Deconvolution of Transmission Images

[Arne Seitz]

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Theoretically it is totally right to assume that one can either increase the sampling frequency or the field of view if the number of pixels are increased.
Practically one cannot increase the field of view in a scanning system without getting nasty side effects like e.g. uneven illumination.  To my understanding this is the reason why vendors tend to go for option one if you increase the number of pixels.

Cheers Arne


---------------------------------------------------------------
Arne Seitz
Head of Bioimaging and Optics Platform (PT-BIOP)
Ecole Polytechnique Fédérale de Lausanne (EPFL)
Faculty of Life Sciences
Station 15, AI 0241
CH-1015 Lausanne

Phone: [phone]
Fax:      [phone]
http://biop.epfl.ch/
---------------------------------------------------------------

> -----Original Message-----
> From: Confocal Microscopy List
> [mailto:[hidden email]] On Behalf Of Guy Cox
> Sent: mercredi 11 avril 2012 15:06
> 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
> *****
>
> Just to add a bit to John's absolutely correct explanation.
>
> It's basically a question of interpretation.  You set up Nyquist imaging at
> 512x512 and then selected 2048x2048, expecting to get the same resolution
> but a 4 times bigger area.  Perfectly reasonable.  But the Leica software
> assumed you now wanted to get 2048x2048 pixels within the same chosen
> field of view.  Also a perfectly reasonable interpretation.  One might, in a
> perfect world, expect the software to ask you which interpretation you
> want, but if it doesn't it's pretty easy to fix.
>
>                                               Guy
>
>
> Optical Imaging Techniques in Cell Biology
> by Guy Cox    CRC Press / Taylor & Francis
>      http://www.guycox.com/optical.htm
> ______________________________________________
> Guy Cox, MA, DPhil(Oxon), Honorary Associate, Australian Centre for
> Microscopy & Microanalysis, Madsen Building F09, University of Sydney, NSW
> 2006
>
> Phone [phone]     Fax [phone]
>              Mobile [phone]
> ______________________________________________
>       http://www.guycox.net
>
>
>
> -----Original Message-----
> From: Confocal Microscopy List
> [mailto:[hidden email]] On Behalf Of John
> Oreopoulos
> Sent: Wednesday, 11 April 2012 10:29 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
> *****
>
> 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

[Johannes Schindelin]

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Hi Mark,

On Sat, 14 Apr 2012, Mark Cannell wrote:

> That's a nice 'rant' but it does of course ignore the fact that many
> cameras have square pixels...

But it is not the square detectors of the camera you are recording. There is
a whole optical path up until then.

Pixels are not the physical dimension of the detector, they are an
abstract construct to describe what the number (or numbers) attached to it
-- the pixel value -- actually mean.

To say that pixels are square because the CCD is organized in a grid is
like saying that the spots the sun is leaving in a forest of trees are as
oddly shaped as the holes made by leaves through which the sun's rays
reach the soil.

Ciao,
Johannes

[Christian Soeller]

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Hi Johannes,

I think you are overstating things quite a bit. Mark has a good point that there is an important difference between point sampling (with a point detector in a scanning confocal) and a camera chip. Point detection essentially samples a field spatially filtered by the PSF. If you sample this too coarsely you can create impressive aliasing artifacts, for example, using a slide with lots of fluorescent beads on it. When using a camera (in say a wide field system) there is an additional low pass filtering by the camera pixels, for CCDs these pixels are typically rectangular (although recent sCMOS will effectively have shapes determined by the capture geometry of the micro lens array). In that sense a camera used below Nyquist for your optical train (characterized by PSF) can avoid some of the aliasing by effectively low pass filtering over the pixel sampling area. You get an image that is lower res than given by your PSF but aliasing should be not so bad/ mostly avoided (this is again a s
light oversimplification).

