[photoptimist]

Are there examples of the same focal length with the same aperture that have differences in light-gathering power (independent of T-stops)? This doesn't immediately make sense to me, unless the tele lens gets more light because of the larger image in the viewfinder. Would a wider-angle lens with a large front element also have brighter stars?

The same focal length with the same numerical aperture always has the same light gathering power (independent of T-stop and corner light fall-off issues caused by the coatings, numbers of elements, materials, and design).

For a given numerical aperture, say f/4, but different focal lengths, the light gathering properties are more complicated.

Think of it this way: each pixel of a telephoto shot at f/4 comes from a smaller chunk of the world (e.g., tinier patch of skin, leaf, or wall) than does a wide-angle shot at f/4 so that seems like less total light. The higher magnification in the telephoto shot makes it dimmer. But, a telephoto lens also has a bigger light-gathering physical aperture than does a wide angle lens (if both are set to the same f-stop), so that's more total light. The two effects cancel so that an f/4 setting has the same sensor signal brightness regardless of focal length. (That's why you can use a standalone light meter that doesn't know the focal length -- f/4 is f/4 on all lenses in terms of light gathering)

But pictures of stars are different. The wide-angle pixel sees the same pin-point star as does the telephoto pixel. Wide angle doesn't see more star the way it sees more skin, leaf, or wall when shooting an image of a surface. Thus for stars, the pixel area advantage of wide angle doesn't counterbalance the physical aperture advantage of telephoto. The net effect is that a telephoto shot of a star gets more light than the wide angle shot of the same star at the same numerical aperture.

Net effect: for astrophotography, telephoto lenses and big telescopes get brighter stars relative to the darkness of the sky.


As for the front element, the light gathering power of the front element defines the upper limit of light gathered, but in most lenses (all but telephoto lenses), only a small fraction of the light gathered by the front element actually makes it to the sensor. Take a look at the front of the typical wide angle lens or a zoom lens at it's wide-angle limit. Behind the big front element you can see a tiny aperture hole surrounded by rings of black metal or plastic that hold all the lens elements in place. Most of the light hitting the front element ends up landing in the black ring zone and only a small amount goes through the center hole (the entrance pupil) to reach the sensor. It's the diameter of the entrance pupil that matters because that is what limits the amount of light gathered and sent to the sensor or film.

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Last edited by photoptimist; 08-13-2020 at 04:28 AM. Reason: typo

[stevebrot]

Are there examples of the same focal length with the same aperture that have differences in light-gathering power (independent of T-stops)? This doesn't immediately make sense to me, unless the tele lens gets more light because of the larger image in the viewfinder. Would a wider-angle lens with a large front element also have brighter stars?

Telescopes in the realm of astrophotography are the usual example.


Steve

[angerdan]

1. Are there examples of the same focal length with the same aperture that have differences in light-gathering power (independent of T-stops)?
2. This doesn't immediately make sense to me, unless the tele lens gets more light because of the larger image in the viewfinder.
3. Would a wider-angle lens with a large front element also have brighter stars?

1. Yes, here:
   Nikon AF-S Nikkor 50mm f/1.4G on Nikon D800E vs Sigma 50mm F1.4 DG HSM A Nikon on Nikon D800E
2. You forget that behind the front lens there're more lenses. Each lens element takes some light on it's way to the sensor. So depending on the number of lens elements and their coating there are differences.
   Even with the same number ol elements, t-stop can be different due to the coating.
   Canon EF 200mm f/2.8L II USM on Canon EOS 5DS R vs Pentax smc DA Star 200mm F2.8 ED (IF) SDM on Pentax K-3
3. No, because it depends on the relation between focal length and lens diameter. The longer the focal lenght, the longer the way light has to travel and gets loss inside the optical elements.
   Side by Side Comparison Sigma 24mm F1.4 DG HSM Art vs. Sigma 50mm F1.4 DG HSM | A: Digital Photography Review

[cometguy]

