Depth of field, print size and sensor size.

[arad85]

No, not another question , more by way of a proof how all this works.

Let's take 2 cameras (one full frame, the other APS-C), 2 lenses (a 50mm and 80mm so that one that has a focal length of 1.6x the other) and some pictures. I'm not sure which combination of camera/lens/subject distance will produce the best results, so I'm going to take 4 pictures.

• The first is with the full frame camera with an 80mm lens. My subject distance is 3metres (3000mm) and for artistic reasons I'm going to use f/5.6. This combination of distance and lens gets my subject to fill the frame nicely.
• The second photo I take is with the APS-C from the same position and with the same lens. OK, the field of view is smaller so my subject is bigger than able to be captured by the APS-C camera, but it's set up now so I'll take the picture.
• The third photo is with the 50mm lens on the APS-C body so I now get the same field of view as I did with the full frame and 80mm combination.
• The fourth photo I decide to take with the 80mm lens on the APS-C body as it's my favourite, so I move to 4.8m away to get a slightly different photo perspective but now my subject still fills the frame.

Because I'm a perfect 'tog , I don't need to do any post processing and can just send them for print them out directly. I'm not really sure how big I want my final print to be, so I print them out at a variety of sizes (6"x4", 9"x6", 12"x8" 15"x10" and 18"x12"). I'm also interested in how sharp the pictures appear, so I'm going to view them all from the same distance.

When I get them back and look at them, I'm shocked that different photos have different depths of field. How can that be - I've taken "the same" photo in 3 of the cases, but the depths of field are different. I'm confused.... so I put together a small spreadsheet that takes the equations from DoFMaster here: http://dofmaster.com/equations.html and plugs the values in that I have used.

Here is the summary of those results:

What can we see from these results? Well:

• If you print the same image bigger and you view it from the same distance, the depth of field shrinks. This makes sense as you are zooming into the picture - you're magnifying the data more.
• For the same lens, aperture and subject distance, and for a given print size the smaller sensor camera produces less depth of field. This is also sensible as to get a given print size from a smaller sensor, you need to magnify it more than that coming from a larger sensor to get the picture printed.
• For the same picture (i.e. same field of view) on the same camera, it doesn't really matter whether you trade focal length for distance, the depth of field is the same. However, as you move further away, the depth of field shrinks as a proportion of the subject distance (that is, the depth of field is the "same" but you are further away). This might help with subject/background isolation for example.
• For the same picture (i.e. same field of view obtained either by use of a different lens or different subject distance) printed at the same size but taken with different sensor sizes, the larger the sensor, the less the depth of field it has.

Can we once and for all put these arguments to bed.

• Depth of field is only relevant when you print an image. You can see this is the case because the print size is used in the depth of field calculations (you may need to look at the definition of Circle of Confusion here: http://en.wikipedia.org/wiki/Acceptable_circle_of_confusion to see that).
• If you have a particular print size in mind, the larger the sensor, the less perceived depth of field there will be in the print for "the same" photo (i.e. if you compensate for the smaller sensor with a shorter lens or moving further from the object.
• If you take a picture of an object from the same place with the same lens but on different format cameras, the smaller sensor will have less depth of field. This is sensible since you have to enlarge the image from the smaller sensor more to get a given print size. The pictures will have very different fields of view though.

Yes, I was bored

 

[woof woof]

There's so much wrong with that (IMVHO - of course) I just don't know where to start So you'll be glad to know that I'll stay well away from this thread I enjoyed reading though

 

[arad85]

There's so much wrong with that (IMVHO - of course) I just don't know where to start So you'll be glad to know that I'll stay well away from this thread I enjoyed reading though

You can stick your fingers in your ears or claim the world is flat as much as you like Alan, but that's what the science says. It's also mirrors my (and other peoples) experience too

 

[StewartR]

Great article, Andy.

