[TDvN57]

The last couple of weeks I decided to dig into why there is difference between FF and MF and how does that impact printing. I first went down the rabbit hole of pixels and comparing pixel pitch with sensor sizes etc etc. That lead me to nowhere. Then I remembered two concepts I had ignored in this attempt: Diffraction and Circle of Confusion (CoC), or better understood as Circle of Least Confusion. Eventually I decided that the deeper dive into diffraction will have to wait for another time.

So here is some of the pathway I travelled:

1. I selected a couple of sensors and 6x7 film and started gathering data.
   
   
2. I corelated some calculated data with known published data and found some discrepancies, such as the sensor sizes published by Sony versus the same sensor sizes published by the camera manufacturers. The camera sensor size was usually smaller, which I ascribed to the "gutter" edges and unusable edges once the sensor was placed in the camera.
   
   
3. I also found some discrepancies in pixel pitch published versus calculated. These are decimal deviances and I opted to use the calculated data, because I am not designing a camera or optics, but rather developing a basis for easier understanding of concepts compared with other cameras, where decimal deviances will not change the essence of the concepts.
   
   
4. From this base set of data followed extrapolations for print size, circle of confusion, etc.
   
   
5. I stumbled upon an article written by Roger Cicala from 2012, where he does a deep dive into many topics around sensor size. I generously learned and concluded much of my understanding based on this article. For those interested I highly recommend reading the article at: Lens Rentals | Blog
   

How large can you print?
With the latest software available in post processing and resampling digital pictures, this has become a near impossible question to answer. Perhaps the best answer is that you can print as large as the resampling software can re-invent data to fill the gaps created when you move data points in the image further apart from each other.

However if we go back to basics and try and understand when we need resampling and when we don't, it may help us optimizing the use of high-tech technology at our disposal, and avoid using it indiscriminately.

Just a short note about image pixels and dots per inch. I know and fully understand that the camera pixels are a long way from the pixel values contained in a RAW file. Then add some more post processing of the pixel values now in the computer and the resemblance between computer based pixels and the original sensor pixels are even further removed from each other.

The computer pixel count of an image (without cropping or resampling) will assume the same number of pixels that it received from the camera. When it comes to printing the same image, I think it is safe to assume that for all practical purposes the dots per inch (dpi) and lines per inch (lpi) can represent the pixels of the computer version of the image. I may refer to the "sensor" size, meaning the digital computer image size.

It seems the important part to making this assumption is that the camera pixels should be a separate discussion, because we are not printing or viewing the camera pixels, but the post processed pixels in the computer.

For the sake of understanding one concept at a time, I conveniently ignored the impact of signal to noise ratios in the sensors (which is likely to get worse with a smaller pixel pitch, and the influence of lenses in resolving details. Since even the best lenses do not have the resolving power of the sensors.

If we assume that we have a printer that can print an unlimited dpi/lpi and we want the absolute theoretical quality in our print, then we should print at a 1:1 ratio, where the dpi matches the pixels per inch. For an uncropped and un-resampled image the print will be the same size as the sensor.

Increasing the size of the printed image will deduct from the hypothetical standard of "ultimate quality". The only question is how much can we increase the image size without seeing any of the degradation from the ultimate quality.

Many, including myself regularly print at 300dpi (x and y axis), and for normal use there does not seem to be any visible degradation. Although I will concede that a side-by-side comparison with a higher dpi print will most likely show differences in quality. The selected dpi depends very much on the viewing distance of the final print. This would also make for an interesting discussion.

So getting back to how large can you print, lets say at +/-300dpi, without resampling or cropping. Here is my "rule-of-thumb" comparison:

The logic so far is somewhat flawed, because it ignores the all important circle of confusion, which most likely will change the above assumptions.

Lets look at the Circle of Confusion (CoC):
Borrowing the formula for the CoC from Roger's article (see link above) I found some interesting results that also explains why and what is the main observable difference between 35mm, 645crop and 6x7. Here is a list of the CoC values for these sensor/film sizes:

Looking at the comparative list, it became clear to me that the most observable differences between FF and MF are in the CoC. It seems as if the larger the CoC the closer the image will start to look realistic (3D) when printed a certain size. I think we should also consider that our eyes and perceptions are somewhat influenced by mostly junk on Instagram and other similar sites, thus seeing and appreciating a realistic image has become more challenging.

