question in the reverse direction of Nyquist sampling

[Zhengmei Mao]

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Dear list,

I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to
image fluorescent oil droplets in water. The droplets can be as large as
several micrometers, but on the small end there is no way to know what's the
smallest they can be. After deconvolution, the individual objects I detect
range in voxel counts from 1 all the way up. My question is: given a certain
voxel size, what is the minimal voxel count that a detected object must have
for me to be able to legitimately identify it an object?

For example, does it need to be 4 pixels across in diameter in x and y? And
what about z?

Your help is greatly appreciated.

Best regards,

Mei

[Chris Tully-2]

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Mei,

I have always told my customers that based on the Nyquist law that the
smallest object that you can reasonably detect with confidence is 2-3
pixels across and seperated from neighboring objects by 2-3 pixels.  
That should hold for X & Y but keep in mind that in most optical systems
the Z axis has a lower resolution (which you have shown based on the
voxel size you are using).

Chris

On 9/16/2013 6:37 PM, Zhengmei Mao wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Dear list,
>
> I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to
> image fluorescent oil droplets in water. The droplets can be as large as
> several micrometers, but on the small end there is no way to know what's the
> smallest they can be. After deconvolution, the individual objects I detect
> range in voxel counts from 1 all the way up. My question is: given a certain
> voxel size, what is the minimal voxel count that a detected object must have
> for me to be able to legitimately identify it an object?
>
> For example, does it need to be 4 pixels across in diameter in x and y? And
> what about z?
>
> Your help is greatly appreciated.
>
> Best regards,
>
> Mei

--
*Chris Tully*
Principal Consultant
240-475-9753


      Image Incyte, LLC

<http:%5C%5Cwww.ImageIncyte.com> [hidden email]
<mailto:[hidden email]>

[Remko Dijkstra]

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**Vendor reply**

Dear Mei,

The previous reply already mentioned that the Nyquist theorem provides a
guideline with which you can determine the optimal sampling for your
microscope system, and hence the smallest objects that you are able to
distinguish.
Defining the ideal sampling in terms of spatial resolution is frequently
done as a rule of thumb ("sample with half the Rayleigh Criterion") but
this is an ambiguous definition (there are many possible criteria for
spatial resolution) and in some cases will lead to undersampling.

In terms of signal analysis the ideal sampling rate is indeed better
defined in terms of the system bandwidth, which is determined by the
Point Spread Function.
This is more precise because it considers the maximum spatial frequency
that the optical system can register, and it guarantees that all
information is properly acquired. This ideal sampling is indeed defined
as the Nyquist rate: http://www.svi.nl/IdealSampling

The online Huygens Nyquist calculator allows you to quickly determine
what would be the optimal sampling rate for your system:
http://www.svi.nl/NyquistCalculator

With ideal sampling and deconvolution, the resolution in your image can
even be increased more than 2 times in x,y and z direction, especially
with a measured PSF. For confocal imaging, deconvolution can increase
the resolution such that objects below 100nm are easily distinguishable
from any remaining noise. Also see:
- Schrader, M., S. W. Hell and H.T.M. van der Voort. (1996) Potential of
confocal microscopes to resolve in the 50-100 nm range. Appl. Phys.
Lett. 69 (24), pp. 3644-3646.

The deconvolution result can be used for object segmentation (for
example based on an intensity threshold). With this segmentation should
be able to efficiently identify the individual objects in your image
since their intensity is much higher than any remaining noise: Huygens
deconvolution typically results in a contrast increase of 10 times for
confocal images. Objects that are close together can be further
distinguished for example with watershed segmentation.

The image of a diffraction limited object will never be smaller than the
point spread function of your imaging system. If the object is
physically small enough, deconvolution can in principle reduce it to
close to a single voxel. Note that this 'size' in voxels does not say
anything about the true physical size of these small objects, as they
are diffraction limited: i.e. they could be as small as 10 nm or as
large as 150 nm, these will all result in a diffraction limited spot in
your image with a typical confocal system. If two small objects are very
closely spaced (within the diffraction limit), you cannot distinguish
these objects in your image.

