http://confocal-microscopy-list.275.s1.nabble.com/Deconvolution-of-Transmission-Images-tp7393699p7463197.html
Excellent points. That paper is a joy to read.
> *****
> To join, leave or search the confocal microscopy listserv, go to:
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>
> Well, to put this in more easily understood terms, Nyquist (at 2B) defines
> the limit - ie the point where you cease to be able to reconstruct the
> wave. So, as Mark says, you need to get beyond this to actually be able
> to get information. The often-quoted 2.3B more or less corresponds to the
> Rayleigh resolution criterion, ie the point at which you can reconstruct
> the wave at usable contrast. However, the other problem we face is that we
> do NOT reconstruct the sine wave, we just look at a map of little squares.
> This is stupid.
>
> Required reading should be:
>
> A Pixel Is Not A Little Square,
> A Pixel Is Not A Little Square,
> A Pixel Is Not A Little Square!
> (And a Voxel is Not a Little Cube)
> Microsoft Technical Memo 6
> Alvy Ray Smith
> July 17, 1995
>
> (Yes, that really is the title)
>
> It's on the Microsoft web site, or I can mail a copy to anyone who is
> interested.
>
>
> Guy
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:
[hidden email]]
> On Behalf Of Mark Cannell
> Sent: Friday, 13 April 2012 5:53 PM
> To:
[hidden email]
> Subject: Re: Nyquist and Image size
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
>
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>
> Please lets not get silly on this. The Nyquist rate is _defined_ as 2
> times the bandlimit. The Nyquist rate is defined by the sufficient
> condition for exact reconstructability: Fs > 2B. 2B _is_ the Nyquist rate
> as David said, it does not mean Fs = 2B is sufficient!
>
> Cheers
>
> On 13/04/2012, at 8:18 AM, Sylvie LeGuyader wrote:
>
> > *****
> > To join, leave or search the confocal microscopy listserv, go to:
> >
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> >
> > Hi everyone
> >
> > "strict Nyquist is a factor of 2."
> >
> > My understanding is that the Nyquist theorem is not arbitrary and that
> the factor is actually >2. So 2.1 would do as well as 2.3. If i understood
> well the >2 comes from this: if you want to describe a periodic signal
> (which is what we do when we acquire an image: we describe a sum of
> periodic signals), you need more than 2 points within 1 full period to
> collect enough information to reconstruct the periodic signal accurately.
> If you only give 2 points per period (e.g. only the crests and troughs),
> you can draw the periodic signal is several ways (e.g. double the frequency
> of the original signal). When we acquire an image we should thus sample
> more than twice the shortest period (the edges) to acquire enough
> information for the computer to properly reconstruct the image. This is why
> the Nyquist criterion is 'more than 2'. Am I right?
> >
> > Sylvie
> >
> > @@@@@@@@@@@@@@@@@@@@@@@@
> > Sylvie Le Guyader
> > Live Cell Imaging Unit
> > Dept of Biosciences and Nutrition
> > Karolinska Institutet
> > Novum
> > 14183 Huddinge
> > Sweden
> > office: +46 (0) 8 5248 1107
> > LCI room: +46 (0) 8 5248 1172
> > mobile: +46 (0) 73 733 5008
> >
> >>
> >> On 11 Apr 2012, at 22:45, "David Baddeley"
> >> <
[hidden email]>
> >> wrote:
> >>
> >>> *****
> >>> To join, leave or search the confocal microscopy listserv, go to:
> >>>
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy> >>> *****
> >>>
> >>>
> >>> The diagonal in z will be much 'straighter' (due to the fact that
> >>> the voxels are
> >> elongated in z rather than being square), making the factor much
> >> closer to 1 (probably something like 1.1) so it can safely be
> >> ignored. When talking about slightly oversampling, 2.3 is already
> >> doing this - strict Nyquist is a factor of 2. It's also worth noting
> >> that you should probably use the theoretical resolution values (ie
> >> ~180x450 for a 1.4 NA objective @500nm and a pinhole of 0.7 AU) and
> >> not the observed PSF width, as these reflect the bandwidth of the
> >> system. I this tend to reccommend a blanket 70x70x200nm pixel size
> >> when using a high NA objective on fixed cells. In live cells, or
> >> other delicate samples you need to exercise a little more discretion
> >> - the artefacts introduced by slight undersampling are likely to be
> outweighed by other considerations.
> >>>
> >>> My 2c,
> >>> David
> >>>
> >>>
> >>> ------------------------------
> >>> On Thu, Apr 12, 2012 3:44 AM NZST Vasseur Monique wrote:
> >>>
> >>>> *****
> >>>> To join, leave or search the confocal microscopy listserv, go to:
> >>>>
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy> >>>> *****
> >>>>
> >>>> Hi John,
> >>>>
> >>>> Indirectly, do you suggest the same for Z sampling if we are
> >>>> interested in 3D measurements? Thanks
> >>>>
> >>>> Monique Vasseur
> >>>>
> >>>> -----Message d'origine-----
> >>>> De : Confocal Microscopy List
> >> [mailto:
[hidden email]] De la part de Lemasters,
> >> John J.
> >>>> Envoyé : 11 avril 2012 09:34
> >>>> À :
[hidden email] Objet : Re: Nyquist and Image
> >>>> size
> >>>>
> >>>> *****
> >>>> To join, leave or search the confocal microscopy listserv, go to:
> >>>>
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy> >>>> *****
> >>>>
> >>>> Please remember that pixel spacing on the diagonal is 1.4 that in
> >>>> the horizontal
> >> and vertical directions. Accordingly to meet the Nyquist criterion
> >> for the diagonal, pixel size should be 2.3 x 1.4 = 3.2. Also, the
> >> Nyquist criterion is an arbitrary threshold, and image quality will
> >> improve somewhat with sampling greater that proposed by Nyquist.
