FZ200 Diffraction Limit - Panasonic Tech Service

Started Aug 27, 2013 | Discussions
Stephen Barrett
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to J C Brown, Sep 2, 2013

J C Brown wrote:

I'm pleased to hear that you are finding my report useful but as I have no idea why you would expect red to give the poorest resolution I'm puzzled by your statement "I find the graph of resolution for the different colours surprising".

The reason that I expected red to have the poorest resolution is that the Rayleigh criterion says the angular resolution is proportional to wavelength.

Visible violet ~ 400 nm
Visible red ~ 650 nm

So the violet end of the spectrum should be able to resolve the smallest angles and red should be poorest.

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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Stephen Barrett, Sep 2, 2013

(continuing previous post)

It occurred to me that a possible reason for red to have the best resolution (in J C Brown's graph) could be related to the sensor rather than the lens. I don't know much about sensors so I Googled "Bayer Array" and was reminded that there are equal numbers of red and blue pixels but twice as many green. So why would red resolve better than green when green has a shorter wavelength and also twice as many pixels as red in the array?

But I guess the green print does not match the wavelength of green in the light spectrum because it is a combination of the cyan, magenta and yellow inks in the printer cartridge. So, I am at a loss in trying to understand the colour-dependence of a camera's resolution.

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J C Brown
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Stephen Barrett, Sep 2, 2013

Stephen Barrett wrote:

J C Brown wrote:

I'm pleased to hear that you are finding my report useful but as I have no idea why you would expect red to give the poorest resolution I'm puzzled by your statement "I find the graph of resolution for the different colours surprising".

The reason that I expected red to have the poorest resolution is that the Rayleigh criterion says the angular resolution is proportional to wavelength.

Visible violet ~ 400 nm
Visible red ~ 650 nm

So the violet end of the spectrum should be able to resolve the smallest angles and red should be poorest.

Thanks very much for the explanation for your comments.

I agree that your statement is correct for the resolution of the lens. However from my understanding of the construction and operation of a digital camera and the evidence of my tests I regard the resolution as being determined by the dimensions of the pixels on the sensor.

For the small sensor in the FZ200 the sides of each of the square pixels have a length of approximately 1.52 microns. As each pixel in the sensor is covered by a red, green or blue filter it receives only light of the colour of the filter which covers it. The colour of each filter depends on its position in the Bayer matrix which as it consists of a square of four pixels will have 3.04 micron long sides.

The colour assigned to each pixel in the final image is determined by a demozaicing algorithm which combines the value for that pixel with the values recorded from adjacent pixels to define the values of the red, green and blue components for that pixel.

I hope that helps.

Jimmy

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sherman_levine
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to J C Brown, Sep 3, 2013

J C Brown wrote:


I too have adopted a relatively simple approach to assessing and measuring the resolution of a digital camera as described in my FZ50 report which is available for download as a 6 MB PDF file from here.

As discussed in Section 2 of that report, due to the effect of the edges of the lines of a black and white grid partially overlapping adjacent pixels, the resolution of a line pair, i.e. one black line and one white line, requires three pixels, i.e. 1.5 pixels per line width. Consequently the maximum resolution of a digital camera can be estimated with reasonable accuracy by dividing the number of pixels in the height of the sensor by 1.5.

Thus for the FZ200 which has a 4000 x 3000 pixel sensor the maximum resolution would be estimated to be 2000 lines per picture height, LPH. That value is within 5% and 10% respectively of the vertical resolution values for the JPEG and RAW images in the DPR FZ200 review.


Jimmy

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J C Brown

Jimmy,

With your most recent stepped-baseline chart, where you select the smallest line in which one E has all 5 bars (B-W-B-W-B) visible, it seems to me that "perfect" zero-diffraction optics would yield one-pixel-per-line resolution (i.e. 1500 B-W pairs in the 3000-pixel high FZ200 sensor).  The 1.5 pixels per line calculation (1000 B-W pairs...) would apply if your criterion were "the smallest line in which all the Es have all 5 bars visible).

Is that not correct?

Thanks

Sherm

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Detail Man
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to sherman_levine, Sep 3, 2013

sherman_levine wrote:

J C Brown wrote:

I too have adopted a relatively simple approach to assessing and measuring the resolution of a digital camera as described in my FZ50 report which is available for download as a 6 MB PDF file from here.

As discussed in Section 2 of that report, due to the effect of the edges of the lines of a black and white grid partially overlapping adjacent pixels, the resolution of a line pair, i.e. one black line and one white line, requires three pixels, i.e. 1.5 pixels per line width. Consequently the maximum resolution of a digital camera can be estimated with reasonable accuracy by dividing the number of pixels in the height of the sensor by 1.5.

