Update to "Resolution" App

[Andrew Barlow]

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Dear Confocal list,


I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.


The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:


Res = 1.22 lambda / 2NA


I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:


Res = 1.22 lambda / NA (obj) + NA (condenser)


My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:


Res = 1.22 lambda / 2  NAmin


Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.


This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.


If you could share your thoughts on this I'd be very grateful.


If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.


Many thanks,


Andy Barlow

[Aryeh Weiss]

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I think 1.22 lambda /(NAobj + min(NAobj, NAcond)) is what you need.

The way you wrote it, a coherently illuminated object with NAcond close
to zero would have no resolution, whereas in fact I think what you lose
is the factor of two.

--aryeh

On 02/02/2017 23:53, Andrew Barlow 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.
> *****
>
> Dear Confocal list,
>
>
> I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.
>
>
> The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:
>
>
> Res = 1.22 lambda / 2NA
>
>
> I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:
>
>
> Res = 1.22 lambda / NA (obj) + NA (condenser)
>
>
> My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:
>
>
> Res = 1.22 lambda / 2  NAmin
>
>
> Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.
>
>
> This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.
>
>
> If you could share your thoughts on this I'd be very grateful.
>
>
> If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.
>
>
> Many thanks,
>
>
> Andy Barlow
>

--
Aryeh Weiss
Faculty of Engineering
Bar Ilan University
Ramat Gan 52900 Israel

Ph:  972-3-5317638
FAX: [phone]

[Steffen Dietzel]

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Andrew,

the Res = 1.22 lambda / 2NA is based on the Rayleigh criterion and that
makes sense for self-luminous objects, so it is good for fluorescence
and dark field microscopy. Or for observing stars, which I believe was
what it was originally described for: How far have to points to be away
from each other... The 0.61 is the radius of the first ring minimum of
the diffraction pattern, 1.22 the diameter. In any case, the condenser
has no influence on this.

Now, if you use a condenser, then you are obviously up to transmission
microscopy. In this case, my understanding is that the Abbe equation is
more appropriate, which assumes a line pattern: How far do the lines in
a grid have to be apart from each other, such that you can resolve them
(i.e. catch the first ring maximum of the diffracted light). Abbe is
usually cited as d=lambda/2 NA. However, more precisely is the following:

d = lambda /(NAobj + NA condenser), where NA condenser must not equal or
smaller than NA objective. So, if NA condenser is bigger than NA
objective, then the formula falls back to d=lambda/2 NAobjective.

While Rayleigh is sort of a convention (why not use Sparrow?) the Abbe
limit is absolute. One condition seems to be that the light is coherent,
which is apparently fulfilled since the light comes from (only) one source.

In summary, I don't think Res = 1.22 lambda / NA (obj) + NA (condenser)
or a derivative form make sense, since it mixes Rayleigh and Abbe. But I
have seen this formula before and I definitely could be wrong, and I am
sure other listers have figured it out :-)


Steffen


Am 02.02.2017 um 22:53 schrieb Andrew Barlow:

> *****
> 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.
> *****
>
> Dear Confocal list,
>
>
> I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.
>
>
> The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:
>
>
> Res = 1.22 lambda / 2NA
>
>
> I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:
>
>
> Res = 1.22 lambda / NA (obj) + NA (condenser)
>
>
> My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:
>
>
> Res = 1.22 lambda / 2  NAmin
>
>
> Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.
>
>
> This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.
>
>
> If you could share your thoughts on this I'd be very grateful.
>
>
> If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.
>
>
> Many thanks,
>
>
> Andy Barlow
>

--
------------------------------------------------------------
Steffen Dietzel, PD Dr. rer. nat
Ludwig-Maximilians-Universität München
Biomedical Center (BMC)
Head of the Core Facility Bioimaging

Großhaderner Straße 9
D-82152 Planegg-Martinsried
Germany

http://www.bioimaging.bmc.med.uni-muenchen.de

[Johannes Helm]

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Dear all,

thank you, Steffen, for your important hint concerning the "microscope
telescope relation". In the classroom and the lab, I use to bring this  
(even) to the (life science) students' attention. What you did not
mention and what I think is important and might be worth mentioning even
in this list:

In (wide field) microscopy, we talk about "resolution" and in general
then refer to what strictly speaking is "lateral resolution", at which
the semantics of this resolution is "minimum resolvable lateral distance
in the object space". (Axial resolution is not so straight forward, to
place it mildly, in wide field microscopy.)

When talking about the telescope, resolution is angular resolution. "By
construction", the latter is not dependent of the "NUMERICAL aperture"
of the objective but by its "aperture". The larger the aperture ("the
opening") of the mirror or lens, the better the angular resolution.
That's why the astronomers like to have large mirrors like the units in
La Silla on the ESO or the large mirror on the Palomar. The resolutions
of these giants are much better than what the aberrations induced by
atmospheric fluctuations allow, and that's why AO is critical for these
telescopes (other than for space based units, e.g.the Hubble). Angular
resolution is also what we think of when talking about the resolution of
the human eye, which then even has legal implications (there are rules
stating what you "must be able to see" and this "minimum mandatory
resolution" is also a criterion for the determination of the size of
traffic signs, advertisements, a. s. o., just as an example).

