Pixels for use at 4-5X on an APS-sized sensor

nernelly · Post by **nernelly** » Tue Jan 31, 2012 3:36 pm

Admin edit: This thread was originally a series of replies in "Lenses for use at 4-5X on an APS-sized sensor".
As suggested by other members, I have split them off from the original thread because this is really a separate and fundamental topic of its own:
How many pixels are needed to capture all of the detail that various lenses can see in a subject that's roughly 5 mm wide?
The discussion continues...

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Rik, thank you very much for this laborious work! It is indeed an impressive demonstration of the quality of the 10xCFI working at 5x. If I got the math correctly, this combination should really start challenging the 15Mpix APS-C sensor. Do you think that in practice the sensor is really becoming the limiting factor?
STeffen

rjlittlefield · Post by **rjlittlefield** » Tue Jan 31, 2012 4:34 pm

nernelly wrote:If I got the math correctly, this combination should really start challenging the 15Mpix APS-C sensor. Do you think that in practice the sensor is really becoming the limiting factor?

Yes, definitely. Consider the following images captured with the Nikon CFI Plan Achromat 10X NA 0.25 (part number MRL00102):

On the far right, we have what the sensor sees at 10X (through a 200 mm tube lens). On the far left, it's what the sensor sees at 5X (through the 100 mm tube lens), expanded to be the same size as 10X. In the middle, there's what a simulated "perfect" sensor would see at 5X, constructed by taking the 10X image and computationally downsampling it to match the pixel count of the actual sensor.

I haven't checked with this particular lens pair, but I'd be very surprised if the optical image at 5X had much less detail than what we see in the captured image at 10X. Certainly what I've seen in the past is that good lenses have no trouble exceeding sensor resolution. (See for example HERE.)

To my eye, the actual sensor is comfortingly close to the simulated "perfect" sensor, and obviously not even a perfect sensor with this pixel count could capture as much detail at 5X as when the image is optically expanded to 10X.

--Rik

Edit: to clarify some wording and more precisely identify the objective.

nernelly · Post by **nernelly** » Tue Jan 31, 2012 5:27 pm

Wow, great you also had the 10x image at hand. Just to make sure I got it right. When you speak of the "perfect" sensor this means perfect given its specific pixel size. When the next sensor generations will find their ways to our setups image detail at 5x might approach the current state of the art at 10x - while preserving the bigger field of view. Nice prospects :-)
STeffen

rjlittlefield · Post by **rjlittlefield** » Tue Jan 31, 2012 7:20 pm

nernelly wrote:Just to make sure I got it right. When you speak of the "perfect" sensor this means perfect given its specific pixel size.

That's correct. I use the simulated sensor as a cross-check on issues like how much degradation there is from the anti-aliasing filter, Bayer demosaicing process, and so on. A sensor of the same mm dimensions but with four times as many pixels would capture the 5X image with essentially the same level of detail that we currently capture the 10X image.

--Rik

seta666 · Post by **seta666** » Wed Feb 01, 2012 1:43 am

rjlittlefield wrote:
nernelly wrote:Just to make sure I got it right. When you speak of the "perfect" sensor this means perfect given its specific pixel size.
That's correct. I use the simulated sensor as a cross-check on issues like how much degradation there is from the anti-aliasing filter, Bayer demosaicing process, and so on. A sensor of the same mm dimensions but with four times as many pixels would capture the 5X image with essentially the same level of detail that we currently capture the 10X image.

