FZ200 Diffraction Limit  Panasonic Tech Service
This just confirms the eternal truth of pocket and bridge cameras fitted with small sensors.... You are perfectly safe at f3.5... Resolutionwise and, most often, bokeh wise for landscapes (everything helplessly in focus).
Ron Tolmie wrote:
Ian:
In my own experience with the ZS20 the resolution at the maximum focal length is substantially worse than at shorter focal lengths. You need to put the camera on a solid tripod and use the timer delay for such shots. Even with the smallest f/ stop the aperture diameter is still nearly 11mm at the longest FL so the image softness cannot be blamed on diffraction.
Hi Ron,
I'm disappointed that you didn't address the quote I posted in my previous reply. Here is a shorter quote from the same source:
"Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the fnumber of your lens, and on the wavelength of light being imaged. " (My emphasis).
So, just to reiterate, it is NOT the case, as you claimed (quoting your first post):
"Since the diffraction is inversely proportional to the diameter the diffraction effects are much less significant at long focal lengths."
In fact, the diffraction effects are very much just as significant at long focal lengths, and the diffraction effects are the same as for short focal lengths for a given f number.
I think you became sidetracked in talking about the way resolution can differ, and certainly does differ for the FZ and ZS cams, at different focal lengths with the same f number setting, quite apart from diffraction effects.
To take an example where diffraction is not a limiting factor on resolution, for the FZ35/38 I carried out detailed resolution testing at different f numbers and FLs as shown here .
The results show that at max zoom (486mm equiv.) and the widest aperture of f/4.4 (which is not diffraction limited) the resolution is lower than at full WA (27mm equiv.) and the same f number. However, and this is the crucial point, the difference in resolution is not due to diffraction, it is due to the lens itself. I think that is the source of your confusion, in addition to your incorrect statement quoted above.
BTW, for my testing I used Jimmy's (JC Brown) coloured Es test chart and I did, of course, use a tripod and the self timer, and with the OIS switched off. I also took replicate shots at each setting to ensure that my results were valid.
Ian
Ianperegian
http://www.ianperegian.com/
Ianperegian wrote:
"Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the fnumber of your lens, and on the wavelength of light being imaged. " (My emphasis).
Ne'er a truer statement wrote in these forums...
One person out of thousands...and thousands!
Well done Ian...
Really there is a God...and He loves you..
FlickR Photostream:
www.flickr.com/photos/46756347@N08/
Mr Ichiro Kitao, I support the call to upgrade the FZ50.
I will not only buy one but two no questions asked...
Ian:
The angular resolution (in arc sec) is inversely proportional to the aperture diameter:
sin (angle) = 1.22 x wavelength/aperture diameter
The focal length is not a factor in determining the angular resolution. If the lenses in a view camera and a miniature camera have the same angular angular resolution they will appear to be equally sharp. If the aperture diameter is 3mm and the lens has no optical aberrations then the image will be acceptably sharp, and it doesn't matter if the focal length of the lens is 4mm or 4000mm. If the aperture diameter is 1mm the image will be soft, irrespective of the focal length.
In comparing lenses that have the same focal length (such as the 50mm lenses used in FF cameras) it is a common practice to resort to a linear measurement (lines per mm) because it is easier to make such measurements. Unfortunately that leads to confusion if you try to compare lenses that have different focal lengths. If you have two lenses of equal quality (i.e. the same angular resolution) but different focal lengths the short FL lens will deliver more lines per mm even though it is not any better than the long FL lens. To make a useful comparison of the lenses you would need to divide the l/mm number by the focal length.
My statement about diffraction as a function of the aperture diameter was correct. If you want to make comparisons between measurements made at different focal lengths then you need to measure the angular resolution, not the l/mm. Otherwise you end up in a state of confusion.
Ron
I'm disappointed that you didn't address the quote I posted in my previous reply. Here is a shorter quote from the same source:
"Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the fnumber of your lens, and on the wavelength of light being imaged. " (My emphasis).
