Sensor size vs max DOF

Yes but then you need a 150mm macro to replace the functon of your 100.

or even worse, how would I replace the functionality of my 150mm macro?  Can you imagine the cost of a 240mm f/2.8 macro lens

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Stop it! You're messing up my carefully constructed rationalization.

And I would need a 500/4 to replace my 300/4.

It's all just to expensive.....

A quick google search:
http://www.answers.com/aperture&r=67

Aperture can be stated in units of length. It's perfectly correct to give an answer "5mm" when asked what aperture was set on a shot. Of course, no photographer would ever say it that way. It's also correct to give it in F-numbers which is the ratio of the focal length to lens diaphragm opening. When stated that way an aperture setting at a given F-number will give the same exposure rate independent of lens focal length or sensor size.

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yes, same f-number = same exposure, as we are dealing with f-numbers when we shoot and, more important here, when we calculate DOF. That was my point.

 
If magnification is not a functon of sensor size, what is your defination of magnification.  My defination of magnification is sensor size / subject size.  Clearly a function of  sensor size.

For example the subject is an 11mm shrimp.  On a small sensor camera this is 22/11 or 2:1.  But on a large sensor camera this is 36/11 or ~3:1 

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1:1 or 2:1 defines the relation between real world size and size on the sensor, not the final print. A smaller sensor does not magnify – it’s “just” cropping. Eric stated in the 5D thread he could put tape on his sensor leaving a small surface in the sensor's centre uncovered. By wrong definition, he would get 5:1 or something:
http://wetpixel.com/...indpost&p=61817

You are right that you need a lens with higher magnification / reproduction ratio in order to fill a full frame (35mm) with the same subject. This is important in order to find out what real life size would fill the frame for the final print. But 1:1 stays 1:1 in terms of optical magnification. And that's what goes into the formula and determines how many millimetres DOF you get. Cropping doesn't change the reproduction ratio / magnification. You don't change the DOF when cropping an image with Photoshop. No difference to what a smaller sensor does all the time compared to full frame (being exactly, DOF would change a little bit if you print a cropped image on the same print size as COCs change a bit, but this has nothing to do with the magnification / reproduction ratio).
As written in the 5D thread:
http://wetpixel.com/...indpost&p=61279

Well then even if it wouldnt work in real life, which effect in theory should be stronger?

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I haven't worked it out. It depends what value of COCs you use for the different sensors. Classic film way would be ~ 0,03mm for 35mm recording surface.
Formula: circle of confusion = sensor/film diagonal (43,27mm for 35mm film) divided by 1500. For a Canon APS-C sensor, this would give ~ 0,018mm. But this is "just" the value when looking at a certain size of print from a certain distance giving the viewer a "sharp" image within the defined DOF. But you won't see the same sharp image if you look at a 13 megapixel image in Photoshop in detail or at a real large print.
You can also use the pixel pitch as COC value. Not easy to state an overall law if you for example compare a 6 megapixel APS-C camera vs. a 13 megapixel 35mm sensor camera and want to give recommendation on effective DOF limits in regards to the different resolutions.

You have to be careful in how you ask the question. Craig Jones and I went back and forth on this awhile back and I think we've managed to converge on the way to look at this question. The best way to look at it is to ask, for the same subject, eg. a 1 cm nudi, a same final print, eg. 24x16", the same diffraction limited resolution, eg 1500 lines across the frame, which sensor has an advantage. For a given resolution, the larger sensor uses a smaller aperture for the same diffraction limited resolution, and this more than offsets the longer focal length lens needed to get the same FOV. The larger sensor has a slight advantage.

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I know that my above statement contradicts to a definition with fixed COCs (adapted to sensor size) as you have mentioned. But I think the different resolutions (6 vs 8 vs 12 MP) and print sizes call for taking different COCs into account. You are absolutely right if you point out the DOF relation based on the same COCs on the final print and provide a comparison between sensor sizes in general. But I think, if you have a 12 MP camera, you want the images to look sharp within DOF @12MP, not just @6MP or whatever. So I would take the used camera into account.
I know my point of view is not very academic. But I have experienced (especially when determining COCs for hyper focal distances) that standard film values like 0,03mm won’t lead to the best results in real life. Especially not if you take a digital camera outresolving film. And even with largely projected slides 0,03mm is kind of weak.
Beside providing an answer which sensor size has an advantage in terms of DOF in conjunction with macro in general, I think it’s difficult to translate this into real life shooting as we are shooting with different resolutions (COCs).