--Rik

I might be wrong but... would not be diffraction the limiting factor then? 40mpx for an APS-C camera sounds like to much.
Would not be better just to removeve the AA filter (which supposedly takes 20-30% of that resolution)
I do like the aproach Fujifilm has taken in his X-1Pro and their new random filter array
http://www.fujifilm.com/products/digita ... /features/

Normally we are working with high effective apertures, so I do not see the point in having a high count mpx camera; the EOS 7D extintion resolution is limited to around f9.8 but will become visible from around f6.5 (a correction of 20-50% more usable f stop can be added because of AA filter)

With my eos 5D mkII I use to downsample images for Zerene Stacker to 17mpx at 5-10X, and use Sraw1 (10mpx) for 40X images and Sraw2 (6mpx) for the few 100X images I have taken

Even with the 10/0.25 at 5X the effective aperture is f10, which is around the limit to get the most of a 10mpx APS-C sensor

In my opinion there are things more important in a sensor than plain resolution like Dynamic Range and ISO
But as I said I might just be wrong

Regards
Javier

rjlittlefield · Post by **rjlittlefield** » Wed Feb 01, 2012 3:35 am

seta666 wrote:Even with the 10/0.25 at 5X the effective aperture is f10, which is around the limit to get the most of a 10mpx APS-C sensor

I'm not sure why our numbers don't agree, but try this.

First see http://www.janrik.net/MiscSubj/2007/Fil ... mages.html, scroll most of the way to the bottom, and see the image that shows f/11 delivers 125 line pairs per mm to the sensor.

Then see http://www.photomacrography.net/forum/v ... php?t=2439 for demonstration that you need around 3 pixels per line pair to avoid significant contrast loss for worst-case positioned detail.

Then do the multiplication: (15 mm * 125 lp/mm * 3 pixels/lp) * (22 mm * 125 lp/mm * 3 pixels/lp) = 46 megapixels.

This line of analysis gives roughly the same answer as the simple downsampling experiment that I described earlier in this thread. If it's wrong, I'll be very interested to hear where I went astray twice.

Where does that number of yours come from, that f/10 is "around the limit" for a 10 mp APS-C sensor? According to http://www.cambridgeincolour.com/tutori ... graphy.htm, a very similar combination of f/11 with an 8 mp sensor would "begin to show diffraction". There's a big difference between softening because the MTF drops below 1 enough to see, and losing the detail entirely because the MTF drops to zero.

--Rik

seta666 · Post by **seta666** » Wed Feb 01, 2012 4:42 am

rjlittlefield wrote:
Where does that number of yours come from, that f/10 is "around the limit" for a 10 mp APS-C sensor? According to http://www.cambridgeincolour.com/tutori ... graphy.htm, a very similar combination of f/11 with an 8 mp sensor would "begin to show diffraction". There's a big difference between softening because the MTF drops below 1 enough to see, and losing the detail entirely because the MTF drops to zero.

--Rik

Rik, I am by no means an expert in this matter as I do think you are; the thing is that a 36mpx APS-C in my opinion is too much
My values come from cambridgeinclour too, second page of that link you just posted

There is an Advanced Diffraction Calculator and shows values for 100% viewing on screen

For a 10mpx x1.6 APS-C sensor (Canon) values are:
Diffraction may become visible at f8.7
Diffraction Limits Extinction Resolution at f10.9
Diffraction Limits Standard Grayscale Resolution f/13.1

For a 18mpx x1.6 APS-C sensor (Canon) values are:
Diffraction may become visible at f6.5
Diffraction Limits Extinction Resolution at f8.1
Diffraction Limits Standard Grayscale Resolution f/9.8

And or a 36mpx x1.6 APS-C sensor (Canon) those values would be:
Diffraction may become visible at f4.6
Diffraction Limits Extinction Resolution at f5.7
Diffraction Limits Standard Grayscale Resolution f/6.9

As Cambridge in colour says "The above values are only theoretical best case scenarios;
actual results will also depend on lens characteristics, demosaicing and subject detail.
Color resolution limits are not listed because these are highly dependent on demosaicing software, image content and color purity; expect these to be at 20-50% higher f-stops for Bayer sensors."

By the way, those links are very good to read; I stll have to go through them few more times as there are loads of information

Regards
Javier

rjlittlefield · Post by **rjlittlefield** » Wed Feb 01, 2012 8:59 am

Javier, thanks for the references. I'll investigate as time permits and see what comes of it.