I had one of those "Eureka" moments the other day when you first spelt this out so clearly:

DoF is only apparent when you render the image, not when you capture it. I can take a photo from any sensor and the depth of field varies depending on how big I print it and how far away I view it.

It's obvious in retrospect, but I had never really appreciated it until then.

I'd like to add something to your thought experiment though. You've decided to look at all your images from the same distance, and you've discovered that they appear to have different depths of field. That's correct. However, we all know that the optimal viewing distance for an image depends on its size - you can't really appreciate a wall-sized image if you stick your nose up to it, and you can't really appreciate a 6"x4" print from the other side of the room. So it's relevant to ask what happens if you look at the print from an appropriate distance - and then something interesting happens.

First of all, what is the "appropriate" distance? There's no hard-and-fast answer. I've seen recommendations for optimal viewing distances ranging from about 75% to 150% of the length of the diagonal of the image, so for convenience I've assumed that the appropriate viewing distance is exactly the same as the diagonal of the image.

So I've re-worked your calculations for your "base case" (full-frame camera, 80mm lens @ 5/5.6), for a variety of print sizes and viewing distances. Encouragingly, when I used a viewing distance of 25cm I got the same results as you (the blue column). Here are the results:

What it shows is that:

• The closer you view a print, the smaller the apparent DOF. That's intuitively right, because when you look at a print more closely you're more easily able to discern the difference between something being in focus and out of focus.
• When you view the print from the appropriate distance (the red figures along the diagonal), you always get the same apparent DOF. Again, that's intuitively right, because in each case you've got the same apparent magnification.

 

[arad85]

Thanks Stewart

Yes, I purposely kept the viewing distance fixed so the print makes up more and more of your field of view to illustrate the point. It's easy to conceptually think of effectively zooming into the print that way.

You've done the other axis of this - changing the viewing distance and you've found the other "rule" that if the print covers the same field of view in your vision, it will have the same perceived DoF (for a given sensor of course).

The other thing to note is that if you have a higher or lower than average visual acuity (i.e. ability to discern detail) then that will also change the perceived depth of field.

 

[HoppyUK]

The reference standard for depth of field calculations is a print 10in wide, viewed from a distance equal to the diagonal, ie about 12in. It then assumes that the finest level of detail that the human eye can differentiate at that distance is 0.2mm wide (the circle of confusion).

The calculations also work for smaller and larger sizes than this, because we automatically alter the viewing distance when looking at different size images (depending on how good your close vision eyesight is, or how long your arms are) though the principle also holds good even for very large prints like street posters when viewed from the other side of the road. The ideal field of view angle that we tend to find most comfortable is around 60 degrees.

TBH, I've never been that happy with 0.2mm as a basic standard since moving to digital, which is capable of much more (it translates to a mere 1mp resolution ). I can look at a 10in print from a normal distance and things don't look quite as sharp as I'd like them to, according to the international standards for DoF. The average PC monitor is capable of more than that, and the standard for magazine reproduction of 300dpi is more than double 0.2mm at around 0.08mm.

There are other 'tricks of the light' going on too, in that if you look at a print with a very sharp hi-res and punchy image, the perceived DoF appears to fall away much more quickly than with a less punchy image taken on a lower-res camera. DoF is an exact science only in theory, and those very precise calculations you get out of DoFmaster don't make that much difference in practise. Subjects don't always suddenly snap in and out of sharp focus, but fade from one to the other very gradually.

 

[specialman]

It's interesting what you've put together and because my tiny mind can't imagine seeing what you've explained, i'm going to have to try it myself, although I'll be doing it with a DX camera in 1.5x and 2x (high-speed crop) modes to save myself having to spend a grand or so on a D700!!!

Although I'd argue that the relevance of DoF isn't limited solely to when an image is in print, this does sound like a very interesting exercise to undertake. I suspect it's one that most of us should do at some point to appreciate how images actually look in print, seeing as many of us rarely bother to actually print our work.....

