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George Kara
7-Sep-2006, 10:30
Just for information would someone please explain how an aperature is determined?
For example, I have a cook 25mm c mount for my super 8 which has a maximum aperature of .95

A canon 200/1.8 L, etc etc.

With large format 4.5 is generally considered very fast (or good for focusing at least).

How are these numbers derived?

George

Ron Marshall
7-Sep-2006, 10:42
The diameter of the lens opening divided by the lens focal length.

Ken Lee
7-Sep-2006, 11:03
Each stop is twice or half the light, depending on which way you go.

Each f/stop divides the area of the circle by 2.

Area = PI * (R squared).

If you want to double the area, you only need to open the diaphragm by the square root of 2, namely 1.4... not 2.

So you get 1.4, 2, 2.8, 4, 5.6, 8, 11, 16.

Leonard Evens
7-Sep-2006, 12:34
As has already been noted, the relative aperture or f-number is the ratio of the focal length to the diameter of the lens opening. (It is actually a bit more complicated since a lens has substantial extension, and the aperture may not be just where you think it might be. But you can assume the lens is confined to a plane and the aperture is a hole in that plane for all practical purposes.)

The relative aperture is used in determining exposure and also in calculating depth of field.

Large forma lenses have largest relative apertures anywhere from f/4.5 to f/9 or more. Generally, the wider apertures (smaller f-numbers) appear in wide angle lenses and the smaller apertures (larger f- numbers) in longer lenses. Longer lenses are easier to focus at the same relative aperture than shorter lenses would be. For example, I have a 75 mm f/4.5 lens and a 300 mm f/8.9 lens.

You would almost never use a large format lens wide open. It is just for focusing.

Patrik Roseen
7-Sep-2006, 12:50
...You would almost never use a large format lens wide open. It is just for focusing.

Leonard is right, however it is fun to occasionally shoot LF wide open for special effects. These were made with a Symmar f5.6/150mm on 4x5".

Slow Motion (http://www.photo.net/photodb/photo?photo_id=4707198&size=lg)
By the waterside (http://www.photo.net/photodb/photo?photo_id=4749717&size=lg)

robc
7-Sep-2006, 13:29
I think the crux of this question is how can you have an aperture of .95. i.e. an aperture which has a diameter of greater than the focal length of the lens?

Marc
7-Sep-2006, 14:03
I think the crux of this question is how can you have an aperture of .95. i.e. an aperture which has a diameter of greater than the focal length of the lens?
Canon did it with their rangefinders, as a 50mm f/0.95
Some details here:
http://www.tet.uni-hannover.de/~kapa/Photo.html
http://www.canon.com/camera-museum/camera/lens/s/data/s_50_095.html

Marc

Ernest Purdum
7-Sep-2006, 14:21
robc, the basic answer is big glass. Besides the Canon, there have been several special purpose lenses with apertures greater than f1.

I want to quibble on one point. It's not the actual aperture that is used in figuring the stop size, it is the apparent aperture, the size the hole seems to be when looking at the front of the lens. The front cell has a magnification factor which has to be taken into account. This has some relevance to robs's question, also.

Besides exmples like those provided by Patrick Roseen, large apertures are sometimes used in portraiture so as to provide shallow depth of field or deal with fidgety kids. Many of the old brass cannons provided selective focus to an extreme.

George Kara
7-Sep-2006, 15:15
So using my 200/1.8 this means that the diameter of the aperature (apparent or actual) is 111.11mm's?
and the cooke 25/.95=26.32mm's?

robc
7-Sep-2006, 15:36
yes, at least close enough for the purpose of the explanation. The iris diameter values will be slightly different because the figures you give are for the entrance pupil which is the magnified iris diameter.

if you set the aperture at .95 and measure the diameter accurately you should be able to find the difference between iris diameter and 26.32mm from where you could calculate the entrance pupil magnifcation if you really wanted to and providing you could measure accurately.

Dan Fromm
7-Sep-2006, 15:57
I think the crux of this question is how can you have an aperture of .95. i.e. an aperture which has a diameter of greater than the focal length of the lens?

Someone care to answer that?Marc, the theoretical limit of relative aperture in air is f/0.5. Microscope objectives intended for high and dry use approach that. Microscope objectives used with oil between the lens and the specimen -- so-called immersion objectives -- have relative apertures of around 0.30.

The fastest photographic objectives that are easily found are so called X-ray lenses, made to transfer images from a fluorescent screen to film. These things run as fast as f/0.7. For most of us, these things are totally useless.