So, just to reiterate, it is NOT the case, as you claimed (quoting your first post):
"Since the diffraction is inversely proportional to the diameter the diffraction effects are much less significant at long focal lengths."
In fact, the diffraction effects are very much just as significant at long focal lengths, and the diffraction effects are the same as for short focal lengths for a given f number.
I think you became sidetracked in talking about the way resolution can differ, and certainly does differ for the FZ and ZS cams, at different focal lengths with the same f number setting, quite apart from diffraction effects.
To take an example where diffraction is not a limiting factor on resolution, for the FZ35/38 I carried out detailed resolution testing at different f numbers and FLs as shown here .
The results show that at max zoom (486mm equiv.) and the widest aperture of f/4.4 (which is not diffraction limited) the resolution is lower than at full WA (27mm equiv.) and the same f number. However, and this is the crucial point, the difference in resolution is not due to diffraction, it is due to the lens itself. I think that is the source of your confusion, in addition to your incorrect statement quoted above.
BTW, for my testing I used Jimmy's (JC Brown) coloured Es test chart and I did, of course, use a tripod and the self timer, and with the OIS switched off. I also took replicate shots at each setting to ensure that my results were valid.
Ron Tolmie
Ron Tolmie wrote:
Ian:
The angular resolution (in arc sec) is inversely proportional to the aperture diameter:
sin (angle) = 1.22 x wavelength/aperture diameter
The focal length is not a factor in determining the angular resolution. If the lenses in a view camera and a miniature camera have the same angular angular resolution they will appear to be equally sharp. If the aperture diameter is 3mm and the lens has no optical aberrations then the image will be acceptably sharp, and it doesn't matter if the focal length of the lens is 4mm or 4000mm. If the aperture diameter is 1mm the image will be soft, irrespective of the focal length.
In comparing lenses that have the same focal length (such as the 50mm lenses used in FF cameras) it is a common practice to resort to a linear measurement (lines per mm) because it is easier to make such measurements. Unfortunately that leads to confusion if you try to compare lenses that have different focal lengths. If you have two lenses of equal quality (i.e. the same angular resolution) but different focal lengths the short FL lens will deliver more lines per mm even though it is not any better than the long FL lens. To make a useful comparison of the lenses you would need to divide the l/mm number by the focal length.
My statement about diffraction as a function of the aperture diameter was correct. If you want to make comparisons between measurements made at different focal lengths then you need to measure the angular resolution, not the l/mm. Otherwise you end up in a state of confusion.
Hi Ron,
Have a look at the mathematical approximations and the correspondng identies in this section:
http://en.wikipedia.org/wiki/Airy_disk#Cameras
What do you think ? It seem (to me) to make sense (for small angles) to be able to restate your the correct identity quoted above to be of the form (in units of distance):
Distance = (Wavelength) * (FNumber)
If you disgaree, I would be very interested in learning from you  as I must have missed something.
The derivation makes an assumption that a (symmetrical, thin) lens is focused at "infinity". The Effective Focal Length being Focal Length (for "infinity" focus) multipled by [ 1 + M/P ] (where M is Image Magnifictaion, and P is Pupillary Magnification factor), it seems that this is the form that one might want to use for analyzing notably "closeup" shooting conditions.
DM ...
LTZ470 wrote:
Received a reply back from Panasonic Tech's on the FZ200 and where the Diffraction limit begins:
Dear Valued Customer
Case Number:30742743Thank you for your inquiry, the diffraction (FZ200) starts 3.5 to 4.0.
We hope this information is helpful.Thank you for contacting Panasonic.Experience is a funny thing, it is hard to beat...so don't believe all the Diffraction Calculators and so called camera experts on the internet...we ourselves can easily determine it from our user experiences...
 hide signature Really there is a God...and He loves you..
FlickR Photostream:
www.flickr.com/photos/46756347@N08/
Mr Ichiro Kitao, I support the call to upgrade the FZ50.
I will not only buy one but two no questions asked...
Cole,
These guys usually read scripts in front of their desks so best is not to take it seriously.
