Max aperture on zoom lenses - stepwise or linear?

Question

When zooming with lenses without a fixed max aperture, the change in aperture* that the camera displays is stepwise, usually in steps of thirds. But, is the max aperture really the same all the way as long as the camera says it's the same, or is there a differense within the same steps? I.e, will the aperture actually be a little bigger at the widest end of such an interval?

And, are there any charts etc available that shows zoom lenses' intermediate max apertures, between longest and shortest focal length? I'm mostly interested in Canon, but other brands as well.

*) edit: I guess F-number is more acurate.

Answer 1

The selected aperture is rarely the actual exact physical aperture of the lens. Usually there is a certain amount of discrepancy between the relative aperture the camera reports, such as f/3.5, and the actual physical area of the current aperture. As such, exposure is rarely exact, and can vary to a measurable (and often visible) degree between samples of a given lens and between a given lens and samples of a given camera. There are also often variations by as much as 1/3rd of a stop or more between camera brands for what would otherwise be exactly the same exposure settings with otherwise equivalent lenses.

The best real-world demonstrations of the difference between a reported aperture and the specification of aperture of a lens required to achieve its design are usually lens patents. Some recent Canon lens patents as reported by Canon Rumors are a great example of some real-world "relative aperture" values for pending lens designs:

Example 1
- Zoom ratio 4.01
- 135.50 – - 290.90mm 72.50 focal length
- Fno 4.66 -. 4.97 – 5.87
- 9.07 – - 4.25deg 16.62 a half angle of view.
- Image height 21.64mm
- 171.47 – - 204.08mm 144.08 full-length lens
- BF 40.08mm
- 18 sheets 12 group lens configuration
- 3 UD glass sheet
- A plane diffraction
- Seven-group zoom positive and negative positive positive and negative polarity
- Inner Focus (Group 6)
- Shake correction (group 2)

Example 2
- Zoom ratio 2.84
- 200.00 – - 292.50mm 103.00 focal length
- Fno 4.67 -. 5.44 – 5.77
- 6.17 – - 4.23deg 11.86 a half angle of view.
- Image height 21.64mm
- 189.12 – - 210.66mm 162.16 full-length lens
- BF 45.16 – 58.25 – 70.16mm
- 13 pieces in 11 groups Lens Construction
- 2 UD glass sheet
- A plane diffraction - Five-group zoom of positive and negative positive positive and negative
- Rear focus

You'll notice the Fno specifications for these two examples of new DO or diffractive optics lens designs. The first example lists the F-Number range as 4.66 to 5.87. Neither of those are standard F#'s, such as f/4.5, f/5 or f/5.6, however they are the specified engineering limits of the lens. You can't actually dial in an exact f/4.5 aperture on Example Lens #1...when you do, you are actually getting an actual f/4.66 aperture. Same deal if you dial in f/5.6, which in reality would mean your getting an actual aperture of f/5.87. (The middle aperture number, if I understand the rather oddball nomenclature of these patents, would be what you get around the middle of the lens, which seems to be the first focal length number, which in the case of Lens #1 is 135mm.)

As you change the focal length of a lens at maximum aperture for a variable aperture lens, the physical size of the aperture DOES NOT change. The diaphragm remains at its widest-possible ("relaxed") setting. The real F-Number's will change smoothly and not in a non-stepped manner. The lens will report the nearest "well-known" 1/3rd stop aperture at one of the specified points (i.e. f/4.5 for f/4.66 @ 72.5mm, f/5 for f/4.97 @ 135.5mm, f/5.6 for f/5.87 @ 290.9mm), and that is what will show up in EXIF as the selected aperture, however the actual apertures (i.e. f/5.87) will often show up in EXIF as "Max Aperture Value" or something similar.

You can usually observe this smooth change in aperture if you point a lens up towards your face with a bright light above your head so it illuminates the inner barrel of the lens, and adjust the focal length. You will see that the camera does not do any kind of micro-adjustment of aperture for you as you zoom. This is always the case at maximum aperture, and usually the case at all other apertures, although sometimes there are slight differences between instances of stopping the lens down to a smaller aperture simply due to the nature of a diaphragms operation. (Use a DOF Preview button to see the behavior at any aperture, including max aperture...otherwise the camera will always remain in a "relaxed" state.)

The same precision differences are present in other aspects of the lens as well. Example Lens #1 is actually a lens with a zoom ratio of 4. Funky nomenclature aside, the lens is actually a 72.5mm to 290mm lens...or a replacement for the 70-300mm f/4.5-f/5.6 DO lens. Similarly, Example Lens #2 is actually a 100-300mm f/4.5-5.6 DO lens.

While these imprecise specifications, at least relative to the idealistic numbers we photographers usually think about, are actually very exact and very necessary to the successful manufacture of a given lens at a given price point. Lens manufacture for DSLR lenses is very complex, and particularly when you get into larger lenses or extremely wide angle lenses, can be very costly due to the physical size of many of the necessary lens elements. Diffractive Optics (DO) lenses have the added complexity of diffraction-grating elements that, while they allow lenses to be made physically smaller, require an extra set of complex manufacturing procedures.

Precise specifications like this allow manufacturers to create a 100-300mm DO lens they can actually sell and make a bit of a profit on, without the discrepancies with their "sales specifications" (i.e. 103mm - 292.5mm rather than a lens that is exactly 100mm - 300mm) really having much of a difference in real-world user. It should be noted that these discrepancies really do not matter in the real-world, and the discrepancies can be larger at longer focal lengths. Some ten millimeters or so difference at supertelephoto lengths, a few millimeters of difference at normal to short telephoto lengths, or a fraction of a millimeter at wide-angle lengths, as well as small discrepancies in F-Number are all indistinguishable by photographers in the real world, so don't let them bother you.

Answer 2

Aperture is measured as a ratio. So as you zoom in the aperture actually has to get bigger in order to show you the same value. In relation to your question, this means that the aperture gets bigger when you zoom in and the camera shows the same number.

Lets say you have an imaginary 10-20mm F/2-F/4 lens, just to use round numbers. At 10mm, F/2 means your aperture is 5mm wide. As you zoom in to say 15mm, then the aperture would need to open up to 7.5mm in order to still be F/2. If 5mm was the max, then at 15mm, it would give you an aperture of F/3 (= 15 / 5) and when you reach 20mm, you would be at F/4 (since 20 / 5 = 4).

Now to keep things simple, most lenses round down to the nearest exposure increment, usually 1/3 or 1/2 EV, otherwise you would get cases where exposure is difficult to set since shutter-speeds are also specified in stops. In plenty of compacts this is not the case and you end up with odd apertures like F/5.8 and correspondingly strange shutter-speeds like 1/427s. Now when the camera indicated the aperture has lowered, then the aperture in fact got smaller. Technically, the camera does not have to this in fixed increments but it makes it simpler.

There are lenses which are known as continuously variable aperture lenses which lets the aperture vary in smaller steps such as 1/16 EV. These lenses are sometimes labelled as HD or Movie-Capable lenses because they provide better transition while recording video where discrete steps are more noticeable. This is the case for the Panasonic Lumix G Vario HD 14-140mm F/4-5.8 ASPH OIS for example.