Airy disk and resolution in confocal microscopy

[u0362565]

Hi all,

I have a question about airy patterns and how these determine resolution in images. So to increase resolution the airy pattern should be made smaller. In microscopy this is achieved by using higher numerical aperture lenses and shorter wavelengths. I have also read that the more diffraction orders the lens can capture the higher the resolution or perhaps its that the image is a more accurate representation of the object. One thing i find confusing is that the zeroth order or central maximum is said to be the light that is undeviated or not diffracted so how is this actually useful information? Secondly, in confocal microscopy it is conventional to set the detection pinhole to one airy unit which i understand to mean that the zeroth order and the 1st order (minimum) is also captured everything outside this is excluded. And in fact making the pinhole smaller than 1 airy unit actually improves resolution. So to me i find these two points contradictory, i.e. you want to capture as many diffraction orders as possible yet with confocal you gain resolution by not doing this.. Can anyone explain if I've misinterpreted something here? I understand that a compromise has to be met when setting the pinhole as allowing too much light through increases the optical section and reduces resolution. I guess I've been thinking about the airy pattern influencing lateral resolution, hence capture more orders yet for axial resolution you'd want to minimise the amount of the airy pattern that you capture..

I'd really appreciate any feedback on this.

Thanks,

Matt

 

[Andy Resnick]

There are a lot of mixed-up concepts here, can you clarify what your question is?

 

[DrDu]

There are two questions here:
First: To extract information on the object, you need the interference pattern of at least two maxima, e.g. the zeroth and the first. So neither the zeroth nor the first order maximum is useful on it's own.
Second: In confocal microscopy you observe fluorescence intensity, not ordinary scattered light. This makes quite some difference in resolution as the optical resolution not only depends on the intensity distribution of the fluorescence light but also on the intensity distribution of the exciting light.

 

[u0362565]

hi guys,

sorry i just kind of typed what was i was thinking at the time without thinking does it actually make any sense.

So i suppose my basic question is, the more diffraction orders you capture with a microscope, the higher the resolution? So with higher numerical aperture lenses they have a wider acceptance angle and thus will capture more orders. But to me this contradicts what is advised when optimising the pinhole diameter in confocal microscopy. 1 Airy unit sets the pinhole to accept light from the airy disk but no more than this. But if resolution is improved by collecting more diffraction orders i.e. more concentric rings away from the airy disk (rather than resolution should i think of the diffraction orders as just adding intensity to the overall image?) then why restrict the confocal pinhole just to the airy disk? I know that the aim of the pinhole is to reject light away from the focal plane and a compromise has to be met somewhere.

Hope this is a bit clearer.

Thanks,
Matt

 

[Andy Resnick]

Imaging doesn't generally collect multiple diffraction orders, just more of the diffracted light. However, there is a particular super-resolution technique called 'structured illumination' that does indeed refer to specific diffraction orders:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1201569/

Confocal imaging is a technique that controls and minimizes the spatial size of the Airy disk to primarily improve depth resolution, although x-y resolution is also somewhat improved. Setting the pinhole size to 1 'airy unit' is an engineering optimization involving throughput and resolution.

Does that help?

 

[u0362565]

Hi Andy,

Yes i think that helps thanks. I think I've been confused by this article:
http://zeiss-campus.magnet.fsu.edu/articles/basics/imageformation.html

In it they use a diffraction grating as the "specimen" and this produces diffraction orders which are spread across the back focal plane of the objective lens. The more orders collected the higher the resolution, so they say. So i took this and applied it to the airy pattern which i think is basically equivalent in that the airy disk represents the zeroth order and subsequent maxima (concentric rings) are higher diffraction orders. Am i at least correct in saying that? So in that sense, the more of the airy pattern you can collect the higher the resolution.

Perhaps i should just accept that the size of the airy pattern is the key thing, the smaller it is, the higher the resolution.

Thanks for your comments.

Matt

 

[u0362565]

Thanks to DRDu also

 

[Andy Resnick]

<snip>So i took this and applied it to the airy pattern which i think is basically equivalent in that the airy disk represents the zeroth order and subsequent maxima (concentric rings) are higher diffraction orders. Am i at least correct in saying that? <snip>

No, that's incorrect. As you later noted, 'resolution' is related to the size of the airy disk (there are several quantitative relationships to choose from- Rayleigh criterion, Sparrow criterion, Strehl ratio, etc.)

 

[u0362565]

Hi Andy,

Ok thanks. Unfortunately this just creates new questions for me..

Diffraction by a sinusoidal grating and by a circular aperture can be thought of as equivalent? In that what results is a diffraction pattern with a bright central area of intensity surrounded by maxima and minima which represents light further from the optical axis undergoing varying degrees of constructive and destructive interference due to increased path length.

Here's an example of diffraction by a circular aperture:
http://www.olympusmicro.com/primer/java/diffraction/index.html

The pattern of light that results on the dark film is the airy pattern? And the article refers to bright maxima away from the central maximum as primary, secondary orders, but these are not orders of diffraction? If a lens can capture more of these maxima and minima what significance does this have on the image? It would just be brighter?

Thanks for all your advice.

Matt

 

[Andy Resnick]

Diffraction by a sinusoidal grating and by a circular aperture can be thought of as equivalent? <snip>

Nope.

 

[u0362565]

Ok andy thanks, i see now that a grating acts to split the light into different beams traveling in different directions.