Regards,
=[ Joms ]=
Ian:
I should have noted that my examples (3mm=sharp, 1mm=soft) apply to long and short focal length lenses that have a normal field of view, equivalent to a 50mm lens for a FF camera. If you narrow the field of view then you will also need to narrow the angular resolution to maintain the same image sharpness. That is why telescopes need large apertures.
Ron
Ron Tolmie
Detail Man wrote:
Ron Tolmie wrote:
Ian:
The angular resolution (in arc sec) is inversely proportional to the aperture diameter:
sin (angle) = 1.22 x wavelength/aperture diameter
The focal length is not a factor in determining the angular resolution. If the lenses in a view camera and a miniature camera have the same angular angular resolution they will appear to be equally sharp. If the aperture diameter is 3mm and the lens has no optical aberrations then the image will be acceptably sharp, and it doesn't matter if the focal length of the lens is 4mm or 4000mm. If the aperture diameter is 1mm the image will be soft, irrespective of the focal length.
In comparing lenses that have the same focal length (such as the 50mm lenses used in FF cameras) it is a common practice to resort to a linear measurement (lines per mm) because it is easier to make such measurements. Unfortunately that leads to confusion if you try to compare lenses that have different focal lengths. If you have two lenses of equal quality (i.e. the same angular resolution) but different focal lengths the short FL lens will deliver more lines per mm even though it is not any better than the long FL lens. To make a useful comparison of the lenses you would need to divide the l/mm number by the focal length.
My statement about diffraction as a function of the aperture diameter was correct. If you want to make comparisons between measurements made at different focal lengths then you need to measure the angular resolution, not the l/mm. Otherwise you end up in a state of confusion.
Hi Ron,
Have a look at the mathematical approximations and the correspondng identies in this section:
http://en.wikipedia.org/wiki/Airy_disk#Cameras
What do you think ? It seem (to me) to make sense (for small angles) to be able to restate your the correct identity quoted above to be of the form (in units of distance):
Distance = (Wavelength) * (FNumber)
If you disgaree, I would be very interested in learning from you  as I must have missed something.
The derivation makes an assumption that a (symmetrical, thin) lens is focused at "infinity". The Effective Focal Length being Focal Length (for "infinity" focus) multipled by [ 1 + M/P ] (where M is Image Magnifictaion, and P is Pupillary Magnification factor), it seems that this is the form that one might want to use for analyzing notably "closeup" shooting conditions.
As well, see these identities relating to FNumber (as opposed to the entrancepupil diameter):
http://en.wikipedia.org/wiki/Diffraction#Diffractionlimited_imaging
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
J C Brown
J C Brown wrote:
...
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.
...
Have you taken this into account?
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 fnumber as being important (which describes focal length relative to aperture size).
http://www.cambridgeincolour.com/tutorials/diffractionphotography.htm
photoreddi wrote:
J C Brown wrote:
...
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.
...
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 fnumber as being important (which describes focal length relative to aperture size).http://www.cambridgeincolour.com/tutorials/diffractionphotography.htm
Jimmy
J C Brown
Jimmy:
I have always discussed angular resolution, not linear resolution, and have noted that basis in my comments. If you try to use linear resolution units then you have to append the focal length to just about every comment you make. For example, you can buy Tessar lenses in many focal lengths from 2 to 800mm and they all have about the same angular resolution but their linear resolutions are radically different. Back in the days when we were using 35mm film cameras and most of us were mainly employing lenses that had a normal field of view the linear resolution values (lines per mm) were useful. Now that we are using many different sensor sizes and a wide range of view angles that method of measurement is obsolete. We need to move on and use a more sensible approach. Most of the confusion surrounding discussions on resolution is attributable to the reluctance to abandon that archaic practice.
