In search of old article / lens frequency band limit doesnt really exist.

[Daniel White-2]

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Hi Sergey,

I've been thinking about this lots recently,
while trying to describe what happens in contrast restoration (by
deconvolution) microscope, and in 3D SIM - because that's what I do

You can see an imageJ/Fiji javascript linked below, that shows a noise free
image blurred by a perfectly known point spread function can be deconvolved
and recover features much smaller than Abbes limit of wavelength / 2NA.
This is because the system is linear and determined and can be simply
inverted. 2+3=5, and 5-3=2.

The OTF doesnt have a sharp edge where it goes to zero.... its just gets
really small after 2NA.

https://raw.githubusercontent.com/chalkie666/imagejMacros/master/DeconvolutionDemos/Convolution_Deconvolution_Demo.js

However, the real resolution limit is the noise and other errors in any
measurement of any real image, and in a real measured point spread function
(OTF, contrast transfer function, modulation transfer function, whatever
you want to call it)
Why?:

When the noise or other error is larger than the OTF at a certain spatial
frequency, that is the effective resolution limit. Cookie cutter, sharp
band limit is a first approximation only.

This is what Abbe effectively observed, and modeled as ray optics (which is
wrong in the same way that Newtonian mechanics is wrong - quantum mechanics
is right). The contrast transfer function (OTF) is so small after about
2NA, that you cant see any finer features with your eyes, or with a camera,
because contrast is too low or lost in noise.

If we could do something about photon shot noise at high signals maybe we
could see more resolution from a given lens. Structured illumination
microscopy and STED work around this limit - 3D SIM turns Abbe's equation
into
d = lambda / 4NA
by frequency mixing modulation. Abbe could not have guessed this is the
real, and easy to access resolution limit, by using only ray optics, but
any signal processing engineer knows this is true.

If an image is really noisy, then the effective resolution is less than
Abbe's limit, because the noise is larger then the contrast transfer
function (OTF) already at lower spatial frequencies than 2NA.

In short -
No Contrast = No Resolution
Noise and other errors kill contrast.
Noise magnitude vs the OTF magnitude is the real resolution limit, and NA
is a part of that, but not the only part.

We should be slightly less obsessed with theoretical band limits (cookie
cutters have sharp edges - OTFs dont - they just get really small), and
worry more about noise, and the fact that the OTF kills contrast of medium
and small features very strongly, and we need to fix that systematic error,
restore that contrast, by a method such as iterative constrained
convolution that can handle the noise. Also true for confocal.

cheers

Dan



Date:    Wed, 3 Aug 2016 09:35:17 +0100
From:    Mark Cannell <[hidden email]>
Subject: Re: In search of old article

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Abbe ?

Cheers
On 2/08/2016, at 10:03 pm, Sergey Tauger <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Thank you, Marco
>
> It seems that is not the article.
> Could you please tell me, who was the first who proved that objective

frequency response is bandlimited to a know frequency? I browsed through
articles cited by Hopkins in 50s and Sheppard in 60s, but I still cannot
get who was the first.
>
> Best,
> Sergey

Mark  B. Cannell Ph.D. FRSNZ FISHR
Professor of Cardiac Cell Biology
School of Physiology &  Pharmacology
Faculty of Biomedical Sciences
University of Bristol
Bristol
BS8 1TD UK

[hidden email]
**********************************************************************

[0000001ed7f52e4a-dmarc-request]

*****
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Interesting discussion, some remarks:

>However, the real resolution limit is the noise
Eric Betzig (and probably many others) illustrates this point quite well in his talks when he draws a wiggly noise line in the OTF graph and shows the limits of the perfect OTF.

>This is what Abbe effectively observed, and modeled as ray optics
As Abbe's theorie of image formation involves the different diffraction orders of an object, I would think it is it is not just ray optics, more fourier optics?

>the same way that Newtonian mechanics is wrong - quantum mechanics is right
Newtonian mechanics is not wrong, it is  good approximation for large quantum numbers (correspondence principle), it gets wrong when you go to high speeds and need to use relativity. Interestingly even locating a single fluorophore with high precision seems to be a problem with higher quantum numbers (the surrounding molecules), otherwise the uncertaincy principle would cause the molecule to be kicked to a different position by its momentum.