Best wishes and have a nice weekend,

Johannes



On 2017-02-03 03:31, Steffen Dietzel 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.
> *****
>
> Andrew,
>
> the Res = 1.22 lambda / 2NA is based on the Rayleigh criterion and
> that makes sense for self-luminous objects, so it is good for
> fluorescence and dark field microscopy. Or for observing stars, which
> I believe was what it was originally described for: How far have to
> points to be away from each other... The 0.61 is the radius of the
> first ring minimum of the diffraction pattern, 1.22 the diameter. In
> any case, the condenser has no influence on this.
>
> Now, if you use a condenser, then you are obviously up to transmission
> microscopy. In this case, my understanding is that the Abbe equation
> is more appropriate, which assumes a line pattern: How far do the
> lines in a grid have to be apart from each other, such that you can
> resolve them (i.e. catch the first ring maximum of the diffracted
> light). Abbe is usually cited as d=lambda/2 NA. However, more
> precisely is the following:
>
> d = lambda /(NAobj + NA condenser), where NA condenser must not equal
> or smaller than NA objective. So, if NA condenser is bigger than NA
> objective, then the formula falls back to d=lambda/2 NAobjective.
>
> While Rayleigh is sort of a convention (why not use Sparrow?) the Abbe
> limit is absolute. One condition seems to be that the light is
> coherent, which is apparently fulfilled since the light comes from
> (only) one source.
>
> In summary, I don't think Res = 1.22 lambda / NA (obj) + NA
> (condenser) or a derivative form make sense, since it mixes Rayleigh
> and Abbe. But I have seen this formula before and I definitely could
> be wrong, and I am sure other listers have figured it out :-)
>
>
> Steffen
>
>
> Am 02.02.2017 um 22:53 schrieb Andrew Barlow:
>> *****
>> 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.
>> *****
>>
>> Dear Confocal list,
>>
>>
>> I'm about to roll out an update for my Android app, "Resolution",
>> which some of you were kind enough to download when I published it
>> late last year.
>>
>>
>> The original version was really designed around fluorescence
>> microscopy, it only gave the user the option to enter a single NA, and
>> it calculates resolution using the following version of Abbe's
>> equation:
>>
>>
>> Res = 1.22 lambda / 2NA
>>
>>
>> I thought it would be helpful to add the ability to characterise a
>> transmitted light objective, with a distinct condenser NA and
>> objective NA, and to calculate resolution based on the following
>> version of the equation:
>>
>>
>> Res = 1.22 lambda / NA (obj) + NA (condenser)
>>
>>
>> My original thought was to just implement this version of the equation
>> exactly as it is, a let the user freely enter the two NAs, and do the
>> calculation.  However, my understanding is that this version of the
>> equation really only applies when the NA of the objective and the NA
>> of the condenser are equal.  Under circumstances in which they are
>> unequal, the true resolution would be:
>>
>>
>> Res = 1.22 lambda / 2  NAmin
>>
>>
>> Where NAmin = the smallest NA of the condenser and objective.  In such
>> cases resolution is constrained by the smaller of the two NAs.
>>
>>
>> This is pretty much what I've implemented, but I don't have the
>> confidence to release this without first checking with this list that
>> this is the right approach.
>>
>>
>> If you could share your thoughts on this I'd be very grateful.
>>
>>
>> If anyone would be interested in taking a look at the beta of the next
>> version I'd be happy to share it with them.
>>
>>
>> Many thanks,
>>
>>
>> Andy Barlow
>>

--
P. Johannes Helm

Voice: ([phone] (office)
Fax: [phone] (office)

[Alex Asanov]

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Hello Andy,

Have you fixed the section for fluorescence brightness? Remember, you used
the equation ~(NA)^4 (X)^-2 for the brightness, which is applicable only for
through-objective epi-fluorescence and through-objective TIRF.

For other methods that employ the excitation lightpath independent from the
emission channel, including prism- and lightguide-based TIRF and other
fluorescence schemes, this equation does not work.  In the latter cases, the
amount of fluorescence quanta collected by an objective will be proportional
to ~(NA)^2 (X)^-1.

I suggest that you introduce an unambiguous definition of the term
"fluorescence brightness," clearly differentiating between through-objective
excitation and independent excitation lightpaths. Respectively, two
different equations should be used to estimate the amount of fluorescence
quanta hitting a CCD camera pixel.

Please send to me the beta of your next version.

Best regards,
Alexander Asanov, Ph.D.
President,  TIRF Labs
Cary, NC 27519
TIRF-Labs.com; TIRFmicroscopy.com
[hidden email]

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On
Behalf Of Andrew Barlow
Sent: Thursday, February 2, 2017 4:54 PM
To: [hidden email]
Subject: Update to "Resolution" App

*****
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*****

Dear Confocal list,


I'm about to roll out an update for my Android app, "Resolution", which some
of you were kind enough to download when I published it late last year.


