## A visual demo on the equivalence of small and large sensors

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rjlittlefield
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### A visual demo on the equivalence of small and large sensors

Recently the issue of DOF versus sensor size has resurfaced in another thread.

As it happens I have handy some old images that may help explain the issues.

Here is a test setup. It consists of a target chart, surrounded by a wire frame with two sides that converge in a convenient point to place the entrance pupil for a couple of different camera setups that have very different sensor sizes.

In operation, one positions a camera so that it sees both of those wire sides end-on, while adjusting zoom so as match framing between the two cameras. Then one sets whatever f-number is needed to run the test, and takes a picture.

Comparing pictures allows one to test various theories about the relationship between f-numbers, sensor size, and DOF.

For the test shown here, the two cameras were:
• Canon Digital Rebel (300D) sensor size 27.3mm diagonal, aspect ratio 3:2
• Kodak DC4800 sensor size called "1/1.8in", actually 8.88mm diagonal, aspect ratio 3:2
The ratio of sensor sizes (linear dimensions) is 27.3/8.88 = 3.07.

Here are three pictures from the archives (2005 in this case):

Comparing images 1 and 2, it is very apparent that the large sensor camera has much less DOF when the lens is set to the same f-number.

But comparing images 2 and 3, it becomes apparent that the large sensor camera develops the same DOF when the f-number is scaled in proportion to the sensor size.

Therein lies the essence of the equivalence. When both cameras are shooting the same subject frame size, and both images are scaled to the same final magnification, then DOF is matched when effective f-number is scaled in proportion to the sensor size.

As standard optics formulas will show, this also results in the same Airy disk size with respect to the subject, so both final images have the same amount of diffraction blur.

I hope this helps.

--Rik

Justwalking
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### Re: A visual demo on the equivalence of small and large sens

rjlittlefield wrote:Recently the issue of DOF versus sensor size has resurfaced in another thread.

As it happens I have handy some old images that may help explain the issues.

I hope this helps.

--Rik
Note. This demo far away from macro range and math behind is very different. That's why it is impossible to take same Dof in range close to 1:1 and above on FF and crop relative to sensor size.

A lens is likely to be diffraction-limited when a large depth of field is required; the larger the format, the more it must be stopped down; hence the more likely it is to be diffraction-limited.
Once a lens is diffraction-limited its resolution is inversely proportional to its f-stop.
Last edited by Justwalking on Sun Aug 19, 2018 1:23 pm, edited 1 time in total.

JohnyM
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### Re: A visual demo on the equivalence of small and large sens

Justwalking wrote: Note. This demo far away from macro range and math behind is very different.
Please, explain how DOF formula is different in "macro range". Please explain what is "macro range". Please quote a reference on this or provide your calculations and experiments.
Justwalking wrote: A lens is likely to be diffraction-limited when a large depth of field is required; the larger the format, the more it must be stopped down; hence the more likely it is to be diffraction-limited.
Once a lens is diffraction-limited its resolution is inversely proportional to its f-stop.
Please explain how one lens (lets assume it's... diffraction limited... which means aberrations free) can provide shallow DOF and "high" resolution, while other lens provide large DOF and equal resolution. Again, please quote a resource or provide your experimental data.

Thank you.

Justwalking
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### Re: A visual demo on the equivalence of small and large sens

JohnyM wrote:
Justwalking wrote: Note. This demo far away from macro range and math behind is very different.
Please, explain how DOF formula is different in "macro range". Please explain what is "macro range". Please quote a reference on this or provide your calculations and experiments.

Thank you.
Macro range when magnification close to 1:2 and higher,
When distance to the object close to lens focal lenght.

This is standart formula based on hyperfocal distance.
(Exerption from wiki)

Let s be the distance at which the camera is focused.
When s is large in comparison with the lens focal length.
Thus, for a given image format, depth of field is determined by three factors: the focal length of the lens, the f-number of the lens opening (the aperture), and the camera-to-subject distance.
___________________________________________________________

When the subject distance s approaches the focal length, using the formulas given above can result in significant errors.
For close-up work, the hyperfocal distance has little applicability, and it usually is more convenient to express DOF in terms of image magnification. Let m be the magnification; when the subject distance is small in comparison with the hyperfocal distance,
so that for a given magnification, DOF is independent of focal length.