Christian

--
Christian Soeller PhD - Dept. of Physiology - Univ. of Auckland
Sent with Sparrow (http://www.sparrowmailapp.com/?sig)


On Sunday, 15 April 2012 at 5:43 AM, Johannes Schindelin wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Hi Mark,
>
> On Sat, 14 Apr 2012, Mark Cannell wrote:
>
> > That's a nice 'rant' but it does of course ignore the fact that many
> > cameras have square pixels...
> >
>
>
> But it is not the square detectors of the camera you are recording. There is
> a whole optical path up until then.
>
> Pixels are not the physical dimension of the detector, they are an
> abstract construct to describe what the number (or numbers) attached to it
> -- the pixel value -- actually mean.
>
> To say that pixels are square because the CCD is organized in a grid is
> like saying that the spots the sun is leaving in a forest of trees are as
> oddly shaped as the holes made by leaves through which the sun's rays
> reach the soil.
>
> Ciao,
> Johannes
>
>

[Mark Cannell]

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Hi Johannes

Sorry I disagree. You are recording an image. The point is that the pixels integrate over their entire face which is square so that this may be represented by square pixels perfectly faithfully. I have no idea what your analogy to the images of the sun through leaves has to do with this, the leavers are apertures.

Cheers Mark


On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:

> Hi Mark,
>
> On Sat, 14 Apr 2012, Mark Cannell wrote:
>
>> That's a nice 'rant' but it does of course ignore the fact that many
>> cameras have square pixels...
>
> But it is not the square detectors of the camera you are recording. There is
> a whole optical path up until then.
>
> Pixels are not the physical dimension of the detector, they are an
> abstract construct to describe what the number (or numbers) attached to it
> -- the pixel value -- actually mean.
>
> To say that pixels are square because the CCD is organized in a grid is
> like saying that the spots the sun is leaving in a forest of trees are as
> oddly shaped as the holes made by leaves through which the sun's rays
> reach the soil.
>
> Ciao,
> Johannes

[JOEL B. SHEFFIELD]

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Hi All,

I posed this puzzle to my class recently, and most of the responses were
similar to Mark's.  And I agree that this is not a bad approximation.  In a
camera, certainly, each of the pixels sums and averages the photons that
eventually fall on it in a given time period.  The approximation fails,
however, when we are counting in very dim light, or single photons, so that
a pixel is only an approximation of the actual location of the source.
This is, as I understand it, the major challenge to many of the
superresolution techniques, which use remarkably large pixel sizes (for
sensitivity), and then calculate back to the original source position.
The solution in these cases is to fit the intensities in the surrounding
pixel array to a gaussian whose peak position indicates the true location
of the source.

I'm open to corrections, of course.

Joel

On Sat, Apr 14, 2012 at 9:35 PM, Mark Cannell <[hidden email]>wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Hi Johannes
>
> Sorry I disagree. You are recording an image. The point is that the pixels
> integrate over their entire face which is square so that this may be
> represented by square pixels perfectly faithfully. I have no idea what your
> analogy to the images of the sun through leaves has to do with this, the
> leavers are apertures.
>
> Cheers Mark
>
>
> On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:
>
> > Hi Mark,
> >
> > On Sat, 14 Apr 2012, Mark Cannell wrote:
> >
> >> That's a nice 'rant' but it does of course ignore the fact that many
> >> cameras have square pixels...
> >
> > But it is not the square detectors of the camera you are recording.
> There is
> > a whole optical path up until then.
> >
> > Pixels are not the physical dimension of the detector, they are an
> > abstract construct to describe what the number (or numbers) attached to
> it
> > -- the pixel value -- actually mean.
> >
> > To say that pixels are square because the CCD is organized in a grid is
> > like saying that the spots the sun is leaving in a forest of trees are as
> > oddly shaped as the holes made by leaves through which the sun's rays
> > reach the soil.
> >
> > Ciao,
> > Johannes
>

--


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

[Christian Soeller]

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The super-resolution techniques you mention work with 'single molecules' but certainly quite far away from 'single-photon' detection scenarios. In practice we require a few hundred photons (ideally about a thousand for good measurements) per single molecule flash for good localization. The pixels sizes we work with are not that large, we typically use around 70-100 nm (depending on wavelength), similar to what you might want for conventional Nyquist sampling.

