FZ200 Diffraction Limit - Panasonic Tech Service

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Stephen Barrett
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Re: Does the Panasonic FZ50 violate the laws of Physics?
In reply to J C Brown, 10 months ago

Thank you Jimmy,

Your post was 5 minutes earlier than mine.  It is a great relief that I made a mistake, rather than having the laws of mathematics and physics violated.

Thanks for the link.  I am learning a lot of new things from your posts and papers.

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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, 10 months ago

Stephen Barrett wrote:

Thank you Jimmy,

Your post was 5 minutes earlier than mine. It is a great relief that I made a mistake, rather than having the laws of mathematics and physics violated.

Thanks for the link. I am learning a lot of new things from your posts and papers.

Thanks for your kind remarks Stephen. It is good to hear that my efforts are appreciated and that you have found my contributions helpful.

Your comments about frequency and space domains in one of your earlier posts brought back memories of several technical meetings during which I had some difficulty in trying to persuade the frequency domain enthusiasts that these methods have limited validity for some problems.

It seems to me that 4000 x 3000 pixel digital image in which every detail must consist of an integer number of pixels may well fall into that category. As you will see from the images in my previous post each of the lines and spaces in the 1.5 pixel Es in the simulation has an integer thickness of either one or two pixels each of a shade of grey which is defined by the percentage overlap.

Thus using an R,G,B scale of 0,0,0, for black and 255,255,255 for white, a black line which overlaps an adjacent row of pixels by 10% of a pixel height has been represented by two rows of pixels with values of 25.5,25.5,25.5 and 229.5,229.5,229.5 respectively.

As will be seen from the following images the situation becomes even more complex when the colours of the Bayer matrix are included in the simulation.

1.5 pixel simulation showing position of Es in relation to the R,G & B filters of the Bayer matrix and theresulting colours for each pixel.

Simulation of 1.5 pixel Es showing the results as grey-scale images and as colour versions determined by their positions in relation to the R,G & B filters of the Bayer matrix.

Jimmy

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J C Brown

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Stephen Barrett
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Re: Does the Panasonic FZ50 violate the laws of Physics?
In reply to J C Brown, 10 months ago

Jimmy,
Thank you for the excellent simulations and comparison with test images from the FZ50. Your simulation of the Bayer array certainly drives home your point that the space domain has some advantages.

In your earlier simulation using 1 pixel per line width, I thought that the letter E looked fairly legible most of the time. If you typed a whole sentence and sampled it with 1 pixel per line width, would the sentence be intelligible?

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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, 10 months ago

Stephen Barrett wrote:

Jimmy,
Thank you for the excellent simulations and comparison with test images from the FZ50. Your simulation of the Bayer array certainly drives home your point that the space domain has some advantages.

In your earlier simulation using 1 pixel per line width, I thought that the letter E looked fairly legible most of the time. If you typed a whole sentence and sampled it with 1 pixel per line width, would the sentence be intelligible?

Stephen,

Thanks very much for your kind remarks. I must say that I am somewhat confused by your statement that you thought that the letter E looked fairly legible most of the time and your question about a sentence sample at one pixel per line width. I assume that the image for which you state that most of the Es are legible is the one for which the Es have a line thickness of 1.5 pixels.

Although I haven't attempted to check it and have very little knowledge of sampling theory I expect that, depending on the colours of the letters and the photographic scale being correct, most of a digital image of a sentence which had been printed using letters with a line thickness of 1.5 pixels would be intelligible.

The same might even be true for letters which have a line thickness 1.4 pixels but not for letters which have a line thickness of 1.3 pixels or less.

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, 10 months ago

J C Brown wrote:

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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J C Brown

OK - Thanks - Sounds like I was wrong about the "look for the line with one visible E and compare that to 1.0" criterion and should use instead the "look for the line with all Es visible and compare that to 1.5 criterion for "perfect"

Is that correct?

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, 10 months ago

sherman_levine wrote:

J C Brown wrote:

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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J C Brown

OK - Thanks - Sounds like I was wrong about the "look for the line with one visible E and compare that to 1.0" criterion and should use instead the "look for the line with all Es visible and compare that to 1.5 criterion for "perfect"

Is that correct?

Sherm

Sherm,

I would recommend that you simply look for the line in which all of the lines and spaces in at least one of the Es are recognisable.

Please bear in mind that the results may vary with the colour of the Es and that as shown in the above 1.5 pixel image, depending on the degree to which they overlap an adjacent row of pixels, the lines and spaces will have a thickness of either one or two pixels.

As you will see from the following image which was taken using a neighbour's Canon EOS 5D MkII some of the 1.3 pixel Es are clearly recognisable. For the 3744 pixel height of its 21 MP sensor that would correspond to a resolution of 2880 LPH.

Crop from a Canon EOS 5D MKII resolution test image. Colour cast removed using PSE.
I hope that helps clarify my recommendations for using my new test chart.

