View Full Version : understanding f-number
Can someone please help stupid me understand this. I've heard it said that in terms of brightness, f/4 at a given focal length is the same whether on an SLR, MF, or LF. However, I'm not quite sure I understand that.
I understand that the same amount of light is collected on a given aperture size. However, for an f/4 lens on an SLR, that light is being put on a 35mm frame. For a LF, it is being put on a 4x5 or 8x10 piece of film. It would seem to me that in terms of "brightness", it certainly isn't the same, even at a given f-number.
Can someone please explain this to me.
f-stop = focal length / lens diameter ...
So, a 150 mmm lens (common on a 4x5 camera) would have to have 3X the lens diameter as a 50 mm lens (common on a 35 mm camera) to pass the same amount of light. That is why most LF lenses have higher minimum f-stops than 35 mm cameras.
There are some other factors such as lens designs, glass used, element shapes, etc. that also factor in ... but that is the basic concept, all things being equal.
It sounds like you are thinking, quite correctly, that, say, a 300mm f 5.6 normal for a 8x10 for instance, throws more light, in total, than the 50mm normal at f 5.6 for a 35mm camera. the 300 5.6 does throw more light.
The thing that makes it all work out so that your metering is accurate for all formats, with no correction for format, is that the longer lens is placed further away from the film and spreads all it's light over a much larger area. It works out that the amount of light in any unit of area at the plane of focus is the same for any lens of a given f stop. The extra total light gathering power of a big longer lens is exactly offset by the greater distance from lens to film, and thus, greater area the light is covering.
f-stop = focal length / lens diameter ...
That's like saying mm = distance. Aperture = focal length / diameter.
The f-stop is a calibrated unit of measurement that allows to have a consistent measurement of how much light a given aperture puts on the film. The idea is that any lens set to a given f/stop will always put the same amount of light on the film (or sensor), yielding the same exposure, no matter the focal length, which is why the f/stop is expressed independently of focal length or film/sensor format.
Not quite, Rakesh, the f-number is dimensionless.
The F in f-stop is actually the focal length, and the "diameter" it should be divided by is the diameter of the entrance pupil of the lens at a given aperture.
So a 360mm lens (F=360) with a 10mm aperture (entrance pupil) would be set at f:36.
Note that the colon in the notation is the European equivalent of a "/", so what it says is that the entrance pupil is 1/36th of the focal length. And since both the focal length and the aperture size are given in the same units of measurement, the f-number is a dimensionless ratio.
Have a read of this it helped my understanding of fstop and shutter speed
This has been explained well here - a given aperture will throw the same amount of light on a given piece of film/sensor, regardless of the focal length. As the lens gets longer, more light is lost in the journey through the lens to the film plane, so the physical aperture (opening) of the lens has to get larger to compensate.
I have a quick and dirty aperture area calculator on my website, for those who are interested:
Aperture area calculator (http://www.petercox.ie/aperture_calc.php)
There are also a few other useful essays and tutorial videos on my photography tutorials (http://www.petercox.ie/tutorials.php) page.
Rather than saying "As the lens gets longer, more light is lost in the journey through the lens to the film plane", you will have more complete understanding you consider that as the lens gets longer the image magnification increases and so the light collected from a given area of the subject is spread over a larger corresponding film area.
Both are correct, really. It's the inverse square law at work, along with the spreading of the image over a larger area. The larger film area only works intuitively if you're talking about going from a smaller to a larger format, but the effect is the same with different lenses on the same format.
But the inverse square law is identically "the spreading of the image over a larger area."
So we've established that we're in violent agreement then.
So we've established that we're in violent agreement then.
If you say so. I was bothered by your use of the word "lost" as if light is dissipated by travels along its path. In fact the light energy is conserved, it is just spread over the larger image area.
The increase in image area exactly accounts for the way the entrance pupil diameter increases with focal length. Doubling the focal length doubles the magnification (for large subject distances) and therefore increases the image area by a factor of four. Doubling the entrance pupil diameter (i.e., keeping a constant F number or keeping the entrance pupil diameter a constant fraction of the focal length) increases the area of the entrance pupil by four.