Since the original post was about astrophotography, I think that exterior glass size (objective diameter) does matter a lot. Regarding the discussed differences between diaphragm-blades aperture (i.e., setting the f-stop from f/1.4 to f/22 or whatever), I would assume that the optics are designed to bend the vast majority of the light through a wide-open aperture (f/1.4 or f/2, etc.), so that the aperture blades are rather negligible in terms of diminishing light-gathering power when wide open (which should, if designed properly) be a function of the outside objective diameter. One key factor not discussed above is the number of lens elements in any given lens, because every lens element absorbs a non-negligible amount of light when considering faint astronomical sources.. When you use fast, small lenses, the sky background will quickly overwhelm faint astronomical objects unless you photograph from a dark-sky site well away from city/town light pollution. Longer-focal-length camera lenses (i.e., 135-mm f/2.5 Takumar vs. a 24-mm f/2 FA) will be way better for any astronomy application in a suburban location with heavy light pollution (no direct light, of course) than will a wide-angle, short-focal-length lens. But the wide-angle lenses are good in a dark site for things like capturing the Milky Way or meteors during a meteor shower. I get great star and planet shots in bright suburbia with my longer-focal-length lenses but can't do anything astronomical, really, with the shorter lenses without going to a dark site.


With astronomical telescopes, the clear aperture of the lens or mirror is the most important thing, followed by the f/-ratio of that objective glass; faint astronomical objects take less time to register on photographic sensors (film, CCD, CMOS, etc.) with lower f/-ratio and with larger clear-objective glass diameter. The top survey telescopes looking for objects near the earth or for distant supernovae typically have mirrors of size 0.5-1.8 meters with low f/-ratios like f/2, and they get very faint with fairly short exposures (45-sec). There are, however, some surveys that basically use large refracting telephoto lenses to discover and monitor comets, cataclysmic variable stars, etc., and there are numerous meteor surveys using wide-angle camera lenses using three or more widely-spaced stations to determine orbits of bright fireballs and search for possible meteorites that survive entry through the atmosphere. I know that some Pentax camera equipment has been used for discoveries by advanced amateur astronomers, especially Japanese observers.

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Last edited by cometguy; 08-15-2020 at 10:55 PM.

[zeebanker]

Since the original post was about astrophotography, I think that exterior glass size (objective diameter) does matter a lot. Regarding the discussed differences between diaphragm-blades aperture (i.e., setting the f-stop from f/1.4 to f/22 or whatever), I would assume that the optics are designed to bend the vast majority of the light through a wide-open aperture (f/1.4 or f/2, etc.), so that the aperture blades are rather negligible in terms of diminishing light-gathering power when wide open (which should, if designed properly) be a function of the outside objective diameter. One key factor not discussed above is the number of lens elements in any given lens, because every lens element absorbs a non-negligible amount of light when considering faint astronomical sources.. When you use fast, small lenses, the sky background will quickly overwhelm faint astronomical objects unless you photograph from a dark-sky site well away from city/town light pollution. Longer-focal-length camera lenses (i.e., 135-mm f/2.5 Takumar vs. a 24-mm f/2 FA) will be way better for any astronomy application in a suburban location with heavy light pollution (no direct light, of course) than will a wide-angle, short-focal-length lens. But the wide-angle lenses are good in a dark site for things like capturing the Milky Way or meteors during a meteor shower. I get great star and planet shots in bright suburbia with my longer-focal-length lenses but can't do anything astronomical, really, with the shorter lenses without going to a dark site.


With astronomical telescopes, the clear aperture of the lens or mirror is the most important thing, followed by the f/-ratio of that objective glass; faint astronomical objects take less time to register on photographic sensors (film, CCD, CMOS, etc.) with lower f/-ratio and with larger clear-objective glass diameter. The top survey telescopes looking for objects near the earth or for distant supernovae typically have mirrors of size 0.5-1.8 meters with low f/-ratios like f/2, and they get very faint with fairly short exposures (45-sec). There are, however, some surveys that basically use large refracting telephoto lenses to discover and monitor comets, cataclysmic variable stars, etc., and there are numerous meteor surveys using wide-angle camera lenses using three or more widely-spaced stations to determine orbits of bright fireballs and search for possible meteorites that survive entry through the atmosphere. I know that some Pentax camera equipment has been used for discoveries by advanced amateur astronomers, especially Japanese observers.

