Analogue lense resolution in pixel by circle of confusion

[pandreas68]

Hi,

I thought about how to estimate the quality of an old analogue lense by pixel counting and ended in the idea of expressing the circle of confusion by a number of pixels:

The resolution of an "analogue" lense may be defined by a maximum number of pixels in within the lense may produce e.g. unsharp pictures or chromatic errors.

This maximum number of pixels may be derived from the maximum diameter of the so called circle of confusion (CoC). The circle of confusion is used in order to achieve a defined depth of field in analogue photography. In general the bigger a film format is the bigger is the allowed maximum CoC diameter. For 24mmx36mm format the diameter is 0.029mm, for 6x6 middle format the diameter is 0.053 mm.

From this diameter, the used resolution of the digital camera and the sensor size the CoC diameter can be calculated as a number of pixels in within the lense may produce unsharpness or chromatic errors.

In general the bigger the film format a lense was calculated for, the bigger the used digital resolution and the smaller the sensor size the bigger is the number of pixels in within the unsharpness and lense errors may be.

The following data show the CoCiPx (CoC in pixel) for different sensor sizes, digital pixel resolutions and film formats respectively CoC the lense originally was calculated for.

For full size sensors (24mmx36mm):

Analogue lenses for full format (CoC: 0.029mm):

10MPx: 3.1Px
12MPx: 3.4Px
24MPx: 4.8Px
42MPx: 6.4Px
50MPx: 7.0Px

Analogue lenses for 6x6 (CoC: 0,053mm):

10MPx: 5.7Px
12MPx: 6.2Px
24MPx: 8.8Px
42MPx: 11.7Px
50MPx: 12.7Px

For APS-C sensors (23.6mm x 15.8mm):

Analogue lenses for full format (CoC: 0.029mm):

10MPx: 4.7Px
12MPx: 5.2Px
24MPx: 7.4Px
42MPx: 9.7Px
50MPx: 10.6Px

Analogue lenses for 6x6 (CoC: 0.053mm):

10MPx: 8.7Px
12MPx: 9.5Px
24MPx: 13.4Px
42MPx: 17.8Px
50MPx: 19.4Px

For MicroFourThird sensors (17.3mm x 13mm):

Analogue lenses for full format (CoC: 0.029mm):

10MPx: 6.1Px
12MPx: 6.7Px
24MPx: 9.5Px
42MPx: 12.5Px
50MPx: 13.7Px

Analogue lenses for 6x6 (CoC: 0.053mm):

10MPx: 11.2Px
12MPx: 12.2Px
24MPx: 17.3Px
42MPx: 22.9Px
50MPx: 25.0Px

All these numbers are calculated using the formula:

CoCiPx = CoCinMillimeter * squareRoot( resolutionInPixel/sensorAreaInSquareMillimeter)

When assuming that 3Pixel is the minimum number of Pixels in within unsharpness and errors may occur due to the nature of digital fotography (sampling, averaging, etc) and that good lenses should have a resolution better than half of the CoC diameter then it can be derived, that good analogue lenses for full format should be useable on full format cameras for at least up to 24MPx resultion while staying within a limit of some 3 Pixels of unsharpness.

Analogue lenses for 6x6 medium format however should be useable for at least 10MPx resolution when using full format sensors.

In reality deviations are reported. Beside the quality of a lense design, the quality of a specific lense copy and the parameters of the particular shot such as e.g. whether a lense shade was used, two other influences are reported:

The quality of a lense may be better than expected by CoCiPx because only the center area of the film format the lense is calculated for is used. This holds true when e.g. a medium format lense is used on full format.

The quality of the lense may be worse than expected by CoCiPx because the lense was calculated for projection on film directly rather than through a flat glass before an sensor. The latter seems to mainly affect lenses calculated for analogue view finder cameras.

I hope this may help in deciding about the quality of a lense and its usability for digital photography.

Andreas

[Lightshow]

Those seem to be some broad assumptions, lens resolution can vary wildly between brands and even within the brand.
I have a few FF lenses that should handle 100MP FF sensor with ease, and a few that struggle with 36MP FF.

I'm still not to sure about the MP war going for much longer, at some point soon most shooters will be asking for smaller resolution options in the menu, I've already started seeing an increased number of requests for it with the A7rIV release.
There are a few that will take every pixel they can get, but I think most will be happy at 50MP, I know a few that think 24MP is the sweet spot.
I know I'm quite happy with 36MP in my A7r for file size vs resolution, I don't covet the sensors in any other camera, only the firmware updates.

