Re: Boosting bright field resolution with dichroic filters

Posted by Smith, Benjamin E. on
URL: http://confocal-microscopy-list.275.s1.nabble.com/Boosting-bright-field-resolution-with-dichroic-filters-tp7583983p7583985.html

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Hey James,
   This site has a nice intro to image FFTs:

https://www.cs.unm.edu/~brayer/vision/fourier.html

   I also recommend this site to my students, because it allows you to modify an FFT and immediately see the impact on the corresponding image:

http://www.brainflux.org/java/classes/FFT2DApplet.html

   In short, as long as the pixel dimensions are scaled correctly in ImageJ, then when you take the FFT, it will give you the spatial frequencies in actual units (i.e. um/cycle).  To read an FFT, the center pixel is the DC component, which you can think of like the offset on a PMT, where it represents the average intensity of the whole image.  As you move the cursor away from the center, you will notice imageJ will give you an angle, amplitude, and frequency.  The angle is the direction the spatial frequency is propagating.  The amplitude is the amplitude (peak to trough) height of that frequency.  Another way to think of this, the greater the amplitude, the greater the contrast of the corresponding feature in the image.  Finally, frequency is the physical peak to peak distance (hence um per cycle, etc.).

   To determine maximum optical resolution, you need to acquire an image where the pixel resolution is much higher than the optical resolution (in this case the pixels were 64nm x 64nm).  If the optical resolution is higher than the pixel resolution, then the FFT cannot show spatial frequencies at the limit of the optical resolution, as they are not contained within the image in the first place.  In other words, in a digital image the highest spatial frequency is 2 pixels, one high, next low, next high, etc.  So, if your pixels are 400nm across and you expect your resolution to be 200nm, then the highest spatial frequency contained within your image is 800nm/cycle so you will never be to resolve down to 200nm.  This is similar to if in an image a person's face is a single pixel, you can't reconstruct the face from that one pixel, no matter what CSI says.

   So, once you have an image where the pixel dimensions are much smaller than your optical resolution, then you take the FFT, and you are looking for the highest spatial frequencies (i.e. the points farthest from the center) where the amplitude of those frequencies is significantly greater than the background amplitude (i.e. look for the pixels that are significantly brighter than the background and farthest from the center).  There is no discrete cut-off, and the amplitude (i.e. contrast) decreases as you approach the resolution limit (this is explained in the link in my original post, in term of the modulation transfer function).  Therefore, I simply looked for a block of high amplitude pixels that were farthest from the center, and measured the spatial frequency at that cutoff.

   You can do the same exercise, with the images posted.  Load the images into ImageJ or FIJI, and make sure the image properties are set to 0.0645um x 0.0645um (ctrl+shift+P).  Then crop the image to remove the scale bar, or the scale bar will show up in the FFT (draw a rectangular selection and press ctrl+shift+X).  Finally, take the FFT of the image (Process->FFT->FFT).  Autocontrast the FFT to make the amplitudes more clear against the background noise (ctrl+shift+C then "Auto").  Then put the cursor over the outer most frequencies that clearly contrast against the background noise.  The bottom of the title bar (the bar with all the menu options) will then automatically give you all the info about the frequency at your cursor position. It should read something like:

r=0.30 micron/c (434), theta= 8.88°, value=121

Where "r" is your resolution, which in this case would be 300nm.  You can also have some fun with the FFT, where you can use the draw tool to black out some of the frequencies and then take the inverse FFT (Process->FFT->Inverse FFT) to see how this modifies the image.  I have found there is no better way to get and intuitive sense of FFTs then to play with them, and see how it effects the image.  FFTs can also be extremely powerful tool in isolating specific features in an image.

For example, take this image of a dandelion: https://drive.google.com/file/d/0B7pDqE0lTjQXbVZjTFlwVWhDT1U/view?usp=sharing

If I asked you to crop the image so that it shows only the dandelion head, it would take years to precisely crop out ever background pixel around every fluff strand.  Conversely, you may notice that the background is blurry (low spatial frequencies), while the fluff is sharp and fine (high spatial frequencies).  Therefore, if rather than cropping out the background positionally (i.e. in an image), you can crop it out via frequency (i.e. in an FFT).  Therefore, in 10 seconds (rather than years) you can use an FFT to separate the fluff from the background based on frequency rather than position and get the following result:

https://drive.google.com/file/d/0B7pDqE0lTjQXU2U0cGZ4OHJlQnM/view?usp=sharing

To recreate this trick exactly.  Open the original image in ImageJ.  Think of this image as a combination of both the high frequency information you want to keep and the low frequency information you want to remove.  To make a purely low frequency version of the image, apply a 20 sigma Gaussian blur to the image (Process->Filters->Gaussian Blur).  Why a Gaussian blur specifically makes a image low frequency only is explained nicely here:

http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm

Then use the image calculator to subtract the blurred image from the original image (Process->Image Calculator).  The math you are doing is basically:
      Original Image    -    Blur Image = Fluff only
                                 OR
(High Freq + Low Freq) - (Low Freq) = High Freq

This is one of the more simple tricks with spatial frequencies, but it drives the point home as to how some problems that are near impossible to solve in positional space (an image) are trivial in frequency space (an FFT).

