View Full Version : calculating infinity.

scott russell

22-Aug-2008, 05:12

I know that when a lens is at its focal length from the film plane, it is focused for infinity. IE and 90mm lens 90mms from the film plane. But how do you find out what the lens to object distance is when that lens is focused toward infinity? What got me thinking about this is the wide angle lenses on 35mm. Now a 16mm fisheye on 35mm will have everything in focus after 3 or 5 feet or something ridiculously short like that, so if the object is 5 feet from the lens, you just set the lens for that sideways 8 and your done focusing. how could i figure this out for a 90mm super angulon?

Are you asking about calculating hyperfocal distance?

Google is your best friend: http://www.google.com/search?client=opera&rls=en&q=hyperfocal+distance

Brian Ellis

22-Aug-2008, 08:13

I know that when a lens is at its focal length from the film plane, it is focused for infinity. IE and 90mm lens 90mms from the film plane. But how do you find out what the lens to object distance is when that lens is focused toward infinity? What got me thinking about this is the wide angle lenses on 35mm. Now a 16mm fisheye on 35mm will have everything in focus after 3 or 5 feet or something ridiculously short like that, so if the object is 5 feet from the lens, you just set the lens for that sideways 8 and your done focusing. how could i figure this out for a 90mm super angulon?

"How do you find out what the lens to object distance is when the lens is focused toward infinity? There's probably a forumula that can tell you how to calculate distance to infinity but when I did some reading before setting the infinity stops on my Linhof Technika I read that focusing on something at least a mile away would put the lens position at infinity. That's probably not precise but it seemed good enough for my purposes so I went out to a highway, found a billboard, drove a mile, and focused on the billboard to set the infinity stops. I'm sure that's not as precise as could be done with the right optical equipment or by applying a mathematical formula but it seemed close enough for practical purposes.

"Now a 16mm fisheye on 35mm will have everything in focus after 3 or 5 feet or something ridiculously short like that, so if the object is 5 feet from the lens, you just set the lens for that sideways 8 and your done focusing. how could i figure this out for a 90mm super angulon?" I'm not sure what you're asking but just because you can focus on something five feet from the lens doesn't mean that you should set the lens to the infinity position for anything five or more feet away or that five feet is infinity. Are you asking how to determine the hyperfocal distance?

aduncanson

22-Aug-2008, 11:51

I think that the hyperfocal distance is the answer to the question posed by the original poster. Focus on an object at the hyperfocal distance, (given in http://www.largeformatphotography.info/articles/IntroToDoF.pdf ) and everything from half that distance to infinity is in focus. (ignoring swing & tilt and who knows what subtleties.)

The question of how distant a subject you need for setting infinity stops is different. I was a little surprised by the 1 mile figure because I recall reading that for lens testing, infinity was taken as anything greater that 43 focal lengths. Evidently that is a very different consideration.

For setting infinity stops, the objective would seem to be to allow an error in the standard's position which is small compared to the allowable focus error per depth of field considerations (less than 5 to 10%.) That allowable error would depend, of course, on all of the usual suspects including: focal length, aperture, degree of print magnification and ones personal standard for sharpness. Making a variety of assumptions, I get numbers between 0.5 and 2.55 miles for a 135mm lens and 1.2 and 5.7 miles for a 210.

I generally just use the moon.

Peter K

22-Aug-2008, 12:58

For the Super-Angulon 1:5.6/90mm the distance at infinity between lensboard and film is 100.6mm, for the f/8 SA it's 99.4mm. So from infinity up to the distance the circle of confusion has a certain dimension is "in focus". This depends of the size the final image will be seen.

Leonard Evens

22-Aug-2008, 14:43

When you are focused at infinity the distance to the object is infinite. You should get that straight before you do anything else, because otherwise you are going to remain hopeless confused. A object would be at infinity if it were further away than any real object can be. There do not exist such objects in the world we see around us, os it is best treated as a mathematical abstraction.

As I said, no real object is at infinity, but if there were such an object it would come to focus in the focal plane. Any object at great distance will come to focus very close to the focal plane, and if it is far enough away, it will come to focus so close to the focal plane that you won't be able to tell the difference. In that case, you could say that the object was `at infinity'. But note that ANY point sufficiently far way can be considered to be at infinity in this sense, so there is still no single distance that can be considered to be at infinity.

Just how far away a point has to be before you consider it effectively at infinity depends on the focal length of the lens and how closely you need to look. Generally shorter focal length lenses are effectively focused at infinity for shorter distances than longer focal length lenses.