Julian

1:1 or 2:1 defines the relation between real world size and size on the sensor, not the final print. A smaller sensor does not magnify – it’s “just” cropping. Eric stated in the 5D thread he could put tape on his sensor leaving a small surface in the sensor's centre uncovered. By wrong definition, he would get 5:1 or something:
http://wetpixel.com/...indpost&p=61817

You are right that you need a lens with higher magnification / reproduction ratio in order to fill a full frame (35mm) with the same subject. This is important in order to find out what real life size would fill the frame for the final print. But 1:1 stays 1:1 in terms of optical magnification. And that's what goes into the formula and determines how many millimetres DOF you get. Cropping doesn't change the reproduction ratio / magnification. You don't change the DOF when cropping an image with Photoshop. No difference to what a smaller sensor does all the time compared to full frame (being exactly, DOF would change a little bit if you print a cropped image on the same print size as COCs change a bit, but this has nothing to do with the magnification / reproduction ratio).

We both agree on this equation magnification = sensor size / subject size

But you are intrepreting it wrong. Magnification is dependent only on sensor size and subject size. The lens you used to make this happen does not matter.

You are jumping to maximum magnification possible. This is a function of lens used and not sensor size or subject size. This is uneffected by changing sensor size. But that is not the same as magnification.

Changing sensor sizes does not change the maximim magnification possible, but it does change the magnification if the subject remains the same.

Not easy to state an overall law if you for example compare a 6 megapixel APS-C camera vs. a 13 megapixel 35mm sensor camera and want to give recommendation on effective DOF limits in regards to the different resolutions.
I know that my above statement contradicts to a definition with fixed COCs (adapted to sensor size) as you have mentioned. But I think the different resolutions (6 vs 8 vs 12 MP) and print sizes call for taking different COCs into account. You are absolutely right if you point out the DOF relation based on the same COCs on the final print and provide a comparison between sensor sizes in general. But I think, if you have a 12 MP camera, you want the images to look sharp within DOF @12MP, not just @6MP or whatever. So I would take the used camera into account.
Julian

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Yes to determine which format is ideal you should be comparing cameras of equal MP. But if it is to much to handle it as theoretically you can use a real example. Comapare the 1Ds with the D2x. Two 12mp cameras with different sensor sizes.

We both agree on this equation  magnification = sensor size / subject size

No, we don't
again, reproduction ratio / magnification is completely independent from sensor size.
If you shoot a critter of 2mm x 2mm @1:1, then it is 2mm x 2mm on your sensor, no matter if your sensor size is 10 x 10mm or 50 x 50 inches.

You can state that an APS-C sensor is filled by a smaller subject than a bigger sensor, but this has nothing to do with reproduction ratio (1:1 for example).
It's only useful for knowing what small critters you can photograph filling you entire sensor.
But we are dealing with DOF here which is dependent on reproduction ratio (Higher magnification = less millimetres DOF). And therefore you have to take the true optical lens' reproduction ratio into the formula.

But if it is to much to handle it as theoretically you can use a real example.  Comapare the 1Ds with the D2x.  Two 12mp cameras with different sensor sizes.

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I understand this is what Herb has worked out, based on "classic" COCs (predicted by the sensor size only, not the camera's resolution / pixel pitch).

Julian

Hi Andy,

That would work if the small sensor cameras could achieve high f-stops, but because of the effects of diffraction, all of them go to a max of F11

So, the short focal length helps, but imagine a 10.5mm fisheye photo shot at f22...That's some serious DOF.

Cheers
James

PS, I agree that it's the photographer that matters, equipment aside. On the other hand, it's important to pick the right tool for the job, and that's what this thread is about. "Talking technical" is important, and doesn't demean the photographer's vision, or the art, but that's just my opinion.

It’s not about the camera but about the photographer’s vision in capturing time and light. 

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Bingo!

PS, I agree that it's the photographer that matters, equipment aside.  On the other hand, it's important to pick the right tool for the job, and that's what this thread is about.  "Talking technical" is important, and doesn't demean the photographer's vision, or the art, but that's just my opinion.

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I completely agree that the right tool helps! But I think that a great misconception out there (especially in these days of annual new camera announcements) is that a better camera will make you a better photographer. Bottomline, a fast, high resolution, accurate and expensive camera will certainly help us take technically perfect photos. Now, what we all strive to obtain (I think) are artistic eye-grabbing photographs that reflect the beauty of the underwater world; the closer to technical perfection those photographs are, the better.

Since Herb wisely suggested that number mavens not stomp on Rand's lovely thread:

<nerd>I shoot whenever I can, and dink around with equations when I can't.

