Re: Nyquist and Image size

Posted by Mark Cannell on
URL: http://confocal-microscopy-list.275.s1.nabble.com/Deconvolution-of-Transmission-Images-tp7393699p7465734.html

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That's a nice 'rant' but it does of course ignore the fact that many cameras have square pixels... so it is justified to represent/describe the data with square pixels in that case ... I kind of wish that Microsoft applied similar 'deep thought' to their software before releasing it tho'

LOL

As a further aside,  I note that no one has so far discussed the issue of A/D conversion resolution in deciding the _actual_  bandlimit. For a n bit converter, the bandlimit occurs when the power spectrum of the Airey disk falls below 1/2 a bit (I think) so it's also amplification and noise dependent...

Cheers
Mark


On 14/04/2012, at 11:05 AM, Guy Cox wrote:

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> http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Renato A. Mortara
> Sent: Saturday, 14 April 2012 2:13 AM
> To: [hidden email]
> Subject: Re: Nyquist and Image size
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
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>
> Hi Guy, it would be great if you could email the article to me:
>
> Thanks again for all the inputs !
>
> Renato
>
>
> Renato A. Mortara
> Disciplina de Parasitologia
> UNIFESP Escola Paulista de Medicina
> R. Botucatu, 862 6o andar
> 04023-062
> São Paulo SP
> Brasil
> [hidden email]
>
>
> Citando "Joel B. Sheffield" <[hidden email]>:
>
>>
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>>
>> Excellent points.  That paper is a joy to read.
>> Joel
>>
>>
>> On Fri, Apr 13, 2012 at 8:36 AM, Guy Cox <[hidden email]> wrote:
>>
>>> *****
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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:
>>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
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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: [phone]
>>>> LCI room: [phone]
>>>> mobile: [phone]
>>>>
>>>>>
>>>>> 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: [phone]
>>>>>>> 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: [phone]
>>>>>>>> Fax:     [phone]
>>>>>>>> email: [hidden email]
>>>>>>>> home page:  
>>> www.ecb.epm.br/~ramortara<http://www.ecb.epm.br/%7Eramortara>
>>>
>>
>>
>>
>> --
>>
>>
>> Joel B. Sheffield, Ph.D
>> Department of Biology
>> Temple University
>> Philadelphia, PA 19122
>> Voice: 215 204 8839
>> e-mail: [hidden email]
>> URL:  http://astro.temple.edu/~jbs
>>
>>