Farrand made an f/0.87 Super Farron in focal lengths to 6". I've held a 76/.87 Super Farron in my hands, declined to buy it for \$200, rue the day.

Among the fastest lenses for large format are the 6"/1.9 and 8"/2.0 Dallmeyer Super Six. I've had a 6".

One of my neighbors has a 400/1.5 Zeiss lens, if he's lucky it will cover 6x6. Weighs 35 kg.

Cheers,

Dan

Ron Marshall
7-Sep-2006, 16:13
Kubrick used a 50mm f0.7 to shoot scenes in Barry Lyndon lit by candlelight.

http://www.theasc.com/magazine/oct99/sword/pg2.htm

Leonard Evens
8-Sep-2006, 04:34
There is no obvious reason why the focal length can't be less than the diameter of the aperture, i.e. relative aperture less than one. It should also be noted that the focal length need not be the distance of any part of the lens to the film plane when focused at infinity. It is the distance of the so called rear principle plane, which need not be within the lens. For lenses of inverted telephoto design, the rear flange focal length---the distance from the front of the lens board to the image plane at infinity---may be considerably greater than the focal length. Lenses meant for use in SLRs often are designed this way in order to allow room for the mirror. Even large format wide angle lenses often have a rear flange focal length greater than the focal length by several mm.

Dan,
I wasn't aware that there was a theoretical lower limit to the f-number. Where can I find a reference that explains that?

Helen Bach
8-Sep-2006, 05:06
Leonard,

It is a qualified limit - the qualification is that the lens is assumed to be well corrected for coma and spherical aberration. In that case, the second principal plane is a portion of a sphere with a radius equal to the focal length of the lens (the Abbe sine condition).

The biggest it can possibly be is therefore a hemisphere sitting on the image plane, and that hemisphere has a diameter of twice the focal length of the lens. I'm sure that this will be in most standard optics references, but if you want a specific reference I'll look later today.

Best,
Helen

Emmanuel BIGLER
8-Sep-2006, 07:25
One reference book about what Helen mentions is simply
Kingslake, Lens Design Fundamentals, Academic Press, San Diego (1978).

I recently got a reprinted copy of this most excellent book, the companion of 'history of the photographic lens'.
Real optical designers will find it obsolete since software design has made tremendous progress since, but some very basic and important rules are clearly explained. Including what happens in a large aperture aplanetic system.

We may add that the actual limit to the properties of concentrating light by any imaging or non-imaging optical systems is the conservation of luminance, which in fact obeys the second principle of thermodynamics, not the first (energy conservation).
It is not possible to concentrate by any means the image of a black body radiator to a target that would heat up above the temperature of the source.
Conical mirrors perform extremely well in concentrating solar radiations although they do not obey Abbe's sine rule. However they cannot concentrate energy beyond the absolute limit stated above.

A legend says that French scientists and engineers when designing a huge mirror named "the solar oven" installed near the Pyrenees in the South of France had expected to get temperatures above the sun's surface temperature before they realised that it was strictly forbidden by the Laws of Physics ;-);-)

Paul Fitzgerald
8-Sep-2006, 08:36
Hi there,

"I want to quibble on one point. It's not the actual aperture that is used in figuring the stop size, it is the apparent aperture, the size the hole seems to be when looking at the front of the lens."

Not to start a flame but apparent to which, you or the film?? Most lenses are measured looking from the front, Voigtlander Heliars are measured looking from the rear thru the lens, the numbers do not work in the other direction.

Is this just a matter of fashion? an advertising ploy? or did they measure the light levels at the focus plane? I've had no problems with exposures using Heliars, they are as they are marked.

Emmanuel BIGLER
8-Sep-2006, 09:14
Voigtlander Heliars are measured looking from the rear thru the lens, the numbers do not work in the other direction.

Voigt&#228;nder Masters knew their stuff so it is impossible to argue against the Great Priests of Gliesmarode, Braunschweig (see below images of The Place).

The question is to know how asymmetrical an Heliar is. To the best of my knowledge, the Heliar derives from the tessar with one additional cemented doublet, so at a first glance a naive approach suggests that the Heliar is weakly asymmetrical as well, the exit pupil and the entrance pupil diameters should be very close to each other. So in principle it should not matter so much from where you look at the pupil. If it actually does matter, it means that the pupillar magnification ratio is on-unit for the heliar.