The explanation about cropping a smaller area of the subject to the same sensor size, thus reducing the light, makes more sense to me than saying the light 'dissipates'. Thank you for that clarification (although I'm sure the light does dissipate to a minor extent, as unless there is a vacuum inbetween the front and rear elements, some of the light will bump into air molecules and be converted into heat).
So, if I want to meter with my 4/3rds camera for my LF camera, I divide both the focal length and the f-number by 7.5 (the crop-factor from 4/3rds to LF), and use the same ISO setting on my 4/3rds camera as my film, right?
So, lets say I have a 150/5.6 LF lens and want to take the image at f/32. In terms of light & angle of view, that is approximately equivalent to 20/4.3 on 4/3rds... So I would set my 14-54/2.8-3.5 to 20 and put the aperture as close to 4.3 as I can, using the same ISO, to meter, right?
What do I do when I can't find an equivalent on my 4/3rds camera? I.e., if I want to shoot wide open with LF at 150/5.6, that's equivalent to 20/0.75 on 4/3rds. There is no such lens, and if there were was, I wouldn't be able to afford it.
You are way over-thinking this. f/32 on your 4/3rds camera (if it had one) would be identical to (provide the same image intensity as) f/32 on your 4x5. So if your DSLR said 1/125 of a second at f/16, then the exposure for the 4x5 would also be 1/125 at f/16 or 1/30 at f/32 (assuming the DSLR ISO was set to match your 4x5 film speed.)
The only subtlety would involve higher order things like the differences in exposure latitude between the film and the sensor or the suitability of the DSLR's metering algorithm for the way you shoot and process your film. There are a number of members of this forum who recommend using a DSLR and its histogram function, as a meter when shooting LF. I don't think I have ever held a DSLR in my hands.
No, you would use the same settings on the 4/3rds camera as on the LF. A 150mm f:5.6 LF lens is roughly equivalent to a 20mm llens at f:5.6 on a 4/3rds camera. The only complication is yhat those dinky little things don't stop down to f:32...
No, that's the whole point behind having standardized and calibrated measurements for aperture -- that's called an "f-stop".
It doesn't matter how you get to the same f-stop setting on your lens, it's the same f-stop. As I pointed out, it's not the same as aperture, it's a measurement. It's functionally identical to measuring distance; 6mm here in Washington is the same as 6mm in New Zealand. f/2 yields the same amount of light on a 1000 mm lens as it does on a 50mm lens -- though such a 1000 mm lens would have to be enormous to gather enough light to match the amount of light a 50mm f/2 lens can gather.
So to meter for a big camera with a small one, match the f/stop and match as closely as you can the field of view, or just use a long lens, treat it like a spot meter, and adjust accordingly since f/stops are f/stops. It's not any different from doubling the exposure by halving the shutter speed, that's also the same amount of light.
Thank you very much for the replies, everyone.
F-stops are calculated values. If you need the exact same exposure when changing lenses, then T-stops are the way to go. The motion picture people are more concerned with this than the 'still' folks.
This thread is drifting a bit.....
I will suggest some clarification....
For the purposes of this discussion, there should be no consideration of light lost through the glass elements. This is a function of the number of glass surfaces, coatings, etc, its not part of the f stop system being discussed here. It's also rarely a major consideration in exposure. Also, for sake of this discussion we should put aside cosine theta fall off for WA lenses, and, exposure compensation for close subjects (macro).
fl = magnification, regardless of format size. This is why a given fl can act as a SWA, WA, Normal, long, or Telephoto, based on the format size its used on. Using the same fl lens, on any format, image size at the film plane will ALWAYS be the identical - assuming same camera to subject distance.
About format size and f stop value....
A 150mm fl lens on 35mm camera and a 150mm lens on a 8x10 camera will produce the same magnification of a subject, (same size at the image plane - assuming same camera position) therefore, at the same f stop, it will produce the exact same subject brightness at the film plane. As you can see, format size is NOT relevant, i.e. a larger / smaller image circle has no bearing on image brightness.
