A little physics

[pnodrog]

Jack's, Ted's and John's are correct but some are illustrating different things.

[Abitconfused]

Thank you. I do not troll. I draw things to try to understand them. If I understand John's image. Every point on a lens contributes to a certain point on the sensor. Would this be the circle of confusion? I guess that depends upon the lens and the sensor but, perhaps, mostly the sensor. When we choose an f-stop such as f/16, we are reducing the number of points available to those nearest the center of the lens. Assuming this is true, how do we get a viable image, as the curvature near the center of a lens is the most subtle??

[pnodrog]

The curvature is consistent over the entire face of the lens. It is just one uniform arc.

P.S. In highly specialised or compound lenses there may well be corrective elements incorporated that are not a simple arc but the diagrams are illustrating the basic theory for simple one element lenses.

[Abitconfused]

Then why is the center of many lenses considered the "sweet spot" of the lens.

[pnodrog]

I think a perfect lens would not have a sweet spot - manufactures simply cannot make the perfect lens. You have switched from theory to practical performance and added in the complexity of an iris.

I know my three wood has a sweet spot that is inherent in the design of the club but that is a completely different subject.

[Abitconfused]

I think you have something there. The three wood's sweet spot may very we'll relate to the frequency generated at that spot in relation to the length of the club. Light frequencies probably react similarly.

[Inkanyezi]

The centre would not need any curvature at all to produce an image. When we make the aperture very small, we can remove all glass and still get an image. The simple hole will not have a focal length, but in essence, all rays that pass will continue in the same direction, as long as we cling to the ray theory for light.

Reality is a bit different, as light is indeed electromagnetic waves and will behave as waves when hitting the little hole. So the hole must be relatively large, compared to the wavelength, in order for any light to continue its straight path. At the sides of the hole, it is - you might have guessed - diffracted. So if the hole is very small compared to the wavelength, light that passes will be distributed more or less evenly on the other side. But for a sufficiently large small hole, an image will be formed on the other side, just as from a lens, and the simple hole, although always adding diffraction, does not have other optical defects.

Circle of confusion is a different thing. As you may suspect from my earlier rant, moving the lens farther away from the sensor would focus it closer. Objects that are not focused are "blurry" then, and the circle of confusion is what blurs them. Objects at larger distances will be focused somewhat before their rays hit the sensor, and the rays will then diverge before it reaches the sensor (as in your second sketch). Objects that are closer will be focused behind the sensor, and where they hit it, they are still converging. So those rays would not meet at a point on the sensor, but fall within a "circle of confusion".

[Glenn NK]

Then why is the center of many lenses considered the "sweet spot" of the lens.

Ed, the "sweet spot" is not just considered sweet, it's reality. The centre is not perfect, but the resolution is better at the centre than elsewhere in the lens.

Looking at the lens tests, it's quite clear that the best resolution is in the central part of the lens, with the edges being not quite as good, and the corners being not as good as the edges (there are of course two different edges with a rectangular image).

A quick peek at the MTF charts shows this (it doesn't matter what brand of lens is looked at - they all display this characteristic:

http://www.photozone.de/canon_eos_ff...8is_5d?start=1

Virtually every lens test I've looked at reveals a difference between the centre and the edges/corners (or border/extreme).


As to your question, the light rays don't have to bend as much at the centre (don't have to bend at all at the actual point of the centre). Different colours (wavelengths) refract different amounts, and where the diffraction is less, the resolution will be better and vice versa - this is at the centre.

Also referring to Urban's post (I'm getting a bit off topic):

The MTF tests also show that as the lens is stopped down, the resolution drops. At first glance, this seems counter-intuitive because stopping down uses less of the edges of the lens to form an image (thereby using relatively more of the centre) so it should get better.

The problem is that diffraction effects (which occur at the edges of the diaphragm - as pointed out by Urban) have more effect as the aperture gets smaller, so the image quality gets worse rather than better.