[pandreas68]

[visualopsins]

I think you are on the right track. Coc is specified, however, for a standard size enlargement (8x10) viewed from a standard distance (arm's length), the eye's resolution limit. You have simply calculated pixel coverage for different density sensors given coc used for format size, however, actual minimum coc produced by the lens on a sensor can be much smaller.

This reminds me why I have to sit so close to see 4k video improvement over 1080p. But if my eyes had greater resolution more megapixels...

[pandreas68]

[pandreas68]

[pandreas68]

Having a problem with resolution respectively sharpness using a Pentacon auto 2.8 200 its time again for me to think about circle of confusion, dpi and so on.

So far I understand the main idea of circle of confusion is, that the human eye can resolve some 1500 lines per the diagonal of the picture held in appropriate distance, that one can see the picture in one view. Therefor in theory it does not really matter how big a picture is printed as long as the appropriate distance is kept to see the picture with one gaze of the eyes.

Looking e.g. on Din A4 it has a format of 297mm times 210mm and a diagonal of sqrt(210^2+297^2)mm = 264mm = 14,32 inch. In turn a resolution of 1500 dots/(14,32inch) = 105 dpi. Of course 150dpi print resolution could yield a better quality for people with over average eyes, while 300 dpi or even 600 dpi should mainly allow for better quality when looking into details but not when looking to the whole picture in one gaze of the eyes.

When it comes now to the sensor or film the 1500 lines per diagonal is calculated to the film or sensor size, and for the standard 1500 lines we yield 0.029mm for 35mm format respectively 0.053mm for square medium format as the diameter of the circle of confusion.

If we want to achieve a higher resolution than 105dpi on A4 or in general more than 1500lines per length of diagonal a smaller diameter of the circle of confusion must be chosen.

In some photographs it is intended to have a maximum depth of field from lowest possible distance to the maximum distance, e.g. infinity, in the picture when the aperture is given. In this case the classical setting is to focus on the most distant point, and to turn this setting now visible at the setting mark to the mark of the intended aperture so that now a smaller distance is at the distance mark.

In other cases a certain depth of field is intended from a minimum distance to a maximum distance, e.g. to catch two faces. In this case the classical setting is to set the minimum distance and "save" it by a pencil mark or in brain, or feeling by the hand, set to the maximum distance, again "save" it, and turn the focus setting ring back in the middle. Now the necessary aperture can be read at the two saved marks (take the bigger aperture value, if two are neighboring).

So far the theory. In practice however it depends how the lens manufacturer has chosen the aperture marks. Setting the Pentacon auto 4/200 (P 4/200au) on the distance mark of 15m according to the aperture marks the depth of field (dof) goes from some 11m to 25m at aperture 22. When using the formulas for depth of field or a respective calculatur, for 35mm film however the dof should only reach from some 12m to 20m. Whats wrong? Obviously they did not use a circle of confusion of 0.029mm but more like 0.053mm which would be leading to some 10,5m to 26m. For the Pentacon Auto therefor an about 1,5 higher aperture setting would be needed. If e.g. for a certain depth of field according to the aperture scale of the P 4/200au an aperture of 8 would be needed an aperture of in between 11 and 16 or higher must be set to achieve a minimum required sharpness in the depth of field.

These considerations should be true for all lenses, also wide angle lenses, and there may be not only Pentacon which did not use the standard circle of confusion for their aperture marks. Knowing about that for the respective lens may help to correct the settings and avoid disappointments especially for pictures which can't be easily repeated.

[pandreas68]

While in the beginning I thought about what to expect from a lens as minimum required quality and how to proove this by pixel counting, the question of this post is, which minimum resolution of lines I need from a lens and what I may expext from a lense which has a higher resolution at a given aperture and in turn which resolution I should use at the camera.

Here I think about what lens resolution I need and what I can do with lenses which support higher resolution that actually needed.

Coming from the circle of confusion I'd expect to have a minimum resolution of 1/0.053mm = 19 lines/mm for 6x6 and 1/0.029mm =35lines/mm for 35mm film / FF.

If I'd have a lens with 70lines/mm then it would mean that I could create crops of a quarter of the area of the original picture and having still the standard resolution defined by the circle of confusion.

