ConfocalSweetestSpot

McNamara 20210301Mon (start) Confocal and Deconvolution Resolution  - confocal Sweetest Spot - 
(a specialized Tips and Procedures)

* inspiration: Jeff Reece (NIH/NIDDK, confocal listserv) likes 0.6 to 0.7 AiryUnits as "confocal sweet spot" (really a range). I have simplified to 0.666 (really 0.66 on the confocal hardware). See also Lam ... Bolte 2017 (box near bottom).

* 20230224F: see "SPLIT-PIN software" box near bottom of this page - part of abstract: "We have recently demonstrated that, instead of closing the pinhole, one can reach a similar level of optical sectioning by tuning the pinhole size in a confocal microscope and by analyzing the resulting image series. The method, consisting in the application of the separation of photons by lifetime tuning (SPLIT) algorithm to series of images acquired with tunable pinhole size, is called SPLIT-pinhole (SPLIT-PIN). Here, we share and describe a SPLIT-PIN software for the processing of series of images acquired at tunable pinhole size, which generates images with reduced out-of-focus background. The software can be used on series of at least two images acquired on available commercial microscopes equipped with a tunable pinhole, including confocal and stimulated emission depletion (STED) microscopes. "

"how low can you go" ... confocal Confocal_xy=0.51*430nm/1.4 then deconvolution DC_xy  = 0.9*0.51*421nm/1.4  with BV421 (or SuperBright 436) on confocal). 
The 430nm is center wavelength of 420-440nm.

In all cases, I think youshould divide the "dxy" value by "approximately 3" (3, 3.3 or 3.5) to get to appropriate pixel size. For example 

Standard 1.0 Airy Unit confocal setting:
Confocal                                   C__xy = 0.51*430nm/1.4 =         156nm
Confocal --> Deconvolution     CD_xy  = 0.9*0.51*430nm/1.4 =  141nm

"Confocal Sweetest Spot" - 0.666 Airy Units, which improves resolution by approximately 5% (maybe a bit more? 6%?) ... Jeff Reece (NIH/NIDDK) jeff.reece@NIH.GOV likes 0.6 to 0.7 AiryUnits as "confocal sweet spot" (really a range). I have simplified to 0.666 (really 0.66 on the confocal hardware), less fluorescence emission (nominally 44% on the Leica SP8 [uses square 'pinhole' aperture, which ends up about the same as a near-circular aperture, but less fuss). A key to success is: not much loss of light through this slightly smaller pinhole, according to a Leica graph at https://www.leica-microsystems.com/science-lab/pinhole-geometry-four-corners-are-perfect (which also explains that Leica uses a square aperture, and claim=argue this is an advantage; i note that area of "square pinhole 1.0" is 1.0, and 0.66^2 = 0.4356; the leica graph online suggests not that much light loss ... in part because the Point Spread Function [PSF] of a focused spot is concentrated). . 

Confocal                                   C__xy(0.66AU) =  0.95*0.51*430nm/1.4 =         148nm
Confocal --> Deconvolution     CD_xy(0.66AU)  = 0.95*0.9*0.51*430nm/1.4  =  134nm

For comparison, classic widefield resolution:
Widefield                                  W__xy = 0.61*500nm/1.4 =         218nm
Widefield --> Deconvolution WD_xy = 0.9*0.61*500nm/1.4 =      196nm
Widefield                                  W__xy = 0.61*430nm/1.4 =         187nm
Widefield --> Deconvolution WD_xy = 0.9*0.61*430nm/1.4 =      168nm

In practice, to get even close to these theoretical calculations you need perfect specimen preparation:
* photostable fluorophore(s) ... BV421 is very good. 
* optimal mounting medium with respect to:
   1. Photostability of fluorophore(s).
   2. refractive index 1.518 to match the immersion oil and the 1.4 NA objective lens specification.
* BLACK background. Nothing fluorescent in the mounting medium. Do not use DAPI with BV421 since overlapping wavelengths (consider BioLegend's Zombie NIR). Put your DNA counterstain in with the primary or secodnary antibodies.
* Perfect specimen preparation with respect to minimizing refractive index changes in the specimen -- any intact lipid membranes will cause R.I. shifts. 
* Perfect antibodies, smFISH probe sets, DNA-PAINT reagents, counterstains.
* Consider moving from classic "zoo" of secondary antibodies to using secodnary Nanobodies to detect any primary antibody. 
* Even better: direct label antibodies, especially Brilliants. The flow cytometry world "went direct" decades ago. BD Biosciences and BioLegend have lots of Brilliant (BV421, others) direct label antibodies, and can conjugate others. They -- and Jackson Immunoresearch -- also have Brilliant Streptavidins (if you want to use streptavidin, you should block any exposed biotins in your specimen before applying reagents).
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Plan T: I am also a fan of tyramide signal amplification. ThermoFisher sell SuperBoost TSA with Alexa Fluor 350 with similar emission spectrum to BV421. ThermoFisher has lots of other fluorophores they can custom conjugate to tyramide, and many catalog tyramides, including Alexa Fluor 488.
https://www.thermofisher.com/us/en/home/life-science/cell-analysis/cellular-imaging/immunofluorescence/tyramide-signal-amplification-tsa.html
Semrock Searchlight with some Brilliants, SuperBrights, AF350   https://searchlight.semrock.com/?sid=8781748e-169f-41ab-bf13-9d4c809e6e3c

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more stuff ... perfect specimen preparation (good luck acheiving that!)

