Dear Marin For electron microscopy, the Rose criterion (a measure of contrast/noise) is sometime used to distinguish low contrast features within polymers (see for example Libera, M. & Egerton, R. (2010). Polymer Reviews. 50, 321-339.). A particular value of the Rose criterion implies a particular information content.
I think this can be directly related to a particular threshold for FSC or FRC. If you can comment on this in your Why-o-Why didactical crusade, I might even register for a twitter account! Regards Colin From: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK<mailto:CCP4BB@JISCMAIL.AC.UK>> On Behalf Of Marin van Heel Sent: 17 February 2020 13:29 To: CCP4BB@JISCMAIL.AC.UK<mailto:CCP4BB@JISCMAIL.AC.UK> Subject: Re: [ccp4bb] [3dem] Which resolution? Dear Petrus Zwart (and all other X-ray crystallographers and EM-ers) Resolution in the sense of the Abbe Diffraction Limit or the Rayleigh Criterion are part of what we would now call the theory of linear systems, and are described by a “transfer function”. “Fourier Optics” covers the theory of linear systems in Optics. These two (essentially identical) resolution criteria state that the smallest details (let us call that “A(r)” for “Airy”) you can possible observe in real-space is inversely proportional to the size of the maximum aperture in Fourier space, i.e., the extent of the transfer function in Fourier space “T(f)”. This defines what “Instrumental Resolution” one could possibly achieve in an experiment, “instrumental” to differentiate it from the “Results Resolution” you actually managed achieve in your data collection/processing experiment [#Why-o-Why #10]. What a linear imaging system will do the image of the object (under the best of circumstances) is described by a (Fourier-space) multiplication of the Fourier transform of the object O(r) [= O(f)] with the (Fourier-space) transfer function T(f) of the instrument, yielding O’(f), which you need to transfer back to real space to obtain the exit wave in the image plane; that is: {O’(f)=T(f)·O(f)}. Note, however, that the properties of the sample, that is, of O(r), does nowhere appear in the transfer function T(f) or in its real-space version A(r)! The very concept of (instrumental) resolution is exactly that it does NOT depend on the object O(r)! The “results resolution” [#Why-o-Why #10], on the other hand, obviously depends on the sample; the illumination; on the radiation dose; the pH of the solvent; the air humidity; and the mood of the person doing the work on the day of preparation… The FRC/FSC “results resolution” measures we introduced in 1982/1986, fit perfectly in the abstract framework of linear systems and Fourier optics. The X-ray metrics like R-factor and phase-residuals and FOMs do NOT fit into that clean mathematical framework. Unfortunately, my EM colleagues started using X-ray metrics like “Differential Phase Residual” and “FOMs” in EM based on some gut feeling that the X-ray scientists know it better because they achieve a higher resolution than us EM blobologists. How wrong my EM colleagues were: the quality of the resolution metric is totally unrelated to the numerical resolution levels we operate at! Seeing 3mm kidney stones in a patient’s tomogram can be equally important as seeing some hydrogen bond length in a cryo-EM density. The FRC/FSC actually make more sense than the indirect and hybrid X-ray ones. This misconception has introduced a very tainted – and still ongoing – discussion in cryo-EM. Now that the fields of X-ray crystallography and cryo-EM are merging it is time to get things right! I guess I cannot yet terminate my #Why-o-Why didactical crusade: I will need at least one more on just this linear-transfer theory issue alone… Marin van Heel, CNPEM/LNNano, Campinas, Brazil On Sun, Feb 16, 2020 at 6:51 PM Petrus Zwart <phzw...@lbl.gov<mailto:phzw...@lbl.gov>> wrote: Hi All, How is the 'correct' resolution estimation related to the estimated error on some observed hydrogen bond length of interest, or an error on the estimated occupancy of a ligand or conformation or anything else that has structural significance? In crystallography, it isn't really (only in some very approximate fashion), and I doubt that in EM there is something to that effect. If you want to use the resolution to get a gut feeling on how your maps look and how your data behaves, it doesn't really matter what standard you use, as long as you are consistent in the use of the metric you use. If you want to use this estimate to get to uncertainties of model parameters, you better try something else. Regards Peter Zwart On Sun, Feb 16, 2020 at 8:38 AM Marin van Heel <0000057a89ab08a1-dmarc-requ...@jiscmail.ac.uk<mailto:0000057a89ab08a1-dmarc-requ...@jiscmail.ac.uk>> wrote: Dear Pawel and All others .... This 2010 review is - unfortunately - largely based on the flawed statistics I mentioned before, namely on the a priori assumption that the inner product of a signal vector and a noise vector are ZERO (an orthogonality assumption). The (Frank & Al-Ali 1975) paper we have refuted on a number of occasions (for example in 2005, and most recently in our BioRxiv paper) but you still take that as the correct relation between SNR and FRC (and you never cite the criticism...). Sorry Marin On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A <pawel.a.penc...@uth.tmc.edu<mailto:pawel.a.penc...@uth.tmc.edu>> wrote: Dear Teige, I am wondering whether you are familiar with Resolution measures in molecular electron microscopy. Penczek PA. Methods Enzymol. 2010. Citation Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8. You will find there answers to all questions you asked and much more. Regards, Pawel Penczek Regards, Pawel _______________________________________________ 3dem mailing list 3...@ncmir.ucsd.edu<mailto:3...@ncmir.ucsd.edu> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem ________________________________ To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 -- ------------------------------------------------------------------------ P.H. 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