Spring 2012

Spring 2012
by ani

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Does the aperture ring lock the apertures beyond, say 5.6 at length lens's telephoto end? Does the lens introduce an obstacle to the aperture ring so the lens can't be opened anymore beyond the aperture at the telephoto end?

And why do lenses behave like this, anyway? Why don't they have constant apertures throughout their focal range?

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It's probably obvious from the answers by now, but there's no difference between what bridge cameras and interchangeable lens cameras do here. – Philip Kendall Jan 8 at 8:24
    
See How do constant aperture zoom lenses work? for essentially the same question in reverse. It particularly addresses the question of why all lenses do not have constant maximum aperture. – mattdm Jan 8 at 13:47

The entrance pupil can not be any larger than the diameter of the front element, and that is what usually restricts the maximum aperture of telephoto zoom lenses - not the physical size of the aperture diaphragm.

The physical size of the diaphragm is only part of what determines the maximum aperture, expressed as an f-number, of a lens. Magnification between the front of the lens and the location of the diaphragm also plays a part. The f-number of an aperture is determined by the ratio of the lens' focal length divided by the diameter of the entrance pupil, often referred to as the effective aperture. In simple language, the entrance pupil diameter is defined by how wide the opening of the diaphragm appears when viewed through the front of the lens.

When constant aperture zoom lenses are moved to change the focal length, the magnification between the front of the lens and the diaphragm is what normally changes, not the physical size of the diaphragm. The change in magnification is what allows the entrance pupil to appear larger at longer focal lengths and smaller at shorter focal lengths. A 70-200mm f/2.8 lens has an entrance pupil 25mm in diameter at 70mm and f/2.8. At 200mm the entrance pupil at f/2.8 is a tad over 71mm wide. The actual physical diaphragm is the same size in both cases. What has changed is the amount of magnification between the diaphragm assembly and the front of the lens.

Note that this same principle is usually in play with variable aperture zoom lenses as well. Take, for example, an 18-300mm f/3.5-5.6 zoom lens. At 18mm the entrance pupil for f/3.5 is roughly 5.14mm wide. At 300mm the entrance pupil for f/5.6 is over ten times that at 53.6mm wide. Notice that most zoom lenses that max out at 300mm and f/5.6 have front elements that are slightly larger than 54mm in diameter. The needed entrance pupil size is the reason! If the entrance pupil at 300mm were still 5.14mm wide as it is at 18mm and f/3.5, the maximum aperture at 300mm would be f/58!

So why don't all zoom lenses use enough magnification to remain at constant aperture throughout the entire zoom range? Primarily the cost associated with the additional size, weight, and complexity needed to produce a constant aperture lens.

An entrance pupil can be no larger than the diameter of the lens' front element. At 200mm an f/5.6 aperture requires an entrance pupil almost 36mm in diameter. Most current interchangeable lenses are at least that large in diameter since the mounting flanges on most contemporary interchangeable lens cameras have diameters roughly 42-54 millimeters. (Please note that we are talking about the width of the hole in the mounting flange, not the distance of the mounting flange in front of the sensor/film plane which is referred to as registration distance.) On the other hand, at 200mm an f/2.8 aperture requires an entrance pupil roughly 71.4mm wide. That requires the lens to be significantly larger in diameter than the hole in the mounting flange.

Not only does the lens barrel and all of the parts of the lens that surround the optical path need to be larger and thus require higher quantities of the raw material from which they are made, but the actual optical elements must also be both larger in diameter and thicker in order to maintain the same refractive angles. The larger lens elements also introduce more aberrations that need correction. Often the most expensive materials in a lens are those used to make these corrective optical elements. Adding elements to correct things such as chromatic aberration can introduce additional problems, such as perspective distortion, than require even more additional elements to correct. So not only does the entire lens and many of the optical elements inside need to be larger, but it also requires more optical components made from even more expensive materials. This means not only is the lens more expensive to design and manufacture, but it is also larger and heavier.

For most folks, unless they really need that larger aperture they would just as soon carry around a lighter, smaller lens for which they paid a lot less.

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Great explanation. I'd add a summary: TL/DR: The issue isn't that the the diaphragm decreases in size, but rather that the front elements aren't large enough to provide a constant aperture. – Caleb Jan 8 at 5:21
    
It is possible for the EP to be larger than the front element. Consider an aperture stop within 1 focal length of a thin positive lens and of the same or nearly the same diameter. The positive lens acts as a magnifier and creates an enlarged image of the stop. This enlarged image will be bigger than the front element. – Brandon Dube Jan 9 at 19:26
    
Then the diameter of the front element is the most restrictive thing in the optical path and thus the true aperture. The entrance pupil is measured by the width of the collimated light parallel to the optical axis allowed to pass through. In the context of this question regarding telephoto lenses there is very little off axis light allowed to pass through the lens in the primary optical path. Off axis light may cause flare with a tele lens, but not a theoretical thin lens (by definition can not be telephoto since it would need to have the actual focal length from the lens to the image plane). – Michael Clark Jan 10 at 8:52
    
@Michael Clark.. Thanks for the answer, but it's a bit tricky for me to understand. Can you please summarize or give in point form? – user152435 Jan 21 at 16:01
    
@user152435 That's pretty much what the parts highlighted in bold are. – Michael Clark Jan 21 at 21:03

The quality of a modern zoom lens is outstanding considering all the manufacturing problems encountered. The maker would love nothing better than to keep the maximum aperture constant throughout the zoom. This is more easily said than done.