The larger image circle is a function of the lens design, ....i.e. it's angle of coverage on the subject side of the lens AND the angular projection on the film side of the lens. No light is lost, because the same composure is NOT being spread over a larger image circle. Instead, the lens simply takes in a greater angular view of the subject and therefore has a wider angular projection (larger image circle). So light is NEVER "diluted" over a larger image circle.... this is SINGLE biggest misconception about exposure.
What is f stop ?
It's the diameter of the apt. opening, calc. by fl / f stop. Why are the stops placed at these distinct values? 2.0, 2.8, 4.0, etc.? Because each stop represents half the light (going up), or 2x the light, going down. This is a result of the area of a circle.... or the apt. opening (even though apertures are not always perfect circles, they are corrected for such)
A 200mm f2.0 lens has a 100mm diam apt. opening (200/2 =100mm). A 100mm diam. apt. has an area of 7854mm (pi * 50^2) . At f2.8, the apt. diameter is 71mm, the apt. area is half of the 100mm diam area. Half the lens opening "area" (not diameter) = half the light. If you go down in f stops, each stop will double the "area" of the aperture circle. If you go up in f stops, each stop will half the "area" of the apt. opening, halving the light.
If the area calcs are not a 100% match, this is because the f stops are abbreviated, example, its not really f11, but f 11.2
What is the relationship between f stop and fl?
When you double the fl, you double the image magnification at the film plane, now image brightness is 1/4 (25%). Once again, this is a result of magnification, NOT angle of coverage (format size)..... so forget format sizes, they are NOT relevant to f stops in ANY way.
Example.... Lets assume you are shooting a cardboard square. When you double the fl, you have doubled the squares dimensions on the image plane. Now the square on the image plane has 4x the area. Since the brightness level of the real square (subject) has remained the same in both scenarios, then by doubling the squares dimensions on the image plane, you have taken the same amount of light from the subject, but now it's spread over an "area" 4x greater. This reduces image brightness by a factor of 4, so the larger magnified square has 1/4 (25%) of the image brightness. To compensate for the light loss of doubling the fl, you must 4x the area of the apt. opening, which equals two full f stops, (2x the f stop value), i.e f4 to f8. It's so simple, double fl, half the f stop..... half the fl, double the f stop.
This is the beauty of the "log" exposure system, it was all predicated on how light levels at the film plane change with magnification. The F stop system removes the magnification variable (lens fl), when determining exposure. It's amazing this system was created in the 1800's. It's was so brilliant, it remains unchanged today!
An brain teaser for f stop and magnification..... Consider this, you scatter every possible format size camera at different camera-to-subject distances. All the format size cameras use a given fl lens to produce the same image size of the subject. They can range from 10mm fl to 1200mm fl. All lenses are set at the same f stop.
If you measure the image sizes on all the ground glasses (or by whatever means you can), and ALL image sizes of the subject are identical, then you can be assured that each image has the EXACT SAME brightness. Even though, one camera might be 5 ft. from the subject and one as far as 600 ft. One might be mini digicam and another might be a 16x20 ULF, (or anything in between) it does not matter.....once again, lens fl and format size is irrelevant. It comes down to this.......
SAME image size, SAME f stop =
SAME IMAGE BRIGHTNESS !
f stop is about image magnification only!
I hope this helps the OP with his question....
Thank you for that informative post. I think that was the clearest description that I have read, and think I finally get it. The f-stop of the lens only determines the intensity of light it gathers.
Now, one other related question: if that is the case, why do different lenses have different image circles? Shouldn't it just be a function of how far the film is placed from the lens, the size of the image circle?
> The f-stop of the lens only determines the intensity of light it gathers.
Yep, same f stop, same light at the image plane ....just don't forget the only caveat.... "same image size".
> if that is the case, why do different lenses have different image circles? Shouldn't it just be a function of how far the film is placed from the lens, the size of the image circle?
I addressed this in my last post..... The Image circle is a function of the angle of coverage of a lens, both the subject side of the lens, and the film side. This is determined during lens design. For example, a 150mm lens designed for a 35mm camera only views a small fraction of a scene vs. a 150mm lens designed for an 8x10 camera. However, if you used the 150mm 8x10 lens, and photographed with a 35mm film back, it would produce the same image on the film back, as the 150mm SLR lens would on a SLR camera. Assuming lens and film are always concentric.