A related but different concept, mentioned by others above, is that of the hyperfocal distance. Whenever you focus, there is a certain range called the depth of field which you would consider adequately in focus. This, of course, depends on how closely you look. Someone looking at a 40 x 50 print from five feet will consider much more adequately in focus than someone putting his nose right up against the print. But once you set your standard for what is sharp enough, you can calculate, from formulas, or using a DOF calculator, the nearest and furthest distance adequately in focus. Thus there will be a certain amount adequately in focus in front of where you focus---called the front DOF---and a certain amount in back of where your focus---called the rear DOF. At a certain distance and beyond, the rear DOF will be infinite. That means that everything in back of where you focus will be adequately in focus. The shortest distance at which this occurs is called the hyperfocal distance. When you hare focused at the hyperfocal distance, everything from that distance to half that distance in front will be in focus and everything in back will be in focus.

Focusing at the hyperfocal distance is not the same as focusing at infinity. If you had a lot of fine detail at great distance from the lens, and you don't much care about what is in focus in the foreground, you should focus at infinity, not at the hyperfocal distance.

The hyperfocal distance depends on the focal length, the f-number, and something called the coc, which is a measure of how closely you will look at a print of the scene. There are lots of DOF calculators on the web which allow you to enter those parameters and tell you hat the hyperfocal distance is.

Alan Davenport

22-Aug-2008, 16:47

"Infinity" for photographic lenses is 1500 X the focal length.

Leonard Evens

22-Aug-2008, 18:10

"Infinity" for photographic lenses is 1500 X the focal length.

It's always nice to have a definite number, but how many of us are going to calculate 1500 x the focal length in units we are familiar with, and then measure out that distance in the scene. Also, as I tried to explain above, there is no one distance which is effectively `at infinity'. It all depends on close you have to be to the focal plane before you can no longer tell the difference. That in turn depends on the focal length and how closely you look as well a what you are trying to accomplish.

Let me give a simple method which anyone can use without making distance measurements. This would apply when you really do want to focus `at infinity' rather than just having infinity adequately in focus, in which case you would use the hyperfocal distance.

Focus on two or three very distant points. See if there is any focus spread on the rail among them. If within the accuracy that you can focus they are all at the same place, then you are focused for all practical purposes at infinity. You won't do better than this by measuring out 1500 X the focal length or 750 X the focal length or 3000 X the focal length or whatever.

Glenn Thoreson

22-Aug-2008, 22:02

Very complicated stuff. I can tell you this much, if it helps - the average hyperfocal distance for a 90mm lens at f/11 will be 19 feet. That's how I set the focus on my home made fixed focus box cameras. At f/11 it covers everything from roughly 9 1/2 feet to infinity and gets better as it's stop down. Is infinity a set distance, or just something far enough away that focus will reach no farther? I don't know if that's the right way to put the question. I don't understand the math related to this.

I'm with you Glenn. We need Buzz Lightyear...anyone who can go "to Infinity...and Beyond!" must be able to calculate infinity, too.

""Infinity" for photographic lenses is 1500 X the focal length." Whoa! That means infinity for a 150mm (6" or .5 foot) lens is 750 feet. A 50 mm (3") lens would be 250 feet -- but on lenses it is usually marked at about 60 feet. Seems a bit much.

Vaughn

Leonard Evens

23-Aug-2008, 09:47

I'm with you Glenn. We need Buzz Lightyear...anyone who can go "to Infinity...and Beyond!" must be able to calculate infinity, too.

""Infinity" for photographic lenses is 1500 X the focal length." Whoa! That means infinity for a 150mm (6" or .5 foot) lens is 750 feet. A 50 mm (3") lens would be 250 feet -- but on lenses it is usually marked at about 60 feet. Seems a bit much.

Vaughn

50 mm is about 2 inches, not 3 inches. If you focused at 60 feet with a 50 mm lens, the image would be about 0.14 mm in front of the focal plane. Such lenses tend to be used in 35 mm cameras, where one doesn't have to worry about moving a standard. The tolerances for such cameras are pretty small, and I suspect the infinity point is set more accurately than 0.13 mm. Because of gearing down, you can certainly control the position of the lens principal point better than that, and using a split image focusing screen, my guess is that you can focus better than that.

On the other hand, 35 mm format has a DOF advantage over larger formats. The CoC is very small, and hence so is the hyperfocal distance for the same relative aperture. So in many situations, where all you need is that infinity still be adequately in focus, it may not matter just how well the infinity point is set. But in critical applications where, for some reason, you really do need to focus at infinity it might.