 >If we could do something about photon shot noise at high signals
Well there is not much you can do about shot noise, light comes in photons, at least when you detect it, but you could limit detctor noise by detecting individual photons (like in Chao et al. Nature Methods, 2013, but this is a localisation based  super-resolution paper)

best wishes

Andreas


 

 

-----Original Message-----
From: Daniel White <[hidden email]>
To: CONFOCALMICROSCOPY <[hidden email]>
Sent: Fri, 5 Aug 2016 9:16
Subject: In search of old article / lens frequency band limit doesnt really exist.

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To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
Post images on http://www.imgur.com and include the link in your posting.
*****

Hi Sergey,

I've been thinking about this lots recently,
while trying to describe what happens in contrast restoration (by
deconvolution) microscope, and in 3D SIM - because that's what I do

You can see an imageJ/Fiji javascript linked below, that shows a noise free
image blurred by a perfectly known point spread function can be deconvolved
and recover features much smaller than Abbes limit of wavelength / 2NA.
This is because the system is linear and determined and can be simply
inverted. 2+3=5, and 5-3=2.

The OTF doesnt have a sharp edge where it goes to zero.... its just gets
really small after 2NA.

https://raw.githubusercontent.com/chalkie666/imagejMacros/master/DeconvolutionDemos/Convolution_Deconvolution_Demo.js

However, the real resolution limit is the noise and other errors in any
measurement of any real image, and in a real measured point spread function
(OTF, contrast transfer function, modulation transfer function, whatever
you want to call it)
Why?:

When the noise or other error is larger than the OTF at a certain spatial
frequency, that is the effective resolution limit. Cookie cutter, sharp
band limit is a first approximation only.

This is what Abbe effectively observed, and modeled as ray optics (which is
wrong in the same way that Newtonian mechanics is wrong - quantum mechanics
is right). The contrast transfer function (OTF) is so small after about
2NA, that you cant see any finer features with your eyes, or with a camera,
because contrast is too low or lost in noise.

If we could do something about photon shot noise at high signals maybe we
could see more resolution from a given lens. Structured illumination
microscopy and STED work around this limit - 3D SIM turns Abbe's equation
into
d = lambda / 4NA
by frequency mixing modulation. Abbe could not have guessed this is the
real, and easy to access resolution limit, by using only ray optics, but
any signal processing engineer knows this is true.

If an image is really noisy, then the effective resolution is less than
Abbe's limit, because the noise is larger then the contrast transfer
function (OTF) already at lower spatial frequencies than 2NA.

In short -
No Contrast = No Resolution
Noise and other errors kill contrast.
Noise magnitude vs the OTF magnitude is the real resolution limit, and NA
is a part of that, but not the only part.

We should be slightly less obsessed with theoretical band limits (cookie
cutters have sharp edges - OTFs dont - they just get really small), and
worry more about noise, and the fact that the OTF kills contrast of medium
and small features very strongly, and we need to fix that systematic error,
restore that contrast, by a method such as iterative constrained
convolution that can handle the noise. Also true for confocal.

cheers

Dan



Date:    Wed, 3 Aug 2016 09:35:17 +0100
From: Mark Cannell <[hidden email]>
Subject: Re: In search of old article

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
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*****

Abbe ?

Cheers
On 2/08/2016, at 10:03 pm, Sergey Tauger <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Thank you, Marco
>
> It seems that is not the article.
> Could you please tell me, who was the first who proved that objective

frequency response is bandlimited to a know frequency? I browsed through
articles cited by Hopkins in 50s and Sheppard in 60s, but I still cannot
get who was the first.
>
> Best,
> Sergey

Mark  B. Cannell Ph.D. FRSNZ FISHR
Professor of Cardiac Cell Biology
School of Physiology &  Pharmacology
Faculty of Biomedical Sciences
University of Bristol
Bristol
BS8 1TD UK

[hidden email]
**********************************************************************

[Zdenek Svindrych-2]

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*****

Hi Daniel,
I hope I'm not alone when I say that Abbe was right and that the resolution
limit in widefield fluorescence microscopy is lambda/2NA (the 'lambda' means
you cannot reach this conclusion using ray optics!).

The reason you can access details up to lambda/4NA in confocal microscopy is
because confocal microscopy IS superresolution technique, at least in your
model case of zero pinhole size (and equal excitation and emission
wavelenghs). With 1 Airy Unit pinhole the information beyond Abbe limit is
truly negligible, and lost in the shot noise long before you even reach that
limit.