An interesting number was how many pixels it takes to cover the area of one CoC. This may be a theoretical number with no real practical application. Although I suspect there is some value in understanding the role of pixels and resolving the details of the CoC. An understanding I still lack. Also keep in mind that our best lenses cannot resolve details to match the pixel pitch of current sensors.

On a side note about 6x7:
I plugged in a fictitious pixel pitch for the 6x7 which then calculated a hypothetical sensor for 6x7. A pixel pitch of 5.31 um (same as 645z) the file size will be 133 mpx with 120 pixels per CoC. At a pixel pitch of 4.60 (same as Hasselblad 100mpx 645FF) the file will be 177mpx (160 pixels per CoC).

This looks as if the 6x7 at 5.31 pixel pitch 133mpx is within reach of existing technology.

On a side note about ideal pixel size:
Roger's article has a link to an article by Farrel at al, about the ideal pixel size, the new link for that article is here: https://web.stanford.edu/~jefarrel/Publications/2000s/2006_Farrell_Feng_Kavusi_SPIE06_final.pdf

My take away conclusion so far:
I would always prefer a larger sensor with a modest pixel pitch, preferably closer to Farrel's ideal sensor size, even though their assessment probably needs an update.


Comments, opinions and contributions to a better understanding will be appreciated.

[Michail_P]

A very technical matter which I have researched just a bit, a while ago. CoC remains a not-so-easily perceived issue, due to the minimal scale of value comparison. Your insight is most interesting and the conclusion even more. Most folks would think “the bigger the better” , but the technological limitations indicate a necessity for balanced aspects.
One particular phrase caught my attention: “our best lenses cannot resolve details to match the pixel pitch of current sensors”.. Now, I get the terminology, pixel pitch etc, but is there really a way to compare lens resolution to sensor pixel pitch ??

[Ian Stuart Forsyth]

Your CoC is dependent on how much you stop down the lens, when you stop down the lens either on a cropped sensor like the K3III or using the 645z for the same amount of DOF you need different ƒ stops thus different CoC. If you are using the same DOF for the both formats then how much of the CoC occupies within final image will be the same. Now with the 645z because it has more pixels within the image for the same CoC the 645z will put more pixels within that CoC and in theory a better recording of how that CoC is being projected and may give you a little bit more detail ..

Now if both sensors share the same amount of pixels for the same DOF both will have the same amount of pixels contained within those 2 different CoC's

---------- Post added 12-30-2021 at 02:33 AM ----------

You also have to remember that CoC is not just one CoC striking the sensor but many of different sizes depending on the wavelength of the the light, so that really there is not a single point of light that will correspond to a patch of photo sites but rather an overlap of many that the sensor will be recording, if you want to record the best information you want as many photo sites recording this overlap as you can. If you can record exactly how each light point is being projected and how they overlap the you will capture the best that lens can project.

[biz-engineer]

Things can get very complicated, such as effect of the lens + pixel density + optimal sharpening and due to the non-linear human perception of sharpness. At certain print sizes and smaller, you may not be able to tell the difference depending how ideal is the post processing. The simple conclusion is the larger the sensor and the more pixels you have the larger you can print, but it comes with diminishing returns in terms of cost or processing time. Diffraction effects are mostly recovered by sharpening. 300PPI can go as low as 200PPI native because above 200PPI the details are so small that the eyes can be fooled into confusing acutance for resolution. My rule for sharp enough prints (my perception of sharp enough) is that if the pixel density is high enough to compete with the lens performance, then I don't enlarge more than 20 x the size of the sensor (other otherwise > 20 x , lens flaws become obvious), with balanced sharpening. So, it's about A3 for micro4/3. A2 for apsc, A1 for full frame and A0 for medium format.

[Ian Stuart Forsyth]

When you get to the point of capturing how each CoC is being projected then you do not need to worry about aliasing as you are using the lens as your anti aliasing filter

There is also the benefit that with more pixels for the same captured resolution (how much will be displayed within your print) that you can stop down the lens even more for the same captured resolution with the sensor that has more pixels and giving your image more DOF over the image captured with less pixels for the same captured resolution.

