Optics Question: What remains constant as we focus closer ?

[Ken Lee]

Let's say we have a 120mm lens. By definition, it requires 120mm of bellows draw at infinity.

When we focus down to 1:1, 240mm bellows draw is required. Some would observe that the focal length is now 240mm.

My question is, what has remained constant: the magnification of the lens ? The angle of view ? I'm not asking about exposure compensation. I understand that.

I ask because a 120mm lens at infinity is a moderately wide angle lens, and when we focus it at 1:1 it continues to give a moderately wide angle of view. How can that be, if the focal length is now doubled ?

[Dan Fromm]

Let's say we have a 120mm lens. By definition, it requires 120mm of bellows draw at infinity.

When we focus down to 1:1, 240mm bellows draw is required. Some would observe that the focal length is now 240mm.

Focal length equals extension only when magnification is zero, i.e., when the subject is at infinity. Focal length is an attribute of the lens that doesn't change when the lens' position changes.

[Tin Can]

Angle of view is unchanged.

[A_Tabor]

The thing that remains constant as you apply extension beyond the focal length distance is the way that light at a given angle is bent when passing through the lens at a given location.

This plays back into depth of how focus and depth of field works. For a given lens there isn't really a single 'point of focus', but rather an infinite number of them that you can see by moving things around on either side of the lens and aligning them properly. (This is why view cameras do their 'thing' when shifting the position of the film and lens around in relation to each other.)


A simplified thought experiment to help understand things:

Draw a simple 'lens' on paper with a () shape. On one side draw your tree, and on the other side draw a line for a focus plane. We know that the tree will be upside down on the focus plane, so draw five lines from the top of the tree to different parts of the lens, and then from the lens to where it would be on your focus plane.

Now draw the tree again, but this time much closer to the lens, and draw five lines from the top of the new tree to different parts of the lens. From experience we know that the second tree is probably out of focus. Why? Because the lines coming out of the lens toward the focus plane would meet up somewhere behind where we've currently drawn it.

Draw a new focus plane somewhere behind the first one, and connect the lines from the lens for the second tree, then extend the lines for the first tree.

What conclusions can you make?

[Will Frostmill]

Well, is focus breathing an issue? With zoom lenses, you can get a situation where the magnification (angle of view) changes depending on how close the focus point is. I assume that's not a problem with traditional LF lenses, but sometimes we work in the near-macro regime, and things are weird there.

[neil poulsen]

That's really interesting, thinking of sharp focus as a matter of what stays constant, what remains invariant.

I don't think that magnification remains constant, since M = i/O. (i => image to lens distance; O=> object to lens distance.) As O gets smaller, i gets bigger, so M must change.

I think what stays constant is the quantity 1/i + 1/O. From the simple lens formula . . .

1/f = 1/i + 1/O . (At least, for simple lenses.)

Since f is a constant of the lens, 1/i + 1/O itself must remain constant. That is, i and O in relationship to each other change in a way to keep the above expression constant.

[IanG]

Angle of view is unchanged.

It's a bit of an an oximoron because coverage improves as you focus closer. I have a 75mm f1.9 Dallmeyer at Infinity might just cover 6x4.5 but at the distance it's optised for it covers 5x4. All terms need to be defined at set standards.

I ask because a 120mm lens at infinity is a moderately wide angle lens, and when we focus it at 1:1 it continues to give a moderately wide angle of view. How can that be, if the focal length is now doubled ?

Now what about a 120mm lens that's a normal FL for Quarter plate at all apertures, a mild Wide Ange for 5x4 at f16, and a good wide angle for 7x5 at f45 (equivqlent to roughly a 28mm on 35m).

Ian

[Ken Lee]

Now what about a 120mm lens that's a normal FL for Quarter plate at all apertures, a mild Wide Ange for 5x4 at f16, and a good wide angle for 7x5 at f45 (equivqlent to roughly a 28mm on 35m).

Sorry, I was unclear. I meant that a 120mm lens is a moderate wide angle for 4x5, and remains moderately wide even at close distance.

Fortunately, the laws of optics aren't constrained by our lack of understanding.

[Emmanuel BIGLER]

Coming late to this discussion. Hi, Ken!

A first remark is that the focal length of a "fixed focal length lens" is ... perfectly fixed ;-)

Hence, the only thing that does not change at all when we re-focus from infinity to the 1:1 ratio at all is the focal length.

The magnification changes from zero to 1 and various distances: subject-to-lens and lens-to-sharp-image change as well, if we keep the focus sharp.

However we don't have to keep the focus sharp; US regulations, to the best of my knowledge, do not prohibit the recording of totally fuzzy images with a LF camera.

Now comes a subtle issue. What happens to the projection of an out-of-focus image, in terms of magnification and perspective rendition?
If the lens is quasi-symmetrical with a pupillar magnification close to one, like many of our faithful, non-telephoto, LF lenses, we can say that the magnification in a fuzzy image is exactly the same as if we had used a pinhole camera, the fuzziest of all imaging systems in LF photography, except when we, intentionnaly, do not re-focus our lens.

A lens does not exactly behave like a pinhole camera, since we have to take into account that the entrance and exit pupils of the lens are located at different points, but usually in a classical quasi symmetrical LF lens, both pupils are close to each other, close the iris and close to the leaf shutter blades.
In a fuzzy image, the location of the pupils determines the magnification of un-sharp pseudo images.
If we neglect the distance between both pupils, the magnification ratio is simply the ratio of the exit-pupil-to-fuzzy-image-plane distance, divided by the object-to-entrance-pupil distance.
Angle of view in a any fuzzy, of sharp image, in a quasi-symmetrical lens is the same as in a pinhole camera.

In a retrofocus or a telephoto, things are slightly different ... the situation is really complicated if we absolutely want we deal with out of focus images in such asymmetric lenses. Difficult to explain in a few words, the problem is that pupils are not located at principal planes. Principal planes determine the position and magnification of sharp images; but for out of focus images, magnification is determined by the position of pupils. Hence the behavior in an assymmetrical lens is really weird with respect to the pinhole camera, our basic model for understanding image magnification and perspective rendition.

Hence, it's much better to focus at best with all our lenses, to avoid a weird behavi(o)ur ;-)

[Struan Gray]

The lens casts a 3D pattern of light behind itself which remains constant provided the lens stays in one place (and the scene is static). Focussing with the rear standard or applying rear movements does nothing but move the position of the ground glass and film so that they intersect different parts of the 3D pattern. When you focus with the rear standard you change nothing optical whatsoever (you change the focus condition of the camera, but no optical rays are changed at all).

Focussing with the front standard or applying front shift/rise/fall will move the entrance pupil. This changes parallax between objects in the scene because the lens 'sees' from the position of the centre of the entrance pupil. Usually this is a small effect (unless you're doing closeups) so here too you can assume the light pattern stays the same and focussing only selects different parts of the 3D light pattern behind the lens to record on film.

Front tilt/swing changes the direction that the optical axis points along. That changes which planes in the scene are perpendicular to the optic axis (and so have a constant focus condition and magnification), it is still the case that focussing merely selects which 2D slice of that tilted 3D light pattern is recorded on the film.

In LF, it's really only the soft focus lenses like the Cookes which do anything much to change the light pattern behind themselves, and even they are unit focussing so the configuration of the elements does not change for focus. Our eyes, and 'IF' 35 mm or digicam lenses, focus by keeping the distance to the film/sensor the same and changing the focal length. This kind of lens does change the pattern of light behind it as it is focussed, but is very rare in LF. The only example I can think of would be a particular kind of overhead projector lens pressed into service for LF.