http://imagej.273.s1.nabble.com/Puncta-quantitation-tp3688664p3688670.html
I took the opportunity to think about this some more. My PSF plugin works by analyzing the optical propagation between aperture of the objective lens and the object point. it actually was developed for the reciprocal propagation case. It assumes the aperture is uniformly illuminated and phased up to focus on the central point. Using this source distribution, it computes the complex field that would occur at each location in the image stack surrounding the point, and takes the magnitude-squared to produce the PSF of a diffraction limited wide-field microscope in the Fraunhofer approximation. In FFT-based deconvolution, this PSF is assumed to be translationally invariant; it is assumed that if the source point were moved, then the entire PSF would move with it without changing shape. This is a good approximation, at least in the transverse directions, when the FOV subtends a small angle. Now consider a confocal microscope. As I understand it, the confocal microscope images a point by first creating the situation in my reciprocal simulation: it distributes light across the aperture so as to focus on the point. The computed PSF therefore describes the illumination, assuming the microscope is diffraction limited. This light then scatters incoherently from the object and is imaged, so the PSF applies a second time. The claim is that the idea of squaring the wide-field PSF to simulate a confocal microscope is exact, assuming the microscope is diffraction limited (in both directions) and the FOV is small enough for the shift-invariant assumption. In this view, your points 1) and 2) are shortcomings of the microscope, not the analytical procedure. Am I missing something?
I see what you mean about squaring the complex field to account for a specular-reflecting object. It is probably not a good to idea image an electron-microscope sample with a light microscope. Would the very bright reflection damage something?
For the fluorescent imaging, maybe the right thing to do is compute two PSFs, one for the wavelength of the illumination and one for the wavelength of the emitted light, and take the product of these two functions.
> Hi Robert and Francis,
>
> almost exactly. The single (unsquared) intensity PSF would apply for a
> "wide-field" illuminated point object, not for a confocal microscope.
> It´s not really that the same "rays" pass twice through the same regions of
> the lens (as is for ex. the case in interferometric testing of an
> objective lens) where you will need to square of the *COMPLEX* (phase and
> intensity) PSF, but the detected intensity in a confocal microscope
> for off-axis points is reduced for two reasons:
>
> 1) The point in question is not as strongly illuminated as if centered, as
> determined by the objective NA and illumination wavelength
>
> 2) Any light scattered back (or fluorecent light) will be detected less
> intense for off axis sources determined by NA, tube lens focal length and
> pinhole diameter as also detection wavelength
>
> For the most simplest case this is equivalent to the "one-pass" intensity
> PSF squared.
>
> Mit freundlichen Grüßen / Best regards
>
> Joachim Wesner
> Projektleiter Optik Technologiesysteme
>
> Leica Microsystems CMS GmbH | GmbH mit Sitz in Wetzlar | Amtsgericht
> Wetzlar HRB 2432
> Geschäftsführer: Dr. Stefan Traeger | Dr. Wolf-Otto Reuter | Dr. David Roy
> Martyr | Colin Davis
> www.leica-microsystems.com
>
>
>
>
> Robert Dougherty
> <
[hidden email]>
> Gesendet von: An
> ImageJ Interest
[hidden email]
> Group Kopie
> <
[hidden email].
> GOV> Thema
> Confocal PSF (was Puncta
> quantitation)
> 01.04.2010 16:32
>
>
> Bitte antworten
> an
> ImageJ Interest
> Group
> <
[hidden email].
> GOV>
>
>
>
>
>
>
> On Mar 31, 2010, at 11:08 PM, Francis Burton
> <
[hidden email]> wrote:
>
>> At 04:46 01/04/2010, Robert Dougherty <
[hidden email]> wrote:
>>>>> Another problem is that, given all of the choices in ImageJ: do I
>>>>> deconvolve the frames and, if so, will this help the program to
>>>>> better
>>>>> identify puncta? Should this be helpful, what would be the best
>>>>> method
>>>>> of deconvolution in ImageJ?
>>>>
>>>>
>>>> It depends on your images but deconvolution can always help.
>>>> Unfortunately I haven't try extensively ImageJ's deconvolution
>>>> plugins
>>>> since I'm working with a LSCM and I can't figure out how to
>>>> compute good
>>>> confocal theorical PSF.
>>>
>>> Have you tried squaring a regular PSF?
>>
>> Bob,
>>
>> Do you mean raising to the power of 2 or making square? What is the
>> rationale for doing that?
>>
>> Francis
>
> Francis,
> Raise to the power 2. The rational is that the light passes through
> the optics of a confocal microscope twice. The regular computed PSF
> (there must be a better name) represents the light from the scanned
> source point reaching the object. Multiplying this function by the
> regular computed PSF accounts for the return trip through the lens to
> the detector. This idea was suggested to me by a user of my PSF and
> deconvolution plugins some time ago, and I have not found a reason to
> dispute it.
> Bob
>
>
>
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