Thus for the FZ200 which has a 4000 x 3000 pixel sensor the maximum resolution would be estimated to be 2000 lines per picture height, LPH. That value is within 5% and 10% respectively of the vertical resolution values for the JPEG and RAW images in the DPR FZ200 review.

Jimmy,

With your most recent stepped-baseline chart, where you select the smallest line in which one E has all 5 bars (B-W-B-W-B) visible, it seems to me that "perfect" zero-diffraction optics would yield one-pixel-per-line resolution (i.e. 1500 B-W pairs in the 3000-pixel high FZ200 sensor). The 1.5 pixels per line calculation (1000 B-W pairs...) would apply if your criterion were "the smallest line in which all the Es have all 5 bars visible).

Is that not correct?

Some relevant thoughts that occur to me are:

Line-pair patterns are composed of a series (of odd integer multiples, amplitude-scaled in inverse proportion to the harmonic-number) spatial frequency "lines" of periodic variations - representing a periodic "square wave" in the spatial domain.

Rather than being a single sinusoidal "line" of periodic variation in space represented in the spatial frequency domain at the Shannon-Nyquist spatial rep-rate that you are proposing (equal to the spatial sampling frequency divided by 2), we are talking about the additional presence of 3rd, 5th, 7th, etc., harmonics that will result in spatial frequency domain aliasing-distortion products.

If the variations are (spatial-frequency) "band-limited" by a composite spatial frequency (MTF) response that decreases with increasing spatial frequency (as is always the case to certain unavoidable extents, in particular because there is no such thing s "perfect zero-diffraction optics"), then we would not expect an ideal, flat magnitude response up to the Shannon-Nyquist spatial frequency limit that you are proposing (or zero or linear phase-shifts, either).

Additionally, one is not ever able to physically line up the rows/column of photosites on an image-sensor with the line-pairs as projected onto the image-sensor surface. Results will be essentiall random (as to the relative phase relationships between the projected image and photosites).

It seems a wonder that an alternating dark/light line-pair can be resolved by only 3 photosites ...

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sherman_levine
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Detail Man, Sep 3, 2013

Detail Man wrote:

sherman_levine wrote:

J C Brown wrote:

I too have adopted a relatively simple approach to assessing and measuring the resolution of a digital camera as described in my FZ50 report which is available for download as a 6 MB PDF file from here.

As discussed in Section 2 of that report, due to the effect of the edges of the lines of a black and white grid partially overlapping adjacent pixels, the resolution of a line pair, i.e. one black line and one white line, requires three pixels, i.e. 1.5 pixels per line width. Consequently the maximum resolution of a digital camera can be estimated with reasonable accuracy by dividing the number of pixels in the height of the sensor by 1.5.

Thus for the FZ200 which has a 4000 x 3000 pixel sensor the maximum resolution would be estimated to be 2000 lines per picture height, LPH. That value is within 5% and 10% respectively of the vertical resolution values for the JPEG and RAW images in the DPR FZ200 review.

Jimmy,

With your most recent stepped-baseline chart, where you select the smallest line in which one E has all 5 bars (B-W-B-W-B) visible, it seems to me that "perfect" zero-diffraction optics would yield one-pixel-per-line resolution (i.e. 1500 B-W pairs in the 3000-pixel high FZ200 sensor). The 1.5 pixels per line calculation (1000 B-W pairs...) would apply if your criterion were "the smallest line in which all the Es have all 5 bars visible).

Is that not correct?

One thought that occurs to me is that line-pair patterns are composed of a series (of odd integer multiples, amplitude-scaled in inverse proportion to the harmonic-number) spatial frequency "lines" of periodic variations - representing a periodic "square wave" in the spatial domain.

So, rather than being a single sinusoidal "line" of periodic variation in space represented in the spatial frequency domain at the Shannon-Nyquist spatial rep-rate that you are proposing (equal to the spatial sampling frequency divided by 2), we are talking about the additional presence of 3rd, 5th, 7th, etc., harmonics that will result in spatial frequency domain aliasing-distortion products.

Additionally, one is not ever able to physically line up the rows/column of photosites on an image-sensor with the line-pairs as projected onto the image-sensor surface. Results will be essentiall random (as to the relative phase relationships between the projected image and photosites).

It seems a wonder that an alternating dark/light line-pair can be resolved by only 3 photosites ...

The characters on Jimmy's chart do not share a single baseline, but rather one which slopes upward by 1/10 of a (projected) pixel per character.

Consequently, the "Which is the smallest line where I can find one good E?" test seems capable of testing the 1:1 situation.