It is a bit technical to prove what happens in a really asymmetrical lens with non-unit pupillar magnification ratio, but in this case you should refer to the entrance pupil. The only really asymmetrical lenses used in LF photography are telephotos, so for this kind of lenses actually it does matter from where you look at the pupil.
It has been mentioned here that the old Telomar had a pupillar magnification ratio of 0.5, so when reversed the lens features a theoretical entrance pupil diameter divided by two with respect to normal use, i.e. it looses 4 f-stops when used reversed !

Helen Bach
8-Sep-2006, 10:26
As is all too often the case, I had overlooked the obvious in favour of the obscure. As Emmanuel points out, at f/0.5 the subject luminance equals the image illuminance, if the right units are chosen. I'd never made the connection that Emmanuel mentions about why that is a limit.

Best,
Helen

Leonard Evens
8-Sep-2006, 17:09
Thanks Helen and Emmanuel! I think I understand both arguments.

It is always nice when two apparently different approaches give the same answer. It reminds us that there really is a physical universe out there that the theories do their best to describe.

Emmanuel BIGLER
9-Sep-2006, 02:19
I made a mistake above un the 0.5 Telomar example.
If the entrance pupil diameter is divided by two when the lens is reversed, the surface is divided by four, 4x is the exposure factor, this is "only" 2 f-stops. Mea culpa.

Another remark is that the f-number defined as the ratio of the paraxial focal length divided by the entrance beam diameter is useful only to quantify the energy density in an image at moderate apertures of a photographic or true imaging system.
For non imaging systems which do not care for Abbe's Sine Condition, you may expand the beam diameter to very high relative values with respect to the paraxial focal length but the actual energy density limit is still limited by the 2-nd law of thermodynamics.
In a parabolic reflector limited to the focal plane and illuminating the focal plane on one side only, the maximum beam diameter for rays reflected at grazing angles to the target is 4 times the focal length (8 times the radius of curvature at the vertex).

If you consider a complete parabolic reflector, that extends far beyond the paraxial focal plane, similar to those used in cars headlights, but used as an energy concentrator, you could argue that allowing light to fall on both sides of the detector could improve the efficiency by a factor 2. In fact when a steady state is reached, and the target heats up and stabilizes in temperature, there is as many enegy re-radiated as there is incident energy, so in a double-sided system you have two sides for capturing energy but also two sides to re-radiate it. So the maximum reachable temperature will not be higher than in a single-sided detector with an absolute insulation at the back.

And back to photographic lenses, my feeling that concentrating light at high f-numbers in super-fast lenses is not practically compatible with a wide field and top-class image quality. The improveent in film granularity and sensitivity, plus the development of low noise silicon image sensors with an equivalent ISO sensitivity in the same range as the best films does not push the engineers to design faster lenses in the f/1 range. Only the problem of diffraction spots for very small photographic sensors imposes that the apertures cannot be too small, but I doubt that we'll see in the near future lots of F/1 zoom lenses for consumer-grade digital cameras with sub-stamp-sized sensors.

Dan Fromm
9-Sep-2006, 02:41
Leonard, Helen, Emmanuel, please see http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html

Cheers,

Dan

Helen Bach
10-Sep-2006, 11:05
Dan,

Thanks. That's the same answer by another route. The maximum theoretical Numerical Aperture in air is unity, which corresponds to f/0.5 for an object at infinity.

Best,
Helen

Emmanuel BIGLER
11-Sep-2006, 01:46
Dan.
The article you mention deals with microscope objectives.
Usually people prefer sharp images and use aplanat lenses ;-) So Abbe's Sine Condition rules.
Immersion in oil will of course allow an increase of the numerical aperture more for resolution purposes than for capturing more light.
And just to re-hash an old story : in many articles dealing with diffraction and lateral resolution, the Airy disc and Rayleigh's criterion are still there in a XIX-st century approach ; many people did not follow the technical progress in optics of the XX-st century : MTF and cut-off frequency instead of the good ol' Rayleigh's criterion ;-)

Dan Fromm
11-Sep-2006, 06:36
Helen, you nailed it. I posted the MicroscopyU link because I think its a useful resource and to make it clear that I didn't make a stupid and arbitrary assertion based on nothing at all.

Emmanuel, a lens is a lens is a lens. You're right that microscopists are concerned with numerical aperture (= 1/2*f number) more for resolution than for illumination, but the bad news is true for all applications. If immersion lenses were practical for general photography, the "my thing exceeds your thing" lunatics would use them and try to lord it over those who didn't.