* specimen is expected to be at the coverglass (if perfect refractive index match, not critical, see Staudt ... Hell 2006 MRT).
* 170 um coverglass ("high performance" - Mattek sells these as imaging dishes, Zeiss as Marienfeld) (if perfect R.I. match, could in theory use thinner coverglass, #0 ~80um  or #1 ~120 um).
* Perfect refractive index match: this matters at the THIRD decimal, that is 1.518 vs 1.515. One challenge is measuring the R.I. of any medium (oil or mounting) to that accuracy and precision. Also, R.I. changes with wavelength ("dispersion") and temperature (our rooms do not have perfectly stable temperature). 
* Leica SP8 HyVolution2 deconvolution uses SVI.nl Huygens, they have online calculator (input your own values), https://svi.nl/NyquistCalculator and would recommend pixel size XY=36nm and Z=108nm where I would recommend ("dxy divide by ~3) of XY 50nm and Z=150nm. I am happy if you use 36nm XY since 50^2 / 36^2 = 1.36 so use spend 1.36x more time and we make 1.36x more money (in practice, we bill in half hour intervals, so we might not generate more revenue). In practice, the Ross building vibrations probably limit our resolution (9th floor; service elevators near by; yes the vibration isolation table works). I suggest instead of slightly smaller pixel size, that you optimize (i) laser power, and (ii) line accumulations (HyD's in photon counting mode). I also note that our Leica SP8's twoHyD's may "perform differently" (that is, one may be better than the other at the same wavelength rang; potentially either may be noisier than the other). More photon counts is better data, better deconvolution.
* Olympus FV3000RS and FISHscope: can be deconvolved on FISHscope PC using cellSens - Process - Deconvolution - Constrained Iterative. Note: requires 2 or more channels to work. If you only have one fluorophore, could turn on a second detector and position it adjacent to the first (GM can set up the light path for you). Note: FV3000RS optimal PMT HV is 500 mV, so if you use some other value (ex 700 mV), you are probably wasting your time and money by generating noisy data. I suggest 16 line average on FV3000RS if aiming to get best possible data (FV3000RS highest NA objective lens is 1.35NA and uses oil RI 1.405, so you should optimize specimen mounting medium for that if you want to use FV3000RS ... or you could buy and donate to the image core a new Olympus X-Line or X-Line HR objective lens that uses 1.518 oil; one of these objective lenses is 1.5 NA, which -- if perfect specimen preparation, would enable a 7% improvement in resolution [1.5/1.4 = 1.07]). 
* If you REALLY need better resolution than what our microscopes "do", MicFac and various research labs have super-resolution fluorescence microscopes.
* if you only have one molecule to detect, and can put it on a high refractive index nanoparticle (ex: Nanodiamond, see Adamas Nano; or Nanogold, or other small AuNP or AgNP) reflected light confocal microscopy could get you spectacular results. And no issues of photobleaching. 

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{due to limitations of our web site, no graphs here}

tale of two traces ... 0.66 Airy units -- aka confocal Sweetest Spot (re: Jeff Reece range 0.6 top 0.7 Airy's) looks like ~6% improvement in XY resolution for 'little' decrease in photon flux ... of course could be measured with HyD detectors in photon counting mode (or S detectors on STELLARI confocals). Additionally (see text later): BV421 (wavelength ~430nm) and deconvolution. 

Leica graph at   https://www.leica-microsystems.com/science-lab/pinhole-geometry-four-corners-are-perfect/
Zeiss graph in a Zeiss appnote on confocal pinhole ... GM has PDF.