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Detail Man
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to sherman_levine, Sep 3, 2013

sherman_levine wrote:

Detail Man wrote:

sherman_levine wrote:

J C Brown wrote:

I too have adopted a relatively simple approach to assessing and measuring the resolution of a digital camera as described in my FZ50 report which is available for download as a 6 MB PDF file from here.

As discussed in Section 2 of that report, due to the effect of the edges of the lines of a black and white grid partially overlapping adjacent pixels, the resolution of a line pair, i.e. one black line and one white line, requires three pixels, i.e. 1.5 pixels per line width. Consequently the maximum resolution of a digital camera can be estimated with reasonable accuracy by dividing the number of pixels in the height of the sensor by 1.5.

Thus for the FZ200 which has a 4000 x 3000 pixel sensor the maximum resolution would be estimated to be 2000 lines per picture height, LPH. That value is within 5% and 10% respectively of the vertical resolution values for the JPEG and RAW images in the DPR FZ200 review.

Jimmy,

With your most recent stepped-baseline chart, where you select the smallest line in which one E has all 5 bars (B-W-B-W-B) visible, it seems to me that "perfect" zero-diffraction optics would yield one-pixel-per-line resolution (i.e. 1500 B-W pairs in the 3000-pixel high FZ200 sensor). The 1.5 pixels per line calculation (1000 B-W pairs...) would apply if your criterion were "the smallest line in which all the Es have all 5 bars visible).

Is that not correct?

One thought that occurs to me is that line-pair patterns are composed of a series (of odd integer multiples, amplitude-scaled in inverse proportion to the harmonic-number) spatial frequency "lines" of periodic variations - representing a periodic "square wave" in the spatial domain.

So, rather than being a single sinusoidal "line" of periodic variation in space represented in the spatial frequency domain at the Shannon-Nyquist spatial rep-rate that you are proposing (equal to the spatial sampling frequency divided by 2), we are talking about the additional presence of 3rd, 5th, 7th, etc., harmonics that will result in spatial frequency domain aliasing-distortion products.

Additionally, one is not ever able to physically line up the rows/column of photosites on an image-sensor with the line-pairs as projected onto the image-sensor surface. Results will be essentiall random (as to the relative phase relationships between the projected image and photosites).

It seems a wonder that an alternating dark/light line-pair can be resolved by only 3 photosites.

The characters on Jimmy's chart do not share a single baseline, but rather one which slopes upward by 1/10 of a (projected) pixel per character.

Consequently, the "Which is the smallest line where I can find one good E?" test seems capable of testing the 1:1 situation.

OK. I was just stating that the sampling mathematics and associated realities do not seem to work (from the get-go). If processing "smoke and mirrors" may convince us that we can violate those facts and still like what we see, that's great - but the perception will have arisen out of the "filters" in our own minds (as well as the "filters" involved in processing). Is that a repeatable observation between individual viewers (or even the same viewer, within differing moods/contexts) ?

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Ianperegian
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Stephen Barrett, Sep 3, 2013

Stephen Barrett wrote:

If aspects such as intensity and the particular shade or hue can move "red" from worst to best, how can the graph be used? My interpretation of the graph is that the average resolution decreases from approx 1800 LP/picture height at f/3 to about 1350 at f/11 and that there are colour/ intensity / hue / tint variations of approximately +/- 200. Would that be a fair interpretation if you were taking a picture of, say, a red flower and could not assess what kind of red it was?

Hi Stephen, in relation to colour resolution/intensity/contrast, some tests I did a while back
using Jimmy's coloured Es chart with different coloured backgrounds might be of interest: http://www.dpreview.com/forums/post/51413807 .

I prepared a table comparing my resolution results with the visual contrast ratio of coloured text on a coloured background according to international standards for webpages. As shown in that table, in most cases, a high contrast ratio corresponded with a high resolution of the Es. However, there were cases where the ratio didn't successfully predict the outcome for resolution.

From the results I prepared a listing of colour combination that gave very good resoluton and those which gave poor resolution, as copied below:

Combinations giving very good resolution:

Red on cyan, or white, or yellow, or pale grey

Green on dark blue Blue on cyan, or white Magenta on white, or pale grey, or yellow

Cyan on dark blue, or black, or dark grey

Yellow on dark blue, or black, or dark grey

Black on white, or green, or pale blue, or pale grey, or cyan.

Combinations giving poor resolution:

Red on dark blue, or magenta, or mid grey

Blue on black, or dark grey

Green on pale blue, or cyan

Magenta on red, or mid grey

Cyan on pale blue, or green Yellow on pale grey, or white

Black on dark blue.

I suggested that optical crosstalk on the Bayer matrix might possibly be implicated in the cases of low resolution.