Cheers,

Dan

GPS
11-Sep-2006, 10:43
Interesting to see that in the heat of the highly theoretical debate nobody noticed that the first answer at the given question is incorrect.;-) Good to know for somebody that takes the thread out of the archive...

Helen Bach
11-Sep-2006, 18:24
Oh, that insignificant error? Easily explained by Abbie's upside-down condition.

Ole Tjugen
12-Sep-2006, 07:12
I noticed it, thought about it, and decided it was correct or not depending on nomenclature only.

if using "F-numbers" it would be wrong, but aperture is properly denoted as a fraction. And that answer would give the correct fraction.

Emmanuel BIGLER
12-Sep-2006, 10:16
I am sure that all the readers of this discussion will insist on getting even more information about weird things related to photographic apertures ;)

So for those who are not satisfied with the consequences of the Second Law of Thermodynamics on their f/0.95 lenses, let me remember the story about double scales engraved on movie camera lenses in the past.
The legend says that some had two scales : the geometric and the photometric.
The geometric was used to determine depth of field and directely related to the apparent diameter of the iris as usual.
The photometric was the same but offset by a suitable amount to take into account the actual transmission factor between the real world and the film inside the camera wich has to take into account... do not know, may be absorption/parasitic reflections in glass ? partially-reflective mirrors that divert a fraction of the main beam to the viewfinder ??

GPS
12-Sep-2006, 10:34
"...but aperture is properly denoted as a fraction" (Ole)
- and less "properly denoted using F- numbers?? Com'on.

Dan Fromm
12-Sep-2006, 11:20
Um, Emmanuel, the manufacturer of a lens for a cine camera can't, in general, predict how light will be taken out for viewing/metering unless he builds the viewing optics into the lens. Examples would be, say, Angenieux and Berthiot zooms with integral "dog leg" finders. So I expect that engraved t/stops reflect losses inside the lens itself.

Some cine cameras with reflex finders use reciprocating mirror (Beaulieu) or rotating mirror (Arri, Doiflex) shutters that send all of the light to the finder when the shutter is closed and all of the light to the film when the shutter is open. I'm not sure what Eclair and son-of-Eclair (Aaton) do. Or Panavision, Anton Bauer, ... , for that matter. Could dig out an ASC handbook, I guess, but all of mine are at home and I'm at the office.

Helen Bach
12-Sep-2006, 15:20
Dan,

Current Aaton, Panavision and Arri movie cameras in all formats all use mirror shutters to the best of my knowledge. The old Eclairs use mirror shutters as well.

Bolex give equivalent shutter speeds that take the beam splitter loss into account, so you can use the T-stop without any other adjustment.

Best,
Helen

Paul Fitzgerald
6-Oct-2006, 19:19
Hi there,

I just found another 'backwards' lens, a B&L 14x17 Tessar IIb (500/6.3). The numbers do not work from the front but are a perfect match from the rear. I don't know what that does to optical theories but it does make a large difference replacing the blades.

Just a note.

C. D. Keth
9-Oct-2006, 08:36
Dan,

Current Aaton, Panavision and Arri movie cameras in all formats all use mirror shutters to the best of my knowledge. The old Eclairs use mirror shutters as well.

Bolex give equivalent shutter speeds that take the beam splitter loss into account, so you can use the T-stop without any other adjustment.

Best,
Helen

It's splitting hairs for this purpose but the spinning mirror in a panaflex isn't actually the shutter ;) They use a seperate shutter of essentially the same design very close to the film plane. They cite the reason as being because the shutter is farther from the film on the top of frame than the bottom, uneven exposure can result under some situations.

I see the theory behind it, but in prctice I've never seen it in many trips out with arris. I just note this as a point of interest, it doesn't actually change the conversation any :P

Helen Bach
9-Oct-2006, 09:27
Absolutely right of course. Re-reading it, I wonder why I used the word 'shutter' at all because I was referring to the reflex viewing system, not the shutter. Just carelessness, I guess.

Best,
Helen

C. D. Keth
11-Oct-2006, 11:06
Absolutely right of course. Re-reading it, I wonder why I used the word 'shutter' at all because I was referring to the reflex viewing system, not the shutter. Just carelessness, I guess.

Best,
Helen

Not a gripe on your accuracy at all; for all practical purposes, they can be spoken about interchangeably. I just thought it was an interesting tidbit to mention. Take care :)