FZ200 Diffraction Limit - Panasonic Tech Service

Started Aug 27, 2013 | Discussions thread
J C Brown
Senior MemberPosts: 1,433
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Re: Diffraction Limit - A bit of revision.
In reply to Ron Tolmie, Aug 28, 2013

Hi Ron,

I’m sorry to say that I’m disappointed in your response to my post and your failure to address the questions raised by Sherm, Ian and myself in this thread. Ron Tolmie / 3mm minimum sensor size

Having used the DPR search facility to search for your original statement I found that on 29 July 2012 you posted this thread The FZ200's unborn sibling in which you wrote:

3mm is the magic dimension!

That is the minimum diameter of the lens diaphragm if you want high resolution images. It doesn't matter if the camera is a tiny digital camera or a huge view camera - the limit is the same, and it is the number that not only defines the resolution but also most of the other optical properties of a camera.”

In response to steven2874’s request for a reference to the magic 3mm dimension you posted this response: “3mm limit” in which you wrote:

“The equation for the diffraction limit is:

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

Note that it is only a function of the aperture diameter and not the focal length of the lens.

I picked the 3mm value by looking at the aperture diameters of lenses that are known to be capable of producing sharp images in large prints. You could also do it by plugging numbers into the equation but then you would need a reference for the angular resolution value you pick.”

As it is many years since I attended an optics course and I wanted to be sure of my facts before responding I decided to do a bit of revision. That consisted of reading the sections on diffraction in the following text books and the lecture notes from an optics course which I attended at Napier University in April 1973:

“A Level Physics”: M Nelkon & P Parker,

“Fundamentals of Optics”: Fourth Edition Francis A Jenkins & Harvey E white

As I expected both of these text books confirmed the above equation for the diffraction limit.

However when I checked the section on diffraction in the Napier University lecture notes I was very pleased to find that in addition to providing the derivation for the above equation for the diffraction limit these confirmed my understanding that in order to relate it to the effect of diffraction at the focal plane it is necessary to take account of the distance from the aperture to the focal plane, i.e. the focal length.

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.

When a plane wave front is incident on an aperture a degree of sideways spreading occurs which is proportional to the ratio lambda/D where lambda is the wavelength of the incident light and D is the diameter of the aperture.

For a circular aperture it can be shown that 1.22 x lambda /D = sin theta

Where theta is half of the angle at the apex of the cone of light which leaves the aperture D.

Thus the image of a point source formed by a theoretically perfect optical system will be a disc of finite diameter, the Airy disc, the diameter of which is easily calculated.

Thus, sin theta = x/v

Where x is half the diameter “d” of the Airy disc and v is the distance from the aperture to the focal plane

Therefore 2x = 2v sin theta = 2v x 1.22 x lambda /D = 2.44 (v/D) x lambda = 2.44 N x lambda

Where N is the F/No. (v/D)

For example:

A point source of wavelength 6.0 x 10^-7 M is photographed at F/8 through a diffraction limited system.

The resulting image diameter d will be:

d = 2.44 x N x lambda = 2.44 x 8 x 6 x 10^-7 M = 11.7 x 10^-6 metres = 11.7 microns

Thus the extent to which the resolution of a digital image will be affected by diffraction will depend on the diameter of the Airy disc “d” in relation to the size of the pixels on the sensor. Consequently a camera with a high pixel count on a small sensor will be affected to a greater extent than a camera with the same pixel count on a large sensor.

For some lenses, especially those with a large diameter and a low F/No there are several other factors which affect the resolution at large apertures. For lenses to which that description applies a plot of Resolution vs. F/No may show an increase in resolution as the effect of these factors is reduced by stopping down followed by a steady reduction in resolution as the effect of diffraction increases with increasing F/No.

Jimmy

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J C Brown

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