The realization that a 3mm aperture size is needed for sharp images is very useful. For any given sensor size you can calculate the minimum f/ stop that will produce sharp images with a lens that has a normal field of view. For example, the FZ200 has an (actual) focal length of 9mm for normal FOV images. At the WA setting the FL is 4.5mm and at the telephoto extreme it is 108mm. For the normal FOV the actual aperture diameter is 3.2mm, slightly greater than the 3mm objective. At the WA setting the actual diameter is 1.6mm, again slightly larger than the 1.5mm objective. At the long FL setting the actual value is 38.6mm, again slightly wider than the 36mm objective (The FL is 12x the 9mm standard FOV so the angular resolution needs to be increased in proportion).
The FZ200 therefore has a rational choice of settings that will yield sharp images providing the lens aberrations do not reduce the resolution. Many cameras (including my own ZS20) do not meet those objectives so the users have to accept lower resolution as an unavoidable consequence of some other design priority, such as building a camera that you can put in your pocket.
The 3mm "standard" produces images that most people would accept as being sharp enough but for those who want the sharpest possible images the aperture needs to be larger. Going beyond the f/2.8 aperture of the FZ200 would be a considerable challenge but if Fujifilm were to put a constant f/2.8 lens on their S2 it could (theoretically) compete with just about anything on the market in terms of sharpness (although it would also need more pixels). The somewhat larger sensor should also deliver lower noise, higher ISO values and a wider choice of apertures so we begin to get a glimpse of where camera development is going.
Ron
Ron Tolmie
J C Brown wrote:
photoreddi wrote:
J C Brown wrote:
...
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.
...
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 fnumber as being important (which describes focal length relative to aperture size).http://www.cambridgeincolour.com/tutorials/diffractionphotography.htm
...
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.
photoreddi wrote:
J C Brown wrote:
photoreddi wrote:
J C Brown wrote:
...
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.
...
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 fnumber as being important (which describes focal length relative to aperture size).http://www.cambridgeincolour.com/tutorials/diffractionphotography.htm
...
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 lenstosensor distance = the focal length.
Take two lenses  50mm and 100mm at constant fstop.
At any given fstop, 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 fstop, because it is a function of both the lenstosensor distance and the aperture diameter.
Sherm
I meant to refer to the Fujifilm XS1, not S2.
Ron
Ron Tolmie
Ron Tolmie wrote:
Jimmy:
I have always discussed angular resolution, not linear resolution, and have noted that basis in my comments. If you try to use linear resolution units then you have to append the focal length to just about every comment you make.
It seems to me that the Effective Focal Length [ EFL = FL * ( 1 + M / P ) ] remains rather close to the Focal Length (when focused at "infinity") in all but rather closeup shooting situations.
For example, you can buy Tessar lenses in many focal lengths from 2 to 800mm and they all have about the same angular resolution but their linear resolutions are radically different. Back in the days when we were using 35mm film cameras and most of us were mainly employing lenses that had a normal field of view the linear resolution values (lines per mm) were useful. Now that we are using many different sensor sizes and a wide range of view angles that method of measurement is obsolete. We need to move on and use a more sensible approach. Most of the confusion surrounding discussions on resolution is attributable to the reluctance to abandon that archaic practice.
How so ? How are linear resolution metrics (pairs/cycles per distance, or per imagesize) "archaic" ?
The realization that a 3mm aperture size is needed for sharp images is very useful. For any given sensor size you can calculate the minimum f/ stop that will produce sharp images with a lens that has a normal field of view. For example, the FZ200 has an (actual) focal length of 9mm for normal FOV images. At the WA setting the FL is 4.5mm and at the telephoto extreme it is 108mm. For the normal FOV the actual aperture diameter is 3.2mm, slightly greater than the 3mm objective. At the WA setting the actual diameter is 1.6mm, again slightly larger than the 1.5mm objective. At the long FL setting the actual value is 38.6mm, again slightly wider than the 36mm objective (The FL is 12x the 9mm standard FOV so the angular resolution needs to be increased in proportion).
The FZ200 therefore has a rational choice of settings that will yield sharp images providing the lens aberrations do not reduce the resolution. Many cameras (including my own ZS20) do not meet those objectives so the users have to accept lower resolution as an unavoidable consequence of some other design priority, such as building a camera that you can put in your pocket.
