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.

[Dan Fromm]

Struan, you opened an interesting question, viz., when not to focus by moving the front standard instead of the camera/lens unit. When shooting closeup most practitioners set extension to get the desired magnification and then move the camera/lens assembly as a unit to focus.

You and I know that there are two magnifications for every film plane to subject distance that exceeds 4f + internodal distance (this is the minimum, gives magnification = 1). This fact has no practical significance for subjects that aren't real close but people who don't know this have problems shooting closeup when they hold film plane-to-subject distance constant and focus by changing extension. Some of them have even complained here.

Cheers,

Dan

[Will Frostmill]

Struan, you opened an interesting question, viz., when not to focus by moving the front standard instead of the camera/lens unit. When shooting closeup most practitioners set extension to get the desired magnification and then move the camera/lens assembly as a unit to focus.

You and I know that there are two magnifications for every film plane to subject distance that exceeds 4f + internodal distance (this is the minimum, gives magnification = 1). This fact has no practical significance for subjects that aren't real close but people who don't know this have problems shooting closeup when they hold film plane-to-subject distance constant and focus by changing extension. Some of them have even complained here.

Cheers,

Dan
Hi Dan,
Could you expand on this a little bit? I've messed around with near macro, but I've never gotten a good intuitive feel for it, nor do I have the kind of technical understanding you are demonstrating. (Or if you could point me to prior threads...?) I think it's pretty important for me, because I'm moving to 8x10 and ULF, and a whole bunch of stuff ends up being 1:2 and 1:1 ratios that would be much smaller on smaller formats.

Will

[Dan Fromm]

Will, here are a few magic formulas:

magnification = f*(1 + film plane-to-rear node distance)

whence film plane-to-rear node distance = f*(magnification + 1)

front node-to-subject distance = f*(magnification +1)/magnification.

film plane-to-subject distance = f*((magnification +1)(1 + 1/magnification) + internodal distance Internodal distances for most LF lenses are small fractions of focal length and many people ignore internodal distance when thinking about closeup work. I mention it for completeness.

You can see that if magnification = 1, film plane-to-subject distance f*2*2 + internodal distance = 4f + ...

To see that the minimum film plane to subject is at m = 1, differentiate the formula with respect to m and solve for the m at which the derivative is 0 or plug the formula into a spreadsheet and calculate ...

To see why people can easily get into trouble, calculate film-to-subject distances for m = 0.5 and m = 2. Actually, they're in trouble for pairs of magnifications (M, 1/M). And now you can see why when M is large it is hard to get enough extension to reach 1/M.

What you really need to do is buy a copy of Lester Lefkowitz' book The Manual of Closeup Photography. Out of print, used copies can be bought at low prices from sellers on abebooks.com, alibris.com, amazon.com ...

[ic-racer]

The focal length of the lens remains constant. The relative aperture, field flatness and field of view [image size on film] change.

[Nodda Duma]

The relative aperture (more commonly referred to as f/#) is a physical property of the lens and therefore also remains static regardless of what is going on in object and image space.

Really the only first order aspects of an imaging system which change are those which are a function of magnification. Aberrations are, as always, simply due to the path the rays take through the system.

[Emmanuel BIGLER]

To add a few details to what Struan explained, you may have a look at the figures in this article, unfortunately the text is in French, but the figures, hopefully, are self-explanatory.

http://www.galerie-photo.com/angle-de-vue.html

Projections (including geometrical distorsions generated by projections on a plane with a perfect distorsion-free lens), image magnification, perspective rendition (i.e. the relative proportions of projected shapes of the subject in the image), all this can be determined considering a pinhole camera, and forgetting about the proper relationship between object-to-lens and lens-to-image distances required to get a sharp image.

See figures 1 to 5 to see what happens in a pinhole camera, nothing new, this is well-known since Renaissance times when conical perspective was used in paintings for the first time.
In those simple ray-tracing diagrams, no focal length is implied, only the distance between the pinhole and the detector determines the magnification of the image, and perspective rendition is the same at all pinhole-to-film distances, the images only change by the magnification factor. Only the distance between the pinhole and the subjet determines perspective rendition.
http://www.galerie-photo.com/angle-de-vue.html#htoc1

See figure 12 for an explanation on how the magnification changes for a slightly defocused image.
http://www.galerie-photo.com/angle-de-vue.html#figure12

If the lens is quasi-symmetrical, the ray tracing diagram valid for a pinhole camera is still valid for a thick compound lens, perspective rendition is determined by the position of the entrance pupil only.

See figure 13
http://www.galerie-photo.com/angle-de-vue.html#htoc15
for an explanation about distorsion in a wide angle lens when taking a picture of a series of identical spheres. Again, the pinhole camera model is sufficient to explain what happens.

Now coming back to the initial subject, what remains constant when we re-focus from infinity to the 2f-2f setup at 1:1 magnification ratio: we can add that if we do not move the lens position with respect to the subject, we do not alter perspective rendition in the image, be it sharp or blurred (at least for a quasi symmetricale lens).
But when the image is extremely defocused, the pinhole ray tracing is useless since the blurred images are transformed in a very low contrast pattern totally different from what a pinhole camera would deliver.