So yes, we need enough photons in a pixel for good images. Otherwise we have a lot of photon noise which effectively degrades our images. None of this invalidates the 'square pixel' integration area.

Cheers,
Christian


--
Christian Soeller PhD - Dept. of Physiology - Univ. of Auckland
Sent with Sparrow (http://www.sparrowmailapp.com/?sig)


On Sunday, 15 April 2012 at 3:03 PM, Joel B. Sheffield wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Hi All,
>
> I posed this puzzle to my class recently, and most of the responses were
> similar to Mark's. And I agree that this is not a bad approximation. In a
> camera, certainly, each of the pixels sums and averages the photons that
> eventually fall on it in a given time period. The approximation fails,
> however, when we are counting in very dim light, or single photons, so that
> a pixel is only an approximation of the actual location of the source.
> This is, as I understand it, the major challenge to many of the
> superresolution techniques, which use remarkably large pixel sizes (for
> sensitivity), and then calculate back to the original source position.
> The solution in these cases is to fit the intensities in the surrounding
> pixel array to a gaussian whose peak position indicates the true location
> of the source.
>
> I'm open to corrections, of course.
>
> Joel
>
> On Sat, Apr 14, 2012 at 9:35 PM, Mark Cannell <[hidden email] (mailto:[hidden email])>wrote:
>
> > *****
> > To join, leave or search the confocal microscopy listserv, go to:
> > http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> > *****
> >
> > Hi Johannes
> >
> > Sorry I disagree. You are recording an image. The point is that the pixels
> > integrate over their entire face which is square so that this may be
> > represented by square pixels perfectly faithfully. I have no idea what your
> > analogy to the images of the sun through leaves has to do with this, the
> > leavers are apertures.
> >
> > Cheers Mark
> >
> >
> > On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:
> >
> > > Hi Mark,
> > >
> > > On Sat, 14 Apr 2012, Mark Cannell wrote:
> > >
> > > > That's a nice 'rant' but it does of course ignore the fact that many
> > > > cameras have square pixels...
> > > >
> > >
> > >
> > > But it is not the square detectors of the camera you are recording.
> > There is
> > > a whole optical path up until then.
> > >
> > > Pixels are not the physical dimension of the detector, they are an
> > > abstract construct to describe what the number (or numbers) attached to
> > >
> >
> > it
> > > -- the pixel value -- actually mean.
> > >
> > > To say that pixels are square because the CCD is organized in a grid is
> > > like saying that the spots the sun is leaving in a forest of trees are as
> > > oddly shaped as the holes made by leaves through which the sun's rays
> > > reach the soil.
> > >
> > > Ciao,
> > > Johannes
> > >
> >
> >
>
>
>
>
> --
>
>
> Joel B. Sheffield, Ph.D
> Department of Biology
> Temple University
> Philadelphia, PA 19122
> Voice: 215 204 8839
> e-mail: [hidden email] (mailto:[hidden email])
> URL: http://astro.temple.edu/~jbs
>
>

[Johannes Schindelin]

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Hi Mark,

On Sun, 15 Apr 2012, Mark Cannell wrote:

> The point is that the pixels integrate over their entire face which is
> square so that this may be represented by square pixels perfectly
> faithfully.

Point is: at the resolution we're operating, PSFs play a role. It does not
matter whether the detector is square. The non-square part happens earlier
in the process, the detector cannot undo it.

All you can safely assume of a pixel is that it has one or more values
(even referring to the value as an "intensity" need not be correct) and
that it has a center. The rest depends on the setup.