I don't think it makes sense to compare DOF of a cropped sensor to a FF sensor at the same distance. I think it's more reasonable to use the same FOV. If you buy that, then the greater sensor-object distance increases DOF for the cropped sensor, partially (but usually not fully) offsetting the larger minimum aperture size for the smaller COC on the little sensor. Of course, this also changes the magnification (less for the little sensor), but to me it makes more sense to hold composition constant when making these comparisons. You are free to disagree, of course.

It's an interesting fact that all focal length lenses have the same DOF for the same FOV -- WA or tele (for the same format and f-stop). If you step back far enough with a 200mm to get the same view as a 14mm, the DOF at the subject plane will be identical. Really.</nerd>

PS, I agree that it's the photographer that matters, equipment aside. On the other hand, it's important to pick the right tool for the job, and that's what this thread is about. "Talking technical" is important, and doesn't demean the photographer's vision, or the art, but that's just my opinion.

Sure but I think we're beyond the point of diminishing returns here. All the current DSLRs provide a system of tools to make to quality images. The differences are miniscule and shouldn't hinder a creative photographer from acheiving his/her vision.

Having seen this debate go back and forth I'm convinced that whatever little difference there is here, it is insignificant compared to other factors that make a great photo.

Don't get me wrong, I love gear for gear's sake but I won't go so far as to confuse my gear lust with what is needed for taking great photos.

I agree in principle about photographic tools.

However, what the current discussion gets right down to, and one of the main points of the discussion in the other thread is that you get .25 inches of DOF with one system and .5 with the other - retaining the same level of sharpness. If you're shooting super-macro, that is a HUGE advantage for the latter system.

It has nothing to do with the photographer's creative abilities - it's the difference between having the subject in focus or not.

Cheers
James

you get .25 inches of DOF with one system and .5 with the other - retaining the same level of sharpness. 

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That's true at the same MAGNIFICATION (who cares?) but not with the same COMPOSITION. The constant-composition calculations (which, I admit, are more complicated) give a much smaller (circa 50 vs 100%) advantage to FF. (You have to recompute distance to preserve the fraction of the diagonal filled in various formats -- always causing you to move back / increase DOF in cropped sensor vs FF cameras, for a given f-stop; then, the effect of larger critical <diffraction> aperture is partly offset by larger distance to object).

CDW

Keep in mind that backing up to achieve the same composition has other consequences underwater.

Cheers
James

I put in some numbers awhile ago and forgotten all about it. So I went back and did it again. A good place to start is the photo.net lense tutorial:

http://photo.net/pho...cs/lensTutorial

I'll first skip to the bottom line for those not so interested in the nerdy equations, and write the equations at the latter part of this post. For a 36mm subject that fills the frame, 1:1 in FF format, 1:1.5 in dx format, the FF sensor has 1.2x DOF of the dx sensor. For this subject at F/22, DOF is 2.64mm for FF. To get the same diffraction limited resolution the dx camera should have the F-stop set to 15 and will have DOF of 2.2mm, not a big difference. These results are independent of the focal length of the lens.

For the shots that Rand was showing us from a 1:1 lens with a 2x teleconverter, the magnification is 2. He shot at F/25, assuming this already takes the teleconverter into account, the DOF is 0.75mm. To get this much DOF, Rand gives up about half the resolution that his 12Mpixel camera is capable of imaging. Had he used a FF camera at F/38 he would have gotten a whopping 1mm DOF, a 33% difference. He would need a lens with 1.5x better magnification to do it.

Here're the calculations. From the photo.net lens tutorial, for macro subjects

DOF = ( c N / M ) * ( 1 + 1/M )

where c is the circle of confusion (about 0.03mm for FF), N is the F-stop, and M is the magnification ( Image size / Subject size ). This is an apporixmation valid for M near 1 or greater, and gives the distance in front or behind the subject that's in focus. Multiply by 2 for total DOF.

The tricky part is deciding how to compare FF and dx sensor shots and what to plug in to get a good comparison. The assumption I'll make is that both sensor have the same number of pixels and that for the part at the center of focus the image is pixel for pixel identical. Scaling the dx sensor relative to the FF under this assumption we get:

c_dx = c / 1.5
N_dx = N / 1.5
and
M_dx = M / 1.5

Since c is roughly the length over which the image can blur and still be considered in focus it is 1.5x smaller for the dx sensor. N has to scale the same way to have the diffraction blur over the same number of pixels, and the magnification clearly scales with the length of the sensor to capture the same image. Pluging in these values gives

DOF/DOF_dx = (1+M)/(1+M/1.5)

from which I calculated some of the numbers above.