While light is not "diluted" with a larger image circle of a lenses of equal fl, resolution IS "reduced" when expanding to a larger image circle. There is many reasons for this, and it will detract from your thread...but the biggest cause of this is, the large image circle lenses must contend with a bulk of its image area, being off-axis rays. The greater the ray angles, the more optical correction required. On longer fl's the problem becomes DOF, so the lens must be optimized at higher f stops, now apt. diffraction becomes the limiting factor of resolution. It's these opposing optical principles that keeps the formats closer in final IQ than the film sizes would suggest.
Thanks again for your reply. I now have a better idea of why it is more difficult to get a LF lens with as high a resolution as a MF or SF lens. However, from reading lpmm lens resolution tests, it seems that the best MF lenses don't return exceptional increases in resolution over good LF lenses (and many of them aren't sharper at all). The other thing I've read is that the limiting factor is often the film.
The greater the ray angles, the more optical correction required. On longer fl's the problem becomes DOF, so the lens must be optimized at higher f stops, now apt. diffraction becomes the limiting factor of resolution. It's these opposing optical principles that keeps the formats closer in final IQ than the film sizes would suggest.
This is interesting, and poses another interesting question that comes to my mind: would this be eliminated with mirror-based "lenses"? I presume optical correction is necessary because of chromatic aberration and color shift that occurs when light goes through a lens. But that doesn't happen with mirrors. (I know there is the problem of "ring" bokeh patterns because of the obstructing secondary mirror; however, there are off-axis "yolo" or mirror designs that don't have an obstructing mirror).
dh003i, have you considered reading a book? Try S. F. Ray's Applied Photographic Optics. I believe, could be mistaken, that the 3d edition is the latest.
And have you considered answering y'r questions with camera, lenses, and film?
I'm not suggesting that you shut up, rather that you'll learn more from a solid authority who writes in chapters and from thoughtful experience than from people who write, at best, in paragraphs. If you're like me, you won't understand everything Ray says at first reading. That's where the equipment and film come in. Do the best you can to understand, then run a little experiment to test your understanding.
> However, from reading lpmm lens resolution tests, it seems that the best MF lenses don't return exceptional increases in resolution over good LF lenses (and many of them aren't sharper at all).
Excellent observation. What you are seeing in these test results, such a Chris Perez's web site, is an evolution of lens design. Technology in photo optics has continued to improve..... particularly in the late mid to late 90's when optical software really started to demonstrate its prowess. But many of the LF lenses have been around for a 100 years, and many still in use today, so their designs are very dated. Most MF lenses never received the full benefit of newer optical designs, like 35mm lenses have, as well as LF lenses. The exception is the Mamiya 7 lenses, they are damn close to the best 35mm lenses made. Within each camera line, you will find a few sharp designs, that often were designed in the mid 90's+ vs. the 70's or 80's designs.
My thoughts on the subject are..... When MF went digital, the LF companies were first out of the gate with "digital lenses"..... the camera makers were in a battle trying to convert to digital, so with these lenses available off-the-shelf, they did not focus on this component of the camera system. As you know, many of the MF makers either folded, merged or are in big trouble....
As for film being the limiting factor.....well, both lens and film are limiting factors. However, the higher aerial resolution lens will always deliver more OFR (On Film Resolution). Do a search for 1/R equation to see how lens and film MTF combine to produce OFR.
> would this be eliminated with mirror-based "lenses"? I presume optical correction is necessary because of chromatic aberration and color shift that occurs when light goes through a lens. But that doesn't happen with mirrors.
Mirror lenses have their own set of optical aberrations the designer must contend with. They are NOT immune to astig., coma, color shifts, etc. In addition, as you mentioned, the secondary mirror is an additional diffraction surface....although the secondary mirror on both Newtonian and SC (Schmidt-Cassegrain) designs reduce image contrast, not resolution, but its substantial vs. a good refractive lens. And mirror designs have opposing forces as well.... the longer the f ratio, the better the IQ...but the light path becomes ridiculously long. A 5" apt. mirror design, well corrected at f10 (vs. f5) has a 50" light path. Not Photo friendly :-(
This secondary mirror forces lower MTF vs. a well designed refractive lens. In addition mirror lenses are limited to long fl's (due to long light travel distances), they can't be designed as zoom lenses, IS is not possible, auto focus would be too complex, etc... and they are often very slow vs. refractive lenses.