In effect, MTF tests show were diffraction starts to degrade the image quality as the aperture is made smaller.

Glenn

[Dulaigh]

What I don't understand is If I take a bite out of the lens the image is not impaired. The whole image is still transmitted Huh ?

[ajohnw]

Thank you. I do not troll. I draw things to try to understand them. If I understand John's image. Every point on a lens contributes to a certain point on the sensor. Would this be the circle of confusion? I guess that depends upon the lens and the sensor but, perhaps, mostly the sensor. When we choose an f-stop such as f/16, we are reducing the number of points available to those nearest the center of the lens. Assuming this is true, how do we get a viable image, as the curvature near the center of a lens is the most subtle??

That's correct so even if a piece is missing it will still do the same thing - less area in that case so it will have less light gathering power.

Sweet spots - generally refer to F ratio settings. Some will generally be better than others. Camera lenses are seldom at there best wide open. As they are stopped down they crisp up at some point and then often get worse when stopped down more.

In complex optics with many pieces of glass each lens is shaped to minimise aberrations. An iris is placed some where that effectively reduces the diameter of the lens. It gets a little complicated as it doesn't usually reduce the size of the glass at the end of the lens. A simple way to look at is that lenses have aberrations and as they get bigger the aberrations get bigger as well. So for instance one lens is 50mm dia and has a focal length of 200mm a lens that is 100mm dia and a focal length of 200mm the aberrations will be worse. The basic reason for this is that the bigger the lens the more the rays entering the increased part of the diameter have to be bent to arrive at the focus.

On camera lenses the whole or most of the front element is generally used what ever F stop is set and the iris placed some where else. This allows improvements in so called off axis performance - rays entering at an angle from the axis of the lens. It best to think of the subject being at infinity to understand that. Say stars. One on centre and another some way away from it. That generated the rays that are entering at an angle. The ones from the central star are parallel lines square to the axis of the lens as often shown in many diagrams.

John
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[xpatUSA]

Thank you. I do not troll. I draw things to try to understand them.

Ed, did you draw that first image? If I had known, I might have held back on the "hogwash" word used earlier!

But it looks like the thread is going off-course slightly :-(

If I understand John's image. Every point on a lens contributes to a certain point on the sensor.

No, that is not so. Consider the middle bit of the lens: light from the scene that is in line (axially) with the middle of the lens goes to the middle of the sensor; however, light from the edge of the scene also passes through the middle of the lens but goes to the edge of the sensor.

Would this be the circle of confusion?

It would not. The circle of confusion is aptly named because in photography it can be calculated several different ways or can simply be made equal to "wot Zeiss said" as if we all still had 35mm film cameras and only printed 8x10" (glurk).

I guess that depends upon the lens and the sensor but, perhaps, mostly the sensor. When we choose an f-stop such as f/16, we are reducing the number of points available to those nearest the center of the lens.

There may be a misconception here. A smaller aperture, right down to a pinhole, will still allow light rays from the edge of the scene to go to the edge of the sensor, but fewer photons/sec will be arriving there. (don't think about diffraction - that will muddy the waters).

Assuming this is true, how do we get a viable image, as the curvature near the center of a lens is the most subtle??

The curvature of a simple lens is equal everywhere on its surface. First, we should learn how images are made with a simple lens. Then learn about more advanced lens shapes later.

The large aperture vs. small aperture can be thought of thus:

Consider a point source of light such as a star. Light pours out in all directions but your lens, even with a large aperture, sees only a small portion of that light (google "solid angle"). In proper focus, the lens brings that portion of light onto one tiny area of the sensor. With a smaller aperture (going to say a stop or two to keep it simple) the light still lands onto that same tiny area but there is less of it, simply because there is less area for the starlight to pass through.

My apologies if I've repeated anyone's prior post content - was trying to do the one-point-at-a-time thing.

[Abitconfused]

Thank you ALL for your comments. I get it now!