[biz-engineer]

Most folks would think “the bigger the better”

The print size has not much to do with better, it's just that a large print doesn't convey the same feeling as a small print. For example, a small print of a waterfall can be good looking , but the viewer in front of the same image printed at A0 feel as if being there at the waterfall location. Higher resolution camera system is just a mean to produce the A0 size so that the user get this immersive feeling. Other examples where print size help convey a feeling to the viewer is for giving the feeling of force or power: being in front of an A0 print of a Lion convey the feeling of strength, force, or fear. A life size print of an elephant convey the feeling of how large is the animal. The same pictures on a mobile phone don't convey any feeling at all.

---------- Post added 30-12-21 at 09:52 ----------

“our best lenses cannot resolve details to match the pixel pitch of current sensors”.

This one is never entirely true , because lenses are continuous systems, the contrast just drops slowly, most lenses still deliver non-zero contrast at 400 lp/mm. Given the pixel density is high enough to pick-up the 400lp/mm contrast from the lens, sharpening can take that small residual contrast at 400lp/mm and pull it up. That's why 100Mpixels on even a full frame sensor is still better than 36Mpixels on the same size sensor. More pixels give more headroom for post processing and the noise to detail tradeoff. If the lens become a limitation, the rectangle edges further out to image circle can be cropped (go to 1:1) to keep only the sharpest part of the lens, which allow to enlarge even more.

---------- Post added 30-12-21 at 09:59 ----------

I would always prefer a larger sensor with a modest pixel pitch, preferably closer to Farrel's ideal sensor size, even though their assessment probably needs an update.

I would still go for the highest possible resolution sensor , provided the total image quality doesn't drop too much (i.e total signal to noise of the image at base ISO). The bottleneck in lenses are the edges and corners, as we enlarge more and more, lens corner issues show much earlier than center issues. Lens contrast at 30lp/mm generally drops between 25% up to 50%, and drops much quicker at 50lp/mm. With the highest possible sensor resolution, even if my sensor pixel density is way too much for the edges of my lens, I can still make use of the square aspect ratio is print my 1:1 images larger then if the sensor had less pixels. My opinion here isn't from theory, I formed that opinion base on experience making print of various sizes, trials & errors and drawing conclusions from observation.

[TDvN57]

A very technical matter which I have researched just a bit, a while ago. CoC remains a not-so-easily perceived issue, due to the minimal scale of value comparison. Your insight is most interesting and the conclusion even more. Most folks would think “the bigger the better” , but the technological limitations indicate a necessity for balanced aspects.
One particular phrase caught my attention: “our best lenses cannot resolve details to match the pixel pitch of current sensors”.. Now, I get the terminology, pixel pitch etc, but is there really a way to compare lens resolution to sensor pixel pitch ??

Hi Michael, There is a simplistic way to get the basic understanding. As with all things technical, there is always a more complicated underlying base of knowledge. However for our purposes as photographers the simplistic methods are usually enough to get a general understanding and appreciation.

You can do some easy internet research for the best commercial and pro lenses, does not have to be 645, can be any format and any brand. Then find the resolving power of the lens at its optimal aperture. Does not matter what the aperture is, for this purpose. That will be a number of line pairs that the lens can resolve within a given distance.

Then consider the pixel pitch and we have to assume that the RAW file will be compiled to the same resolution as the pixel pitch. This is most likely not the case, but for the sake of understanding the concept, lets make that assumption.

Take the sensor pixels across the sensor and assume it is technically capable of resolving a perfect vertical line from top to bottom on every second column of pixels. This will fill the sensor with line pairs across.

We know that the 645z sensor has 8,256 pixels across. Divide by 2 equals to 4128 "line pairs". We know the width of the sensor is +/-43.8mm which will result in +/-94 line pairs per mm (not inch BTW). You will struggle to find a lens that can resolve more than 30 line pairs per mm.

Thus, there is a gap between what the best lenses can resolve versus what sensors can resolve. Perhaps the larger CoC is the important issue here instead of the pixels.

My apology if I dragged this out too much step by step.

---------- Post added 2021-12-30 at 05:26 PM ----------

Your CoC is dependent on how much you stop down the lens, when you stop down the lens either on a cropped sensor like the K3III or using the 645z for the same amount of DOF you need different ƒ stops thus different CoC. If you are using the same DOF for the both formats then how much of the CoC occupies within final image will be the same. Now with the 645z because it has more pixels within the image for the same CoC the 645z will put more pixels within that CoC and in theory a better recording of how that CoC is being projected and may give you a little bit more detail ..