Best regards,

Remko

--
***********************************************************
Remko Dijkstra, MSc
Imaging Specialist/Account Manager
Scientific Volume Imaging bv
Tel: + 31 35 642 1626
www.svi.nl
***********************************************************
For support matters contact: [hidden email]




On 09/17/2013 02:30 AM, Chris Tully wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Mei,
>
> I have always told my customers that based on the Nyquist law that the
> smallest object that you can reasonably detect with confidence is 2-3
> pixels across and seperated from neighboring objects by 2-3 pixels.  
> That should hold for X & Y but keep in mind that in most optical
> systems the Z axis has a lower resolution (which you have shown based
> on the voxel size you are using).
>
> Chris
>
> On 9/16/2013 6:37 PM, Zhengmei Mao wrote:
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> Dear list,
>>
>> I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to
>> image fluorescent oil droplets in water. The droplets can be as large as
>> several micrometers, but on the small end there is no way to know
>> what's the
>> smallest they can be. After deconvolution, the individual objects I
>> detect
>> range in voxel counts from 1 all the way up. My question is: given a
>> certain
>> voxel size, what is the minimal voxel count that a detected object
>> must have
>> for me to be able to legitimately identify it an object?
>>
>> For example, does it need to be 4 pixels across in diameter in x and
>> y? And
>> what about z?
>>
>> Your help is greatly appreciated.
>>
>> Best regards,
>>
>> Mei
>
>

[Kevin Ryan]

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http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
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Keep in mind the difference between _detection_ and _resolution_. It's quite possible to detect a sub-resolution object without being able to separate two objects that are closer together than the system resolution. If your droplets are dispersed you will be able to detect very small dots. [This is the basis of localization microscopy, PAML/STORM etc., locating a single fluorescent molecule.]

This is one of the resolution tests I have on occasion used - observing crossing fluorescently labeled microtubules (25nm in width, below normal optical resolution but quite detectable), using their extended shape to estimate the angle of convergence, and looking at the inter-tubule distance where they become indistinguishable.


Kevin Ryan
Media Cybernetics, Inc.


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Zhengmei Mao
Sent: Monday, September 16, 2013 6:37 PM
To: [hidden email]
Subject: question in the reverse direction of Nyquist sampling

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Dear list,

I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to image fluorescent oil droplets in water. The droplets can be as large as several micrometers, but on the small end there is no way to know what's the smallest they can be. After deconvolution, the individual objects I detect range in voxel counts from 1 all the way up. My question is: given a certain voxel size, what is the minimal voxel count that a detected object must have for me to be able to legitimately identify it an object?

For example, does it need to be 4 pixels across in diameter in x and y? And what about z?

Your help is greatly appreciated.

Best regards,

Mei    

[Paul Herzmark]

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Mei,

The way you phrase your question it is hard to tell if the problem is 1)
detection of a tiny oil drop, 2) separation (resolution) of multiple oil
drops, 3) detection (counting) of multiple, overlapping oil drops, or 4)
measurement of the size of tiny oil drops. Each of those questions have
different answers. Kevin Ryan mentioned several of those.

I'll comment on number 4.

In most discussions of resolution we talk about separating two small
objects. The Nyquist sampling theorem is easy to apply to that situation
because there is nothing in between. Just look for a dip in the signal.
However, to measure the diameter of an object you need to resolve both
edges separately and what is in between looks exactly like the edges. There
is no dip in the signal to tell you if the edges are resolved.

Theoretically you could find the diameter limit of detection in a sample
with objects both larger and smaller than the limit. In such a sample
objects smaller than the limit would have the same size image (the size of
the PSF). Images at that small limit can represent objects of any size
equal to or smaller than the limit. The images of bigger things would
increase in size as the objects got bigger.

In practice I'll bet it is hard to distinguish differences in diameter of
the objects from differences in brightness of the objects. Dimmer things
will probably have smaller images.