For a 35 mm camera with a 50 mm lens, 1500 X the focal length might be about right. In that case the image point would be about 0.033 mm in front of the focal plane, which may be withing the tolerances. I guess that the 1500 X the focal length camera originated from advice about 35 mm photography, which at one time constituted the great majority of what was done. One often sees such advice applied to large format photography without the realization that what works for one format may not work for another.

But, as I noted above, we may be arguing about the equivalent of `angels on the head of a pin'. In practice, you are focused at infinity if you can't tell the differences in focusing at several different distant points.

ic-racer

23-Aug-2008, 12:18

"Infinity" for photographic lenses is 1500 X the focal length.

I am not sure where you are going with that statement. When a technician (or common lens owner) sets a lenses infinity stop using an industrial or homemade collimator the device produces PARALLEL rays entering the lens. Light rays from 1500 feet are close but technically not PARALLEL.

I'm focussing right now on an object at infinity, but due to the inverse square law, the intensity of light from that object has now dropped to zero, so it can't been seen, lest focussed on a view screen. :)

Thanks, Leonard, for your always accurate and thorough explanations. Close enough is close enough.

~Joe

ic-racer

23-Aug-2008, 17:53

I'm focussing right now on an object at infinity, but due to the inverse square law, the intensity of light from that object has now dropped to zero, so it can't been seen, lest focussed on a view screen. :)

You could just be focused on a point so many light years away that the universe was so young, no light source was present (yet still not quite be to infinity!):eek:

I just read the posts and consider that the Restaurant at the end of the universe qualifies for infinity -- but only if the lights are on.

1500x's the focal length does seem a useful practical idea. So --- if I shoot with a 150 mm lens on my 5x4 the Restaurant at the end of the universe is 225 metres from my camera :) Easy walking distance.

Alan Davenport

23-Aug-2008, 22:28

Light rays from 1500 feet are close but technically not PARALLEL.

Light rays from 1500 light years away are technically not parallel, either, but I bet they're darn close. When the rays are close enough to parallel, that the divergence does not affect the resulting image, that's close enough to call it "infinity" for the lens. For photographers, that takes into account allowable circle of confusion, acuity of vision, etc. I was taught to use 1500X the focal length.

Kirk Fry

23-Aug-2008, 22:34

Hey guys, they are called view cameras for a reason. Get that loupe out and LOOK!!!

Yikes no calculation needed.

K

50 mm is about 2 inches, not 3 inches.

That teaches me about posting late at night! Thanks!

Kirk -- not all LF cameras are view cameras...such as fixed-focus point and shoot 8x10's (Hobo Cameras, for example). Or if one used a Speed Graphic w/o a rangefinder as a point-and-shoot.

As long as we all are having fun!

Vaughn

Leonard Evens

24-Aug-2008, 09:35

I doubt if anyone will be interested, but I've written a (tentative) article about infinity in photography, particularly view camera photography. It is at

www.math.northwestern.edu/~len/photos/pages/Infinity.pdf

It discusses the issues that have been raised here as well as some others. One point I make is that the space which we see about us, and in which the scenes we photograph exist, is not the same as physical reality as described by modern physics and astronomy. But it does correspond pretty well to the geometries that mathematicians have been describing from Euclid on. Another point is that while infinity is not attainable on the subject side of the lens, it is attainable on the image side, in terms of vanishing points and the focal plane. Another point which I tried, perhaps not successfully, to make is that when we look at a scene we accept as a matter of course distortions of distances and angles. This is something built into our visual system, and if it weren't, photographs would be unintelligible as representations of the scene. An example of this is that any pair of parallel lines receding into the distance does appear to converge to a point, although if you tried to reach that point you would never get there. In the photograph, that point is a vanishing point, and we accept it as the image of `something' without thinking about it. That `something' is an example of what we mean by a point at infinity.

The article is tentative in the sense that I am not sure that anything in it will be of use to the intended audience. I am also not sure I managed to say what I intended clearly. In addition, there are some grammatical and other errors that need correcting. If you found the article interesting and have some suggestions that would help improve it, please let me know.

ic-racer

24-Aug-2008, 10:28

Light rays from 1500 light years away are technically not parallel, either, but I bet they're darn close. When the rays are close enough to parallel, that the divergence does not affect the resulting image, that's close enough to call it "infinity" for the lens. For photographers, that takes into account allowable circle of confusion, acuity of vision, etc. I was taught to use 1500X the focal length.

