There is a lot of misunderstanding out in the world of photography about focal length, aperture, field-of-view (FOV), and depth of field (DOF). If there's one thing I hate arguing about, writing about, and educating people about, it's these topics—especially DOF. Misunderstanding of DOF is ineradicable. Arguments always follow assertions about it. It was that way in 1910, and 1940, and 1980, and it's that way now, and it will be that way in 2030 and 2050—regardless of what I or anybody else might say about it, now or ever. I edited a technical magazine about photography for six years; take my word for this.
When "translating" a focal length, all we're doing is bringing back a FOV crop to a context that is more or less readily understandable to people because it's familiar and/or standardized. With digital's multiplicty of format sizes, it's become conventional to "translate" FOV crops into 35mm equivalents—and it amazes me that anyone still questions this, since it's a widespread practice with digicams, many of which use the 35mm equivalent focal lengths in their menu systems or even engraved on their lens barrels.
When I write that a 150mm ƒ/2 lens on 4/3rds format is "equivalent" to a 300mm ƒ/2 lens in 35mm, no, the actual focal length of the lens hasn't changed—it's still 150mm. And no, the aperture doesn't change either. You don't have to "translate" that ƒ/2 to ƒ/4 or ƒ/5.6 to "be consistent." There's one thing that does change, and that's DOF, and yes, you would have to stop down the lens on the larger format to get the same DOF for identical scene FOVs—but aperture is not primarily a control of, or a measure of, DOF; it's primarily a measure of exposure. It's highly misleading to say that a 150mm ƒ/2 lens in 4/3rds should be "translated" to a 300mm ƒ/5.6 in 35mm just because the DOF of those two apertures might match more closely. DOF is a "side effect," one might say. As an exposure control, ƒ/2 is ƒ/2 is ƒ/2. For a given exposure, aperture is independent of format.
When "translating" focal lengths, all we're talking about is FOV. It's true that it's not rigorous. We do it that way because we don't have a better way to do it. We don't all have any other concept in common. And it's not even possible to come up with a completely rigorous scientific nomenclature, because aspect ratio matters as well. If you want to "translate" lens focal lengths as a means of understanding FOV between, say, 8x10 film and 35mm film, you have to choose whether you're going to compare the long dimensions, or the short dimensions, or the diagonal measures—and none of the three results in an exactly accurate equivalence.
For myself, for instance, I always compare the longer dimensions of different formats to each other, but that's because that's how I see. How "wide" a lens is to me depends on how much it takes in from side to side, not on its height when held horizontally.
So let's say I want to know what a 110mm lens on 2 1/4 square format would be in 35mm terms. A square MF neg has an image area of 56 x 56mm, so I'd compare the long dimension of the 35mm film to the square and I'd "translate" the focal length/FOV to about 70mm in 35mm terms. There would be some height "added" to the square, is all. (When Lee Friedlander was asked how the Hasselblad he switched to was different than the Leica he previously used, he said something like there's more sky.) But someone else might be more sensitive to image height. That person might compare the short dimension of the 35mm frame to the square, and might be more comfortable thinking of that 110mm lens as being "equivalent" to about a 50mm lens on the 35mm, but with the ends cropped off!
Who's right? Neither, obviously. (Well, actually, both, but neither more than the other.) And to compare the film diagonals is not completely rigorous either, since that's just a rather crude means of splitting the difference.
The point is that it's just best not to get too bent out of shape with FOV "equivalents" and focal length "translations" and all the attendant issues that come up in their wake. It's just a rough, seat-of-the-pants means of giving you a general idea of the angle of view the lens is going to take in. It's no more important than that. And that really isn't worth arguing about.
________________
Mike
Amen!
Posted by: John | Wednesday, 22 August 2007 at 02:02 PM
Amen.
Posted by: Robert Roaldi | Wednesday, 22 August 2007 at 02:05 PM
Did Friedlander make the "more sky" comment in reference to the Hasselblad SWC? Perhaps the comment was a reference to both the change in aspect ratio and focal length? I'm not nitpicking, I'm just curious!
Cheers,
Joe
Posted by: Joe Reifer | Wednesday, 22 August 2007 at 02:26 PM
Yeah, but...
Just kidding. You are correct, no matter what some of the the numbskulls over at dpreview say.