It means also that according to the ability of a lens and to the intended resolution the resolution of a digital camera may be selected appropeately: When assuming that it makes sense to use twice the x and y resolution in the sensor than the signal has then we'd achieve 24*2*36*2/(0.029^2) = 4Mx as sensful Minimum resolution. When the lens is sharp enough to allow for a circle of confusion of 0.015mm we'd achieve a necessary resolution of some 16MPx.

In turn it means that if using a camera as a Sony 7S with some 12MP a lens (and aperture) which supports sqrt(12MPx/(4*24*36))= 60lines/mm is sufficient and this even allows for a certain "cropability" while still staying in standard quality definition.

60 lines then corresponds to 30 line pairs. Next step is how to correspond this to MTF charts...

[DConvert]

[visualopsins]

[kymarto]

There is a lot more to lens performance than raw resolution. Lens designers have to balance design for resolution vs contrast. A lens with good microcontrast will often appear better than one with higher resolution, before we even begin to talk about Seidel aberrations. There are very few situations when any viewer can actually tell any difference in raw resolution between two lenses under normal viewing conditions.

[visualopsins]

[kymarto]

Well, what is the resolution of your mepg-1 vids? 480x640 pixels?

I has some exhibitions a few years ago with photos taken with a 12mp Canon powers hot and a 36mp Nikon D800 with pro lenses. The photos were about 60x90cm. At a viewing distance of one meter there was no noticeable difference. If you got really close you could see a bit more detail in the Nikon images.

[visualopsins]

[Ernst Dinkla]

[kymarto]

Just to add to the discussion: New software algorithms like Topaz Sharpen AI and the discontinued but powerful Piccure Plus can improve sharpness and microcontrast greatly with few artifacts. I have not tested them for absolute resolution using charts, but the effects are striking.

[visualopsins]

https://www.discovery.com/science/mexapixels-in-human-eye

[Ernst Dinkla]

https://plex.page/The_Equivalent_Megapixels_Of_The_Human_Eye

for international members.

[pandreas68]

[pandreas68]

[Ernst Dinkla]

Andreas,

The discussion I gave a link to shows quite well that this is complex field to explore. I am more interested in the data of print quality that would add to the total chain of reproduction quality. Replacing MTF measurements of lenses with what looks to me as a simpler but less telling rating is not something I am interested in.

[Ernst Dinkla]

[pandreas68]

Which specific size of print would you suggest to support with 450ppi, Ernst?

[Ernst Dinkla]

[pandreas68]

Thanks Ernst for the links.

Yes it is not that easy. Maybe I missunderstood you with the 450ppi. I thought you mean it directly as print resolution.

I guess I need to find some more time to think about; I will start with https://www.imatest.com/support/docs/5-2/sharpness/interpreting-mtf50/

So far I understand with not too much of additional thinking and thus the strong risk of making a mistake is that the 150 line withs/inch in the left column actually is the print resolution. And the example with the EOS 10 D with coming from 2048Px picture hight when printing on 12.3inch high paper results in 167 dpi print resulution which is seen as high print resolution. This results in the sentence: "There’s little reason go to a 12+ megapixel camera likie the EOS 5D, unless you plan to print larger" which I can support from both my observations and calculations. So my Sony Alpha II is usually switched to 10MPx, but I have no professional requirements. A3 paper size is maybe too small for professional application and/or if stronger crops are required.

"MTF50" of 150lines/inch I would interpret, that 150lines per inch are assumed, if its transfer function is 50%. The problem with calculating this down to pixel resolution of lenses and MTFs may be that digital pictures always somehow interpolate some three pixels in one dimension, but for this issue there may be those algorithms mentioned above. If we use now the 2048 on a sensor height of 24mm then we achieve some 2048/24 = 85 lines/mm respectively some 40lp/mm. I guess there are some vintage lenses which deliver 40lp/mm with a MTF at or better than 50.

Vintage lenses: When trying to take vintage style photographs, for my taste somehow also the original rules of taking pictures somehow need to be applied; but this requires that the old theory still holds true which somehow hardly relies on the diameter of the circle of confusion (CoC). Since the 80ies however when the MTF charts got chick there were some hobby photographers which looked upon their negative film stripes or slides with some 10x magnifiers, but not using anymore the depth of field in their pictures because they hunted for absolute sharpness.

So maybe there is a need to come to new definitions of CoC, or even different sets of CoC for different applications.
Best regards, Andreas