Re: Diffraction Limit - A bit of revision.

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?

I had hoped that as indicated by my use of a bold font I'd made it clear that it is only the angular size of the airy disc that is independent of the focal length and that for any specific aperture diameter the linear size is directly proportionalto the focal length.

Consider the case of two lenses with an aperture D of 25 mm but focal lengths of 50 mm and 100 mm.

As the diameter of the aperture is the same for both they will both have the same angular resolution "1.22 x lambda/25". However as the focal length of the 100 mm lens is double that of the 50 mm lens the linear size, i.e. the diameter of the Airy disc for the 100 mm lens will be double that for the 50 mm lens.

However as both have a 25 mm aperture the 100 mm lens is an F/4 lens while the 50 mm lens is an F/2 lens. If the aperture of the 50 mm lens is reduced to 12.5 mm to make it an F/4 lens then its angular resolution will become "1.22 x lambda/12.5" and so double the linear size of its Airy disc to match that of the 10 mm lens, thus confirming that the linear diameter of the Airy disc is directly related to the F/No.

I hope that helps clarify your understanding of diffraction focal length and F/No.

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.

Thanks for your kind remarks about my TZ30 resolution thread. Although the absolute values of the resolution of your ZS7 will differ from my TZ30 results I would expect their variation with F/No to be very similar. If you are keen to check the resolution of your ZS7 you are welcome to download my test chart as a JPEG file and print copies for your own use. Although its dimensions are outwith the limits set for uploading to the DPR gallery it can be downloaded from here.

Jimmy