[Nodda Duma]

How confident are you that you are not simply predicting perspective distortion? Your post indicates the pinhole lens predicts geometric distortion, which is a third order effect most apparent in a fisheye.

[Emmanuel BIGLER]

Your post indicates the pinhole lens predicts geometric distortion, which is a third order effect most apparent in a fisheye.

Hi !

I'm not sure that I properly understand what you mean.

Call it as you wish, my point is that perspective distorsion or whichever it is called in proper technical English, can be simulated by the traditional diagram of a pinhole camera. All perspective rendition effects can be simulated by a simple ray tracing, the basic pinhole ray tracing, for all quasi-symmetrical lenses and even for slightly defocused images.
Fish-eye effects and intrinsic lens distorsion is not something I'm considering here.
The fact that a rectangle can be projected slanted, or spheres projected as ellipses, is simply the consequence of standard conical projection and not an effect due to intrinsic lens distorsion.

But this is off-topic with respect to the initial question raised by Ken dealing with a good lens with virtually no intrinsic distorsion.
We also can add that as a rough approximation, the image circle of a LF lens is doubled when focusing to 1:1 / 2f-2f configuration, hence the total diagonal angle of view does not change ivery much if we use a bigger film size at 1:1.

I do not know if we have properly answered Ken' questions!

[Ken Lee]

I suspect my question has been answered.

If I understand correctly, we can discard a number of potentially confusing factors and the problem becomes simple to model.

To paraphrase and combine, we can imagine a simple lens which is stationary, while the subject and film plane can be adjusted freely. The lens doesn't know whether the subject or the film have been moved: it behaves the same way at all times. The focal length doesn't change, nor does the aperture.

What confused me was that in earlier conversations, it was suggested that as we focus closer, the focal length of the lens changes, and the effective aperture is correspondingly decreased. I see now that this was wrong.

Thank you for your most helpful and erudite explanations ! This forum is lucky to have such a high level of expertise among the members !

[Dan Fromm]

Ken, you're still mistaken. Effective aperture changes with magnification.

The magic formula is: effective aperture = (aperture set)*(1 + magnification)

Incidentally, I made a small slip in post #13 above. All of the distances are measured in focal lengths but I didn't indicate that.

[Struan Gray]

Dan: I suspect not moving the position of the lens to focus becomes important if you want to avoid the objects in the scene moving with respect to each other. Despite my perpetual twig obsession, macro photography of complex 3D scenes is not something I have experience of, so I don't know how important it is in practice. Some of my denser woodland photographs depend on a precise placement of the lens' seeing, and often disappoint if I move an inch or two from where my eye was when I spied the composition. I don't know if anybody but me would care though.

Ken: in photography it is usual to talk of the effective aperture, but that is just because photographers are used to working out exposures using f-numbers. A close up photograph of an object spreads the light coming from it over a larger area, so it's dimmer and needs more exposure to record the same density on film. You can express this in terms of effective apertures, as is conventional in photography, or in terms of the inverse square law operating on the light emerging from the exit pupil to form the image. Both descriptions work - they say the same thing - but the photographic one implies that something is happening to the aperture. It's not, you're just moving the film further away from the source of the light.

[Dan Fromm]

Struan, I understand your concern. I've done much of my closeup work with 35 mm SLRs. With them I dial in the magnification I want and move the camera/lens assembly to get the composition I want with the plane of best focus where I want it. I use electronic flash for illumination so can shoot handheld.

I've never done closeup work with 4x5, have with 2x3 Graphics. Shooting them handheld closeup is impossible so I use a variety of approximations to three axis translators to get the composition I want with the plane of best focus where I want it. In the worst case, pick the tripod up and move it a little. Its very slow and tedious work but the results are sometimes worth the effort.

[Struan Gray]

Dan, I think that when you get into real macro work, the depth of field is so thin that you naturally think in terms of photographing 2D patches of the world. The constant magnification approach then makes sense, especially if you know the size of your subject beforehand. It makes sense when stacking too, as it keeps the magnification of whatever is in focus the same.

I've taken the odd flower or soil close-up or semi-close-up, usually with meadow-like flora with a lot of 3D structure. Having a monorail with full front and back movements makes fine-tuning relatively easy - you don't get locked into the pointing axis of the camera. Putting the lens where I wanted to see from became the primary issue. Everything else could be adjusted after the fact.

Ken: when you wind the focus helical on a small-format camera it looks and feels as if you are doing something to the lens. If it's an IF one, you are, but with most older unit-focussing primes all you are doing is moving the entire lens structure back and forth, exactly as with using focus on the front standard of a LF camera. Things are more obvious with LF: I take my Norma to show to undergrad physicists in optics practicals to help them understand how unit focussing actually works.

[Tin Can]

I think of this as a box that may move back and forth within the 'angles' of view. I was going to make a gif demonstrating that, but this is a text based forum.