Ian

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Detail Man
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Ianperegian, Sep 3, 2013

Ianperegian wrote:

Stephen Barrett wrote:

If aspects such as intensity and the particular shade or hue can move "red" from worst to best, how can the graph be used? My interpretation of the graph is that the average resolution decreases from approx 1800 LP/picture height at f/3 to about 1350 at f/11 and that there are colour/ intensity / hue / tint variations of approximately +/- 200. Would that be a fair interpretation if you were taking a picture of, say, a red flower and could not assess what kind of red it was?

Hi Stephen, in relation to colour resolution/intensity/contrast, some tests I did a while back
using Jimmy's coloured Es chart with different coloured backgrounds might be of interest: http://www.dpreview.com/forums/post/51413807 .

I prepared a table comparing my resolution results with the visual contrast ratio of coloured text on a coloured background according to international standards for webpages. As shown in that table, in most cases, a high contrast ratio corresponded with a high resolution of the Es. However, there were cases where the ratio didn't successfully predict the outcome for resolution.

From the results I prepared a listing of colour combination that gave very good resoluton and those which gave poor resolution, as copied below:

Combinations giving very good resolution:

Red on cyan, or white, or yellow, or pale grey

Green on dark blue Blue on cyan, or white Magenta on white, or pale grey, or yellow

Cyan on dark blue, or black, or dark grey

Yellow on dark blue, or black, or dark grey

Black on white, or green, or pale blue, or pale grey, or cyan.

Combinations giving poor resolution:

Red on dark blue, or magenta, or mid grey

Blue on black, or dark grey

Green on pale blue, or cyan

Magenta on red, or mid grey

Cyan on pale blue, or green Yellow on pale grey, or white

Black on dark blue.

I suggested that optical crosstalk on the Bayer matrix might possibly be implicated in the cases of low resolution.

And I think that you seem to have made a reasonably good case. On a pure pixel-pitch level, one might thing that the FZ50 image-sensor (with ~ 2 Micron photosites) might (possibly, for that reason) fare better than the smaller image-sensors models (with ~ 1.5 Micron photosites).

However, I would think that such inter-channel "crosstalk" probably also is very much related specific photodetector placement geometries (and micro-lenses, if present along with the unique to each image-sensor's "filter stack") - and becomes harder to avoid as photosite sizes shrink.

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Ianperegian
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Detail Man, Sep 3, 2013

Detail Man wrote:

On a pure pixel-pitch level, one might thing that the FZ50 image-sensor (with ~ 2 Micron photosites) might (possibly, for that reason) fare better than the smaller image-sensors models (with ~ 1.5 Micron photosites).

However, I would think that such inter-channel "crosstalk" probably also is very much related specific photodetector placement geometries (and micro-lenses, if present along with the unique to each image-sensor's "filter stack") - and becomes harder to avoid as photosite sizes shrink.

Thanks DM. I think that would seem to be the case, judging from some recent results that Jimmy kindly sent me from tests he carried out on a DSLR with large pixels compared with his FZ50.

In those tests the poor resolution and colour spreading for certain coloured Es such as yellow appeared to be far less for the DSLR.

Ian

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Stephen Barrett
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to Ianperegian, Sep 3, 2013

This is a most interesting thread!
Thank you, J C Brown and Ianperegian for all the testing you have done. I had not thought about all the complications of various colour combinations and did not know about "crosstalk".

The discussion of how many pixels are required per line-pair is also very interesting (J C Brown, sherman_levine & Detail Man).

If I may summarize some of the suggestions:

  1. In his paper, J C Brown has proposed 3 pixels per line-pair, also citing Helmhotz' use of this criterion. (I am a big fan of Helmholtz's book "On the Sensations of Tone".)
  2. sherman_levine has suggested 2 pixels per line-pair.
    This is what I used in my crude calculations of (lens + sensor) resolution. My reason for using 2 was that full extinction of the pattern would be rare, occurring only with a precise alignment of the camera with the target. This "sensor resolution" of 2 pixel-widths was then combined with the lens resolution (~9% MTF) by taking the square root of the sum of the squares. The results seem to match my test results surprisingly well for my Canon SX30. This thread is making me wonder how that is possible.
  3. Detail Man says that "it seems a wonder" that 3 photosites per line-pair are enough. If I understand his argument, 2 per line-pair is not enough because of the distortions that result from aliasing and because of "filters" that the camera uses in processing. My impression is that the rest of us are thinking predominantly in the space domain, whereas Detail Man's descriptions are mostly in the frequency domain, using MTFs, which is a fundamentally more powerful way of analysing the combination of all the complicated systems in a camera.
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Stephen Barrett
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Are 2 pixels per line-pair enough?
In reply to Stephen Barrett, Sep 3, 2013

J C Brown's assessment of the FZ50 (Section 7 of his paper for Black & white resolution) is that it can resolve at least 1850 lpph (line-pairs per picture height).

