Technical question on focusing

[kheong sann chan]

I thought I understood telescope focusing until I started trying to convert some of my telephoto lenses into telescopes by mounting eyepieces on them. Maybe someone can help check and correct my understanding. (I've found a cheap way to do that, basically by cutting a 1.25" hole in the end of my camera rear dust caps just big enough to squeeze the eyepiece. The dust caps are only about $1 each online, so I can afford to mess up, and I make 1 per eyepiece. The tools for drilling the 1.25" hole are also cheap, so this is a nice way to convert all my lenses into telescopes. I can point people to online vendors if there's interest.)

My understanding is that in telescopes, focus is achieved by moving the eyepiece (or the CCD) back and forth until the eyepiece (or CCD) is at the point where the rays from a certain distance all focus at the CCD plane. That distance is different for different subject distances. For telescopes, nothing is changing in the lens (or mirror) setup but only in where we place the detector.

Is this mechanism the same for camera lenses? in a camera lens, the lens-to-CCD distance doesn't change, it's held fixed by the camera mount. The front objective position isn't changing either. Generally you see the front piece of glass in a fixed position as you focus. So what's happening during focusing in a camera? The only thing I can think is that the glass inside the lens is moving so as to focus light from different distances in front of the lens, onto the CCD (which is at a fixed distance from the main objective). Since the definition of the focal length is the point at which parallel rays from infinity are focused, and we are changing that point during the focusing, does that effectively mean we are changing the focal length of the lens as it is focused? That doesn't seem right to me, but I can't see where I'm going wrong in my analysis.

Is the main objective in a camera lens the front-most piece of glass?

[Tim]

Never really thought about it before, but would assume the WHOLE lens assembly in compound lenses moves together, even if just a little bit, probably the length of the lens tube is extended/shortened.

If individual lenses moved within the housing, colour correction, and field flatness would be affected.

The focal length of the lens is primarily determined by the objective (front most) glass, as I understand it, but different eyepieces will come to focus at different positions.

[Tim]

Yep, the helical focuser on the lens extends or shortens the tube.

[ronin]

Most camera lens will be several bits of glass and yes they move to achieve focus. They are actually fairly complex as you really want to alter focal length without altering focus. This is difficult so you generally find that altering focal length will alter focus a little.

The front bit of glass is generally refered to as the main objective but that may be convention more then accuracy. It could as easily be looked on as a sort of "collector" that collects light over a larger angle then presents the light to the objective. This is the case on a few eyepieces. The problem is that in a compound lens of say 12 lens in 7 groups which is the objective?

Concerning the focal length and where the image is:

If you have 2 simple lens in contact (an approximation) then the total focal length is:

1/F = 1/F1 + 1/F2

Where F1 and F2 are the focal lengths of the individual lens.

Easy enough.

If however they are seperated by a seperation D then you have:

1/F = 1/F1 + 1/F2 - D/(F1F2)

So you see that by moving the second lens the overall focal length alters, thus your image plane moves.

The above is the simplified thin lens approach.

What you would (might) do in the above is to alter the seperation between the 2 lens to get the focal length required, then you move the whole lens assembly forward or back to get a sharp focus. Probably why a zoom lens has seperate zoom and focus bits. (No idea what to call them, so bits will have to do)

[IanL]

If you think of a telescope equipped with a Barlow lens (a magnifier) that will increase the effective focal length of the scope (and thus the 'magnification') without a correspondingly large increase in the focus point distance  from the objective.  Similarly for a reducer, the effective focal length is reduced (and so the magnification), again without a large decrease in the focus position.

Furthermore, if you vary the distance between the sensor and the Barlow or the reducer, you can change the magnification or reduction factor (though reducers are generally designed to work at an optimal distance so that you get a flat field across the whole image).

I'm not an expert in camera lenses, just peeked in to the front of a few cheap zooms, and it seems to me that some of the internal elements are moving with respect to the front objective and the rear element at the same time to achieve the required change in magnification whilst keeping the image in focus.

[kheong sann chan]

Most camera lens will be several bits of glass and yes they move to achieve focus. They are actually fairly complex as you really want to alter focal length without altering focus. This is difficult so you generally find that altering focal length will alter focus a little.

The front bit of glass is generally refered to as the main objective but that may be convention more then accuracy. It could as easily be looked on as a sort of "collector" that collects light over a larger angle then presents the light to the objective. This is the case on a few eyepieces. The problem is that in a compound lens of say 12 lens in 7 groups which is the objective?

Concerning the focal length and where the image is:

If you have 2 simple lens in contact (an approximation) then the total focal length is:

1/F = 1/F1 + 1/F2

Where F1 and F2 are the focal lengths of the individual lens.

Easy enough.

If however they are seperated by a seperation D then you have:

1/F = 1/F1 + 1/F2 - D/(F1F2)

So you see that by moving the second lens the overall focal length alters, thus your image plane moves.

The above is the simplified thin lens approach.