I guess my question is "how do you use that number 1500x the focal length?" As an estimate of infinity for setting lens stops? (In which case it seems like a reasonable thing.)

Kirk Fry

24-Aug-2008, 19:18

Vaughn,

I too use a crown as point a shoot, but I calibrated infinity by looking with a loupe before hand and marking it on my rails. I think a hobo has a regular ground glass back for which you can check that your lens mount is set correctly. A pure calculation is tricky because you need to know the exact optical center of your lens and be able to accurately measure it. I still think looking beats calculating but each to his own, obviously this is a captivating subject to a number of folks. K

timparkin

25-Aug-2008, 06:32

Light rays from 1500 light years away are technically not parallel, either, but I bet they're darn close. When the rays are close enough to parallel, that the divergence does not affect the resulting image, that's close enough to call it "infinity" for the lens. For photographers, that takes into account allowable circle of confusion, acuity of vision, etc. I was taught to use 1500X the focal length.

If two parralel lines converge at infinity, lines that diverge from a point should be parralel once they are an infinite distance away?

Anyway, given a closed universe, you could just turn around and infinity should be right in front of you...

Tim

aduncanson

25-Aug-2008, 09:07

"Infinity" for photographic lenses is 1500 X the focal length.

Using 1500 focal lengths rather than some literally astronomical distance results in a focus error that could limit resolution in an 11x14 (3x) print from 4x5 to approximately 6 LP/mm at f/5.6, or 19 LP/mm at f/16 with a 150mm lens. In other words it is a perfectly acceptable approximation.

My earlier, much greater suggestions for infinity were based on the premise that the CoC due to error in infinity should be much less than the allowable total CoC. Very likely it would be impossible to focus accurately enough to gain any improvement on the 1500 focal lengths estimate.

ic-racer

25-Aug-2008, 13:24

If two parralel lines converge at infinity, lines that diverge from a point should be parralel once they are an infinite distance away?

I think if they met they would not be parallel. Perhaps this is a question of semantics or mathematical theory.

Anyway, given a closed universe, you could just turn around and infinity should be right in front of you...

Tim

A mobius universe ? :)

I think if they met they would not be parallel. Perhaps this is a question of semantics or mathematical theory.

A mobius universe ? :)

Now you're just getting all loopy and twisted out of shape...

Stuck inside a mobius with the Memphis Blues again...

Leonard Evens

27-Aug-2008, 13:01

Using 1500 focal lengths rather than some literally astronomical distance results in a focus error that could limit resolution in an 11x14 (3x) print from 4x5 to approximately 6 LP/mm at f/5.6, or 19 LP/mm at f/16 with a 150mm lens. In other words it is a perfectly acceptable approximation.

My earlier, much greater suggestions for infinity were based on the premise that the CoC due to error in infinity should be much less than the allowable total CoC. Very likely it would be impossible to focus accurately enough to gain any improvement on the 1500 focal lengths estimate.

It would depend on the focal length and the format. With a 450 mm, if you focused at 1500 times the focal length, you would be focusing about 0.30 mm in front of the focal plane. With 4 x 5 format, using 4 X loupe, that might be just barely in the depth of focus. On the other hand with a 150 mm lens, it the displacement would be about 0.10 mm, which would almost certainly be undetectable.

But, as I keep saying, how in the world would you determine that something was at 1500 times the focal length from the lens without some fancy range finding equipment? You could of course guess, but it seems easier just to focus on several distant points and decide you have effectively focused at infinity if you can't see any focus spread among them.

Glenn Thoreson

28-Aug-2008, 20:13

I'll just stick with the Buzz Lightyear theory. :D

But, as I keep saying, how in the world would you determine that something was at 1500 times the focal length from the lens without some fancy range finding equipment?

.

Wow! 450mm x 1500 = 675 m. How do you find out that something is more than 675 m away from you??? Take a wild guess...! And if is further away from you than 700 yards - it's still more that 675 m away. Imagine..!

Alan Davenport

6-Sep-2008, 08:06

If two parralel lines converge at infinity, lines that diverge from a point should be parralel once they are an infinite distance away?

True, but we're only talking about 1500 light years, NOT infinity...

ic-racer

6-Sep-2008, 10:22

I'm going to interpret it as follows and add it to my list of mantras...

'Anything 1500 times the focal length away or more, can be used to set infinity stops with reasonable accuracy, based on accepted circles of confusion.'

seawolf66

6-Sep-2008, 12:11

Where is Spock when you need him: [LOL]

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