Paul Herzmark
Specialist
[hidden email]

Department of Molecular and Cell Biology
479 Life Science Addition
University of California, Berkeley
Berkeley, CA  94720-3200
[phone]
[phone] fax




On Tue, Sep 17, 2013 at 6:39 AM, Kevin Ryan <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Keep in mind the difference between _detection_ and _resolution_. It's
> quite possible to detect a sub-resolution object without being able to
> separate two objects that are closer together than the system resolution.
> If your droplets are dispersed you will be able to detect very small dots.
> [This is the basis of localization microscopy, PAML/STORM etc., locating a
> single fluorescent molecule.]
>
> This is one of the resolution tests I have on occasion used - observing
> crossing fluorescently labeled microtubules (25nm in width, below normal
> optical resolution but quite detectable), using their extended shape to
> estimate the angle of convergence, and looking at the inter-tubule distance
> where they become indistinguishable.
>
>
> Kevin Ryan
> Media Cybernetics, Inc.
>
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]]
> On Behalf Of Zhengmei Mao
> Sent: Monday, September 16, 2013 6:37 PM
> To: [hidden email]
> Subject: question in the reverse direction of Nyquist sampling
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Dear list,
>
> I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to
> image fluorescent oil droplets in water. The droplets can be as large as
> several micrometers, but on the small end there is no way to know what's
> the smallest they can be. After deconvolution, the individual objects I
> detect range in voxel counts from 1 all the way up. My question is: given a
> certain voxel size, what is the minimal voxel count that a detected object
> must have for me to be able to legitimately identify it an object?
>
> For example, does it need to be 4 pixels across in diameter in x and y?
> And what about z?
>
> Your help is greatly appreciated.
>
> Best regards,
>
> Mei
>

[George McNamara]

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Hi Mei,

if your fluorescence labeling is consistent for all droplets, you should
be able to use integrated intensity, regardless of spatial resolution.

I can think of a lot of reasons why this "fluorescence proportionality"
could fail, including:
* O2 quenching of molecules near the surface (smaller droplets having
higher proportion of surface area to volume)
* photobleaching
* non-quantitative acquisition: saturated pixels -- most likely of big
droplets; insensitivity to fluorescence in the smallest droplets.
* non-quantitative deconvolution -- an undergraduate I worked with this
summer evaluated many ImageJ deconvolution routines, to make a long
story short, they ranged from "too good to be true" compared to confocal
or widefield (which is actually the goal), good, bad and ugly. Bruce and
Butte's CUDA deconvolution was pretty good, with the virtue of being
fast (on an NVidia GPU card - the point of the algorithm), but I more
recently found that increasing the number of iterations (3x or 10x of
their default) produced nicer results, and increasing even further (1000
iterations) produced awful results.

In the flow cytometry world, there are fluorescent bead sets of
different intensities that good flow cores and labs use routinely. You
could use those (if only available in "cell size". could emulate by
using a low mag lens on your microscope). You could also do the
experiment on an EMD Millipore AMNIS ImageStream or FlowSight (has a big
advantage over flow in being continuous flow stream, not droplets ... if
you have good rapport with a local rep, they might be able to arrange
samples to be run at AMNIS HQ if you do not have an instrument at your
place or locally), or on a flow cytometer (there are a lot more flow
cytometers than ImageStreamX's).

***

Plan D (for diffusion): big droplets diffuse slower than smaller
droplets. This is quantitative (assuming you do not have bulb flow or
edge effects of imaging right at the coverglass or some other surface).
The smallest droplets may diffuse too fast for your hardware (if you do
not have a resonant scanner ... maybe even if ou do). You could go to
line scan mode, though may be hard to interpret the data. this can all
be tested by comparing different fluorescent bead sizes (ex. 40 nm vs
100 nm vs 400 nm).

Look up single particle tracking (SPT) papers by: K. Braeckmans, in
particular:

    K. Braeckmans (*), H. Deschout, J. Demeester, and S.C. De Smedt
    Laboratory of General Biochemistry and Physical Pharmacy, Ghent
    University, Harelbekestraat 72, 9000 Ghent, Belgium
    e-mail: [hidden email]
    A. Diaspro (ed.), Optical Fluorescence Microscopy,
    DOI 10.1007/978-3-642-15175-0_9, # Springer-Verlag Berlin Heidelberg
    2011

            K. Braeckmans et al 2011 Fluorescence single particle
tracking for sizing of nanoparticles in undiluted biological fluids.
Proc. of SPIE Vol. 7908, 79080B


Another option: The Vutara SR-200 has a single (molecule) particle
tracking option (it is usually bought for 3D single molecule
localization. You could use that, or work with your sales rep to have
demo samples sent to that company. Two more items for the listserv:
* Vutara just announced SR-350 ... looks like will be sCMOS based and
since Joerg Bewersdorf is a cofounder, may have the full sCMOS
calibration published earlier this year in Nature Methods (Huang et al
2013).
* I was told that Abberior.com's FLIP 565 works well in PBS for single
molecule(s) localization on the Vutara SR-200. That is, could be used
for live cell surface antibody labeling.