The original version was really designed around fluorescence microscopy, it
only gave the user the option to enter a single NA, and it calculates
resolution using the following version of Abbe's equation:


Res = 1.22 lambda / 2NA


I thought it would be helpful to add the ability to characterise a
transmitted light objective, with a distinct condenser NA and objective NA,
and to calculate resolution based on the following version of the equation:


Res = 1.22 lambda / NA (obj) + NA (condenser)


My original thought was to just implement this version of the equation
exactly as it is, a let the user freely enter the two NAs, and do the
calculation.  However, my understanding is that this version of the equation
really only applies when the NA of the objective and the NA of the condenser
are equal.  Under circumstances in which they are unequal, the true
resolution would be:


Res = 1.22 lambda / 2  NAmin


Where NAmin = the smallest NA of the condenser and objective.  In such cases
resolution is constrained by the smaller of the two NAs.


This is pretty much what I've implemented, but I don't have the confidence
to release this without first checking with this list that this is the right
approach.


If you could share your thoughts on this I'd be very grateful.


If anyone would be interested in taking a look at the beta of the next
version I'd be happy to share it with them.


Many thanks,


Andy Barlow
***** To join, leave or search the confocal microscopy listserv, go to:
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Hi Alex,




Thanks for the message.




Yes, I used (NA)^4 (X)^-2 for brightness, this value is divided by the
brightness of a 10x 0.25 objective, which I'm using as "standard brightness"
to give the value scale.




Your suggestions for TIRF are really interesting, and I'd like to discuss
these in more detail "off list".




Thanks,

Andy














----------------------------------------------------------------------------
----

From: Confocal Microscopy List <[hidden email]> on behalf
of Alex Asanov <[hidden email]>
Sent: 12 December 2016 18:24
To: [hidden email]
Subject: Re: Android Tool for Microscopy
 
***** To join, leave or search the confocal microscopy listserv, go to:
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Hi Andy,
 
Your tool will be useful for many microscopists, including TIRF users. We
need it for iPhones too. Unfortunately, I do not have Android and was not
able to see which equation did you use for fluorescence brightness. How you
define the fluorescence brightness? Did you use for fluorescence brightness
~(NA)^4 (X)^-2? This equation is good for epi-fluorescence and
objective-TIRF, when both excitation and emission use the objective. In the
case of prism- and lightguide-TIRF, where the excitation lightpath is
independent from the emission channel, however, the amount of emitted
fluorescence collected  by an objective to a pixel of CCD camera is
proportional to the square of numerical aperture and reverse proportional to
magnification ~(NA)^2 (X)^-1. If you distinguish between these TIRF
geometries, you will benefit the entire microscopists community. Prism- and
lightguide-TIRF are becoming indispensable tools for super-resolution
microscopies and single molecule studies, becasue they provide "clean" TIRF
effect, unlike o-TIRF, which is contaminated with 15-20% of stray light.
It is important to distingushe between p-, lg-, and o-TIRF geometries.
Your app is very much needed tool! Thank you.
 

Best regards,

Alexander Asanov, Ph.D.
President,  TIRF Labs
Cary, NC 27519
Tel: [phone] TIRF-Labs.com; TIRFmicroscopy.com
Mobile:  [phone]  [hidden email]

 



----------------------------------------------------------------------------
----
From: Confocal Microscopy List [mailto:[hidden email]] On
Behalf Of Andrew Barlow
Sent: Monday, December 12, 2016 4:45 AM
To: [hidden email]
Subject: Re: Android Tool for Microscopy


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Thanks Sylvie!




That's much appreciated!  Please let me know if you have any suggestions for
improvement or new functionality.




Regards,

Andy











----------------------------------------------------------------------------
----

From: Confocal Microscopy List <[hidden email]> on behalf
of Sylvie Le Guyader <[hidden email]>
Sent: 12 December 2016 09:27
To: [hidden email]
Subject: Re: Android Tool for Microscopy
 
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Cool app! Thanks Andrew! :-)

Med vänlig hälsning / Best regards

Sylvie

@@@@@@@@@@@@@@@@@@@@@@@@
Sylvie Le Guyader, PhD
Live Cell Imaging Facility Manager
Karolinska Institutet- Bionut
Hälsovägen 7,
Novum, G lift, floor 6
14157 Huddinge
Sweden
mobile: [phone]
office: [phone]
LCI website

---- Andrew Barlow wrote ----


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Dear Confocal Microscopy List,

I'd like to draw your attention to a new tool for microscopists I've
developed for Android devices, "Resolution".

After entering magnification, immersion medium, lambda, and NA the App will
calculate resolution (actual and theoretical), axial resolution and
fluorescence brightness of your objective.

Each objective entered can be easily saved and restored.

You can select your camera, binning and additional magnification to
determine if you're sampling at Nyquist frequency.

All information generated get be easily shared via e-mail, MMS, LinkedIn or
even Facebook (it could with the share button.

The App is free to download and compatible with phones or tablets running
Android 4.0 or above.

I hope you find it useful!