Jimmy

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Stephen Barrett
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Re: Does the Panasonic FZ50 violate the laws of Physics?
In reply to J C Brown, 10 months ago

Stephen,

Thanks very much for your kind remarks. I must say that I am somewhat confused by your statement that you thought that the letter E looked fairly legible most of the time and your question about a sentence sample at one pixel per line width. I assume that the image for which you state that most of the Es are legible is the one for which the Es have a line thickness of 1.5 pixels.

Jimmy,

When I said that the E looked legible most of the time with 1 pixel per line width, I was referring to your greyscale simulation, not the actual camera test. There are 11 Es at different heights with respect to the pixels and 10 of them are recognizable as Es. Only the middle one lost its arms and looks like a letter I.

The question that I asked was stupid, as a result of posting in a hurry before I had to go somewhere. What I had in mind was some telephoto tests that I did with my Canon SX30, resolving about 30 microradians (~9% MTF line-pair resolution using the USAF test chart). At the same time, I did some tests with printing "The quick brown fox jumped over the lazy dog." using various fonts. With simple fonts, the printing became legible at a height corresponding to 55 microradians. This is probably a poor test because I knew the words ahead of time and, even if I that were not the case, one could probably guess a lot of the words from a few legible letters and the shape of the word. So your tests with a single letter make more sense.

In spite of my the obtuseness of my question, I think that you answered it when you said that 1.4 pixels per line width might be enough for intelligibility, but not 1.3.
Thank you.

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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, 10 months ago

Stephen Barrett wrote:

Stephen,

Thanks very much for your kind remarks. I must say that I am somewhat confused by your statement that you thought that the letter E looked fairly legible most of the time and your question about a sentence sample at one pixel per line width. I assume that the image for which you state that most of the Es are legible is the one for which the Es have a line thickness of 1.5 pixels.

Jimmy,

When I said that the E looked legible most of the time with 1 pixel per line width, I was referring to your greyscale simulation, not the actual camera test. There are 11 Es at different heights with respect to the pixels and 10 of them are recognizable as Es. Only the middle one lost its arms and looks like a letter I.

The question that I asked was stupid, as a result of posting in a hurry before I had to go somewhere. What I had in mind was some telephoto tests that I did with my Canon SX30, resolving about 30 microradians (~9% MTF line-pair resolution using the USAF test chart). At the same time, I did some tests with printing "The quick brown fox jumped over the lazy dog." using various fonts. With simple fonts, the printing became legible at a height corresponding to 55 microradians. This is probably a poor test because I knew the words ahead of time and, even if I that were not the case, one could probably guess a lot of the words from a few legible letters and the shape of the word. So your tests with a single letter make more sense.

In spite of my the obtuseness of my question, I think that you answered it when you said that 1.4 pixels per line width might be enough for intelligibility, but not 1.3.
Thank you.

Stephen

Thanks for clarifying your comments about the 1 pixel per line width images. Having looked again at these images I realised immediately that the legibility of the Es in the simulation is very much higher than in the recorded image and that the difference is due to the large difference in the shades of grey in the adjacent pixels, with those in the recorded image much darker.

As explained in my previous post the shades of grey used in my simulations are in direct linear proportion to the percentage overlap and were calculated using an R,G,B scale of 0,0,0 for black and 255,255,255 for white.

In contrast the shade/colour of each pixel in the image recorded by my FZ50 has been derived from the amount of red, green or blue light received by that pixel and several adjacent pixels and combined by a demozaicing algorithm the properties of which as Detail Man suggests are known only to Panasonic.

Though I am not familiar with the USAF test chart I seem to recall that it consists of several sets of five parallel lines with the line thickness of each set progressively reduced to allow the resolution to be assessed in line pairs per mm.

As I have been used to working with milli and micro radians since the early 1970s I found it interesting to discover that you also are familiar with measuring resolution in micro radians and relating the height of a font to a subtended angle in micro radians. It is almost six years since I joined the Panasonic forum and this is the first time that I have come across someone else who thinks in these terms.

Jimmy

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Stephen Barrett
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FZ50 Test Images
In reply to J C Brown, 10 months ago

Jimmy
It seems natural to use angular resolution for telephoto, but I like to use microns for macro (line-pair separation on the subject, not on the sensor).

The way that you handle the greyscale sounds quite reasonable to me. In your FZ50 test images, is any of the blur from diffraction or is that negligible?

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J C Brown
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Re: FZ50 Test Images
In reply to Stephen Barrett, 10 months ago

Stephen Barrett wrote:

Jimmy
It seems natural to use angular resolution for telephoto, but I like to use microns for macro (line-pair separation on the subject, not on the sensor).

The way that you handle the greyscale sounds quite reasonable to me. In your FZ50 test images, is any of the blur from diffraction or is that negligible?

Stephen,

Thanks for your comments. As the FZ50 crops included in my response to Sherm were from images recorded at F/4 the contribution from diffraction should not be significant.

Jimmy

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