 

[arad85]

It's interesting what you've put together and because my tiny mind can't imagine seeing what you've explained, i'm going to have to try it myself, although I'll be doing it with a DX camera in 1.5x and 2x (high-speed crop) modes to save myself having to spend a grand or so on a D700!!!

You can see the effect of rendering size simply by pixel peeping. I posted a file here that was taken at f4 @ 17mm on a full frame camera. DoFmaster says it should have a DoF that extends to infinity. Looking at it zoomed out on a 24" monitor so you can see the whole picture as a 12"x8" (approx) size and it does. Pixel peep (so it's the equivalent of a print about 60"x40") from the same distance and all of a sudden it has a real DoF in that the further away objects are, the more out of focus they are. Clearly, that won't do the different size sensor but will demosnstrate the maths translates into the real world (even if, as Richard points out, the absolute values can be argued).

Here's the image (in case you haven't seen it): http://www.arad85.co.uk/hosted/talkp/_8439.jpg

Although I'd argue that the relevance of DoF isn't limited solely to when an image is in print

I used "print" to suggest outputting the image. The same effect can be seen on the screen as "print" really means rendered.

this does sound like a very interesting exercise to undertake. I suspect it's one that most of us should do at some point to appreciate how images actually look in print, seeing as many of us rarely bother to actually print our work.....

Yup. And it's why I'm going to have to redo some of my prints. I added some gross grain on some pictures I wanted to have a grungy feel to them. I didn't look at them on screen at a representative size before printing. Result: they looked OK on screen but too soft when printed. Dial back the grain so it's better at a representative size and Bobs your uncle. Classic example of how viewing conditions set how sharp we perceive things.

 

[HoppyUK]

Edit: crossed post with Andy

It's interesting what you've put together and because my tiny mind can't imagine seeing what you've explained, i'm going to have to try it myself, although I'll be doing it with a DX camera in 1.5x and 2x (high-speed crop) modes to save myself having to spend a grand or so on a D700!!!

It's simply that if you look more closely at a print, the more detail you can see, so therefore any changes in sharpness due to DoF will be more apparent.

Although I'd argue that the relevance of DoF isn't limited solely to when an image is in print, this does sound like a very interesting exercise to undertake. I suspect it's one that most of us should do at some point to appreciate how images actually look in print, seeing as many of us rarely bother to actually print our work.....

Yes, DoF is always present to a greater or lesser extent, and relative changes are just as important. It's just that in order to measure it you need to define the viewing parameters, and PC monitors are often not good enough to show the level of detail necesary, but a high quality print is. If you just enlarge everything on screen to 100%, as we often do these days, all DoF calcs go straight out of the window.

When comparing the DoF changes between full frame and crop format (with all other paremeters equalised) the difference is only a smidge over one stop. As a subjective comment, that's not a huge amount when you see it for real and those folks that dither over the difference between f/2.8 and f/3.5 for example are often kidding themselves I think. For example, if the meter says f/5.6 and I want a shallow DoF effect to be obvious, I will try to lower the f/number by a couple fo stops at least to f/2.8, and vice versa to f/11 for very deep depth of field.

 

[arad85]

There's so much wrong with that (IMVHO - of course) I just don't know where to start

In case Alan is looking in... I'm actually interested how you define Depth of Field.

Given that ANYTHING off the precise plane of focus is, by definition, out of focus (so actual depth of field is really infinitesimally small), how do you define what the depth of field is (i.e. the distance that appears in focus) in your prints?

 

[specialman]

....For example, if the meter says f/5.6 and I want a shallow DoF effect to be obvious, I will try to lower the f/number by a couple fo stops at least to f/2.8, and vice versa to f/11 for very deep depth of field.

That is a great point. I buy that. If i want to throw the background out on, say my 70-200mm at 200mm, then I know f/4 or thereabout will give me some good blur providing the background is far enough away. plus it'll be a sweeter spot on the lens. If I accidentally change it to f/3.5 then I won't lose sleep, although the time when it is of importance is when reaching my max sync speed with flash, but that's another story...