I think the bit about "aperture is not primarily a control of, or a measure of, DOF; it's primarily a measure of exposure" is what throws most people off. They're so used to hearing that f/2.8 gives you much less depth of field than f/11, which is not exactly the whole story. Maybe you should write a little treatise on that one, Mike.
Posted by: Nerdie McSweatervest | Wednesday, 22 August 2007 at 03:07 PM
I think Mike hit the nail on the head when he said this has come up because all of a sudden lots of "regular" folks are feeling the need to compare the many significantly different formats now available.
Several years ago, it was only the relatively well-versed MF and LF shooters that might have given this much thought--nearly everybody else whether it was a compact or an SLR or a rangefinder was shooting 35mm. The MF/LF community could accept and probably deal with these differences in a (relatively) intelligent manner without being compelled to standardize.
Now, from tiny digicam sensors to APS-C D-SLRs, the marketers had to make sure that their potential customers knew that their compact, shorter-focal-length lenses had similar ability to capture the same images as their old 35mm cameras. It is unfortunate that way back, 35mm didn't use something a little more versatile or portable (like Mike's somewhat imperfect but practical horizontal angle-of-view) as the primary means of describing their lenses.
All in all, 35mm equivalence isn't as useless as another term being bandied about in the digicam world--3x zoom, 10x zoom, etc. These *sort* of work only because the wide end is nearly the same (~35mm equiv.) on so many digicams. Some of us alternatively take this term to roughly determine how much the lens being described has been compromised from 'ideal' (e.g. 10x zoom is likely to have much more distortion, slower performance, vignetting issues, soft corners, etc. than a more conservative 3x zoom). This of course is only a rule of thumb and doesn't take into account actual lens design quality.
Aren't binoculars generally sold by magnification? Convenient but doesn't much address any differences in field-of-view, does it?
Posted by: Andrew Gilchrist | Wednesday, 22 August 2007 at 03:14 PM
Amen. Thanks be to Mike.
Posted by: Matthew Allen | Wednesday, 22 August 2007 at 03:21 PM
"Did Friedlander make the 'more sky' comment in reference to the Hasselblad SWC?"
Hi Joe,
Yes. I'd have to look for the source, but that's my memory.
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 03:22 PM
Well, I erred in the comment about DOF that I sent to your previous article. Good thing you didn't publish it. (grin)
Wrotniak has a good article about DOF in the digital age here:
http://www.wrotniak.net/photo/tech/dof.html#FRAME
and a handy chart for fourthirds users to calculate DOF here:
http://www.wrotniak.net/photo/tech/dof-43.html
I would argue that DOF is more than a "side effect" when considering focal lengths in the sense that photographers would like to have a handy way to predict DOF now that the old 35mm standard we all kept in the back of our heads is mostly unusable and lens makers seem to have stopped embossing those little guides on their lenses.
Of course, digital allows for lots of trial and error.
Posted by: mikeinmagog | Wednesday, 22 August 2007 at 03:38 PM
I guess the question is whether using these "35mm equivalents" makes people smarter or dumber about things like FOV and DOF. Maybe it would just make more sense to specify the actual focal length and format, and qualify the field of view descriptively--"moderate wide-moderate tele zoom," "normal," "super tele," etc. After all, no one thinks of the 15mm lens on a Minox, the 80mm lens on a Hasselblad, and the 300mm lens on an 8x10" camera all as "50mm equivalent" lenses.
Perhaps APS-C and other small-format digital shooters would be smarter, if they understood that they were shooting a smaller format than 35mm, and how that relates to the actual focal length of the lens, field of view, and depth of field.
Posted by: David A. Goldfarb | Wednesday, 22 August 2007 at 03:41 PM
Andrew has a good idea in using format-independent measures to describe lenses. He's also right that these would probably never catch on, but I'm interested in how to do it anyway:
Instead of using focal length, we could use angle of view. Manufacturers actually specify this for some of their lenses.
For light transmission ("brightness"), Mike is right that aperture is already format-independent.
I'm not aware of a format-independent way of describing the DOF of a lens at a given aperture. Is there a good one?
Or we can just go around saying, "my lens has the angle of view of a 82mm lens on 35mm film, an aperture range of f/2.8-f/22, and the DOF of an f/4-f/32 lens on 35mm film." (Speaking of the long end of my Nikon 17-55/2.8 DX, for example.)