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A couple of references (and their math):

Lambda = wavelength (in vacuum), n=refractive index, NA=numerical aperture.
Klaus Weisshart , Thomas Dertinger , Thomas Kalkbrenner , Ingo Kleppe and Michael Kempe 2013 Super-resolution microscopy heads towards 3D dynamics.  Adv. Opt. Techn. 2013; 2(3): 211–231. DOI 10.1515/aot-2013-0015
Resolution equations:
widefield
dxy = Lambda / 2n sin(alpha) = Lambda / 2 NA, n=refractive index, NA=numerical aperture.
dz   = 2 lambda / (n sin(alpha))^2

Kubalov I, Nemeckova A, Weisshart K, Eva Hribova E, Schubert V 2021 Comparing Super-Resolution Microscopy Techniques to Analyze Chromosomes. Int J Mol Sci 22(4):1903. doi: 10.3390/ijms22041903.
==> also has STED, SIM, SMLM equations. 
Widefield ("conventional")
Rayleigh XY = 0.61 * Lambda / NA
Rayleigh Z   = 2 * Lambda / NA^2

Deconvolution XY = (0.61 * Lambda / NA) / sqrt(2) = (0.61 * Lambda / NA) / 1.414
  GM: sqrt(2) would be ~30% improvement  (XY*0.707) ... this is more than is realistic.
Confocal XY = (0.61 * Lambda / NA) / sqrt(2)
   GM: weird that confocal (implicitly 1.0 Airy unit) same as deconvolution. Also they did not report deconvlution of confocal data.
My take (see also above): 
  standard confocal  (1.0 Airy unit)  XY:           0.51 * Lambda / NA
  Confocal --> deconvolution             XY: 0.9 *  0.51 * Lambda / NA
with caveat that an "ocean of uniform fluorescence" cannot be usefully deconvolved -- that is, some specimens may result in nonsense for deconvolution (whether widefield or confocal).

1.40 vs 1.45 NA objective lenses

* ignoring for this table deconvolution, which can improve an additional ~10% resolution. Table added 20211007 because we are demo'ing the Olympus 150x/1.45NA objective lens (hopefully find money some day to buy it ... ideally Olympus would introduce X-line or X-Line-HR version), widefield lambda = 500nm d = 0.61 * 500 / 1.40 = 218nm   d = 0.61 * 500 / 1.45 = 210nm    ... 150x/1.45NA lens   confocal, pinhole 1.0 Airy Unit,  lambda = 500nm d = 0.51 * 500 / 1.40 = 182nm   d = 0.51 * 500 / 1.45 = 178nm    ... 150x/1.45NA lens   confocal, pinhole ~0.666 Airy Unit ("confocal sweetest spot", re Jeff Reese "confocal sweet spot" range 0.6-0.7 A.U.} ,  lambda = 500nm d = 0.475 * 500 / 1.40 = 170nm   d = 0.475* 500 / 1.45 = 164nm    ... 150x/1.45NA lens   confocal, pinhole 0.5 Airy Unit,  lambda = 500nm d = 0.44 * 500 / 1.40 = 157nm   d = 0.44 * 500 / 1.45 = 151nm    ... 150x/1.45NA lens   confocal, pinhole 0.5 Airy Unit,  lambda = 440nm for Brilliant Violet BV421 d = 0.44 * 440 / 1.40 = 140nm   d = 0.44 * 440 / 1.45 = 135nm    ... 150x/1.45NA lens

reviist widefield widefield lambda = 500nm d = 0.61 * 500 / 1.40 = 218nm   d = 0.61 * 500 / 1.45 = 210nm    ... 150x/1.45NA lens ORCA-FLASH4.0LT is 6.5x6.5 um pixel size, so: 6.5 um / 100 (mag) = 65nm  6.5 um / 150 (mag) = 43nm This might have benefit for super-resolution on widefield microscopy.

Goodwin PC 2014 Quantitative deconvolution microscopy. Methods Cell Biol. 123:177-92. doi: 10.1016/B978-0-12-420138-5.00010-0. PMID: 24974028

* Pawley J 2006 Handbook of Confocal Microscopy.

* Sanderson J 2019 Understanding Light Microscopy.

Sweetest Spot Confocal re AiryScan central detectors (2/2022: Abberior Instruments introduced MATRIX detector)

20210805 note Preprint mentioned that the seven central detectors of AiryScan (and AiryScan2) have a diameter of 0.6 Airy Unit. Then clever math (Zeiss or this preprint - see also SVI.nl Huygens) is done with respect to all three rings. One consequence of 7 or all 32 detectors is noise adds. this suggests to me that for dim signal, one extremely good detector (i.e. avalanche photodiode or Leica STELLARIS confocal "S" SiPM) with 0.6 (or 0.666...) Airy Unit could outperform the 32-channel detector. Prigent 20210802 bioRxiv - High-resolution reconstruction and deconvolution of array detector images https://doi.org/10.1101/2021.08.02.454749 Each individual sub-detector has a diameter of 0.2 AU (Airy Unit). The inner hexagonal patch gathering the 7 central detectors has a diameter of 0.6 AU. The inner ring gathering the sub-detectors 8-19 has a diameter of 1 AU. The whole array of 32 sub-detectors has a diameter of 1.25 AU.