The most sensible camera lens is the SC design, which has the highest f ratio of all, due to the light traveling 3 alternating directions. But the benefit is their shorter length...hence why Sony introduced a new mirror 500mm f8 last month, which is probably the sweet spot for a mirror lens on a SLR.
> there are off-axis "yolo" or mirror designs that don't have an obstructing mirror
yes, there is off-axis mirror designs, and this does eliminate the secondary mirror being in the light path of the primary mirror. However, as you can imagine they present a new set of problems, as the mirrors are no longer spherical, and/or require secondary refractive optical corrections. Therefore the mirror build has tremendous complexity. They also require very tight mechanical tolerances when placed into the tube. Cost are exorbitant. If you want to learn more about these different types of mirror designs, hit some astronomy web sites, as this where such designs make more sense.....and even the off-axis designs are built today. Of course in the end, if any of these lenses made good economical sense in the photo field, they would be used for camera lenses today... I am impressed with Sony's new Reflex offering, but never used it.
An interesting side note....before digital became vogue, many telescopes were designed to accept 6x7, 6x9 and 4x5 film backs (for astrophotography)....so these designs would function OK for terrestrial use also, but the results would be less than stellar compared to a modern LF lens. I have a Nikkor 1200mm lens that covers 8x10.... Most mirror scopes are in this fl range, but will NOT cover 8x10... and the ones that cover 4x5 would be no match for LF lenses. Of course, if you needed a VERY long lens, there is no reason it can not be utilized today.
Thanks for the book suggestion for Applied Photographic Optics; but to me, the price seems a little bit exorbitant -- in line with the outrageous rip-off prices of college textbooks (which I presume is what it is). I had forgotten the insane price of college textbooks.
For now, I'll stick with reading through Adams' The Camera, which at $25, is more in line with what I'm willing to spend on a book.
Just a thought here. The f stop is indeed a universal indication of the ability of a given lens to illuminate the film at the same level for whatever lens. However when using the lens to focus close, on a LF camera typically, one needs to increase the distance between the lens and the film plane. This means that the true f stop is smaller than that indicated on the aperture ring. If the distance between the two exceeds the focal length of the lens by 2x (that is 300mm for a 150mm lens) then an f4 lens becomes an f8 at that extension. Hence the charts that are available for so called macro work. It isn't magic, it all comes down to logic in the end.
On the matter of image circle coverage: this is a matter of for which format the lens is designed. The lens is placed more or less at its focal length away from the film. at that distance, when focused sharply, the image circle will illuminate the intended film format adequately from corner to corner. At larger extensions, the image circle is also larger but it is unlikely to be so large that the lens can be used on the next format up. So a lens intended for 5x4 will be unlikely to give good coverage on 5x7 or 10x8.
> However when using the lens to focus close, on a LF camera typically, one needs to increase the distance between the lens and the film plane.
Fully agreed, I stated this and other exposure issues, in my original post....
"For the purposes of this discussion, there should be no consideration of light lost through the glass elements. This is a function of the number of glass surfaces, coatings, etc, its not part of the f stop system being discussed here. It's also rarely a major consideration in exposure. Also, for sake of this discussion we should put aside cosine theta fall off for WA lenses, and, exposure compensation for close subjects (macro)."
While on the subject of exposure.... here is another "gotcha" exposure issue. Some lenses actual do consume light.... each glass surface will consume some light through reflection, as well as some very minor losses within the glass. With modern coatings this reflection issue has been minimized to the point of it being a non-issue. However, with some of the more high tech lenses with 12 - 20 elements, the number of surfaces add up fast. These small losses at each surface, which will not produce noticeable light loss in a 4 element design, but can have noticeable light loss in a 15+ element design. I was burnt by this once, using a standard light meter to set exposure on a 35mm film shoot (tricky lighting).... the lens was consuming almost a 1/2 stop of light, it had 18 elements. Punchline - the f number of a lens represents the apt. diameter, not the light throughput. Exposure meters assume 100% light throughput.