Now if both sensors share the same amount of pixels for the same DOF both will have the same amount of pixels contained within those 2 different CoC's

---------- Post added 12-30-2021 at 02:33 AM ----------

You also have to remember that CoC is not just one CoC striking the sensor but many of different sizes depending on the wavelength of the the light, so that really there is not a single point of light that will correspond to a patch of photo sites but rather an overlap of many that the sensor will be recording, if you want to record the best information you want as many photo sites recording this overlap as you can. If you can record exactly how each light point is being projected and how they overlap the you will capture the best that lens can project.

From my understanding Circle of Least Confusion is a better description of the concept, since there will always be some imperfection. My impression was that the diameter of the CoC does not change with aperture. The angle of the "cone" of light to the point of focus is just flatter with a smaller aperture, hence deeper DoF.

You are right there are an almost infinite numbers of CoC on the sensor/film representing everything in the image including the frequency range of "colors", some in focus other not. CoC also overlap each other, hence suggestion of a near infinite number of CoC.

Yet to understand the behaviors of matters such as this, it helps to isolate only one scenario at a time. Think about the behaviors of waves, where a single point is considered to map out the wave behavior. The same concept applies in this instance.

[biz-engineer]

The simply answer to all this, for me is: the larger the sensor and the more megapixels the better it is for images, but the heavier the equipment, the less usable it becomes and the more expensive it is. The physics come into play, and there is no way physics can be changed. Everything else is mental stretch to keep peace of mind and bank account.

[Ian Stuart Forsyth]

CoC does not change with aperture

Diffraction is what changes the size of the CoC, as you stop down the lens the the larger the CoC will become ignore

[biz-engineer]

Diffraction is what changes the size of the CoC, as you stop down the lens the the larger the CoC will become

I thought the CoC is what we start from from the print size, viewing distance and viewer eyes performance (i.e if the viewer has cataract, the CoC is much larger than if the viewer has 20/20 vision). The we take that print CoC and shrink with sensor enlargement ratio to figure what the equivalent resolution should be on the camera sensor level. Isn't that correct?

[Ian Stuart Forsyth]

I thought the CoC is what we start from from the print size, viewing distance and viewer eyes performance (i.e if the viewer has cataract, the CoC is much larger than if the viewer has 20/20 vision). The we take that print CoC and shrink with sensor enlargement ratio to figure what the equivalent resolution should be on the camera sensor level. Isn't that correct?

Had a little bit of a brain fart here at 3am

CoC and Airy disk mixup

You are correct

[TDvN57]

I thought the CoC is what we start from from the print size, viewing distance and viewer eyes performance (i.e if the viewer has cataract, the CoC is much larger than if the viewer has 20/20 vision). The we take that print CoC and shrink with sensor enlargement ratio to figure what the equivalent resolution should be on the camera sensor level. Isn't that correct?

That is a unique approach, I must say :-)

I suppose you can ride the horse that way too. The only important thing is to get the horse to go to your destination.

[GUB]

but is there really a way to compare lens resolution to sensor pixel pitch ??

and the influence of lenses in resolving details. Since even the best lenses do not have the resolving power of the sensors.

Another person interested in Michail's question.
I think that good lenses easily out resolve sensors - especially taking into account the guesswork of the bayer array. I would love to have some good information to either confirm or deny this.

[biz-engineer]

The problem with how good prints look is a qualitative thing, and it even differs from paper surface to paper surface, paper brand to paper brand. Then people have tried to quantify perceived quality via conceptualization and math. Limiting factors stack on top of each other to lesser how good a print looks, it starts with lens diffraction, lens aberration, pixel density, bayer interpolation, non-ideal post processing, loss of information from raw capture to printable file format (compression), printer resolution ink droplet size, printer speed settings, paper inner surface (how much the ink smear when in contact with paper fibers), and how good is the lighting of the print when it is displayed. So, if you tweak each step to the best possible setting, you end up with an overall better looking print. But it's not like the image become unappealing as soon as you cross the CoC threshold, it's not working like mathematical models.

---------- Post added 30-12-21 at 12:16 ----------

I think that good lenses easily out resolve sensors - especially taking into account the guesswork of the bayer array. I would love to have some good information to either confirm or deny this.

Lens rental has done some lens measurements way beyond conventional 10lp/mm, 30lp/mm and 45lp/mm specified for lenses, he's done test up to 200lp/mm, the results are very interesting: https://www.lensrentals.com/blog/2017/07/experiments-for-ultra-high-resolution-camera-sensors/. The big picture for me is that all lenses resolve best in the center and show bell shapes contrast figures going towards the edges. Shooting square give the best possible enlargement of the short size of the sensor.