The f-number is a ratio. Mathematically we divide the focal length by the working aperture diameter to compute the f-number. We need this value to be a ratio because a ratio is dimensionless. In other words, an f/4 lens passes the same light energy to film or sensor regardless of the dimensions of the lens. As an example a 100mm lens with an aperture of 25mm diameter, functions at f/4. This lash-up delivers the same image brightness as an astronomical telescope system with a focal length of 4000mm with a working aperture of 1000mm. Both expose the same vista the same.

We need the f-number system because it takes away the chaos. Any lens set to the same f-number as any other lens, delivers the same image brightness. This is because focal length and aperture diameter are intertwined. As you zoom to higher and higher magnifications the image dims. Think about moving a projector further and further from a white wall. As you back the projector away from the wall, the projected image on the wall gets bigger and, because the light must cover more surface area, the image gets dimmer. Same with a zoom lens.

Somehow the lens maker must compensate or a constant f-number cannot be maintained throughout the zoom. Most zooms cannot maintain a constant f-number. It becomes it becomes too expensive to make and sales will be lost because you have priced yourself out of the market.

How to maintain a constant f-number throughout the zoom? The iris diaphragm is set behind the moving group of lenses. The front group acts like a magnifier to cause the apparent diameter of the iris to look bigger as seen from the front. This placement allows more and more light to transit the iris as the lens zooms to higher and higher magnifications. Such placement and action of the forward lens elements induce distortion and aberrations that must be corrected. This correction requires complex lens elements that must move with precision. This adds to the cost. The bottom line is a constant aperture zoom is very expensive to make.

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"Any lens set to the same f-number as any other lens, delivers the same image brightness." Is this true? What if the the elements of one lens were all made from the same material used in ND filters? Stupid example, but surely the tranmission properties of the lens element materials effect image brightness? How about if one lens is catadioptric? – dav1dsm1th Jan 9 at 21:57
    
Within reason, any lens set to the same f/# delivers the same amount of light as any other lens set to the same f/# regardless of design or size. Yes, variations exist but generally they are of no coinsurance. Many lens makers us a T-stop which stands for True – stop. The iris diaphragm diameter is computed using a light meter. The f-stop is computed by dividing the focal length by the working diameter. It is likely impossible to set a camera closer than 1/3 of an f-stop due to mechanical limitations of the iris adjustment (gear backlash etc.). Adjustments 1/6 f-stop are achievable sometimes. – Alan Marcus Jan 20 at 18:25

Whether a zoom lens is constant aperture or variable aperture has first to do with the design, a secondly to do with mechanical factors like opening or closing a diaphragm.

A zoom lens works by having some elements move to change the focal length. This works because of the equation for the focal length of a thick lens:

(1) Phi = phi_1 + phi_2 - (t/n)*phi_1*phi_2

(2) EFL = 1/Phi

Where Phi is the total optical power of the thick lens, phi_1 and phi_2 are the optical power of the first and second surface, t is the thickness between them, and n is the refractive index of the lens. EFL stands for effective focal length and is what is colloquially referred to by saying focal length.

Any optical system containing any number of elements can be modeled accurately as a single thin lens. This equation also works for thin lenses, but the t/n term disappears, as t=0. A 50mm f/1.8 lens can be modeled as a single thin lens of focal length 50mm, as can an 18-300mm lens set to 50mm.

You can also use this formula to model 2 thin lenses. As long as the lenses are positive, you can see that by pushing them further apart the t/n term will get larger. As it grows, the power decreases and the focal length gets larger.

This is the essence of a zoom lens.


As soon as you introduce an aperture stop into an optical system, you have what are known as entrance and exit pupils. The entrance pupil is the image of the aperture stop formed by the elements in front of it, and the exit pupil is the image of the aperture stop formed by the elements behind it.

The pupils have a position and size just like a lens element or the actual aperture stop itself. The f/# of a lens can be approximated by

(3) f/# = EFL/EPD

Where f/# is the 'focal ratio', EFL is the effective focal length, and EPD is the entrance pupil diameter.

Let's stick an aperture stop in the middle of two thin lenses separated by air. If we increase the EFL of the lens system by moving the lens in front forward, the EPD will change with it. If we increase the EFL of the lens by moving the lens in the back backwards, the EPD will not change with it, since that lens does not affect the entrance pupil in any way.

It happens to be the case that unless you make an extremely large zoom range, the magnification of the aperture stop responsible for the EPD increases at the same rate as the focal length. Since both the numerator and denominator of (3) changed by the same relative amount, the ratio is still the same and thus our lens may have moved from 70mm to 200mm and maintained an aperture of f/4.

If we moved the lens in the back, the lens would have slowed down to about f/10 or so by zooming from 70mm to 200mm.


A modern zoom lens has 3 or 4 zoom groups, so it is more complicated than this simple explanation. If all of them are in front of the aperture stop, this is still true. If most of them are in front of the aperture stop, the manufacture will tend to program the diaphragm to open/close while the lens zooms and just cheat the gap to make it behave like a constant aperture lens.

You may wonder why not just put all of the groups in front of the stop and be done with it - there are two key motivations:

1) If you force all of the zooming to happen in front of the aperture stop, the lens is necessarily longer than if it could zoom on both sides.

2) It is easier to design a well-corrected lens if you are allowed to alter the position of the elements on both sides.

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