Ciao,
Johannes

[Guy Cox-2]

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OK, I think I know Mark well enough that I can just say bollocks.

Representing a sample as a square (ie presenting a sine wave as a square wave) is introducing a whole series of (every alternate) higher harmonics which contribute absolutely NOTHING to the image.   This is really fundamental to understanding digital imaging.

                                                                               Guy

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Mark Cannell
Sent: Sunday, 15 April 2012 11:35 AM
To: [hidden email]
Subject: Re: Nyquist and Image size

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Hi Johannes

Sorry I disagree. You are recording an image. The point is that the pixels integrate over their entire face which is square so that this may be represented by square pixels perfectly faithfully. I have no idea what your analogy to the images of the sun through leaves has to do with this, the leavers are apertures.

Cheers Mark


On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:

> Hi Mark,
>
> On Sat, 14 Apr 2012, Mark Cannell wrote:
>
>> That's a nice 'rant' but it does of course ignore the fact that many
>> cameras have square pixels...
>
> But it is not the square detectors of the camera you are recording.
> There is a whole optical path up until then.
>
> Pixels are not the physical dimension of the detector, they are an
> abstract construct to describe what the number (or numbers) attached
> to it
> -- the pixel value -- actually mean.
>
> To say that pixels are square because the CCD is organized in a grid
> is like saying that the spots the sun is leaving in a forest of trees
> are as oddly shaped as the holes made by leaves through which the
> sun's rays reach the soil.
>
> Ciao,
> Johannes

[Mark Cannell]

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Hi Guy

Thanks a lot! You have got the wrong end of the stick. I am not talking about image reconstruction but displaying raw pixel data...

Cheers


On 15/04/2012, at 11:33 AM, Guy Cox wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> OK, I think I know Mark well enough that I can just say bollocks.
>
> Representing a sample as a square (ie presenting a sine wave as a square wave) is introducing a whole series of (every alternate) higher harmonics which contribute absolutely NOTHING to the image.   This is really fundamental to understanding digital imaging.
>
>                                                                               Guy
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Mark Cannell
> Sent: Sunday, 15 April 2012 11:35 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
> *****
>
> Hi Johannes
>
> Sorry I disagree. You are recording an image. The point is that the pixels integrate over their entire face which is square so that this may be represented by square pixels perfectly faithfully. I have no idea what your analogy to the images of the sun through leaves has to do with this, the leavers are apertures.
>
> Cheers Mark
>
>
> On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:
>
>> Hi Mark,
>>
>> On Sat, 14 Apr 2012, Mark Cannell wrote:
>>
>>> That's a nice 'rant' but it does of course ignore the fact that many
>>> cameras have square pixels...
>>
>> But it is not the square detectors of the camera you are recording.
>> There is a whole optical path up until then.
>>
>> Pixels are not the physical dimension of the detector, they are an
>> abstract construct to describe what the number (or numbers) attached
>> to it
>> -- the pixel value -- actually mean.
>>
>> To say that pixels are square because the CCD is organized in a grid
>> is like saying that the spots the sun is leaving in a forest of trees
>> are as oddly shaped as the holes made by leaves through which the
>> sun's rays reach the soil.
>>
>> Ciao,
>> Johannes

[Mark Cannell]

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Hi Johannes

I can see we are talking at crossed purposes, I was referring to the article "Pixels are not square". If you have to display your data, then the square display pixel representing the integrated intensity over that area in the camera pixel is _perfectly_ correct -it has nothing to do with trying to 'undo' an instrument PSF. I recall publishing a paper some time ago where the detector pixels were visible in the image. The production editor complained that the image was too low a resolution and insisted that it be retaken ay a higher resolution. I pointed out that the square pixels he could see were actually made up of many smaller pixels (as required to meet their 600 dpi printing requirement) and that it was not appropriate to reprocess the image to hide the actual detector/instrument resolution  (I eventually got the image accepted by him but it was a protracted email fight).  I have also seen 'images' representing 2D histograms that have been smoothed and displayed at much higher pixel resolution than the underlying histogram data without rescaling the intensity calibration. This is, in my opinion, a form of scientific fraud, it leads the reader to assume that there was much more data obtained than was actually present and a false sense of reliability in the underlying data set (but I bet the production editor was happy)...