The Cameralabs review says 2100 lpph at f/4.0.
http://www.cameralabs.com/reviews/PanasonicFZ50/page4b.shtml

The sensor has 3648 x 2738 pixels, so the number of pixels per line-pair is
2738 pixels / 2100 line-pairs = 1.3 pixels per line-pair. This seems to give somewhere around 10% MTF total camera resolution, including the sensor, lens and and all the "filters", demosaicing algorithms and crosstalk etc.

In view of this, 1.3 pixels per line-pair appears to be enough to give approximately 10% MTF total resolution, and possibly more than enough for the sensor alone.  A large number of lines in a test pattern would probably exhibit aliasing and other distortions, but the pattern would not be extinguished everywhere.

Some Crude Calculations
With my Canon SX30 at full optical zoom f/5.8 (wide open for full zoom) and infinite focus, the camera resolution (approx 10% MTF) is approximately 30 microradians.

30 x 10 ^ -6 radians x 150.5 mm = 0.0045 mm (test value)
4.55 mm sensor height / 3240 pixels = 0.0014 mm per pixel

Lens resolution (old Zeiss formula for white light & nearly-perfect optics)
= 1600 / 5.8 = 276 line-pairs / mm or 0.0036 mm line-pair separation.

Sensor resolution assuming 2 pixels per line-pair = 2 x 0.0014 mm = 0.0028 mm

Total resolution (approx 10% MTF) from square root of the sum of the squares
= 0.0046 mm or approx 30 microradians, in good agreement with the test result.
Frequency = 1 line-pair / 0.0045 mm = 222 line-pairs / mm.

Even though the this method seems to give good agreement with several types of tests (telephoto, macro & telemacro) for my camera, I am not satisfied with it because it is hard to justify the 2 pixels per line-pair in the calculation when the final image on the sensor has about 3 pixels per line-pair. The MTF calculations (frequency domain) that Detail Man advocates do not suffer from such inconsistencies.

Better Calculations in the Frequency Domain
At the observed frequency of 222 line-pair per mm, the lens has more than 10% MTF, and so does the sensor with approximately 3 pixels per line-pair. When the MTFs of the lens, sensor and all the "filters" are all multiplied together , the result is the total MTF. This computation can be performed as a function of frequency until the estimated test value of approximately 10% is obtained. The corresponding calculated frequency, which is a measure of the resolution, can then be compared with the test value of 222 line-pairs per mm.

Tentative Conclusion

Tentatively, I would conclude that in my tests, I was obtaining approximately 10% MTF total resolution at frequencies corresponding to about 1 line-pair per every 3 pixels. J C Brown and Camerlabs showed some test results on the Panasonic FZ50 with similar resolution at frequencies above 1 line-pair per every 1.5 pixels. We are looking at fairly poor resolution, close to extinction but, for that purpose, it appears that 2 pixels per line-pair are sometimes enough.

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sherman_levine
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Re: Are 2 pixels per line-pair enough?
In reply to Stephen Barrett, Sep 3, 2013

I finally found the image I was looking for, from here:

http://www.dpreview.com/forums/post/51215396

If you look at this image (of which I've taken a screenshot and re-posted)

you see that the red line identifies one letter which is quite clear, while the surrounding ones on the same line are progressively less so, and no E is clearly visible on a smaller line.

Now, I'd expect that the "all characters are visible" line would need to be 1.5 times as large as the "one character is visible" line - but that does not appear to be the case here.

Sherm

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J C Brown
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Re: FZ200 Maximum Desirable F-Number to achieve adequate "Sharpness"
In reply to sherman_levine, Sep 3, 2013

sherman_levine wrote:

Detail Man wrote:

sherman_levine wrote:

J C Brown wrote:

I too have adopted a relatively simple approach to assessing and measuring the resolution of a digital camera as described in my FZ50 report which is available for download as a 6 MB PDF file from here.

As discussed in Section 2 of that report, due to the effect of the edges of the lines of a black and white grid partially overlapping adjacent pixels, the resolution of a line pair, i.e. one black line and one white line, requires three pixels, i.e. 1.5 pixels per line width. Consequently the maximum resolution of a digital camera can be estimated with reasonable accuracy by dividing the number of pixels in the height of the sensor by 1.5.

