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Measurable values are for the birds. Give us subjective pictures. (*sic)

-Josh

Thanks for the math Barry. I've seen this discussed with numbers in the past, but have always hoped to see a field test with side by side comparisons of each sensor size DoF. Although, I've shot with most and have a pretty good idea what it would look like, but still think it would be nifty to see.

"For a 1/3" camera to match to 2/3" - open up 1 2/3 stops."

That isn't much difference. The other factor is the length of the lens. I've always thought that with only an 8x zoom the fixed scarlet isn't going to beat an A1 in DOF with a 20x zoom.

In fact, my rough calculation before was that an 8x fixed Scarlet at full zoom is about the same as an A1 at 3/4 zoom (16x) at the same aperture. Or at the same zoom its 1 2/3 stops different albeit with a change in the FOV. Not a huge difference.

Of course 1/3" sensors with only 10-14x zoom will be beaten in DOF control by the Scarlet all the time.

If that's right then an A1 will beat a fixed scarlet for DOF control at the far end of the zoom, if you have the room to back up.

Another factor is whether the A1, which goes to f1.6, will go wider than the Scarlet fixed. I heard a rumor of T3, which is about f2.8. Thats approximately a stop and a half and DOF difference is listed here as 1 2/3, which is pretty close right off the bat. That would make wide angle DOF very close in both cameras, and the tele DOF better on the A1.

The Scarlet fanbois will probably be sharpening their pitch forks and getting out their torches for that statement, but resolution should be another matter.

Nice concise article Barry.

Just to get a little more clarity (pun intended) on how you derived the CoC figures, what numbers did you use for viewing resolution and magnification calculations?

The formula I've seen for the CoC calculations is: ( 1 / Viewing Resolution ) / ( Print Size / Image Size ) which of course the denominator being Magnification Ratio or Print Size / Image Size or Image Diagonal.

Just guessing, but looks like you may have used the conventional 5 line pairs of viewing resolution at 250mm viewing distance?

For 35mm FF, that would translate to: ( 1 / 5 ) / ( 250 / 43.3 ) = roughly .03 or exactly .03464 for the CoC.

Is that correct?

Thanks,

The analogy to analog photography is a little complex. DOF in distance units is different from the DOF LOOK differences which Barry calculated.

In analog photogaphy an infinite projection resolution is assumed (not true for pixel based digital displays) and resolution is limited by viewing distance (our vision). The DOF equations calculate the area of acceptable sharpness and not the DOF LOOK.

These cameras all have different resolution, even if the sensor size is the same. If you assume that the material from each camera is viewed at its native resolution, the COC which has to be connected to the pixel size in digital cameras, can be 1 pixel or 0.5pixel depending on what you accept as sharp. It also has to be lowered if the viewing resolution is lower, because once the material is sharp enough for the delivery resolution, the image is as sharp as it will get. So, we have to use different COC for each camera, even if the sensor size is the same. As an example, a 2/3" sensor could be 1920x1080 and another 720x405 SD. The 1080p camera has a smaller COC and a shallower DOF in distance units. But the LOOK of dof is identical if you scaled both focal length and relative aperture by the crop factor. The out of focus circles have the same diameter. But the in focus area which DOF quations calculate is different.

If you project these two cameras on a 720x405 screen you will get the same DOF and the same DOF LOOK.

If you project these two cameras on a 1080P screen, you will get different DOF but the same DOF LOOK.

Things are very simple, if we ignore the camera resolution and the DOF in distance units, and focus on the DOF look. This is what Barry effectively did. Assuming a COC for one sensor size, scale the COC for the other sensor sizes.

But what is a COC of 0.03mm? For a full frame sensor it represents 36/0.03=1/1200 of the screen width. It is 675lines PPH in 16:9 which is indeed quite sharp. But what about the 1080p and 4k cameras with 2k lines PPH and an ultra sharp lens? The COC must change.