20220216W: Abberior Instruments (cofounded by Stefan Hell) introduced MATRIX detector with 20 "sub-detectors" (unclear if to 20 APDs or perhaps more likely to a SPAD). Same day early Feb 2022 introduced TIMEbox (fluorescence lifetime meets rainbow)

 

Lam ... Bolte 2017 like 0.6 Airy Units

Lam F, ... Bolte S 2017 Super-resolution for everybody: An image processing workfl ow to obtain high-resolution images with a standard confocal microscope. Methods 115 (2017) 17–27. http://dx.doi.org/10.1016/j.ymeth.2016.11.003 We furthermore showed that the fixed biological tissue has an overall refractive index that is close to that of the optical system (1.518), rendering the tissue very transparent. {gm note: live cells R.I. ~1.40} Resolution improvement by closing the pinhole aperture We then wanted to test if we could increase resolution of the confocal microscope by closing the detection pinhole. We compared resolution at the coverslip and in a depth of 60 lm with the detector pinhole set to 0.6 AU (Fig. 1C, Table 1) and after deconvolution of the data. Our choice of the 0.6 AU pinhole size was based on several tests on our biological data. We acquired the same type of biological sample with different pinhole sizes, from 1 AU to 0.4 AU and observed that 0.6 AU is the threshold where we discard enough diffraction signal without photo-bleaching and with a good contrast. Since the result depends largely on the quality and the photo-stability of the biological sample the optimal pinhole value has to be evaluated for each biological sample.  For the AF1+-medium {R.I. 1.518}, lateral resolutions of 106 nm ± 4 nm (coverslip) and 120 nm ± 7 nm (depth) and axial resolutions of 164 nm ± 8 nm (coverslip) and 192 nm ± 17 nm (depth) were measured. Closing the pinhole indeed increased lateral and axial resolution 1.3–1.4-fold. These results are in good agreement with data measured by Cox and Sheppard [28], who observed a 1.4-fold increase in resolution after closing the pinhole aperture to 0.5 using a Leica TSC SP2 confocal microscope.  By optimizing sample preparation, image acquisition parameters and performing deconvolution, our workflow allowed us to obtain a considerable gain in lateral and axial resolution throughout the sample thickness. We used AF1 (Citifluor, UK), a commercially available mounting medium with a refractive index of 1.463 and AF1+, a modified AF1 solution harbouring a refractive index of 1.518. The refractive index increase of AF1+ solution was obtained by adding 83% (w/w) of Methyl-Phenylsulfoxid (Sigma-Aldrich, #261696) to AF1-solution. Refractive indices were verified at 21 C using a refractometer (Mettler Toledo, Switzerland). * [17] C. Fouquet, J.-F. Gilles, N. Heck, M. Dos Santos, R. Schwartzmann, V. Cannaya, M.-P. Morel, R.S. Davidson, A. Trembleau, S. Bolte, PLoS ONE (2015), http://dx.doi.org/10.1371/journal.pone.0121096

20230224F update SPLIT-PIN software enabling confocal and super-resolution imaging with a virtually closed pinhole Elisabetta Di Franco, Angelita Costantino, Elena Cerutti, Morgana D’Amico, Anna P. Privitera, Paolo Bianchini, Giuseppe Vicidomini, Massimo Gulisano, Alberto Diaspro & Luca Lanzanò  Scientific Reports volume 13, Article number: 2741 (2023)  https://www.nature.com/articles/s41598-023-29951-9 In point-scanning microscopy, optical sectioning is achieved using a small aperture placed in front of the detector, i.e. the detection pinhole, which rejects the out-of-focus background. The maximum level of optical sectioning is theoretically obtained for the minimum size of the pinhole aperture, but this is normally prevented by the dramatic reduction of the detected signal when the pinhole is closed, leading to a compromise between axial resolution and signal-to-noise ratio. We have recently demonstrated that, instead of closing the pinhole, one can reach a similar level of optical sectioning by tuning the pinhole size in a confocal microscope and by analyzing the resulting image series. The method, consisting in the application of the separation of photons by lifetime tuning (SPLIT) algorithm to series of images acquired with tunable pinhole size, is called SPLIT-pinhole (SPLIT-PIN). Here, we share and describe a SPLIT-PIN software for the processing of series of images acquired at tunable pinhole size, which generates images with reduced out-of-focus background. The software can be used on series of at least two images acquired on available commercial microscopes equipped with a tunable pinhole, including confocal and stimulated emission depletion (STED) microscopes. We demonstrate applicability on different types of imaging modalities: (1) confocal imaging of DNA in a non-adherent cell line; (2) removal of out-of-focus background in super-resolved STED microscopy; (3) imaging of live intestinal organoids stained with a membrane dye. A user-friendly version of the Matlab (The MathWorks) code is available at https://github.com/llanzano/SPLITPIN. A step-by-step description of this user-friendly version is available as Supplementary Text.