Thus for the FZ200 which has a 4000 x 3000 pixel sensor the maximum resolution would be estimated to be 2000 lines per picture height, LPH. That value is within 5% and 10% respectively of the vertical resolution values for the JPEG and RAW images in the DPR FZ200 review.

Jimmy,

With your most recent stepped-baseline chart, where you select the smallest line in which one E has all 5 bars (B-W-B-W-B) visible, it seems to me that "perfect" zero-diffraction optics would yield one-pixel-per-line resolution (i.e. 1500 B-W pairs in the 3000-pixel high FZ200 sensor). The 1.5 pixels per line calculation (1000 B-W pairs...) would apply if your criterion were "the smallest line in which all the Es have all 5 bars visible).

Is that not correct?

One thought that occurs to me is that line-pair patterns are composed of a series (of odd integer multiples, amplitude-scaled in inverse proportion to the harmonic-number) spatial frequency "lines" of periodic variations - representing a periodic "square wave" in the spatial domain.

So, rather than being a single sinusoidal "line" of periodic variation in space represented in the spatial frequency domain at the Shannon-Nyquist spatial rep-rate that you are proposing (equal to the spatial sampling frequency divided by 2), we are talking about the additional presence of 3rd, 5th, 7th, etc., harmonics that will result in spatial frequency domain aliasing-distortion products.

Additionally, one is not ever able to physically line up the rows/column of photosites on an image-sensor with the line-pairs as projected onto the image-sensor surface. Results will be essentiall random (as to the relative phase relationships between the projected image and photosites).

It seems a wonder that an alternating dark/light line-pair can be resolved by only 3 photosites ...

The characters on Jimmy's chart do not share a single baseline, but rather one which slopes upward by 1/10 of a (projected) pixel per character.

Consequently, the "Which is the smallest line where I can find one good E?" test seems capable of testing the 1:1 situation.

Sherm,

Your assessment that "Consequently, the "Which is the smallest line where I can find one good E?" test seems capable of testing the 1:1 situation" is entirely correct.

Unfortunately in order to achieve that in practice, even with a perfect lens and sensor, it would be necessary for the image of the vertical scale line to be exactly 400 pixels long and for the edges of the image of the first and last E in each group of eleven to be in exact register with the edges of the pixels on the sensor. IMHO even in the best of laboratory condition it would be extremely difficult if not impossible to achieve that.

The following image shows a comparison between a group of eleven 1.0 pixel black Es, a graphical simulation of the response of a grey-scale only sensor and crop from an FZ50 test image for which the scale and the alignment had been adjust very carefully to meet the requirements described above.

FZ50 test image compared with image of 1.0 pixel section of test chart and a graphical simulation of the response of a grey-scale only sensor to the 1.0 pixel Es.

As can be seen from the lower part of the above image even with very careful adjustment of the photographic scale and alignment my FZ50 has failed to record an accurate image of any of the eleven E in the test chart.

The following image shows an equivalent comparison between a group of eleven 1.5 pixel black Es, a graphical simulation of the response of a grey-scale only sensor and crop from the same FZ50 test image.

FZ50 test image compared with image 1.5 pixel section of test chart and graphical simulation of the response of a grey-scale only sensor to the 1.5 pixel Es.

As can be seen from the above image the FZ50 has succeeded in recording fairly accurate representations of the 1.5 pixel Es all of which are recognisable as an E and IMHO very similar in appearance to the graphical simulations of the expected images.

I hope that you will find the above images and comments helpful in explaining the reasoning behind the design of my test chart.

Jimmy

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Stephen Barrett
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Re: Are 2 pixels per line-pair enough?
In reply to Stephen Barrett, Sep 3, 2013

Something is wrong with my last post.  The test result of 1.3 pixels per line-pair for the FZ50 doesn't make sense.  Either the test is too good or I blundered in my calculation.  Too bad i have to go out now.  It's going to drive me nuts.

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Detail Man
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Re: Are 2 pixels per line-pair enough ?
In reply to Stephen Barrett, Sep 3, 2013

Stephen Barrett wrote:

Something is wrong with my last post. The test result of 1.3 pixels per line-pair for the FZ50 doesn't make sense. Either the test is too good or I blundered in my calculation. Too bad i have to go out now. It's going to drive me nuts.

It's heartening to see such rampant and unabashed "nerdism" (a good thing in my book) at play.

Fear not, by the end of today I plan to provide you with the spreadsheet tools to (directly) surf in the spatial frequency domain. With all knowledge comes some suffering, but also deeper insights.

You will find that arbitrary MTF "lower thresholds" are only metaphors for situations where (depending on the Signal/Noise Ratio) image-data information may potentially not be adequately "recoverable" in processing. The MTF of an Airy disk diameter of 2.44 * Wavelength * F-Ratio happens to be arouns 8.9 %. That is only one of the several factors that multipy to generate the net composite system spatial frequency (MTF) response.