What you would (might) do in the above is to alter the seperation between the 2 lens to get the focal length required, then you move the whole lens assembly forward or back to get a sharp focus. Probably why a zoom lens has seperate zoom and focus bits. (No idea what to call them, so bits will have to do)

So you're saying that we _do_ change the focal length of the camera lens as it is focused? I thought the focal length determines how much magnification we observe (eg: 400mm lens has more magnification than a 50mm lens), but I don't think that as we change the focus, the magnification changes...

I've seen this 1/F=1/F1 + 1/F2 before, but in that context, F is the focal length of a single lens, F1 is the distance of the lens to the subject and F2 is the distance of the lens to the image produced. I'm not too sure how to interpret this equation in the context of 2 lenses as you're describing. This equation is quite useful in my context because I'm trying to determine how far back I need to put my eyepiece, and where to set the focus on my lens. I am constrained by the mounting mechanism to a limited range of distances to put the eyepiece. I'm hitting one more snag in that one of the lenses I'm trying to use does not allow me to focus it when it is not mounted on a camera... which is a pain. so I'm focusing it with a camera mounted, taking the camera off and then mounting the eyepiece and trying to find a good position for the eyepiece in the limited range I have. I think the lens equation above helps me to gauge where I should be focusing and where I should be mounting the eyepiece... Anyway, it's a learning experience and it exposed weaknesses in my understanding that I previously didn't know were there.

I'm  going to buy some macro tube extensions. That will give me more control over where I can place the eyepiece.

[kheong sann chan]

Most camera lens will be several bits of glass and yes they move to achieve focus. They are actually fairly complex as you really want to alter focal length without altering focus. This is difficult so you generally find that altering focal length will alter focus a little.

The front bit of glass is generally refered to as the main objective but that may be convention more then accuracy. It could as easily be looked on as a sort of "collector" that collects light over a larger angle then presents the light to the objective. This is the case on a few eyepieces. The problem is that in a compound lens of say 12 lens in 7 groups which is the objective?

Concerning the focal length and where the image is:

If you have 2 simple lens in contact (an approximation) then the total focal length is:

1/F = 1/F1 + 1/F2

Where F1 and F2 are the focal lengths of the individual lens.

Easy enough.

If however they are seperated by a seperation D then you have:

1/F = 1/F1 + 1/F2 - D/(F1F2)

So you see that by moving the second lens the overall focal length alters, thus your image plane moves.

The above is the simplified thin lens approach.

What you would (might) do in the above is to alter the seperation between the 2 lens to get the focal length required, then you move the whole lens assembly forward or back to get a sharp focus. Probably why a zoom lens has seperate zoom and focus bits. (No idea what to call them, so bits will have to do)

So after re-reading your post and thinking some more, I'd like to clarify that I'm not talking about zoom-lenses. I'm talking about prime lenses that are not supposed to change their focal length. But my analysis is (I think wrongly) suggesting that the focal length changes as we change the focus, which is what is puzzling me. Let's take the example of a 100mm prime lens. The definition of f=100mm means that parallel rays from infinity converge 100mm behind the lens, forming the image there. Non-parallel rays coming from a nearer subject actually focus further away 100mm, so you'd need to put your CCD at  for example 105mm to bring a non-infinity subject into focus. When a telescope focuses, it moves the CCD plane from 100mm to 105mm in order to bring a nearer subject into focus in which case the infinity point goes out of focus. In a camera, you can't move the CCD plane because it's fixed by the mount. My assumption is that the objective is not moving, but this might be wrong, or ill-defined because as (I think it was) TIm mentioned, how do you tell which is the objective in a multi-glass system? At any rate, if the objective is not moving relative to the CCD, what _is_ changing is the position that we are bringing into focus from let's say infinity to 10m. When we bring 10m into focus infinity necessarily goes out of focus. Infinity is now focusing somewhere else, not at 100mm any more. By the definition of focal length (where infinity focuses), the focal length of the lens has changed (and note, this is not a zoom, but a prime lens). So this is where I feel something is wrong, because when we say a 50mm prime lens, we don't mean it's a 45mm at near focus, but 50mm at infinity focus. It means 50mm regardless of where it's focused.

I think the way to get around this conclusion is to say that the objective lens in the multi-lens system is moving as we focus. The focal length of the system remains constant but the objective to CCD distance changes, just like in a telescope, even though the mount is holding everything in place, internally I think we must say the "effective objective" lens is moving relative to the CCD.

[IanL]

Let's be clear that I said the 'effective' focal length deliberately: So a refractor with an objective 1,000mm focal length plus a 2x Barlow would have an effective focal length of 2,000mm.  In other words it would have the same image scale as a refractor with an objective focal length of 2,000m, despite the fact the actual distance from the objective to the focal plane is only 1,000mm plus the physical length of  the Barlow.

It's no different that needing to use the objective focal length and the eyepiece focal length to determine the magnification for visual observing.

For a simple non-zoom camera lens, if the position of the sensor is fixed (which it is) the only way it can focus is by moving the objective - the focus ring is just a helical focuser and makes the lens body longer or shorter.

For a multi-element lens it's going to be more complicated; as I said I don't know the mechanics/optics having not really cared to this point, but on the zoom lenses I have, the body definitely moves the objective when twisting the focus ring, and appears to move the inner elements when you slide it to zoom in and out.