Posted by: Stefan Pharies | Wednesday, 22 August 2007 at 04:07 PM
"Perhaps APS-C and other small-format digital shooters would be smarter, if they understood that they were shooting a smaller format than 35mm, and how that relates to the actual focal length of the lens, field of view, and depth of field."
David,
Point taken, but it really isn't easy. The names of the "tiny formats" are opaque, and there are a number of them. It means that the people with the least serious cameras (digicams/digital point-and-shoots)--most of whom don't know what "focal length" even means--would need to be the most aware of the sensor sizes and they way focal lengths related to those sensor sizes. It seems a lot to ask.
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 04:36 PM
Doesn't a 110mm lens on 2 1/4 square format translate into a 170 mm lens on a 35mm format [110x(56/36)]?
Posted by: Peter P. | Wednesday, 22 August 2007 at 04:43 PM
Stefan,
Given that apparent depth of field is dependent on a large number of factors and a large number of variables--not only aperture but focus distance, degree of enlargement, and even the sharpness of the in-focus image (the less sharp the plane of focus is, the more similar to it slightly out-of-d.o.f. objects will appear), I'd say that "finding a format independent way of describing DOF" would be impossible....
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 04:43 PM
"Doesn't a 110mm lens on 2 1/4 square format translate into a 170 mm lens on a 35mm format [110x(56/36)]?"
Peter,
No. Written the way you have it, the correct equation would be [110x(36/56)].
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 04:47 PM
I've always hated the term "crop factor" although I understand its use. I prefer "format/focal length relationship" which is more descriptive but, most likely, more confusing to those photographers more familiar with 35mm.
Posted by: Dogman | Wednesday, 22 August 2007 at 05:16 PM
Mike writes:
When "translating" a focal length, all we're doing is bringing back a FOV crop to a context that is more or less readily understandable to people because it's familiar and/or standardized.
Hmmmmmm.....well --koff, koff-- actually.....
to many of us Children of the Digital Age,
"it" is neither a familiar nor an accepted standard.
Lament this as you will, but our concept of a 50mm lens
was formed by its use over a 23.7 x 15.7mm sized sensor.
So we have a different frame of reference (so-to-speak).
But that doesn't make us naive or stupid about things.
(Not, of course, that I think any of you all thought it did.)
We do "get it" -- that is, to "make the same photo"
on a larger "35mm" sensor would require us
to use some foot zoom and make other necessary adjustments.
Assuming that our 50mm lenses were not DX, of course,
and could actually be used over a larger sensor.
It's all relative, I think the man once said.
Posted by: Andrea B. | Wednesday, 22 August 2007 at 06:13 PM
When you look at the info on different Leica lenses from the company (in pdf format), they illustrate different FOVs graphically, depending on aperture and distance to the object in focus. This isn`t perfect, but I guess it gives you pretty much of an idea of how a given lens work.
Or rather gave. Because with the 1.3X crop factor of the M8, things change. I think Leica would do the M8 users a favor, by providing separate graphical illustrations regarding that camera.
And in an ideal world, every camera- and lens maker should provide the same for their equipment, printed on paper, so people could carry it around during the first weeks of trying out a different format from what they were used to.
Also, they could add, as a standard formula, that other factors, like the above mentioned enlargement of the image and the sharpness of the plane of focus, also play a role.
At least I think it would give people an idea, and be quite helpful in all this confusion.
(I know that there are FOV calculators on the net, but this really should be provided on print with the box, like the info printed with films in the...eh film days.)
Posted by: Paul Norheim | Wednesday, 22 August 2007 at 06:15 PM
Dear Stefan,
Unfortunately, there's no clean rule that relates DoF to format size. The approximation I've given-- that the f/# scales up with the format-- is VERY crude. It fails in a lot of cases. It's a useful factoid to have in the back of your head, that you need to stop down more with larger formats to get the same DoF, but the amount is highly variable.
DoF is very complicated. Blanket rules are at best qualitative, and sometimes they're entirely wrong. For example, it's not true that 1/3 of the DoF lies in front of the subject and 2/3 behind it. At close distances, DoF is symmetric; as you approach the hyperfocal distance, the back/front ratio climbs from 1:1 to infinity. Another example-- DoF field is NOT independent of focal length (when on-film magnification is held the same). It's true for close working distances/large apertures. The further away you get and the more you stop down, the more DoF depends on actual focal length as well as magnification.
