I have only now got my head around this as I last studied optics in the early seventies. Below are four pictures.
The first is an image of a star and is what you see if you telescope is diffraction limited.
The second is a 3d representation of the Airy Disk
The third is airy disks resolved and fourth are airy disks unresolved
If you imagine the peaks a lot smaller then even in the unresolved case they would be resolved. This is also the reason bright stars are bigger than dim ones, as for really bright stars the dim rings (or Bessel function maxima) become quite evident and seem to merge.
Hope this makes it clearer.
I had forgotten I knew this. Everything is much clearer now.
I think I get it Bert, less brightness at any point makes the peaks finer/narrower/smaller and there will be less overlap between the peaks and hence better resolution between them...?
I think I get it Bert, less brightness at any point makes the peaks finer/narrower/smaller and there will be less overlap between the peaks and hence better resolution between them...?
Bert, I'm not sure about this interpretation - it may be ok but I have not seen the airy disk presented this way (in 3D).
The equations I've seen for the size of the airy disk only talk about mirror diameter and the wavelength of light, not brightness. But your explanation implies that the airy disk size can be made smaller by decreasing the brightness.
e.g. in my copy of the Suiter book on star testing, he gives the formula for the size of the airy disk as:
r = 1.22Lf/D
L=wavelength, f=focal length, D=diameter of mirror or objective.
Am I interpreting your comments correctly?
regards, Bird
edit - I think I understand your comment now, are you saying that a dimmer object will have a smaller central bright spot and a larger dark gap, but the overall size of the airy disk remains constant...
Applying this idea to extended objects like planets is a bit interesting, you might divide the object into an infinite number of very dim points, leading to some odd conclusions.
That gives the resolution limits for two point sources (stars) of equal magnitude. The first minima is the border of the Airy disc. With a dimmer object the minima will be broader and for a real case less than the noise.
With planetary imaging a smooth part is fine, it is at the border between light and dark features you want resolution. And as you said that is about a quarter of the diameter of the Airy disk. So the border is blurred by this amount.
What set me thinking was that the Airy disk for F64 was 43 micron which for a ToUcam is 8 pixels. Yet the detail I have been seeing seems to be far better than that. This has been a worthwhile exercise in understanding what is happening.
So by your criteria the resolution limit by diffraction is really about 2 pixels for F64 and for F32 1 pixel, Is this what you actually see with very good seeing.
The Airy disk is not uniform. The intensity follows a bessel function for a circular aperture. The 3D picture has intensity as the vertical variable.