Thanks Cometguy. My thoughts on the physical diameter of the objective for astrophotography mirror (pun intended) yours. Obviously a reflecting telescope (or a simple refracting one for that matter) has fewer optical elements that a 1:1 comparison to cameras is not possible, without making broad generalizations. I instinctively (or from experience) knew what you are saying about using a telephoto lens vs. wide prime lens for urban vs. dark site photography.

[stevebrot]

With astronomical telescopes, the clear aperture of the lens or mirror is the most important thing...

Thanks for your excellent and very clear explanation. I will reiterate, though, that with an on-camera photographic lens, the clear (absolute) aperture is no wider than the entrance pupil diameter with the iris wide open. I note that purely for clarification since it is that point of comparison with telescopes that creates a lot of the confusion. The same is basically true for refracting telescopes as well.


Steve

[Sykil]

1) Apertures: As other have said, the numerical aperture and physical aperture are related by the focal length. In fact, that's why many write the F-stop as "f/" some number and might refer to a 50mm f/1.4 lens as a 50/1.4 lens.


2) Light gathering power: When it comes to image brightness and setting exposures in photography of surfaces, numerical aperture is king. It's all you need to know for getting the right exposure. A 50mm lens set to f/5.6 and a 500mm lens set to f/5.6 will both render a surface (skin, paint, leaf, etc.) as the same brightness despite the huge difference physical aperture.

When it comes to object brightness and setting exposures in photography of point light sources (e.g., stars), physical aperture is king because the area of the light-gathering aperture determines the total star light collected. A 500mm f/5.6 lens (i.e., a small telescope with a 90mm objective and physical aperture) will gather over 6X more star light (over 2.66 stops more star light) than a 50mm set at f/1.4 (only a 36mm physical aperture). In fact, for a given exposure time, the 500/5.6 will render the stars as brighter and the sky blacker than will the 50/1.4. (However, the 50/1.4 will render diffuse objects such as nebulae and comets brighter than will the 500/5.6).

Note: the effect of numerical and physical aperture on the brightness of line-like sources of light (e.g., meteors) is also determined by the physical aperture more so than the numerical one but the strength of the effect if half way between that of area and point light sources.


3. Objective element size versus physical aperture: For longer focal length lenses, the physical size of the front element and the optical entry pupil are almost the same. For wider angle lenses, the wider angle of view means the fan of light rays from the scene are wider where they enter the first element than when they pass through the aperture deep inside the lens. Thus, the front element is wider than the aperture. This phenomenon can be quite extreme in ultra-wide angle lenses. For example, the physical aperture of the Samyang 14 mm f/2.8 is a tiny 5 mm but the front objective element is 77mm across. That huge bulbous element is needed to bend a 114° wide field of view into a bundle of rays that are projected on to the sensor.

The f-number is not calculated from the physical diaphragm opening measure. The Samyang 14/2.8 for example has a physical diaphragm that is larger than 5mm; the entrance pupil or effective aperture are 5mm as viewed from the objective. This is specifically why wide angle lenses are rarely that fast, which is somewhat counter-intuitive. After all, any 14/1.4 would only need a 10mm diaphram, right? That seems relatively easy to design and manufacture compared to a 50/1.4 which would need a ~35mm opening. But on full-frame where this indicates a wide angle, the objective shrinks the apparent aperture, which is what actually matters. That is why the lens has to be so huge for a measly f/2.8 5mm aperture. It's why you can find 25/0.95 lenses for Micro 4/3, but not full-frame: on micro 4/3, the appearance of the physical diaphragm opening is enlarged. On full-frame, it's shrunk.

Sorry, this is false. The F-stop opening of a lens is only a function of focal length and has nothing to do with sensor size.

A 50 f/1.4 lens designed for a crop sensor (or even a micro4/3rds camera) will have the identical aperture pupil diameter as will a 50 f/1.4 lens designed for a full frame sensor.

What may be true is that the diameter of the front element may be larger on lenses for larger sensor cameras because they are wider-angle lenses.