Andrew L. Barlow



Please use the link below on your Android device to install:

https://play.google.com/store/apps/details?id=com.Barlowax.resolutionfragmen
ts

You can also find it on the Play Store by searching for the Keywords
"Resolution Objective"




   

[jerie]

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Dear Andrew,

I just read a recent publication from
Colin J. R. Sheppard
DOI: 10.1002/jemt.22834
which may be interesting in this respect.

Kind regards, Jens

On Thu, Feb 2, 2017 at 7:53 PM, Andrew Barlow <[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.
> *****
>
> Dear Confocal list,
>
>
> I'm about to roll out an update for my Android app, "Resolution", which

some of you were kind enough to download when I published it late last year.
>
>
> The original version was really designed around fluorescence microscopy,
it only gave the user the option to enter a single NA, and it calculates
resolution using the following version of Abbe's equation:
>
>
> Res = 1.22 lambda / 2NA
>
>
> I thought it would be helpful to add the ability to characterise a
transmitted light objective, with a distinct condenser NA and objective NA,
and to calculate resolution based on the following version of the equation:
>
>
> Res = 1.22 lambda / NA (obj) + NA (condenser)
>
>
> My original thought was to just implement this version of the equation
exactly as it is, a let the user freely enter the two NAs, and do the
calculation.  However, my understanding is that this version of the
equation really only applies when the NA of the objective and the NA of the
condenser are equal.  Under circumstances in which they are unequal, the
true resolution would be:
>
>
> Res = 1.22 lambda / 2  NAmin
>
>
> Where NAmin = the smallest NA of the condenser and objective.  In such
cases resolution is constrained by the smaller of the two NAs.
>
>
> This is pretty much what I've implemented, but I don't have the
confidence to release this without first checking with this list that this
is the right approach.
>
>
> If you could share your thoughts on this I'd be very grateful.
>
>
> If anyone would be interested in taking a look at the beta of the next
version I'd be happy to share it with them.
>
>
> Many thanks,
>
>
> Andy Barlow

[Sylvie Le Guyader]

*****
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*****

Dear list and Andrew



I have a question concerning the calculation for the brightness of an objective (NA4/mag2).



I understand why in a widefield/epifluorescence context, the brightness of the objective depends on the total magnification since if we change magnification, photons will be projected onto more or less pixels, leading to a brighter or dimmer intensity per pixel so a brighter or dimmer image.



However I do not understand how/if this calculation applies to single-point scanning confocals, i.e. not camera-based but e.g. PMT-based confocals. In this case the detector is like 1 single large pixel. All photons are being collected by the detector at each point that is being scanned. Is that not independent of magnification? So is it correct to say that in the case of a single-point confocal, the calculation is simply NA4?



Thanks



Med vänlig hälsning / Best regards



Sylvie



@@@@@@@@@@@@@@@@@@@@@@@@

Sylvie Le Guyader, PhD

Live Cell Imaging Facility Manager

Karolinska Institutet- Bionut Dpt

Hälsovägen 7,

Novum, G lift, floor 6

14157 Huddinge

Sweden

mobile: [phone]

office: [phone]

LCI website







-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Andrew Barlow
Sent: den 2 februari 2017 22:54
To: [hidden email]
Subject: Update to "Resolution" App



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*****



Dear Confocal list,





I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.





The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:





Res = 1.22 lambda / 2NA





I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:





Res = 1.22 lambda / NA (obj) + NA (condenser)





My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:





Res = 1.22 lambda / 2  NAmin





Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.





This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.





If you could share your thoughts on this I'd be very grateful.





If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.





Many thanks,





Andy Barlow

[Tim Feinstein]

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Are confocals being modeled in the Android version of the app?  The iOS version* has transmitted light and epi-fluorescence only.  I would imagine the calculations for a confocal would be a greater challenge, with many variables to consider and many potential scope types.  

(*) BTW, thank you Andrew!

Best,


Tim

Timothy Feinstein, Ph.D.
Research Scientist
University of Pittsburgh Department of Developmental Biology


On 5/2/17, 6:06 AM, "Confocal Microscopy List on behalf of Sylvie Le Guyader" <[hidden email] on behalf of [hidden email]> wrote:

    *****
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    Post images on https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0 and include the link in your posting.
    *****
   
    Dear list and Andrew
   
   
   
    I have a question concerning the calculation for the brightness of an objective (NA4/mag2).
   
   
   
    I understand why in a widefield/epifluorescence context, the brightness of the objective depends on the total magnification since if we change magnification, photons will be projected onto more or less pixels, leading to a brighter or dimmer intensity per pixel so a brighter or dimmer image.
   
   
   
    However I do not understand how/if this calculation applies to single-point scanning confocals, i.e. not camera-based but e.g. PMT-based confocals. In this case the detector is like 1 single large pixel. All photons are being collected by the detector at each point that is being scanned. Is that not independent of magnification? So is it correct to say that in the case of a single-point confocal, the calculation is simply NA4?
   
