of incidence.  Its speed changes with direction.  The index of refraction for the extraordinary ray is a continuous function of direction.  The index of refraction for the ordinary ray is independent of direction.  When the ordinary index of refraction is plotted against wavelength, the dispersion curve for the ordinary ray is a single unique curve.  The dispersion curve for the extraordinary ray is a family of curves with different curves for different directions.  A ray normally incident on a birefringent crystalline surface will be divided into two rays at the boundary, unless it is in a special polarization state or unless the crystalline surface is perpendicular to an optic axis.  The extraordinary ray will deviate from the incident direction while the ordinary ray will not.  The ordinary ray index n0 and the most extreme extraordinary ray index ne are together known as the principal indices of refraction of the material.  The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed.

Wow, I also would like to join in saying that those structures are really cool. I have no breakthrough advice for the direct problem with rotation though, my cursory thoughts would go to 1) extracting a small ROI of the overlapping region, 2) applying MultiStackReg to automatically register these two small sub-images (rigid), 3) extracting the transformation matrix and noting the angular values.

Circularlypolarized light

I’ve discovered the problem with my image stitching is that the images are slightly rotated in each image and if I rotate these images then the stitching works fine. However, at first I was having to guesstimate the amount of rotation needed for each pair of images, rotate, see if the rotation looks good and attempt to stitch. If the stitched image still looks blurred rotate again and repeat (even a rotation of 0.2 can give a less blurred image). Now I am drawing lines between two landmarks on the images, measuring these angles and then getting the lines roughly equal but this still takes time. There are plugins that do the rotation automatically (e.g. align image by line ROI) but I can’t see the rotation used to align the images.

Polarization

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Changing the field of view option to Moving (warped) tells bigwarp: “transform the image, see where it ends up, and make sure the output contains the transformed image” which I think is pretty much what you need.

A more extreme example to show what that option does: rotating at ~45 degrees and selecting the above export options gets me this: image793×830 63.7 KB

If a beam of linearly polarized monochromatic light enters a birefringent crystal along a direction not parallel to the optical axis of the crystal, the beam will may be divided into two separate beams.  Each will be polarized at right angles to the other, and they will travel in different directions.  The intensity of the original beam will be divided between the two new beams in a manner which depends on the original orientation of the electric field vector with respect to the crystal.  The ratio or the intensities of the two orthogonally polarized beams can have any value.

In other devices the changes in direction of propagation between the two rays is used to separate the incoming beam into two orthogonally polarized beams as in the Wollaston and Thompson beam-splitting prisms.

I was mistaken about the export, it does keep all 6 channels, it just put them all in grey scale which confused me for a moment.

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That does not really solve the issue as 90% of image 7 has been cut. What I really need is a result where the images overlap as they are then used to reconstruct the whole biofilm. Doing it by hand I got number 15 and then eventually I end up with my result (these don’t have the channels due to upload size limit). It just takes an hour to do one biofilm as these have between 2-13 parts depending on the strain and I really want to find a way to streamline the process.

Bigwarp does work as advertised. This issue with cropping is because the software transforms the image as well so it does look cropped but you can move the image with the right click and all the information is there. I’ve had some really good results with the exported warped images I got. If there are still issues with the registration of the images for stitching I use the Align4 plugin from G. Landini to get the coordinates for where my images overlap (mostly this is where there are small, distinct areas of overlap so mostly smooth biofilms where most of the middle is the same but the edges don’t match up on stitching or where there is very, very little overlap).

The two beams within the birefringent crystal are referred to as the ordinary and extraordinary ray, respectively.  The polarization of the extraordinary ray lies in the plane containing the direction of propagation and the optic axis, and the polarization of the ordinary ray is perpendicular to this plane.

Electric polarization

A quarter-wave plate δ = π/2 can be used to convert linearly polarized light to circularly polarized light.  The incident linearly polarized light must be oriented at 45o to the wave plate's axes.  A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

Lastly, the direction of polarization of an electromagnetic wave is defined as the direction in which the electric field oscillates. Note that there is no ...