Two photosites cannot be enough - simply because of the spatial frequency spectrum of periodic line-pairs (a "square wave" containing higher order harmonics as well as a fundamental spatial frequency), the Shannon-Nyquist sampling theorem, and the random-phase of aligning projected periodic line-pairs onto an image-sensors array of photosite locations. It's that simple.

DM ...

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Stephen Barrett
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Does the Panasonic FZ50 violate the laws of Physics?
In reply to Detail Man, Sep 4, 2013

Detail Man wrote:

Stephen Barrett wrote:

Something is wrong with my last post. The test result of 1.3 pixels per line-pair for the FZ50 doesn't make sense. Either the test is too good or I blundered in my calculation. Too bad i have to go out now. It's going to drive me nuts.

Two photosites cannot be enough - simply because of the spatial frequency spectrum of periodic line-pairs (a "square wave" containing higher order harmonics as well as a fundamental spatial frequency), the Shannon-Nyquist sampling theorem, and the random-phase of aligning projected periodic line-pairs onto an image-sensors array of photosite locations. It's that simple.

DM ...

Thanks Detail Man.
That is the reason that I said something was wrong with my previous post.
The question is:
How can you explain J C Brown's and Cameralab's test results?
By my calculations in my previous post, they seem to be resolving above the Nyquist freqency.
Cameralabs claims a resolution of 2100 line pairs per picture height for the Panasonic FZ50. The sensor height has 2737 pixels ==> 1.3 pixels per line-pair, so how do they get that resolution? If you click on the Cameralabs link that I posted, you can see the evidence. Also J C Brown's test is similar, claiming slightly less resolution, corresponding to 1.5 pixels per line-pair. So, what is going on? Did I drop a factor of 2 somewhere? Or, does the Panasonic FZ50 sensor violate the laws of physics to get twice the resolution of the sensor in my Canon SX30?

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Re: Does the Panasonic FZ50 violate the laws of Physics ?
In reply to Stephen Barrett, Sep 4, 2013

Stephen Barrett wrote:

Detail Man wrote:

Stephen Barrett wrote:

Something is wrong with my last post. The test result of 1.3 pixels per line-pair for the FZ50 doesn't make sense. Either the test is too good or I blundered in my calculation. Too bad i have to go out now. It's going to drive me nuts.

Two photosites cannot be enough - simply because of the spatial frequency spectrum of periodic line-pairs (a "square wave" containing higher order harmonics as well as a fundamental spatial frequency), the Shannon-Nyquist sampling theorem, and the random-phase of aligning projected periodic line-pairs onto an image-sensors array of photosite locations. It's that simple.

Thanks Detail Man.
That is the reason that I said something was wrong with my previous post.
The question is:
How can you explain J C Brown's and Cameralab's test results?
By my calculations in my previous post, they seem to be resolving above the Nyquist freqency.
Cameralabs claims a resolution of 2100 line pairs per picture height for the Panasonic FZ50. The sensor height has 2737 pixels ==> 1.3 pixels per line-pair, so how do they get that resolution? If you click on the Cameralabs link that I posted, you can see the evidence. Also J C Brown's test is similar, claiming slightly less resolution, corresponding to 1.5 pixels per line-pair. So, what is going on? Did I drop a factor of 2 somewhere? Or, does the Panasonic FZ50 sensor violate the laws of physics to get twice the resolution of the sensor in my Canon SX30?

Well, (somehwere) I recently posted that such numbers games were more a subjective and variable "art" than a science. Bear in mind that (in-camera, RAW, or post) processing (with Sharpening and NR) are also most frequently involved. All proprietary parameters and methods. No way to compare the processing-chains of any of the individual units tested. Completely muddy.

Jimmy publicly raised a prime example of the unreliability of such subjective "judgement calls" here:

http://www.dpreview.com/forums/post/41438422

If I recall correctly, there was zero response in return.

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J C Brown
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Re: Does the Panasonic FZ50 violate the laws of Physics?
In reply to Stephen Barrett, Sep 4, 2013

Stephen Barrett wrote:

Detail Man wrote:

Stephen Barrett wrote:

Something is wrong with my last post. The test result of 1.3 pixels per line-pair for the FZ50 doesn't make sense. Either the test is too good or I blundered in my calculation. Too bad i have to go out now. It's going to drive me nuts.

Two photosites cannot be enough - simply because of the spatial frequency spectrum of periodic line-pairs (a "square wave" containing higher order harmonics as well as a fundamental spatial frequency), the Shannon-Nyquist sampling theorem, and the random-phase of aligning projected periodic line-pairs onto an image-sensors array of photosite locations. It's that simple.