   
   
    Thanks
   
   
   
    Med vänlig hälsning / Best regards
   
   
   
    Sylvie
   
   
   
    @@@@@@@@@@@@@@@@@@@@@@@@
   
    Sylvie Le Guyader, PhD
   
    Live Cell Imaging Facility Manager
   
    Karolinska Institutet- Bionut Dpt
   
    Hälsovägen 7,
   
    Novum, G lift, floor 6
   
    14157 Huddinge
   
    Sweden
   
    mobile: [phone]
   
    office: [phone]
   
    LCI website
   
   
   
   
   
   
   
    -----Original Message-----
    From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Andrew Barlow
    Sent: den 2 februari 2017 22:54
    To: [hidden email]
    Subject: Update to "Resolution" App
   
   
   
    *****
   
    To join, leave or search the confocal microscopy listserv, go to:
   
    https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=oZUDH%2FB9hQvuyrLAJgWjWawVcgNvNlbhVRQmLzleMkw%3D&reserved=0
   
    Post images on https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0 and include the link in your posting.
   
    *****
   
   
   
    Dear Confocal list,
   
   
   
   
   
    I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.
   
   
   
   
   
    The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:
   
   
   
   
   
    Res = 1.22 lambda / 2NA
   
   
   
   
   
    I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:
   
   
   
   
   
    Res = 1.22 lambda / NA (obj) + NA (condenser)
   
   
   
   
   
    My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:
   
   
   
   
   
    Res = 1.22 lambda / 2  NAmin
   
   
   
   
   
    Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.
   
   
   
   
   
    This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.
   
   
   
   
   
    If you could share your thoughts on this I'd be very grateful.
   
   
   
   
   
    If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.
   
   
   
   
   
    Many thanks,
   
   
   
   
   
    Andy Barlow
   

[Eric Marino]

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*****

Good Morning Andrew,

You may have answered this question already, what is the name of the IOS version of your app. I tried searching for “Resolution” “Microscope Resolution” with no results.

Eric Marino
[hidden email]

> On May 2, 2017, at 9:21 AM, Feinstein, Timothy N <[hidden email]> wrote:
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy <http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy>
> Post images on http://www.imgur.com <http://www.imgur.com/> and include the link in your posting.
> *****
>
> Are confocals being modeled in the Android version of the app?  The iOS version* has transmitted light and epi-fluorescence only.  I would imagine the calculations for a confocal would be a greater challenge, with many variables to consider and many potential scope types.  
>
> (*) BTW, thank you Andrew!
>
> Best,
>
>
> Tim
>
> Timothy Feinstein, Ph.D.
> Research Scientist
> University of Pittsburgh Department of Developmental Biology
>
>
> On 5/2/17, 6:06 AM, "Confocal Microscopy List on behalf of Sylvie Le Guyader" <[hidden email] <mailto:[hidden email]> on behalf of [hidden email] <mailto:[hidden email]>> wrote:
>
>    *****
>    To join, leave or search the confocal microscopy listserv, go to:
>    https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=oZUDH%2FB9hQvuyrLAJgWjWawVcgNvNlbhVRQmLzleMkw%3D&reserved=0 <https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=oZUDH%2FB9hQvuyrLAJgWjWawVcgNvNlbhVRQmLzleMkw%3D&reserved=0>
>    Post images on https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0 <https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0> and include the link in your posting.
>    *****
>
>    Dear list and Andrew
>
>
>
>    I have a question concerning the calculation for the brightness of an objective (NA4/mag2).
>
>
>
>    I understand why in a widefield/epifluorescence context, the brightness of the objective depends on the total magnification since if we change magnification, photons will be projected onto more or less pixels, leading to a brighter or dimmer intensity per pixel so a brighter or dimmer image.
>
>
>
>    However I do not understand how/if this calculation applies to single-point scanning confocals, i.e. not camera-based but e.g. PMT-based confocals. In this case the detector is like 1 single large pixel. All photons are being collected by the detector at each point that is being scanned. Is that not independent of magnification? So is it correct to say that in the case of a single-point confocal, the calculation is simply NA4?
>
>
>
>    Thanks
>
>
>
>    Med vänlig hälsning / Best regards
>
>
>
>    Sylvie
>
>
>
>    @@@@@@@@@@@@@@@@@@@@@@@@
>
>    Sylvie Le Guyader, PhD
>
>    Live Cell Imaging Facility Manager
>
>    Karolinska Institutet- Bionut Dpt
>
>    Hälsovägen 7,
>
>    Novum, G lift, floor 6
>
>    14157 Huddinge
>
>    Sweden
>
>    mobile: [phone]
>
>    office: [phone]
>
>    LCI website
>
>
>
>
>
>
>
>    -----Original Message-----
>    From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Andrew Barlow
>    Sent: den 2 februari 2017 22:54
>    To: [hidden email]
>    Subject: Update to "Resolution" App
>
>
>
>    *****
>
>    To join, leave or search the confocal microscopy listserv, go to:
>
>    https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=oZUDH%2FB9hQvuyrLAJgWjWawVcgNvNlbhVRQmLzleMkw%3D&reserved=0 <https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=oZUDH%2FB9hQvuyrLAJgWjWawVcgNvNlbhVRQmLzleMkw%3D&reserved=0>
>
>    Post images on https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0 <https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com&data=01%7C01%7Ctnf8%40PITT.EDU%7C1d04de5f755144882f3608d4914305e5%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1&sdata=A46Ok3vJWrpoXvdWLk%2FrNrF7iuTZazqzS76xt4VmhXY%3D&reserved=0> and include the link in your posting.
>
>    *****
>
>
>
>    Dear Confocal list,
>
>
>
>
>
>    I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.
>
>
>
>
>
>    The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:
>
>
>
>
>
>    Res = 1.22 lambda / 2NA
>
>
>
>
>
>    I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:
>
>
>
>
>
>    Res = 1.22 lambda / NA (obj) + NA (condenser)
>
>
>
>
>
>    My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:
>
>
>
>
>
>    Res = 1.22 lambda / 2  NAmin
>
>
>
>
>
>    Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.
>
>
>
>
>
>    This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.
>
>
>
>
>
>    If you could share your thoughts on this I'd be very grateful.
>
>
>
>
>
>    If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.
>
>
>
>
>
>    Many thanks,
>
>
>
>
>
>    Andy Barlow