Justwalking
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### Re: A visual demo on the equivalence of small and large sens

JohnyM wrote: Please explain how one lens (lets assume it's... diffraction limited... which means aberrations free) can provide shallow DOF and "high" resolution, while other lens provide large DOF and equal resolution. Again, please quote a resource or provide your experimental data.

Thank you.
DoF is not the function of the lens itself if it is not microscope objective with
fixed WD etc parameters. It depends of projection size and other many things including pixels density on sensor that is not lens at all.

JohnyM
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OK. What "close to 1:2 and higher" means? What does "distance to the object close to lens focal lenght" means?
DoF is not the function of the lens itself if it is not microscope objective with fixed WD etc parameters. It depends of projection size and other many things including pixels density on sensor that is not lens at all.
For sake of this discussion, lets assume that both mentioned lenses are NOT sensor limited. Or that image is projected on matte glass with very fine grain and we're skipping sensor as part of imaging system. My question still stands:
How one lens can provide shallow DOF and "high" resolution, while other lens provide large DOF and equal resolution. Again, please quote a resource or provide your experimental data.

Additionaly now, how exactly does a MICROSCOPE OBJECTIVE differs from the lens you have in mind.

Thank you.

Justwalking
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Last edited by Justwalking on Wed Aug 15, 2018 5:20 pm, edited 1 time in total.

Justwalking
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Lou Jost wrote:Justwalking, my trust in Rik's understanding of DOF is based on (among other things) the fact that his depth of field tables which he constructed from theory match my experience (and everyone else's) when stacking, where knowledge of DOF is critical to get the correct step size.

Lou, i'm not against your trust and even Rik's table in absolute mm. Only thing i want to say that the difference will be significant when you start to see resized 4/3 frame and FF on the screen and even more with 1/2.3" sensor.
1mm DoF on 36 mm frame and 1mm on 6mm with same FoV of subject looking on monitor screen - big difference.

I hope it help to understand:
http://resourcemagonline.com/2014/02/ef ... eld/36402/
Btw you probably well know the author of the article also.

According to Rik's table 2-A on your link my 0.8X Moritex must give me about 0.35-0.4 mm DoF.... but Oops - you have seen my first thread here. Probably my lens is abnormal for this table. (

ray_parkhurst
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It looks to me like the equivalent image concept is getting in the way of understanding and agreement. There is talk and calculation about sensor sizes and depths of field, but ultimately what matters for the comparison is the final size the image is viewed at. This is what Rik showed in both threads through example, and in the other thread by calculation. For sure this concept is a paradigm shift from the various articles and discussions, but it is critical to understanding why a small sensor can produce the "equivalent" image vs a large sensor.

rjlittlefield
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ray_parkhurst wrote:It looks to me like the equivalent image concept is getting in the way of understanding and agreement.
I disagree.

I think the difficulty is that Justwalking has somehow developed a fanatical commitment to the mistaken idea that small and large sensors cannot possibly capture images that have the same DOF and sharpness. Any evidence to the contrary must therefore be denied, ignored, or re-interpreted, regardless of how ludicrous that effort becomes. It's like trying to convince a flat-earther that he actually lives on a sphere.

But maybe I'm wrong. One more try, coming up.

--Rik

rjlittlefield
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Here is some new material that may help some readers.

What I've done here is to image an 8.5 x 6.4 mm FOV, at NA 0.04, on two sensors that are different in size by a factor of 5.57. To be precise, one sensor is nominal 1/2.5", 5.744 x 4.308 mm, native 4:3 aspect ratio, and the other sensor is fullframe cropped to 4:3 aspect ratio, so 32 x 24 mm.

With this FOV and NA, the maximum usable content of the optical image is around 2400 x 1800 pixels on both sensors, using lambda=0.55um and Nikon's rule of 2 pixels per cycle at diffraction cutoff.