As far as assigning a data value to a spatial point within the detector pixel, that is quite problematic as the pixel integrates the signal over its area -I think we agree on that. Unless the pixel were very small compared to the width of the instrument PSF then it's value does not 'correctly' assign the intensity recorded to the center of the pixel (or anywhere else over the area of the pixel). Perhaps one way of thinking about this is to imagine a narrow spike being detected by a single camera pixel (yes, the sampling frequency is slightly greater than twice the bandwidth) the camera pixel reports the local integrated amplitude/energy of the spike function correctly but the phase information (needed for reconstruction) is uncertain due to the width of that single pixel. The problem disappears if you know you are looking at a single Airy disk (or other known bandlimited waveform with 2B < Fs) as only one solution for the position of the disk centre will fit the intensities recorded over the width of  several pixels (I'm ignoring the uncertainty due to noise).  It is the extra pixels around the pixel of interest that supply the extra information needed to assign an intensity to a _position_ within that pixel from the integrated signal over the pixels. This is why super resolution microscopy becomes possible. BUT to display _raw_ camera data, I still think you should use square pixels for square pixel cameras to show that you don't know how to assign (or have not yet determined the assignment (it's raw data)) the intensity to a point...

Perhaps a non-mathematical, intuitive way of describing the situation is this: You need to pieces of information for determining a sinusoid: It's amplitude and phase. So you need 2 measures to solve the equation and that is given by the values of 2 adjacent pixels for a sinusoid just under Fs/2. If you move the phase of highest frequency sinusoid both pixel intensities change (note that both pixels always have different intensity).  It's the ability to solve the phase component that makes super resolution microscopy possible. BUT to display _raw_ camera data, I still think you should use square pixels for square pixel cameras to show that you don't know how to assign (or have not yet determined the assignment (it's raw data)) the intensity to a point...

Hope this clears up the confusion between our POVs for others reading this.

For those interested in how to display super resolution data when you only have intensities at points and not pixels, we published a nice (IMO) method that may not corrupt spatial information as much as assigning a Gaussian or square to each point:

Baddeley D, Cannell MB, Soeller C. Visualization of Localization Microscopy Data. Microsc. Microanal. 2010 Jan. 18;16(01):64.  

Cheers Mark


On 15/04/2012, at 6:24 AM, Johannes Schindelin wrote:

> Hi Mark,
>
> On Sun, 15 Apr 2012, Mark Cannell wrote:
>
>> The point is that the pixels integrate over their entire face which is
>> square so that this may be represented by square pixels perfectly
>> faithfully.
>
> Point is: at the resolution we're operating, PSFs play a role. It does not
> matter whether the detector is square. The non-square part happens earlier
> in the process, the detector cannot undo it.
>
> All you can safely assume of a pixel is that it has one or more values
> (even referring to the value as an "intensity" need not be correct) and
> that it has a center. The rest depends on the setup.
>
> Ciao,
> Johannes

[Guy Cox-2]

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To join, leave or search the confocal microscopy listserv, go to:
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Precisely.

                            Guy

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Mark Cannell
Sent: Sunday, 15 April 2012 9:17 PM
To: [hidden email]
Subject: Re: Nyquist and Image size

*****
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Hi Guy

Thanks a lot! You have got the wrong end of the stick. I am not talking about image reconstruction but displaying raw pixel data...