[Martin Wessendorf-2]

*****
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*****

Dear Dr. Le Guyader--

I think that the answer is no.  Consider the case of increasing the
magnification by making the  pixels smaller.  If you do that--and you
don't change the time you take to scan a unit of distance--the time per
pixel (and brightness) will decrease linearly with the number of pixels,
i.e. with the square of the magnification.  You'd have to scan more
slowly (i.e. you'd need to keep the time-per-pixel the same rather than
the time-per-unit distance the same) to get the same number of photons.

With regard to comparing the brightness of a point-source viewed with
two objectives having the same NA but different magnification (and using
equal pinhole sizes for the two objectives, as measured in Airy units)
and sampled for equal times, you will be correct. BUT if in both cases
you were scanning at Nyquist resolution (which is a function only of
NA), the size of your pixels would be identical...and thus your total
magnification would be identical. If you change total magnification,
you'd be sampling your source for different periods of time and would be
collecting different numbers of photons.

Hope that this helps--or if my explanation is incorrect, that some of
the better minds on the List will rise to the occasion and correct things!

Martin Wessendorf



.
On 5/2/2017 5:06 AM, Sylvie Le Guyader wrote:

> Dear list and Andrew
>
>
>
> I have a question concerning the calculation for the brightness of an objective (NA4/mag2).
>
>
>
> I understand why in a widefield/epifluorescence context, the brightness of the objective depends on the total magnification since if we change magnification, photons will be projected onto more or less pixels, leading to a brighter or dimmer intensity per pixel so a brighter or dimmer image.
>
>
>
> However I do not understand how/if this calculation applies to single-point scanning confocals, i.e. not camera-based but e.g. PMT-based confocals. In this case the detector is like 1 single large pixel. All photons are being collected by the detector at each point that is being scanned. Is that not independent of magnification? So is it correct to say that in the case of a single-point confocal, the calculation is simply NA4?
>
>
>
> Thanks
>
>
>
> Med vänlig hälsning / Best regards
>
>
>
> Sylvie
>
>
>
> @@@@@@@@@@@@@@@@@@@@@@@@
>
> Sylvie Le Guyader, PhD
>
> Live Cell Imaging Facility Manager
>
> Karolinska Institutet- Bionut Dpt
>
> Hälsovägen 7,
>
> Novum, G lift, floor 6
>
> 14157 Huddinge
>
> Sweden
>
> mobile: [phone]
>
> office: [phone]
>
> LCI website
>
>
>
>
>
>
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Andrew Barlow
> Sent: den 2 februari 2017 22:54
> To: [hidden email]
> Subject: Update to "Resolution" App
>
>
>
> *****
>
> 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.
>
> *****
>
>
>
> Dear Confocal list,
>
>
>
>
>
> I'm about to roll out an update for my Android app, "Resolution", which some of you were kind enough to download when I published it late last year.
>
>
>
>
>
> The original version was really designed around fluorescence microscopy, it only gave the user the option to enter a single NA, and it calculates resolution using the following version of Abbe's equation:
>
>
>
>
>
> Res = 1.22 lambda / 2NA
>
>
>
>
>
> I thought it would be helpful to add the ability to characterise a transmitted light objective, with a distinct condenser NA and objective NA, and to calculate resolution based on the following version of the equation:
>
>
>
>
>
> Res = 1.22 lambda / NA (obj) + NA (condenser)
>
>
>
>
>
> My original thought was to just implement this version of the equation exactly as it is, a let the user freely enter the two NAs, and do the calculation.  However, my understanding is that this version of the equation really only applies when the NA of the objective and the NA of the condenser are equal.  Under circumstances in which they are unequal, the true resolution would be:
>
>
>
>
>
> Res = 1.22 lambda / 2  NAmin
>
>
>
>
>
> Where NAmin = the smallest NA of the condenser and objective.  In such cases resolution is constrained by the smaller of the two NAs.
>
>
>
>
>
> This is pretty much what I've implemented, but I don't have the confidence to release this without first checking with this list that this is the right approach.
>
>
>
>
>
> If you could share your thoughts on this I'd be very grateful.
>
>
>
>
>
> If anyone would be interested in taking a look at the beta of the next version I'd be happy to share it with them.
>
>
>
>
>
> Many thanks,
>
>
>
>
>
> Andy Barlow