The native resolution of the 1/2.5" sensor is 3072 x 2304, which modestly over-samples the optical image. The native resolution of the FF sensor is 7360 × 4912, which grossly over-samples the optical image. For purposes of visual comparison, I have downsampled the FF image to match the pixel count of the 1/2.5" .

I have also gone to considerable effort to eliminate distracting but irrelevant differences. The same front end optics are used in both cases, differing only in the shape of the aperture. Aperture placement is matched in the two cases, which matches perspective. I've matched exposure and color rendition. The effect is make the resulting captured arrays of pixel values as similar as I can, so as to fully emphasize whatever fundamental effects the difference in sensor size might have.

Here are the images, first as whole frame (4:3 aspect ratio) and then as actual-pixel crops from images of size 3072 x 2304 pixels. (Make your browser window wide or zoom out, to see the images side by side.)

Now, here's the catch. I'm not going to tell you which is which, and the order may be random.

If sensor size matters, then given the 5.57X difference in sensor sizes, it should be immediately and overwhelmingly apparent which is which. But I submit that these two images are so similar that it's very difficult to tell them apart, let alone to clearly label which one goes with each size sensor.

In both cases, the front-end optics facing the subject consisted of an old Pentax-A 50 mm f/1.7 SMC lens, used as an infinite objective, stopped down to NA 0.04 by the addition of a 4 mm diameter external aperture.

The rear-end optics, facing the sensors, were of course different. For the 1/2.5" sensor, the rear-end optics consisted of the built-in lens of the Canon A710 camera containing the sensor, zoomed out to its maximum optical length and set to nominal f/8. In this case the limiting aperture was the iris built inside that lens, which gives a 4 mm diameter entrance pupil as shown below. For the FF sensor, the rear-end optics consisted of a Raynox DCR-150 on bellows, slightly tweaked from infinity focus to match FOV. In this case the limiting aperture was an external iris in M42 mount, adjusted to 4 mm diameter, and positioned with respect to the Pentax front end lens in the same place as the entrance pupil of the A710 optics.

Here is a schematic description of the optics, together with calculations of their effective f-numbers and diffraction limits:

To take the photos, I set up as follows:

One last bit of detail, here are photos with scales, of the two different apertures that were used:

The discerning reader will notice that although the two apertures are the same overall size, they are different shapes. The iris built inside the small-sensor camera is hexagonal, while the external iris that I used with FF is almost circular. That difference in shape does in fact cause one clear difference between the two whole-frame images: the far background bokeh is different. I will leave as an exercise for the reader, to use that information to figure out which image is which.

I hope this is helpful to at least some readers. Of course I will happily entertain coherent discussion on this topic.

--Rik

Justwalking
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rjlittlefield wrote: What I've done here is to image an 8.5 x 6.4 mm FOV, at NA 0.04, on two sensors that are different in size by a factor of 5.57. To be precise, one sensor is nominal 1/2.5", 5.744 x 4.308 mm, native 4:3 aspect ratio, and the other sensor is fullframe cropped to 4:3 aspect ratio, so 32 x 24 mm.

With this FOV and NA, the maximum usable content of the optical image is around 2400 x 1800 pixels on both sensors, using lambda=0.55um and Nikon's rule of 2 pixels per cycle at diffraction cutoff.

--Rik
If the DOF is to be the same for both formats the required f-number is in direct proportion to the format size.

You can easily get more Dof at 1/2.5" but you won't because in this case your FF with same FoV and DoF will look too diffraction limited with same MP as on 1/2.5"

So you experiment is not clear. It is about how to show that the dof can looks the same in both cases, but not about maximum Dof you can take on different sensors.
To take it clear you can repeat it with two coins and compare if you want but with same sensor resolution. It must show that math behind is correct, but not your imagination that Dof is independent of magnification.
For purposes of visual comparison, I have downsampled the FF image to match the pixel count of the 1/2.5" .
Is it correct for comparision? This means that downsampling can have the apparent effect of increasing depth-of-field.