For the stitching Pairwise is often better than Grid I’ve found as Pairwise has an option to ignore 0 values (the black bits in the rotated images) where as with Grid there are often large black areas or toned down areas where the empty bit overlaps with the other image. Pairwise also uses the images in situ rather than the saved files so I can quickly make adjustments if needed and without risking mucking anything up and not having hundreds of back ups required.

Linearpolarization

Thanks for the recommendations however neither of them are appropriate. With the interactive rigid I need to be able to rotate the image in relation to another and I have no reference point when I am rotating the image (for example I have a triangle in my biofilms I can’t see if this has been lined up correctly in relation to the same triangle in the second image ready for stitiching). It also has the unexpected effect of dragging the channels in the image out of sync with each other so the image itself gets distorted once I start rotating it.

Is there a way to see how much the image was rotated in one of these align tools/plugins? I can’t just just the align plugins as they tend to crop the images which is not what I want as I am making a bigger image out of component images. The image also have 6 channels so I prefer to rotate and then stitch either pairwise or gridwise so these channels don’t get blended together.

Linearpolarization example

Linearly polarized light is a special case of elliptically polarized light.  If the light is linearly polarized, then the two components oscillate in phase,  for example Ex = E0xexp(i(kz - ωt)), Ey = E0yexp(i(kz - ωt)), φ = 0.  The direction of E and the direction of propagation define a plane.  The electric vector traces out a straight line.  For example, E = Ei = E0xexp(i(kz - ωt))i.

You can manually rotate by dragging the points around. Press to choose the rotation. and it also prints a rotation matrix. It’s possible to extract the angle from that if you need. (Let us know if that would be helpful and I’m sure someone can help with that)

Polarization oflight

The electric field vector E can always be resolved into two perpendicular components.  The light is elliptically polarized, then the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation.

If you’re using bigstitcher, it may have some built-in ways to apply rotations, but I havn’t used it much. Maybe this is worth checking out:

However, if I have used Align4 I need to use the Grid option “Positions from file” and I can modify the TileConfiguration file with the coordinates I received from Align4 to get the images stitched where I want them without the computer being confused.

In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in ...

Elliptical polarization

i wouldn’t blame you, that’s not very nice behavior for the export :-/ - feel free to create a new issue about this if you’d like (if you don’t i might).

The plugin also has an option of “no underlying grid” which will increase computational time and RAM use but it might be worth a try.

With the Bigwarp. I am not sure what is happening but again I get the issue of the software cropping my pictures when it does the alignment which is not what I want. However, the main problem here is that if I export the images from the plugin they become one channel and I lose the brightfield and 3 fluorescent channels from the images.

I used your exemplary images and guessed an overlap of 10% and the fused image looks pretty good. Resized to ~ 1/4 of the number of pixels to be able to upload it.

The rotation center can be set by making a selection and selecting Image>Transform>Rotate… It looks like that rotates a selection about its center.

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In the Glan-Taylor polarizing prism shown on the right the rejected (ordinary) ray is absorbed by black mounting material in the prism housing.

ED12_RT_6.tif (15.8 MB) ED12_RT_7.tif (15.8 MB) So here are two images I need to stitch as part of my biofilm. Number 6 is on the left and 7 on the right. In the middle there is a thin strip of overlapping material (if you look at the bottom of the biofilm from the right of the first big ridge from the right of 6 until the next big ridge in 7). In Bigwarp I selected 4 landmarks in this overlapping area and selected it to use the rotation option when I press F2. When I press T I get the image shown in Bigwarp_image. As you can see most of the image has gone with only the overlapping part remaining. I was mistaken about the export, it does keep all 6 channels, it just put them all in grey scale which confused me for a moment. The exported image is in Bigwarp_export. Bigwarp export.tif (15.8 MB)

Lapping machines: Lapping machines are used for fine polishing and finishing of optical surfaces to achieve sub-micron surface roughness and flatness. They ...

image1104×974 89.7 KB I draw an ellipse over a known circular area, rotate and scale till the selection is circular in order to simulate a 3D alignment. image1037×519 37.8 KB