DM ...

Thanks Detail Man.
That is the reason that I said something was wrong with my previous post.
The question is:
How can you explain J C Brown's and Cameralab's test results?
By my calculations in my previous post, they seem to be resolving above the Nyquist freqency.
Cameralabs claims a resolution of 2100 line pairs per picture height for the Panasonic FZ50. The sensor height has 2737 pixels ==> 1.3 pixels per line-pair, so how do they get that resolution? If you click on the Cameralabs link that I posted, you can see the evidence. Also J C Brown's test is similar, claiming slightly less resolution, corresponding to 1.5 pixels per line-pair. So, what is going on? Did I drop a factor of 2 somewhere? Or, does the Panasonic FZ50 sensor violate the laws of physics to get twice the resolution of the sensor in my Canon SX30?

Hi Stephen,

You are correct in suspecting that you dropped a factor of 2 somewhere. As explained below the resolution figures you quote are for lines per picture height not line pairs per picture height.

In your previous post "http://www.dpreview.com/forums/post/52101765" you wrote:

"J C Brown's assessment of the FZ50 (Section 7 of his paper for Black & white resolution) is that it can resolve at least 1850 lpph (line-pairs per picture height).

The Cameralabs review says 2100 lpph at f/4.0.
http://www.cameralabs.com/reviews/PanasonicFZ50/page4b.shtml

The sensor has 3648 x 2738 pixels, so the number of pixels per line-pair is
2738 pixels / 2100 line-pairs = 1.3 pixels per line-pair. This seems to give somewhere around 10% MTF total camera resolution, including the sensor, lens and and all the "filters", demosaicing algorithms and crosstalk etc."

If you check section 7 of my FZ50 report you will see that all of my measurements are in LPH, lines per picture height as defined here: http://www.dpreview.com/glossary/digital-imaging/resolution. The maximum resolution measured in any of my FZ50 tests was 1954 LPH, 2736/1.4.

The  "1.5 pixels per line" rule of thumb in my FZ50 report was based on a relatively crude graphical simulation which as I recall I prepared in 2001 or 2002. Based on the results of my subsequent tests I would regard a figure of "1.4 pixels per line" as more accurate.

It seems that your confusion may have been caused by the use of the abbreviation "lpph" instead of "LPH" in the Cameralabs review definition of resolution.

If the 2100 lpph at f/4.0 figure which you quote from the Cameralabs review was correct a resolution of 2100 line pairs per picture height would correspond to a picture height of 4200 line which for a sensor height of 2736 pixel is clearly impossible.

If you haven't already seen it you may find the comparisons between my graphical simulations and the corresponding sections of my test images in the following post of interest.

See: http://www.dpreview.com/forums/post/52102009

Jimmy

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J C Brown

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Stephen Barrett
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Factor of 2 Found
In reply to Detail Man, Sep 4, 2013

Thank you Detail Man for drawing my attention Jimmy's post. It is certainly worth reading in detail.

Quoting from that same post:
"the following image which shows crops from the DPR test charts for FZ30 and FZ50 both with an assessed resolution of 1800 LPH."

Apparently,
LPH means lines per picture height (meaning LINE WIDTHS per picture height)
LPPH also means "lines per picture height" (meaning LINE WIDTHS per picture height)
LP/PH means line pairs per picture height

So there is my factor of 2. I thought LPPH meant line pairs per picture height, but it doesn't unless there is a slash in it: LP/PH.

http://www.normankoren.com/Tutorials/MTF.html

Line pairs or lines?
All MTF charts and most resolution charts display spatial frequency in cycles or line pairs per unit length (mm or inch). But there are exceptions. An old standard for measuring TV resolution uses line widths instead of pairs, where there are two line widths per pair, over the total height of the display. When dpreview.com recommends multiplying the chart values in its lens tests by 100 to get the total vertical lines in the image, they refer to line widths, not pairs. Confusing, but I try to keep it straight. Imatest SFR displays MTF in cycles (line pairs) per pixel, line widths per picture height (LW/PH; derived from TV measurements), and line pairs per distance (mm or in).

Revision of Standard to Avoid Confusion

http://www.image-engineering.de/index.php?option=com_content&view=article&id=483

The following table and explanation will be part of the upcoming revision of ISO 12233 and was created by Don Williams.

LW/PH = Line width per picture height
LP/mm = Line pairs per millimetre
L/mm = Lines per millimetre
Cycles/mm = Cycles per millimetre
Cycles/pixel = Cycles per pixel
LP/PH = Linepairs per picture height

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