> >> Considering diagonal sampling, I suggest using a pixel size that is one
> fourth of the resolving limit for the most critical work.
> >>>>
> >>>> John
> >>>>
> >>>> --
> >>>> John J. Lemasters, MD, PhD
> >>>> Professor and GlaxoSmithKline Distinguished Endowed Chair Director,
> >>>> Center for Cell Death, Injury & Regeneration Departments of
> >>>> Pharmaceutical & Biomedical Sciences and Biochemistry & Molecular
> >>>> Biology Medical University of South Carolina
> >>>> DD504 Drug Discovery Building
> >>>> 70 President Street, MSC 140
> >>>> Charleston, SC 29425
> >>>>
> >>>> Office: 843-876-2360
> >>>> Lab: 843-876-2354
> >>>> Fax: 843-876-2353
> >>>> Email:
[hidden email]
> >>>>
http://academicdepartments.musc.edu/ccdir> >>>>
> >>>>
> >>>> -----Original Message-----
> >>>> From: Confocal Microscopy List
> >>>> [mailto:
[hidden email]] On Behalf Of John
> >>>> Oreopoulos
> >>>> Sent: Wednesday, April 11, 2012 8:29 AM
> >>>> To:
[hidden email]
> >>>> Subject: Re: Nyquist and Image size
> >>>>
> >>>> *****
> >>>> To join, leave or search the confocal microscopy listserv, go to:
> >>>>
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy> >>>> *****
> >>>>
> >>>> Renato,
> >>>>
> >>>> Whether you have 256x256, 512x512 or 2048x2048, the "optimum"
> >>>> Nyquist
> >> sampling rate (ie: pixel dimensions) does not change since your
> >> objective lens did not change. The quoted pixel size at 2Kx2K you
> >> mentioned (22.5 nm x 22.5 nm) means you are oversampling the image
> >> (and not gaining anything). Your image may look smoother but it
> >> contains no more information than the 512x512 image with 90x90 nm
> >> pixel sizes. Presumably the scan speed is the same between
> >> 512x512 and 2Kx2K.
> >>>>
> >>>> You should decrease the galvometric mirror scan zoom setting to get
> >>>> back to
> >> an effective pixel size of 90x90 nm with 2Kx2K pixels in your image.
> >> Effectively, you will be imaging (and properly sampling) a larger
> >> field of view then. I'm not familiar with the Leica laser scanning
> >> confocals so I'm not sure if it will allow you to do this. On other
> >> systems, like the Olympus FV300 for example, you can set your image
> >> pixel dimensions (256x256, 512x512, etc.) and your scan zoom
> independently.
> >>>>
> >>>> Just out of curiosity, why image 2K x 2K when you can't easily
> >>>> display that on
> >> a standard computer screen or present it in a published paper without
> downsizing?
> >> I rarely departed from 512x512 in my laser scanning days, except when
> >> I wanted to see a larger field of view.
> >>>>
> >>>> Cheers,
> >>>>
> >>>>
> >>>> John Oreopoulos
> >>>> Research Assistant
> >>>> Spectral Applied Research
> >>>> Richmond Hill, Ontario
> >>>> Canada
> >>>> www.spectral.ca
> >>>>
> >>>>
> >>>> On 2012-04-11, at 7:22 AM, Renato Mortara wrote:
> >>>>
> >>>>> *****
> >>>>> To join, leave or search the confocal microscopy listserv, go to:
> >>>>>
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy> >>>>> *****
> >>>>>
> >>>>> Dear all,
> >>>>>
> >>>>> Having attended the first Pawley course in Vancouver I feel highly
> >>>>> embarassed to ask this, but I would really appreciate a
> clarification:
> >>>>>
> >>>>> When estimating the highest zoom users should apply to their
> >>>>> sample in order to accommodate for the Nyquist theorem, I
> >>>>> estimated the optimum pixel size value by dividing the lateral
> >>>>> resolution (eg: 0.2
> >>>>> microns) by 2.3 so that the value is approxiametely 90 nm.
> >>>>>
> >>>>> The doubt: if the image size is increased from 512x512 (having
> >>>>> adjusted the zoom to the pixel size of 90nm) to 2Kx2K, the
> >>>>> resulting pixel size (displayed by the system - Leica) the pixel
> >>>>> size decreases
> >>>>> 4 fold, to 22.5 nm. Since the resolution obviously did not change
> >>>>> but only the image size, what happens to Nyquist and the optimum
> >>>>> pixel size
> >> at 2Kx2K ?
> >>>>>
> >>>>> Many thanks !
> >>>>>
> >>>>> Renato
> >>>>>
> >>>>> Renato A. Mortara
> >>>>> Parasitology Division
> >>>>> UNIFESP - Escola Paulista de Medicina Rua Botucatu, 862, 6th floor
> >>>>> São Paulo, SP
> >>>>> 04023-062
> >>>>> Brazil
> >>>>> Phone: 55 11 5579-8306
> >>>>> Fax: 55 11 5571-1095
> >>>>> email:
[hidden email]
> >>>>> home page: www.ecb.epm.br/~ramortara<
http://www.ecb.epm.br/%7Eramortara>
>
Joel B. Sheffield, Ph.D