Hope this helps,
  Ben Smith


Benjamin E. Smith, Ph.D.
Samuel Roberts Noble Microscopy Laboratory
Research Scientist, Confocal Facility Manager
University of Oklahoma
Norman, OK 73019
E-mail: [hidden email]
Voice   405-325-4391
FAX  [phone]
http://www.microscopy.ou.edu/
 





________________________________________
From: WAINWRIGHT James [[hidden email]]
Sent: Friday, July 10, 2015 9:24 AM
To: Smith, Benjamin E.
Subject: RE: Boosting bright field resolution with dichroic filters

Hi Benjamin,

Cool post!

Hope you don't mind me asking how you worked out the resolution from the FFT?

Bear in mind that I'm not a mathematician nor computer scientist.

I can kind of see that the FFT of the blue image has a larger "bright" area / distance from centre, but I'm not sure what that means and how you then show the resolution of the original?

Thanks for any explanation you can provide or handy website for explaining FFTs...

Best regards,

James

James Wainwright
Product Support Engineer (Microscopy Systems)
Europe, Middle East & Africa

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-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Smith, Benjamin E.
Sent: 10 July 2015 14:59
To: [hidden email]
Subject: Boosting bright field resolution with dichroic filters

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Hey microscopists,
    I had a student ask if the department had a 1.4NA condenser for high resolution imaging of diatoms.  This is a pretty specialized piece of equipment, and the highest NA condenser I could find on hand was 0.9NA, so I started thinking about how we could get a comparably high resolution with our setup.

    For a 1.4NA objective and a 1.4NA condenser, with white light BF illumination, one would calculate the lateral resolution to be approximately:

   (0.6 * 575nm) / ((1.4 + 1.4) / 2) = 246nm

    For a 1.4NA objective and a 0.9NA condenser, with white light BF illumination, one would calculate the lateral resolution to be approximately:


   (0.6 * 575nm) / ((1.4 + 0.9) / 2) = 300nm

    However, if you then simply put a blue emission filter (such as a DAPI filter cube) into the light path, then one would calculate the lateral resolution to be:


   (0.6 * 445nm) / ((1.4 + 0.9) / 2) = 232nm

     Which is now a slightly better lateral resolution then even the 1.4NA condenser setup.

    I tested this out on a diatom slide, and the results perfectly matched the theory, with the white BF image maxing out at 300nm resolution, and the blue BF image maxing out at 230nm resolution.  You can also clearly see additional detail in the blue BF image:

White BF Image - https://drive.google.com/file/d/0B7pDqE0lTjQXT3VKc2Y0ckFEU2s/view
Blue BF Image - https://drive.google.com/file/d/0B7pDqE0lTjQXVUhBODJ4NUZMS3c/view
FFT of White BF - https://drive.google.com/file/d/0B7pDqE0lTjQXb2lBR2dwRXEzVVE/view
FFT of Blue BF - https://drive.google.com/file/d/0B7pDqE0lTjQXZU5GQWNaTE5aUGM/view

   Upon further investigation, I found this great write-up by René van Wezel discussing the same and other ideas for boosting resolution:
http://www.microscopy-uk.org.uk/mag/indexmag.html?http://www.microscopy-uk.org.uk/mag/artapr09/rvw-contrast.html


   However, in my hands, annular illumination generated a ringing artifact, although this is likely because the NA of the condenser is much lower than the NA of the objective.  All in all, I'm sure for experienced microscopists this is likely an obvious solution, but for newer microscopists, it may be surprising just how much higher the resolution becomes simply by putting a short wavelength dichroic filter into the light path (especially when comparing the FFTs), and serves as a reminder that transmitted light resolution isn't primarily about NA alone.  I know for myself, I qualitatively knew that blue light would boost resolution, but it wasn't until I did out the math, and verified it experimentally, that I realized that blue light with a conventional dry condenser can even out-perform white light with a 1.4NA oil immersion condenser.

Have a great Friday,
   Ben Smith

Benjamin E. Smith, Ph.D.
Samuel Roberts Noble Microscopy Laboratory Research Scientist, Confocal Facility Manager University of Oklahoma Norman, OK 73019
E-mail: [hidden email]
Voice   405-325-4391
FAX  [phone]
http://www.microscopy.ou.edu/


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