Re: Diffraction Limit - A bit of revision.

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photoreddi wrote:

J C Brown wrote:

photoreddi wrote:

J C Brown wrote:

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As you have correctly stated:

The equation for the diffraction limit is

sin(angular resolution) = 1.22x(wavelength/aperture diameter)

However it is important to recognise that the above equation defines an “angular” limit

To relate that to the corresponding linear limit at the focal plane it is necessary to take account of the focal length. What follows is based on my Napier University lecture notes.

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Have you taken this into account?

Yes I have. If you read my post again carefully you should find that it is entirely consistent with the Cambridge in colour Technical Note which you quote.

In particular if you check the final equation for the diameter of the Airy disc "d" you will see that d = 2.44 x N x lambda defends only on the F/No N and the wavelength lambda and is therefore independent of focal length.

Perhaps I should have emphasised that fact and stated that the analysis I presented was entirely consistent with the results of ianperegians resolution tests and with the resolution tests that I've done with my FZ50 and TZ30. See for example: Resolution measurements - TZ30 (ZS20) - Many images

Technical Note: Independence of Focal Length

Since the physical size of an aperture is larger for telephoto lenses (f/4 has a 50 mm diameter at 200 mm, but only a 25 mm diameter at 100 mm), why doesn't the airy disk become smaller? This is because longer focal lengths also cause light to travel further before hitting the camera sensor -- thus increasing the distance over which the airy disk can continue to diverge. The competing effects of larger aperture and longer focal length therefore cancel, leaving only the f-number as being important (which describes focal length relative to aperture size).

http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm

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I agree with both your assertion that the size of the Airy disc "independent of focal length." and CinC's tech. note that states the same. But I don't see how this jibes with your earlier statement :

As you have correctly stated:

The equation for the diffraction limit is

sin(angular resolution) = 1.22x(wavelength/aperture diameter)

However it is important to recognise that the above equation defines an “angular” limit

To relate that to the corresponding linear limit at the focal plane it is necessary to take account of the focal length.

Which appears to be saying that the diffraction limit is a function of the focal length. Am I misinterpreting something or did you not state this quite as well as you intended?

Bye the way, I found your "Resolution measurements - TZ30 (ZS20)" post interesting and it shows a prodigious amount of effort, but you ended it with "I hope that the information and test results provided in this post will be of some value to owners of TZ30 (ZS20) and similar cameras." and from reading many reviews it seems that my ZS7 is sufficiently inferior optically that your ZS20 data probably won't tell me much about the ZS7.

It took a while for the aperture/Airy disc diameter to sink through for me also. Perhaps this will help:

For a thin lens focused at infinity, the lens-to-sensor distance = the focal length.

Take two lenses - 50mm and 100mm at constant f-stop.

At any given f-stop, the aperture of the 50mm lens is half the diameter, of the 100mm lens' aperture, hence the diffraction angle is twice as large.

However the 50mm lens is half the distance to the sensor, so the diffraction distance as measured at the sensor is the same in the two cases.

Hence the diffraction distance appears to depend only on the f-stop, because it is a function of both the lens-to-sensor distance and the aperture diameter.

Sherm