The 3mm "standard" produces images that most people would accept as being sharp enough but for those who want the sharpest possible images the aperture needs to be larger. Going beyond the f/2.8 aperture of the FZ200 would be a considerable challenge but if Fujifilm were to put a constant f/2.8 lens on their S2 it could (theoretically) compete with just about anything on the market in terms of sharpness (although it would also need more pixels). The somewhat larger sensor should also deliver lower noise, higher ISO values and a wider choice of apertures so we begin to get a glimpse of where camera development is going.
photoreddi wrote:
J C Brown wrote:
photoreddi wrote:
J C Brown wrote:
...
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.
...
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 fnumber as being important (which describes focal length relative to aperture size).http://www.cambridgeincolour.com/tutorials/diffractionphotography.htm
...
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
J C Brown
Hi Ron,
Thanks for your further comments and analysis.
Having used a variety of optical measuring techniques throughout my career in mechanical engineering R&D I am very familiar with both linear and angular measurements and well aware of the advantage of using angular measurements to compare the resolution of lenses.
However as the final recorded image takes the form of a flat two dimensional surface it is necessary to use the focal length of the lens in order to relate the angular resolution of the lens to the linear dimensions of the sensor and vice versa. As the flat two dimensional surface is the final form of a digital photograph I prefer to use the focal length to convert the angular values from the lens to their linear equivalents on the sensor.
While I agree that the wide range of sensor sizes, aspect ratios and pixels densities makes comparing resolution more complicated I don’t have any significant problems in making comparisons based on LPH (lines per picture height) and lp/mm line pairs/mm data.
The resolution of any digital camera in LPH can be estimated fairly accurately by dividing the number of pixels in the height of the sensor by 1.5. To convert that figure to a 35 mm equivalent lp/mm figure it is only necessary to divide by 48. IMHO both of these calculations can easily be done with sufficient accuracy using simple mental arithmetic.
After using a spreadsheet to calculate the angular resolution and the diameter of the Airy disc and create a table of results for a range of aperture diameters and focal lengths I examined the results. In view of the wide range of pixel dimensions associated with the range of sensor sizes and pixel densities I failed to notice any evidence to justify your choice of a 3 mm aperture as having any particular advantage in terms of the size of the Airy disc in relation to the range of pixel pitches in the various available camera models.
With regard to the resolution of your ZS20 it may interest you to know that when I examined at high magnification a hand held shot taken at maximum zoom I found that I could just detect the cables attached to the sides of a TV transmitter mast which was about 12 miles away.
Jimmy
J C Brown
Jerry:
What the equation states is that if you want to achieve a given angular resolution then there is a corresponding aperture dimension that will produce that resolution so long as some other factor (like optical aberrations) does not override the consideration.
Looking at it the other way around, if the aperture diameter is 3mm and the lens is intended to be used for imaging a "normal" field of view (equivalent to what you get with a 50mm lens on a full frame camera) then the image will be sharp, and it doesn't matter what the focal length of the lens is. You might have a different opinion on what constitutes a "sharp" image, but in that case the dimension might be a little bigger or a little smaller than 3mm, but the point is that there is a particular diameter that will satisfy your objective.
Cameras like the FZ200 and ZS20 have pushed the choice of sensor size right down to the point where diffraction is a critically important design consideration (although certainly not the only one!). They work well, especially if you apply some simple post processing. I printed up a batch of 11x14" ZS20 prints this afternoon and they were sharp enough to satisfy me. However, I did not print any of the images that had used the longest telephoto settings because they were not sharp enough for my tastes.
I would argue that these cameras are operating right at the limit of what is practical. Examining the impact of diffraction is one of the most basic considerations that determine if they perform satisfactorily  or do we need to revert to using much larger sensors like M4/3 or full frame?
What the equation implies is that we really only need to make modest changes in the aperture size (and hence the camera size) to get away from the diffraction limitation. A really big sensor may offer other advantages, such as wider ISO settings and a wider choice of apertures, but I am happy to give up those advantages if it means that I can put a widezoom camera in my pocket.
Ron
Ron Tolmie

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