--
Martin Wessendorf, Ph.D.                   office: [phone]
Assoc Prof, Dept Neuroscience                 lab: [phone]
University of Minnesota             Preferred FAX: [phone]
6-145 Jackson Hall, 321 Church St. SE    Dept Fax: [phone]
Minneapolis, MN  55455                    e-mail: [hidden email]

[George McNamara]

*****
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*****

Hi Sylvia, Martin et al,

I encourage to initially think about the reflection (aka backscatter)
case, since brightness of a fluorescent specimen is going to depend on
the location of the fluorophores that are in vs out of focus, as well as
autofluorescence. David Piston has promoted the worst case scenario for
widefield (possibly also widefield + deconvolution) of a solid
fluorescent specimen with a bleached region, i.e. fluorescent plastic
slide with multi-photon bleached "object". My expectation is that Apps
are going to get the wrong answer.

A pretty ood - but by no means perfect -- article on improving images is:

https://www.ncbi.nlm.nih.gov/pubmed/27826080

Lam F, Cladière D, Guillaume C, Wassmann K, Bolte S
Super-resolution for everybody: An image processing workflow to obtain
high-resolution images with a standard confocal microscope.
Methods. 2017 Feb 15;115:17-27. doi: 10.1016/j.ymeth.2016.11.003.
(open access)
http://www.sciencedirect.com/science/article/pii/S1046202316304364

In the presented work we aimed at improving confocal imaging to obtain
highest possible resolution in thick biological samples, such as the
mouse oocyte. We therefore developed an image processing workflow that
allows improving the lateral and axial resolution of a standard confocal
microscope. Our workflow comprises refractive index matching, the
optimization of microscope hardware parameters and image restoration by
deconvolution. We compare two different deconvolution algorithms,
evaluate the necessity of denoising and establish the optimal image
restoration procedure. We validate our workflow by imaging sub
resolution fluorescent beads and measuring the maximum lateral and axial
resolution of the confocal system. Subsequently, we apply the parameters
to the imaging and data restoration of fluorescently labelled meiotic
spindles of mouse oocytes. We measure a resolution increase of
approximately 2-fold in the lateral and 3-fold in the axial direction
throughout a depth of 60μm. This demonstrates that with our optimized
workflow we reach a resolution that is comparable to 3D-SIM-imaging, but
with better depth penetration for confocal images of beads and the
biological sample.

Highlights
• We propose a workflow that allows obtaining confocal super-resolution
images.
• We improve the resolution of confocal imaging 2-fold in the lateral
direction.
• Axial resolution is improved 3-fold up to a depth of 60 μm.
• We evaluate two different deconvolution algorithms and denoising on
the deconvolution result.
• With our approach, super-resolution may be obtained in the meiotic
spindle of mouse oocytes.

///

The Lam paper has flaws, for example, they argue for slow scanning (400
Hz), but do not "do the right thing" which would be to scan each pixel
for equal time (example: 800 Hz scan should be scanned twice and summed,
correcting for noise). This scan speed --> sum issue was highlighted for
me by one of Leica's applications scientists who walked me through an
evaluation of many different scan speeds on one of the leica SP5
confocal microscopes I used to manage (Miami, FL). Ushot was that SP5
resonant scan mode, 8000 Hz, greatly outperformed very slow scan speeds
(default 400 Hz, vague recollection we might have been able to operate
the SP5 at 80 or 100 Hz). On Lam et al's deconvolution:  I am unclear of
whether the deconvolution algorithm they used is quantitative (correctly
reassigns signal, no data in the paper testing this --
acknowledgement=disclosure: this issue was brought to my attention by
someone at one of the other deconvolution companies, and one of my
favorite datasets is on that vendor's image gallery).

Additional key issues with respect to fluorescence:

* irreversible photobleaching: that is, dead fluorophores emit no more
photons.

* reversible "shelving" of fluorophore(s) into a dark state ... and
there are lots of dark states, as easily demonstrated by dark states
winning part of the Nobel Prize for super-resolution (PALM/STORM, I note
that STED is also a "dark state").

More excitation energy --> usually more dark state(s). ... point
illumination with high power laser can easily achieve this. Researchers
have been FRAPing for decades, even before confocal, so it is possible
to reversibly "dark state(s)" and/or irreversibly bleach with widefield
(arc lamp) excitation.