---------- Post added 30-12-21 at 12:40 ----------

I suppose you can ride the horse that way too. The only important thing is to get the horse to go to your destination.

The circle of confusion are given for normal viewer looking at a 8x10" print from 15" distance. So if you use these circles of confusion to determine how large you can print, all you can print (in principle) is 8"x10" (approx. A4), in whoch case 6x7 133Mpixels is a total overkill. The way you calculate CoC is based on viewer's acuity, print size and viewing distance, which gives you an approximate number of useful pixel count. https://www.photopills.com/calculators/coc . Take CoC = 2 pixels (bayer interpolation). So for example, according to this calculator , with 645Z, 50Mpixels, corresponds to a 90 x 70 cm print viewed from 25cm and sensor level CoC of 0.011mm (11 micrometer ~ 2 x basic sensor cell geometry) using Zeiss standard visual acuity. If you now take a GFX100, for the visual CoC at 25cm viewing distance to match 2 x pixel pitch, you can print 140x100cm (sensor level CoC = 0.007mm), assuming no diffraction and a perfect lens without any aberration corner to corner, AND assuming the subject matter contains details/edges at the limit of camera system resolving power (moving clouds and moving water in seascapes can be printed super large even from an entry level ILC camera, given that the image is up-sampled to avoid pixelation).

[ProfessorBuzz]

I feel late to the party!

2. I corelated some calculated data with known published data and found some discrepancies, such as the sensor sizes published by Sony versus the same sensor sizes published by the camera manufacturers. The camera sensor size was usually smaller, which I ascribed to the "gutter" edges and unusable edges once the sensor was placed in the camera.

CMOS APS sensors specifications are a bit tricky. You have to refer to the actual data sheet for the sensor. There are "total pixels", "effective pixels" and lastly "active pixels" which are the usuable ones that capture the image. The effective pixels includes the actve ones and additional horizontal and vertical overscan border pixel areas used for reference and diagnostics. Total pixels sometimes include dead, masked, black reference or other pixels.

3. I also found some discrepancies in pixel pitch published versus calculated. These are decimal deviances and I opted to use the calculated data, because I am not designing a camera or optics, but rather developing a basis for easier understanding of concepts compared with other cameras, where decimal deviances will not change the essence of the concepts.

Likely due to the active pixel vs effective/total pixels. I find it best to take the datasheet pixel size (e.g. 3.69um) and multiply by active pixel row/column numbers to get the actual. Note also some manufacturers include dimensions of the whole silicon chip, not the imaging area.

On a side note about 6x7:
I plugged in a fictitious pixel pitch for the 6x7 which then calculated a hypothetical sensor for 6x7. A pixel pitch of 5.31 um (same as 645z) the file size will be 133 mpx with 120 pixels per CoC. At a pixel pitch of 4.60 (same as Hasselblad 100mpx 645FF) the file will be 177mpx (160 pixels per CoC).

This looks as if the 6x7 at 5.31 pixel pitch 133mpx is within reach of existing technology.

The IMX161 in the 645Z has a pixel pitch of 5.30um. For a simple listing, visit this Wikipedia page (and it is correct for the 161): https://en.wikipedia.org/wiki/Exmor

I would always prefer a larger sensor with a modest pixel pitch, preferably closer to Farrel's ideal sensor size, even though their assessment probably needs an update.

Thanks for the link to the SPIE FFK paper - really dated examples in there considering how fast the tech has matured in just 15 years! The article mentions ImagEval.com which was founded by Farrell and Brian Wandell. The domain is gone, but the software lives on: Home · ISET/isetcam Wiki · GitHub


A big issue (especially for astronomers and low-light photographers) is the electron well depth of the pixel. Bigger pixels hold more charge, so you can do longer exposures and collect more photons. This gives more range.

There's also the problem of oversampling/undersampling - bigger pixels are better suited to longer focal lengths.

Astronomers often refer to the Sparrow diffraction limit (Rayleigh, Abbe, then Sparrow) which is were 2 point sources of light can be distinguished. It's even tighter than the Abbe, at d = 0.47/(n sine theta).
Ref: https://articles.adsabs.harvard.edu/pdf/1916ApJ....44...76S



Enjoyed your analysis. I like bigger pixels and lots of them.