For full frame 1080p cameras and near distance 1080p projection a coc of 0.01875 is a true 1080p. It represents an accetable sharpness of 1 pixel diameter which is a blur radius of 0.5 pixel. For a 2/3" there is a 36/9.6mm=3.75 crop factor, so it should be 0.01875/3.75=0.005mm which is the same with the pixel size of a 1080p 2/3" sensor.

Digital cameras projected at their native resolution have a COC equal to their pixel size. This represents the maximally sharp area in the native resolution. For 1080p delivery and comparisons, I recommend a COC of 0.01875/CropFactor where crop factor is 36mm/SensorWidthInMM.

For DOF LOOK comparisons (what Barry was after) the COC is not important at all, as long as the one chosen for full frame is scaled for the different sensor sizes (by the crop factor if full frame is the base size).

My goal was equating the look of the DOF based on the different sensor sizes, using a common viewing size, as Otis has elucidated. I was trying to deliver an effective simulation of how to make one camera look like another, and what the f-stop differences are needed to accomplish that.

Thanks Otis/Barry, very interesting discussion...

Otis, what I was ultimately trying to do is 'back into' or reverse-engineer the 'common viewing' size used for the calculations just for reference.

Barry, I apologize if I missed it, but what did you use for the common viewing size?

Thanks again for the info Otis/Barry...

It doesn't really matter what the common viewing size is, because the amount of relative magnification will always be the same. So the amount of f-stop compensation is the same.

But, with that said, it was based off the theatrical projection size, which is what 35mm film's Circle of Confusion is always calculated for.

Viewing size is relative itself In still photography, there are different standards.

Human viewing provides a luma resolution of about 1 linepair per 2 arcmininutes. This is 1 pixel per minute of angle of view, which is 60 pixels for each degree of angle of view. This is scientifically accepted and Kodak and others use it. It is more demanding than the standards for still photography by Zeiss and others. The chroma resolution is usually accepted as being 1/2 that of luma since the relative bandwidth of chroma is Y:RG:YB = 8:5:3.

So a 1080p is good for 1920/60=32 degrees horizontal angle of view. This is a distance of 1.5*ScreenDiagonal. 60 inches for a 40" TV, 15meters for a 10meter diagonal 16:9 projetion etc. The color resolution is half that so 4:2:0 will do the job at this distance if there are no artifacts (alias or compression).

THX theaters require a minimum angle of view (furthest seat) of 26degrees and recommend 36degrees. The best seat in the house is roughy 45 degrees. Seating there, one can aproximately resolve a 2700x1148 luma and 1350x574 chroma. In a 16:9 projection, that is 2041x1148 and 1020x574 which is 16:9 2K 4:2:0. The COC for this would be 0.01764 but good luck finding a theater that can actually output an image of this quality

It is probably a surprise to many that the old 1080p standard in 4:2:0 distribution covers 94% of the human resolution capabilities in a 16:9 THX projection and 71% even if you crop the 16:9 1080p to scope.

The actual resolution visible in cinemas is even lower, because THX uses 16 foot lamberts which is only about 54nits of brightness in a dark room and the low brightness limits resolution even after the eye adjusts (try evaluating noisy video in 20% and 100% brightness on a display). Then you need to add the losses on the projection system which is not ideal (about 700lines PPH in most theaters in one study due to optical issues). Setting an office display or true 1080p broadcast monitor to typical brightness (200nits and more sometimes) and sitting at normal distance (closer than 1.5xscreen diagonal), shows a lot more than will be visible in a theatrical projection. In simple words, pixel peeping a monitor is not representative to the resolution of a theatrical projection, that's why even 720p 4:2:0 looks better than it ought to look when projected theatrically. You will not see more just because the projection size is larger, only angle of view is important.

A COC of 0.03 for full frame is 675lines PPH, so Barry is both conservative and realistic on that choice.

Thanks again Otis, that is some really great practical information. I rarely get deep into pixel peeping but it definitely pays to know the science and math behind the technology and helps to keep things in the right 'perspective' when shooting :-)