Al Blaker wrote a whole book on the subject-- Applied Depth of Field. Kinda the Bible of the field, and even he missed a number of important bits.
There's no way you can be "smart" about this, unless you can solve DoF equations in your head easily. All you can do is crunch the numbers when you need specific results.
pax / Ctein
Posted by: Ctein | Wednesday, 22 August 2007 at 06:59 PM
How about a "Perspective Ratio"?:>)
Normal, i.e. 42mm on 35mm film, would be "1".
Posted by: Joe | Wednesday, 22 August 2007 at 07:01 PM
One thing I'm always noticing (on silly arguments at dpreview, or pick your favorite forums site) is that the weenies always think that shallower DOF is an unalloyed good thing. Probably because (a) it's something their SLRs have that the other guy's compact doesn't, and (b) because of the argument that you can always increase your DOF by stopping down, but you can't decrease it past the lens' maximum aperture.
What they're forgetting is that there are huge swathes of photography for which limited DoF is a curse, not a blessing. It's the limited DoF that makes very wide-aperture (f/1.2 or f/1.0) lenses not a practical solution for a lot of photographic purposes for which they'd sure be useful from a light-gathering point of view. While it can occasionally be neat to have one eye in focus while the other isn't, and the nose and ears of your subject heavily blurred, it's not if that's not the effect you need.
Macro shooters want more depth of field, not less. Long shutter speeds risk movement of the subject, either by itself or by wind movement, camera/tripod shake, etc etc.
Long-telephoto shooters would also love a bit more depth of field, too.
Quite apart from the weight and size savings, I can see that as a bonus to e.g. Four Thirds, not a disadvantage.
Posted by: Matthew Brown | Wednesday, 22 August 2007 at 07:25 PM
Oh, my -- remember when I wrote this to you just short of two years ago:
"My brain fell out today reading some horrible threads/flames/rants/insanity on DPReview about DOF and crop factors.
[...]
Anyway, can you *please* bring back the SMP, a photo blog, or something??? Really now, the world needs you."
And here we are -- back to DOF and crop factors. I guess you're right --it never goes away!
Posted by: Mike Sisk | Wednesday, 22 August 2007 at 08:01 PM
The reason I brought up DOF is this: I have long wondered why Olympus could make an f/2 constant-max-aperture zoom when nobody else seems to make one faster than f/2.8. So I was interested to realize that Oly's f/2 zoom would *not* get you less DOF than, say, Canon's f/2.8. And, of course, since f is lower for the same FOV, the aperture is not necessarily larger in absolute terms ...
Posted by: Ben Rosengart | Wednesday, 22 August 2007 at 08:14 PM
"the weenies always think that shallower DOF is an unalloyed good thing."
Matthew,
It's as you say...for most photographers for most of photography's history it's been the opposite.
Either way, though, you can learn to use your tools. If they want shallower depth of field, they should just get a longer lens and/or move closer. It's not only aperture that matters. I've taken plenty of "shallow DOF" shots with a digicam.
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 08:27 PM
Ben,
You're not getting this. The aperture IS greater in absolute terms. It absolutely is. An f/2 lens wide open will allow you to shoot with one stop faster shutter speed than will an f/2.8 lens wide open. Aperture is not a measure of depth of field!! It is a measure of how much light is coming through the lens. An f/2 lens is always one stop faster than an f/2.8 lens, regardless of the format.
Mike
Posted by: Mike | Wednesday, 22 August 2007 at 08:49 PM
As mentioned above, the problem lies with the internet-mixture of first-timers and experienced professionals, and what lies in between. To give an idea of the FOV of a lens, a relatively accessible standard is needed.
That said, I think the reviewer in the linked article went with an elegant solution by speaking of "Long telephoto lenses (less than 10 degree diagonal viewing angle) ...", giving the information that really matters and is not dependent on external factors such as FOV crops. Since the relationship between mm focal length and expected FOV is arbitrary anyway, perhaps it is time to change to a more universal look at lens specifications.
All you'd need is a little chart (available on the internet) in the beginning to convert the mm-degrees values for a certain format. Once it sticks in your mind, you're set to go.
Posted by: Elmer | Wednesday, 22 August 2007 at 09:13 PM