Bill, losing only half a stop with a coated 18 element lens isn't bad. An uncoated triplet with only six glass-air interfaces loses roughly half a stop too. Evaluate .95^6.
Consider the Angenieux 8x8B, an 8-64/1.9 zoom lens that was fitted to Beaulieus, Leicinas, etc. Mine t-stopped around t/3.4. Truly a lens for high noon and few other times of day. I found the 7-70/1.4 on a Nikon R-10 similarly dim, and test reports on the camera reported that it t/stopped much slower than the nominal f/stop. Also a camera for high noon.
> Bill, losing only half a stop with a coated 18 element lens isn't bad. An uncoated triplet with only six glass-air interfaces loses roughly half a stop too. Evaluate .95^6.
Well, we all assume the ultra high transmissive value of coatings today would eliminate any throughput issue.... but I agree, with 36 surfaces elements, you start gangin losses on top of losses. This issue is rarely raised, so it can fly under the radar, till you get your film processed :-( Of course, manufacturers will NEVER provide this data, as many people buy fast lenses, because of the fast ss they need.... loosing a 1/2 stop in throughput is not a good way to sell an expensive, and often very heavy lenses.
I have never used / collected older LF lenses... I was going to ask in previous post.... I am curious about vintage LF lenses and the number of elements vs. transmissive losses. Do you have a feel for these losses through several eras of LF lenses? I understand that even the early early coatings of the 70's were much inferior vs. what we have today, but never knew to what extent. Maybe you can elaborate....
The uncoated Dialytes and double-gausses are about the worst LF lenses where light loss is concerned. Eight surfaces means you lose almost a stop of image-forming light - although you "get it back" as shadow-lifting haze. ;)
I have two 130mm f:4.5 Rodenstock Eurynars, one of which has been coated at a later date. The difference is stunning!
On the other hand I have a 150mm f:3.5 Xenar Typ D with natural bloom. The light transmission is visibly better than an uncoated Tessar of about the same age. So while the earlier (or even unintended) coatings really are inferior compared to modern coatings, you won't see any significant differences wiht LF lenses. Now with a 24-elements-in-18-groups superduperzoom lens, it's a different matter.
Bill, I haven't looked at Rodenstock's lens data sheets for a while, but Schneider's usually show transmission, and by wavelength too.
My experience with uncoated older lenses is limited to tessar types, triplets, dialytes and 6/4 double Gauss types. The emulsions I shoot are a little forgiving and it could be that my leaf shutters run a little slow. The upshot is that I've had no underexposure problems with any of my old lenses in or in front of shutter or, for that matter, any of my post-WWII coated ones.
I have had flare problems with one modern single coated lens, in the form of Ole's shadow-lifting haze, that could be controlled by a lens hood. 210/9 Konica Hexanon GRII. This one, not the 150/9 GRII and possibly not the others as well, is 6/6. More than sharp enough, but needs to be used with care.
Re Ole's comment on has 130/4.5 Eurynars, the VM says much the same about a pair of f/1.9 (6/4 double Gauss) Dallmeyer Super Sixes, one coated, the other not. But I don't recall flare or underexposure problems with the uncoated 50/2 Xenons (same design family) on my old Retinas. Could be that my memory is failing.
> Bill, I haven't looked at Rodenstock's lens data sheets for a while, but Schneider's usually show transmission, and by wavelength too.
I should have been more specific.... .I was referring to the super dooper zoom lenses with 36+ surface lenses for DSLR's.... LF lenses today, do not have enough surfaces for this to be a big issue. Modern coatings remove this issue for LF lenses...
Interesting about the Eurynars... a guess the saving grace is....back in the days before coatings, lens designs were not complex, limited number of elements, so while they may have ate light like a hungry rat....overall, not a deal-breaker. A stop is a lot, but I was wondering if some were even worse, but I guess not enough surfaces. Between the ultra slow film and slow lenses back in the day..... I guess we have it easy, vs. the pre 1960's era.
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