Upshot: fluorescence is complicated, especially at high energy flux.

enjoy,

George


On 5/2/2017 10:05 AM, Martin Wessendorf 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.
> *****
>
> Dear Dr. Le Guyader--
>
> I think that the answer is no.  Consider the case of increasing the
> magnification by making the  pixels smaller.  If you do that--and you
> don't change the time you take to scan a unit of distance--the time
> per pixel (and brightness) will decrease linearly with the number of
> pixels, i.e. with the square of the magnification.  You'd have to scan
> more slowly (i.e. you'd need to keep the time-per-pixel the same
> rather than the time-per-unit distance the same) to get the same
> number of photons.
>
> With regard to comparing the brightness of a point-source viewed with
> two objectives having the same NA but different magnification (and
> using equal pinhole sizes for the two objectives, as measured in Airy
> units) and sampled for equal times, you will be correct. BUT if in
> both cases you were scanning at Nyquist resolution (which is a
> function only of NA), the size of your pixels would be identical...and
> thus your total magnification would be identical. If you change total
> magnification, you'd be sampling your source for different periods of
> time and would be collecting different numbers of photons.
>
> Hope that this helps--or if my explanation is incorrect, that some of
> the better minds on the List will rise to the occasion and correct
> things!
>
> Martin Wessendorf
>
>
>
> .
> On 5/2/2017 5:06 AM, Sylvie Le Guyader wrote:
>> Dear list and Andrew
>>
>>
>>
>> I have a question concerning the calculation for the brightness of an
>> objective (NA4/mag2).
>>
>>
>>
>> I understand why in a widefield/epifluorescence context, the
>> brightness of the objective depends on the total magnification since
>> if we change magnification, photons will be projected onto more or
>> less pixels, leading to a brighter or dimmer intensity per pixel so a
>> brighter or dimmer image.
>>
>>
>>
>> However I do not understand how/if this calculation applies to
>> single-point scanning confocals, i.e. not camera-based but e.g.
>> PMT-based confocals. In this case the detector is like 1 single large
>> pixel. All photons are being collected by the detector at each point
>> that is being scanned. Is that not independent of magnification? So
>> is it correct to say that in the case of a single-point confocal, the
>> calculation is simply NA4?
>>
>>
>>
>> Thanks
>>
>>
>>
>> Med vänlig hälsning / Best regards
>>
>>
>>
>> Sylvie
>>
>>
>>
>> @@@@@@@@@@@@@@@@@@@@@@@@
>>
>> Sylvie Le Guyader, PhD
>>
>> Live Cell Imaging Facility Manager
>>
>> Karolinska Institutet- Bionut Dpt
>>
>> Hälsovägen 7,
>>
>> Novum, G lift, floor 6
>>
>> 14157 Huddinge
>>
>> Sweden
>>
>> mobile: [phone]
>>
>> office: [phone]
>>
>> LCI website
>>
>>
>>
>>
>>
>>
>>
>> -----Original Message-----
>> From: Confocal Microscopy List
>> [mailto:[hidden email]] On Behalf Of Andrew Barlow
>> Sent: den 2 februari 2017 22:54
>> To: [hidden email]
>> Subject: Update to "Resolution" App
>>
>>
>>
>> *****
>>
>> 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.
>>
>> *****
>>
>>
>>
>> Dear Confocal list,
>>
>>
>>
>>
>>
>> I'm about to roll out an update for my Android app, "Resolution",
>> which some of you were kind enough to download when I published it
>> late last year.
>>
>>
>>
>>
>>
>> The original version was really designed around fluorescence
>> microscopy, it only gave the user the option to enter a single NA,
>> and it calculates resolution using the following version of Abbe's
>> equation:
>>
>>
>>
>>
>>
>> Res = 1.22 lambda / 2NA
>>
>>
>>
>>
>>
>> I thought it would be helpful to add the ability to characterise a
>> transmitted light objective, with a distinct condenser NA and
>> objective NA, and to calculate resolution based on the following
>> version of the equation:
>>
>>
>>
>>
>>
>> Res = 1.22 lambda / NA (obj) + NA (condenser)
>>
>>
>>
>>
>>
>> My original thought was to just implement this version of the
>> equation exactly as it is, a let the user freely enter the two NAs,
>> and do the calculation.  However, my understanding is that this
>> version of the equation really only applies when the NA of the
>> objective and the NA of the condenser are equal.  Under circumstances
>> in which they are unequal, the true resolution would be:
>>
>>
>>
>>
>>
>> Res = 1.22 lambda / 2  NAmin
>>
>>
>>
>>
>>
>> Where NAmin = the smallest NA of the condenser and objective. In such
>> cases resolution is constrained by the smaller of the two NAs.
>>
>>
>>
>>
>>
>> This is pretty much what I've implemented, but I don't have the
>> confidence to release this without first checking with this list that
>> this is the right approach.
>>
>>
>>
>>
>>
>> If you could share your thoughts on this I'd be very grateful.
>>
>>
>>
>>
>>
>> If anyone would be interested in taking a look at the beta of the
>> next version I'd be happy to share it with them.
>>
>>
>>
>>
>>
>> Many thanks,
>>
>>
>>
>>
>>
>> Andy Barlow
>

--


George McNamara, PhD
Houston, TX 77054
[hidden email]
https://www.linkedin.com/in/georgemcnamara
https://works.bepress.com/gmcnamara/75   (may need to use Microsoft Edge or Firefox, rather than Google Chrome)
http://www.ncbi.nlm.nih.gov/myncbi/browse/collection/44962650