Cheers


On 15/04/2012, at 11:33 AM, Guy Cox wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> OK, I think I know Mark well enough that I can just say bollocks.
>
> Representing a sample as a square (ie presenting a sine wave as a square wave) is introducing a whole series of (every alternate) higher harmonics which contribute absolutely NOTHING to the image.   This is really fundamental to understanding digital imaging.
>
>                                                                              
> Guy
>
> -----Original Message-----
> From: Confocal Microscopy List
> [mailto:[hidden email]] On Behalf Of Mark Cannell
> Sent: Sunday, 15 April 2012 11:35 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
> *****
>
> Hi Johannes
>
> Sorry I disagree. You are recording an image. The point is that the pixels integrate over their entire face which is square so that this may be represented by square pixels perfectly faithfully. I have no idea what your analogy to the images of the sun through leaves has to do with this, the leavers are apertures.
>
> Cheers Mark
>
>
> On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:
>
>> Hi Mark,
>>
>> On Sat, 14 Apr 2012, Mark Cannell wrote:
>>
>>> That's a nice 'rant' but it does of course ignore the fact that many
>>> cameras have square pixels...
>>
>> But it is not the square detectors of the camera you are recording.
>> There is a whole optical path up until then.
>>
>> Pixels are not the physical dimension of the detector, they are an
>> abstract construct to describe what the number (or numbers) attached
>> to it
>> -- the pixel value -- actually mean.
>>
>> To say that pixels are square because the CCD is organized in a grid
>> is like saying that the spots the sun is leaving in a forest of trees
>> are as oddly shaped as the holes made by leaves through which the
>> sun's rays reach the soil.
>>
>> Ciao,
>> Johannes

[Mark Cannell]

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Precisely? What do you mean? Lets say you have a nine pixel camera. How would you recommend displaying the raw data reported by the camera in terms of x-y position and intensity?

Cheers Mark


On 15/04/2012, at 1:26 PM, Guy Cox wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Precisely.
>
>                            Guy
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Mark Cannell
> Sent: Sunday, 15 April 2012 9:17 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
> *****
>
> Hi Guy
>
> Thanks a lot! You have got the wrong end of the stick. I am not talking about image reconstruction but displaying raw pixel data...
>
> Cheers
>
>
> On 15/04/2012, at 11:33 AM, Guy Cox wrote:
>
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> OK, I think I know Mark well enough that I can just say bollocks.
>>
>> Representing a sample as a square (ie presenting a sine wave as a square wave) is introducing a whole series of (every alternate) higher harmonics which contribute absolutely NOTHING to the image.   This is really fundamental to understanding digital imaging.
>>
>>
>> Guy
>>
>> -----Original Message-----
>> From: Confocal Microscopy List
>> [mailto:[hidden email]] On Behalf Of Mark Cannell
>> Sent: Sunday, 15 April 2012 11:35 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
>> *****
>>
>> Hi Johannes
>>
>> Sorry I disagree. You are recording an image. The point is that the pixels integrate over their entire face which is square so that this may be represented by square pixels perfectly faithfully. I have no idea what your analogy to the images of the sun through leaves has to do with this, the leavers are apertures.
>>
>> Cheers Mark
>>
>>
>> On 14/04/2012, at 6:43 PM, Johannes Schindelin wrote:
>>
>>> Hi Mark,
>>>
>>> On Sat, 14 Apr 2012, Mark Cannell wrote:
>>>
>>>> That's a nice 'rant' but it does of course ignore the fact that many
>>>> cameras have square pixels...
>>>
>>> But it is not the square detectors of the camera you are recording.
>>> There is a whole optical path up until then.
>>>
>>> Pixels are not the physical dimension of the detector, they are an
>>> abstract construct to describe what the number (or numbers) attached
>>> to it
>>> -- the pixel value -- actually mean.
>>>
>>> To say that pixels are square because the CCD is organized in a grid
>>> is like saying that the spots the sun is leaving in a forest of trees
>>> are as oddly shaped as the holes made by leaves through which the
>>> sun's rays reach the soil.
>>>
>>> Ciao,
>>> Johannes