--Rik

ChrisLilley · Post by **ChrisLilley** » Wed Feb 01, 2012 9:30 am

To add some Nikon values:

12.1 MPx 1.0 crop (Nikon D3S)
f/12.7 Diffraction May Become Visible
f/15.9 Diffraction Limits Extinction Resolution
f/19 Diffraction Limits Standard Grayscale Resolution

16.2 MPx 1.0 crop (Nikon D4)
f/11 Diffraction May Become Visible
f/13.7 Diffraction Limits Extinction Resolution
f/16.4 Diffraction Limits Standard Grayscale Resolution

10.2 MPx 1.0 crop (Nikon D200)
f/9.1 Diffraction May Become Visible
f/11.4 Diffraction Limits Extinction Resolution
f/13.6 Diffraction Limits Standard Grayscale Resolution

24.5 Mpx 1.0 crop (Nikon D3X)
f/8.9 Diffraction May Become Visible
f/11.1 Diffraction Limits Extinction Resolution
f/13.4 Diffraction Limits Standard Grayscale Resolution

16.2 MPx 1.5 crop (Nikon D7000)
f/7.2 Diffraction May Become Visible
f/9.1 Diffraction Limits Extinction Resolution
f/10.9 Diffraction Limits Standard Grayscale Resolution

edit: these numbers are wrong because the D800 is full frame. Numbers left, because follow-on discussion referred to them.

36 MPx 1.5 crop (Nikon D800)
f/4.8 Diffraction May Become Visible
f/6.1 Diffraction Limits Extinction Resolution
f/7.3 Diffraction Limits Standard Grayscale Resolution

correct numbers

36 MPx 1.5 crop (Nikon D800)
f/7.4 Diffraction May Become Visible
f/9.2 Diffraction Limits Extinction Resolution
f/11 Diffraction Limits Standard Grayscale Resolution

seta666 · Post by **seta666** » Wed Feb 01, 2012 11:53 am

Also, could the confusion be caused by the way we look at line pairs?

If line pairs overlay should be something like this, right?

and if they do not should look like this

I may just be completely wrong again, but I do not remember seeing any drawing explaining it
Regards
Javier

Charles Krebs · Post by **Charles Krebs** » Wed Feb 01, 2012 2:35 pm

I'm going to throw a question or two into this discussion. (This is strictly in regard to "resolution", not other potential advantages/disadvantages of pixel dimensions). I'll refer to two cameras chosen from ChrisLilley's list, same sensor size but very different pixel density:

CAMERA "A"
10.2 MPx 1.5 crop (Nikon D200)
f/9.1 Diffraction May Become Visible
f/11.4 Diffraction Limits Extinction Resolution
f/13.6 Diffraction Limits Standard Grayscale Resolution

CAMERA "B"
36 MPx 1.5 crop (Nikon D800)
f/4.8 Diffraction May Become Visible
f/6.1 Diffraction Limits Extinction Resolution
f/7.3 Diffraction Limits Standard Grayscale Resolution

Let's look at the "Diffraction may become visible" number... f/9.1 for "A" and f/4.8 for "B". I've read discussions (elsewhere... not in our bastion of knowledge

) where people will assume that camera "B" will look much worse than camera "A" if both are shot in the same situation at f/9.1. My impression is that "B" will not look worse, it is just that at f/9.1 you are not taking advantage of the higher pixel density and thus potential resolving power of the sensor. (In other words, camera "B" has the capability of recording far more detail than camera "A", but when you are at f/9.1 you are effectively giving up that potential increase in resolution due to diffraction.... you just don't really need more pixels than "A" has). With camera "B" you may be flogging yourself, your computer storage, and processing time by having more "pixels" than can be utilized to produce additional detail, but you are not really sacrificing final image resolution.

But with camera "B", when the optics and situation is such that you can make use of the higher resolution potential, you can get images that show detail that could not be recorded with camera "A".

Is my thinking correct?