Sensor size absolutely matters, like I just mentioned. 50/1.4 means nothing on its own because it does not indicate an angle of view; you need an image circle diameter for that. It may be relatively easy to design, inexpensive to manufacture, and practically sized on full-frame and below - but if you want one for 6x7, where it has the field of view of a ~24mm full-frame lens, it doesn't exist. The objective and diaphragm will need to be much larger. In fact, you'd be hard-pressed to find a lens that just gives you the equivalent depth of field at the same focal length or an equivalent that gives the same FoV. On 6x7 that would be f/3. I don't think you can even find it for modern digital "645" where it's f/2.2.

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Last edited by Sykil; 08-16-2020 at 03:47 PM.

[stevebrot]

Sensor size absolutely matters, like I just mentioned.

Image circle has nothing to do with entrance pupil size nor with exit pupil size nor even the rear element diameter. Field angle of view is determined by frame size (i.e. crop) as applied to image circle and as such effects nothing directly. After all, a crop is a crop is a crop.


Steve

(...simplistic, I know...)

[Sykil]

This has nothing to do with cropping, which only works in one direction. You need an image circle diameter in tandem with focal length to describe the angle of view of a rectilinear lens. A 24mm Micro 4/3 lens doesn’t suddenly capture a 83° field of view just because you put it on a full-frame body. You can magnify the image circle by moving it farther away or some other optical trickery and it still won’t capture a wider angle. Nor does simply scaling up the physical dimensions of the lens make it one; the design has to change, which changes the magnification of the diaphragm as seen from the objective, which puts even stricter practical limits on the f-stops the lens is capable of.

Like I said, the same physical diaphragm mechanism can be in two lenses of the same focal length and indicate different f-stops depending on the angle of view the lens is intended to capture. Look at the f-numbers for wide-angle medium format lenses. Why aren’t they the same as normal full-frame lenses if all that matters is focal length? What you said is that f-stop is a function of focal length alone, which is false. Focal length does not tell you the magnification of the diaphragm, which changes based on what type of angle the lens captures, which is not a function of focal length alone.

[stevebrot]

Like I said, the same physical diaphragm mechanism can be in two lenses of the same focal length and indicate different f-stops depending on the angle of view the lens is intended to capture.

I believe you are mistaken.


Steve

[Sykil]

I am not. F-number is calculated by the diameter of the entrance pupil, which is an optical image of the physical opening, not the opening itself.

Remove the front element of a wide angle-lens and you’ll see that the diaphragm is larger. Remove the front element from a normal lens and you’ll see that the diaphragm is smaller. 50mm can mean wide-angle, normal, telescopic — it depends on the image circle (and thus angle of view) that the lens is intended for. The f-numbers will be different in each case even if the physical opening inside is the same diameter.

[coondog]

See what you started you have to be careful what you say around these guys & gals there are a lot of sharp cookies in this jar! Ihave learned a lot from them. Also I have heard of a disease you can acquire reading to much info on the Pentax Forum I am sure I contracked it as I now own about 60 lenes. Some one will tell us what it is called. Great people here!!!!!!

[photoptimist]

The f-number is not calculated from the physical diaphragm opening measure. The Samyang 14/2.8 for example has a physical diaphragm that is larger than 5mm; the entrance pupil or effective aperture are 5mm as viewed from the objective. This is specifically why wide angle lenses are rarely that fast, which is somewhat counter-intuitive. After all, any 14/1.4 would only need a 10mm diaphram, right? That seems relatively easy to design and manufacture compared to a 50/1.4 which would need a ~35mm opening. But on full-frame where this indicates a wide angle, the objective shrinks the apparent aperture, which is what actually matters. That is why the lens has to be so huge for a measly f/2.8 5mm aperture. It's why you can find 25/0.95 lenses for Micro 4/3, but not full-frame: on micro 4/3, the appearance of the physical diaphragm opening is enlarged. On full-frame, it's shrunk.

First, thanks for catching my error on the 14/2.8. You are right. The diameter of the physical aperture inside a lens is almost always different from the entry pupil size and it is the entry pupil size that determines the f-stop. The design of the optical elements in front of the aperture will determine whether the physical aperture appears larger or smaller than it actually is.