About your calculation. That is only show how much counts of Airy disk diameter can be resolved by the sensors at f/8 and f/47 on FF. In both cases ut will be about 500x380 dots.
I did not know where you find the "Nikon Rule" about 4.88. Pixels can be only integer.

Now it is time to calculate the DoF correctly due to your explanation of theoretical ("pixels size matched" but real sensor did not have them) did not say anything about the DoF.

rjlittlefield
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Justwalking, I see that you have returned with all your old confusions intact.

You and I have discussed all this before. Obviously you did not understand it before. I don't expect you to understand it this time either.

But because there may be new people reading this thread, I will take time to explain it again one more time.

You wrote:
If the DOF is to be the same for both formats the required f-number is in direct proportion to the format size.
Excellent! I agree with that statement, assuming that "required f-number" means the effective f-number, from the standpoint of the sensor.

Given that agreement, we should be only one step away from complete agreement. This is because when the effective f-number is in direct proportion to the format size, then the Airy disk diameter is also in direct proportion to the format size. So everything scales together: the image of the subject, the out-of-focus blur circles due to geometry, and the Airy disk blurs due to diffraction. The optical image on the large sensor is identical to the optical image on the small sensor, except for overall size.

From my standpoint, this seems to be a simple concept, well supported by both theory and practice.

But for some reason, you seem to be either unable to understand it, or unable to accept it. I cannot tell which. In either case, you reject all evidence and respond with nonsense.

I tire of this exercise, but I did promise to respond, so here we go.

You wrote:
You can easily get more Dof at 1/2.5" but you won't because in this case your FF with same FoV and DoF will look too diffraction limited with same MP as on 1/2.5"
We can easily get more DOF on either size sensor, by stopping down more. To go along with the more DOF, the increased blurring due to diffraction will also be the same on both sizes of sensor. Your belief that it won't is apparently based entirely on imagination and scrambled math. There is no correct math or physical evidence to support it.
So you experiment is not clear. It is about how to show that the dof can looks the same in both cases, but not about maximum Dof you can take on different sensors.
I guess you imagine that stopping down more would make the FF image blurred, while leaving the 1/2.5" image sharp.

I agree that this particular demonstration is not clear on that point.

But earlier, I showed you the image pair at http://www.photomacrography.net/forum/v ... 033#236033. In that test I stopped down to about NA 0.01. The images clearly showed that both sensors still had the same DOF and resolution, even though both were then obviously limited by diffraction.

Your response then was to deny the evidence of that demonstration also, by claiming that those images were too deep in diffraction!

The pattern seems clear: given any image comparison, you just find some way to deny the evidence in front of your eyes.
For purposes of visual comparison, I have downsampled the FF image to match the pixel count of the 1/2.5" .

Is it correct for comparision?
Of course it is correct.

What would you have me do, compare 36 megapixels on FF against 6 megapixels on 1/2.5"?

I would happily compare 36 megapixels on 1/2.5" against 36 megapixels on FF, if I had a 36 megapixel 1/2.5" sensor to work with.
I did not know where you find the "Nikon Rule" about 4.88.
It seems your memory is as bad as your comprehension. We went over this at http://www.photomacrography.net/forum/v ... 512#235512 . That discussion is too long to reproduce here for your convenience.
Pixels can be only integer.
Of course. But their dimension is arbitrary. "4.88 pixels per Airy disk diameter" really means "Pixel width equal to Airy disk diameter divided by 4.88 ."
Now it is time to calculate the DoF correctly due to your explanation of theoretical ("pixels size matched" but real sensor did not have them) did not say anything about the DoF.
Sure, I'm happy to calculate DOF again.

DOF ~ 2F'c/M^2, where F' - working number, c - circle of confusion, M - magnfication.
Using standard numbers for COC:
on the FF sensor, we have F' = 47, c = 0.030, M = 3.74,
on the 1/2.5" sensor, we have F' = 8.5, C = 0.0054, M = 0.68.