For my microscope cameras this is an extremely pertinent question. With a 1.67X projection photo-eyepiece I could make good use of a 27Mp APS sensor with a 4/0.20 Plan Apo objective. With a 100/1.30 objective I would only really need 1.8Mp on an APS sized sensor! (This puts the same number of pixels (3) across the smallest resolvable detail.

g4lab · Post by **g4lab** » Wed Feb 01, 2012 3:13 pm

I will leave your question for Rik to answer definitively but I think you are correct.

There is a calculator for such things at diagnostic instruments dot com.

The number of pixels required by a digital camera in order to use all the resolution availble in various objectives is shown on a table. It is not terribly intuitive either.

http://www.spotimaging.com/iq/SpotLight ... sSep06.pdf

http://www.spotimaging.com/iq/imaging_concepts.html

seta666 · Post by **seta666** » Wed Feb 01, 2012 3:21 pm

Charles Krebs wrote:
Let's look at the "Diffraction may become visible" number... f/9.1 for "A" and f/4.8 for "B". I've read discussions (elsewhere... not in our bastion of knowledge ) where people will assume that camera "B" will look much worse than camera "A" if both are shot in the same situation at f/9.1. My impression is that "B" will not look worse, it is just that at f/9.1 you are not taking advantage of the higher pixel density and thus potential resolving power of the sensor. (In other words, camera "B" has the capability of recording far more detail than camera "A", but when you are at f/9.1 you are effectively giving up that potential increase in resolution due to diffraction.... you just don't really need more pixels than "A" has). With camera "B" you may be flogging yourself, your computer storage, and processing time by having more "pixels" than can be utilized to produce additional detail, but you are not really sacrificing final image resolution.

But with camera "B", when the optics and situation is such that you can make use of the higher resolution potential, you can get images that show detail that could not be recorded with camera "A".

Is my thinking correct?

For my microscope cameras this is an extremely pertinent question. With a 1.67X projection photo-eyepiece I could make good use of a 27Mp APS sensor with a 4/0.20 Plan Apo objective. With a 100/1.30 objective I would only really need 1.8Mp on an APS sized sensor! (This puts the same number of pixels (3) across the smallest resolvable detail.

Camera B will never look worse than A, but there won't be any resolution benefit either when working with high efffective apertures; I can see a beneffit when working with a 1X lens like the Rodagon-D 75/4 wide open

Well, I think in macro we normally work with effective apertures higher than f9.1 Mitutoyos 5X and 10X work at f18 at their designed magnification. So in my opinion camera "A" will be enough for 95% of our macro work.

Even the 4/0.20 works at effective aperture of f10 at 4X so I do not understand your numbers with the 4/0.20. Adding the 1.67X photo eyepiece has the same effect (or pretty similar) as adding a 1.7X teleconverter, right? so effective apperture should rise by 1 stop or so

Regards

nernelly · Post by **nernelly** » Wed Feb 01, 2012 3:39 pm

I think there might be two points mainly contributing to the big difference in Mpix numbers mentioned above: 1) different resolution criteria and 2) the potentiation when converting pixel size into Mpix count.

This reference discusses many relevant aspects of the topic http://luminous-landscape.com/tutorials ... tion.shtml. At the bottom it presents optimal pixel sizes for two different scenarios based on different resolution criteria (table 2, columns (3)&(4)). The optimal pixel sizes given for e.g. f/11 would be in case A) 7.4mu, in case B) 3.7mu (for green light). Converting these numbers to pixel counts on an APS-C sensor results in A) 7Mpix (cf. table 3) and B) 28Mpix.

The important difference between the two scenarios is the resolution criterion applied. Case B) seems to correspond to the classical Rayleigh criterion (cf. figure 5). This requires a separation between two airy discs that is by a factor 2 smaller than the one used in case A) (cf. figure 7). This factor gets transferred into the optimal pixel sizes and squared when calculating the Mpix count.

Hope I got this right (and comprehensible). Already quite late here...

seta666 · Post by **seta666** » Wed Feb 01, 2012 3:53 pm

nernelly wrote:Hope I got this right (and comprehensible). Already quite late here...

thank you, another nice article I will have to calmly read