You may think of confocal microscopy as an extreme (but definitely not
optimal) case of structured illumination microscopy. Image Scanning
Microscopy (Muller and Enderlein, Phys. Rev. Lett. 104 (2010) 198101) that
materialized as Zeiss AiryScan (among others) is building on that.

To conclude, there IS a well defined and sharp band limit in microscopy
(lambda/2NA for homogeneous illumination and lambda/4NA for structured
illumination through the same lens) that you can overcome only with
nonlinear techniques (meaning emission intensity is not proportional to
illumination intensity) - STED, STORM / PALM, SOFI, etc, etc. 

Best, zdenek



---------- Původní zpráva ----------
Od: Daniel White <[hidden email]>
Komu: [hidden email]
Datum: 5. 8. 2016 4:16:46
Předmět: In search of old article / lens frequency band limit doesnt really
exist.

"*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
Post images on http://www.imgur.com and include the link in your posting.
*****

Hi Sergey,

I've been thinking about this lots recently,
while trying to describe what happens in contrast restoration (by
deconvolution) microscope, and in 3D SIM - because that's what I do

You can see an imageJ/Fiji javascript linked below, that shows a noise free
image blurred by a perfectly known point spread function can be deconvolved
and recover features much smaller than Abbes limit of wavelength / 2NA.
This is because the system is linear and determined and can be simply
inverted. 2+3=5, and 5-3=2.

The OTF doesnt have a sharp edge where it goes to zero.... its just gets
really small after 2NA.

https://raw.githubusercontent.com/chalkie666/imagejMacros/master/
DeconvolutionDemos/Convolution_Deconvolution_Demo.js

However, the real resolution limit is the noise and other errors in any
measurement of any real image, and in a real measured point spread function
(OTF, contrast transfer function, modulation transfer function, whatever
you want to call it)
Why?:

When the noise or other error is larger than the OTF at a certain spatial
frequency, that is the effective resolution limit. Cookie cutter, sharp
band limit is a first approximation only.

This is what Abbe effectively observed, and modeled as ray optics (which is
wrong in the same way that Newtonian mechanics is wrong - quantum mechanics
is right). The contrast transfer function (OTF) is so small after about
2NA, that you cant see any finer features with your eyes, or with a camera,
because contrast is too low or lost in noise.

If we could do something about photon shot noise at high signals maybe we
could see more resolution from a given lens. Structured illumination
microscopy and STED work around this limit - 3D SIM turns Abbe's equation
into
d = lambda / 4NA
by frequency mixing modulation. Abbe could not have guessed this is the
real, and easy to access resolution limit, by using only ray optics, but
any signal processing engineer knows this is true.

If an image is really noisy, then the effective resolution is less than
Abbe's limit, because the noise is larger then the contrast transfer
function (OTF) already at lower spatial frequencies than 2NA.

In short -
No Contrast = No Resolution
Noise and other errors kill contrast.
Noise magnitude vs the OTF magnitude is the real resolution limit, and NA
is a part of that, but not the only part.

We should be slightly less obsessed with theoretical band limits (cookie
cutters have sharp edges - OTFs dont - they just get really small), and
worry more about noise, and the fact that the OTF kills contrast of medium
and small features very strongly, and we need to fix that systematic error,
restore that contrast, by a method such as iterative constrained
convolution that can handle the noise. Also true for confocal.

cheers

Dan



Date: Wed, 3 Aug 2016 09:35:17 +0100
From: Mark Cannell <[hidden email]>
Subject: Re: In search of old article

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
Post images on http://www.imgur.com and include the link in your posting.
*****

Abbe ?

Cheers
On 2/08/2016, at 10:03 pm, Sergey Tauger <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Thank you, Marco
>
> It seems that is not the article.
> Could you please tell me, who was the first who proved that objective

frequency response is bandlimited to a know frequency? I browsed through
articles cited by Hopkins in 50s and Sheppard in 60s, but I still cannot
get who was the first.
>
> Best,
> Sergey

Mark B. Cannell Ph.D. FRSNZ FISHR
Professor of Cardiac Cell Biology
School of Physiology & Pharmacology
Faculty of Biomedical Sciences
University of Bristol
Bristol
BS8 1TD UK

[hidden email]
**********************************************************************"