It is true that wide angle lenses tend to have negative diopter front assemblies but that does not mean the physical aperture diaphragm has to be infeasibly large. In fact, the physical size of the diaphragm is usually no larger than the larger of the focal length divided by the f-stop or the rear nodal distance divided by the f-stop.

Sensor size absolutely matters, like I just mentioned. 50/1.4 means nothing on its own because it does not indicate an angle of view; you need an image circle diameter for that. It may be relatively easy to design, inexpensive to manufacture, and practically sized on full-frame and below - but if you want one for 6x7, where it has the field of view of a ~24mm full-frame lens, it doesn't exist. The objective and diaphragm will need to be much larger. In fact, you'd be hard-pressed to find a lens that just gives you the equivalent depth of field at the same focal length or an equivalent that gives the same FoV. On 6x7 that would be f/3. I don't think you can even find it for modern digital "645" where it's f/2.2.

50/1.4 does mean something even if the image circle is unknown. It means that 0.001 radians of angular width in the center of the scene resolves as exactly 0.050 mm of linear width on the sensor or film (regardless of image circle or f-stop). It means the lens has the image exposure properties of an f/1.4 lens (regardless of focal length or image circle size). It means the lens has the starlight gathering power of a 35.7 mm aperture (regardless of image circle). It even tells you what the DoF will be as long as you determine DoF using a given size of circle of confusion in microns (not relative to the frame size).

A 50/1.4 that covers a 6x7 image circle isn't hard to make at all -- a single element will do but it will have horrible aberrations and field curvature. It will also be incompatible with the long register distance of 6x7 SLRs. It's not the diaphragm size that causes problems for designing fast, wide-angle, medium format lenses. It's correcting all the aberrations over both the wide FoV and the large aperture. That takes a lot of elements on both sides of the aperture to make a decent image. And the stack of elements in front of the aperture must fan out according to the width of the FoV.

Both Sigma and Canon make high quality 24/1.4 lenses. Simply doubling all the dimensions of every element of this design would create a decent 48/1.4 with an image circle that works on a 6x7. Note that doubling all the dimensions creates a lens with 8X the mass. The lens would tip the scales at over 5 kg and have a 154mm filter diameter. One can only imagine the cost!

[pschlute]

Focal length does not tell you the magnification of the diaphragm, which changes based on what type of angle the lens captures, which is not a function of focal length alone.

But surely the angle of view that a lens is capable of projecting onto a surface has a fixed constant maximum...ie a given lens may have an image circle that will only serve aps-c format, or it may be wider like FF format. But that is a property of the lens alone. The Focal length and magnification of a 50mm 1.4 is the same whether the lens is aps-c or FF. The light gathering properties are the same too.

I can put the same 50mm f1.4 lens on my K1 or K10D. At f1.4 or whatever aperture I choose, they both produce identical exposures.

[Sykil]

But surely the angle of view that a lens is capable of projecting onto a surface has a fixed constant maximum...ie a given lens may have an image circle that will only serve aps-c format, or it may be wider like FF format. But that is a property of the lens alone. The Focal length and magnification of a 50mm 1.4 is the same whether the lens is aps-c or FF. The light gathering properties are the same too.

I can put the same 50mm f1.4 lens on my K1 or K10D. At f1.4 or whatever aperture I choose, they both produce identical exposures.

Subject magnification is measured relative to the size of the sensor, so it does not stay the same. And that's just how crops work; it doesn't have much to do with the lens otherwise. The rest doesn't really have anything to do with my point, which is that if you have a 50mm wide angle lens with the same physical diaphragm as a 50mm normal lens, the 50mm wide angle will have a higher maximum f-stop (e.g. smaller maximum entrance pupil) due to the necessary differences in the way they're designed and the effect that has on the entrance pupil.

The same lens is the same lens. Exposure is the same because they're literally looking at the same image circle, so the crop is exposed to the same degree as that portion of the full-frame sensor. But I'm not talking about identical lenses.