Then running the numbers through the formula:
on FF we have 2*47*0.030/(3.74^2) = 0.20,
and on 1/2.5" we have 2*8.5*0.0054/(0.68^2) = 0.20,
just the same.

These numbers are rounded. If we plug exact numbers into exact formulas (that effort not shown here), again the results are the same.

So even your own math says that the DOFs are identical. Your own math also shows that diffraction blur is identical -- same number of Airy disk diameters across the frame. And anybody with clear eyes can see that the images look the same.

But it seems you are so passionately faithful to the idea that small sensors are magic, you ignore all this evidence and just keep saying "La la la la la, small sensors give more DOF!"

As I told Ray, talking with you about sensor size and DOF seems like trying to convince a flat-earther that he is actually living on a sphere. The effort is pointless, except for whatever insight other people may get from witnessing the conversation.

--Rik

Justwalking
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rjlittlefield wrote:
We can easily get more DOF on either size sensor, by stopping down more. To go along with the more DOF, the increased blurring due to diffraction will also be the same on both sizes of sensor. Your belief that it won't is apparently based entirely on imagination and scrambled math. There is no correct math or physical evidence to support it.
You probably did not understand that Dof formula with magnification just ignore the diffraction effect at all. Even you can get the same Dof large sensor goes much far inside diffraction compared with small.
Your FF diffraction limited f/14.5 not the f/47.
I agree that this particular demonstration is not clear on that point.
I would happily compare 36 megapixels on 1/2.5" against 36 megapixels on FF, if I had a 36 megapixel 1/2.5" sensor to work with.
Easy to compare 16MP FF that exists in real world than to find 1/2.5" 36MP.
Sure, I'm happy to calculate DOF again.

DOF ~ 2F'c/M^2, where F' - working number, c - circle of confusion, M - magnfication.
Using standard numbers for COC:
on the FF sensor, we have F' = 47, c = 0.030, M = 3.74,
on the 1/2.5" sensor, we have F' = 8.5, C = 0.0054, M = 0.68.
Then running the numbers through the formula:
on FF we have 2*47*0.030/(3.74^2) = 0.20,
and on 1/2.5" we have 2*8.5*0.0054/(0.68^2) = 0.20,
just the same.
Yiu have missed that your 1/2.5" sensor Coc is not the 0.0054 but 0.00498 according to pixel pitch and 0.027 for cropped FF.
No matter. It must be around the same in absolute size.
I'm completely agree. Congrats.
Of course that must be the same, but F'=8.5 is not the same as F'=47 for
diffraction effect.
System with your small sensor become diffraction limited at f/5.6 and FF with f/14.6.
f/8.5 compared to f/5.6 and f/47 compared to f/14.6. Do you see the difference? As we know manipulation with resampling also have effect of resizin diffraction blur, so your comparision by picture is incorrect to see
the difference.
But it seems you are so passionately faithful to the idea that small sensors are magic, you ignore all this evidence and just keep saying "La la la la la, small sensors give more DOF!"

--Rik
It's not idea. It's a math.
Yes, small sesor can give in macro same Dof with less diffraction. or more Dof with same diffractioin, or both at same time.
You fail already with pen picture at f/64. Also i can't trust to your last picture with safety match. They do not looks like your previous in parallel thread, sorry.

Rik, I bet you can't take same image with any lens you want on FF when 1/2.5" take the single shot at 2X Mag when you will try it with 11X on FF.
Sure instead i will see from you just La-la-la and that their Dof must be the same and that it is the reason that they must looks the same despite that you will go to around F/100.

Regards.

JohnyM
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Do you realise that 16mpx FF pixel is way bigger than 16mpx 1/X" sensor?
Yes, small sesor can give in macro same Dof with less diffraction. or more Dof with same diffractioin, or both at same time
Only if you use low resolution sensor that is severly limiting overall resolution, yes. Someting like 1mm diagonal 1 pixel sensor, infinite DOF regardless of magnification!

P.S:
Single pixel camera is actually a thing.
https://www.ams.org/publicoutreach/math ... -pixel.pdf