George


On 9/17/2013 5:07 PM, Paul Herzmark wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Mei,
>
> The way you phrase your question it is hard to tell if the problem is 1)
> detection of a tiny oil drop, 2) separation (resolution) of multiple oil
> drops, 3) detection (counting) of multiple, overlapping oil drops, or 4)
> measurement of the size of tiny oil drops. Each of those questions have
> different answers. Kevin Ryan mentioned several of those.
>
> I'll comment on number 4.
>
> In most discussions of resolution we talk about separating two small
> objects. The Nyquist sampling theorem is easy to apply to that situation
> because there is nothing in between. Just look for a dip in the signal.
> However, to measure the diameter of an object you need to resolve both
> edges separately and what is in between looks exactly like the edges. There
> is no dip in the signal to tell you if the edges are resolved.
>
> Theoretically you could find the diameter limit of detection in a sample
> with objects both larger and smaller than the limit. In such a sample
> objects smaller than the limit would have the same size image (the size of
> the PSF). Images at that small limit can represent objects of any size
> equal to or smaller than the limit. The images of bigger things would
> increase in size as the objects got bigger.
>
> In practice I'll bet it is hard to distinguish differences in diameter of
> the objects from differences in brightness of the objects. Dimmer things
> will probably have smaller images.
>
> Paul Herzmark
> Specialist
> [hidden email]
>
> Department of Molecular and Cell Biology
> 479 Life Science Addition
> University of California, Berkeley
> Berkeley, CA  94720-3200
> [phone]
> [phone] fax
>
>
>
>
> On Tue, Sep 17, 2013 at 6:39 AM, Kevin Ryan<[hidden email]>  wrote:
>
>    
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> Keep in mind the difference between _detection_ and _resolution_. It's
>> quite possible to detect a sub-resolution object without being able to
>> separate two objects that are closer together than the system resolution.
>> If your droplets are dispersed you will be able to detect very small dots.
>> [This is the basis of localization microscopy, PAML/STORM etc., locating a
>> single fluorescent molecule.]
>>
>> This is one of the resolution tests I have on occasion used - observing
>> crossing fluorescently labeled microtubules (25nm in width, below normal
>> optical resolution but quite detectable), using their extended shape to
>> estimate the angle of convergence, and looking at the inter-tubule distance
>> where they become indistinguishable.
>>
>>
>> Kevin Ryan
>> Media Cybernetics, Inc.
>>
>>
>> -----Original Message-----
>> From: Confocal Microscopy List [mailto:[hidden email]]
>> On Behalf Of Zhengmei Mao
>> Sent: Monday, September 16, 2013 6:37 PM
>> To: [hidden email]
>> Subject: question in the reverse direction of Nyquist sampling
>>
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> Dear list,
>>
>> I am using 100nm x 100nm x 200nm voxel size of a confocal microscope to
>> image fluorescent oil droplets in water. The droplets can be as large as
>> several micrometers, but on the small end there is no way to know what's
>> the smallest they can be. After deconvolution, the individual objects I
>> detect range in voxel counts from 1 all the way up. My question is: given a
>> certain voxel size, what is the minimal voxel count that a detected object
>> must have for me to be able to legitimately identify it an object?
>>
>> For example, does it need to be 4 pixels across in diameter in x and y?
>> And what about z?
>>
>> Your help is greatly appreciated.
>>
>> Best regards,
>>
>> Mei
>>
>>      
>    

--



George McNamara, Ph.D.
Single Cells Analyst
L.J.N. Cooper Lab
University of Texas M.D. Anderson Cancer Center
Houston, TX 77054
http://works.bepress.com/gmcnamara/26/

[Zhengmei Mao]

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http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Thank you all very much for your helpful comments!

Best regards,

Mei