Large aperture and Sweet Spot

[alhazen]

Hi,

The sweet spot of a lens usually can be achieved by using the aperture about 2 stop smaller from the largest aperture. An aperture that is too small is not useful because of the diffraction. But, why the largest aperture can't get the sweet spot?

Thanks in advance for your answer!

[Inkanyezi]

The simple answer is that no lens is perfect, because we have not found a way to correct all imaging errors in a lens.

A somewhat longer answer is that lenses are corrected for imaging errors to a certain degree, where a balance is met between production costs and imaging quality as well as specifications. There is no theoretical optical law that impedes the sweet spot to be found at the largest aperture. You could for example imagine a lens where the diaphragm cannot open more than two steps stopped down; like a 2,8 lens that is limited to 5,6 as its largest aperture. That lens would of course have its sweet spot at largest aperture. We would acquire such a lens by making the individual lens elements smaller, so the same lens would not have a larger aperture at all, and its imaging performance would be decreased by stopping down. A lens designed designed from scratch to have that aperture might lack some imaging quality at its largest aperture, but would have its sweet spot somewhat more stopped down, and it would be sharper than the crippled lens designed for a larger aperture.

Lenses are made to suit their intended purpose, so it would not make sense to limit their performance in that way, considering the possibility to reach a two stops larger aperture with reasonable quality. Those two stops enable the photographer to shoot at lower light without missing a lot. So instead of aiming the lens to have its sweet spot at its largest aperture, the designer aims at a larger aperture to make a lens that can take in more light. Mind that the "sweet spot" is a point that is not clearly defined; it is where various parameters that govern image quality have a minimum of errors. The most notable optical error that is alleviated by stopping down is spherical aberration, and all lenses have it. By stopping down we alleviate spherical aberration, as well as vignetting, but we cannot do much about chromatic aberration. At a certain point, varying with focal length, errors introduced by stopping down become more prominent and decrease image quality. Hence the point where sharpness is estimated to be best is what we call the "sweet spot" of the lens.

[alhazen]

Inkanyezi,

Thank you very much for your explanation. You made it very clear for me now. It's very hard to find this kind of information all over the internet. Earlier, I suspect Circle of Confusion (CoC) is the factor, but I guess CoC is only related to Depth of Focus, it's not the cause of large aperture unable to attain sweet spot.

Anyway, thanks again for your answer. I salute your deep knowledge about the optics theory.

[John C]

An aperture that is too small is not useful because of the diffraction.

I think the significance of the sweet spot may be overrated. Most modern lenses provide excellent photos at apertures well into the range affected by diffraction and at the widest apertures. I do a lot of macro photography and have no qualms using f/16 and f/22 with my macro lenses.

Regarding the sweet spot being 2 stops from the largest aperture, I think that is old general rule of thumb to use when you don't know much about a lens. A lot of lenses tend to be less sharp and have other defects (chromatic aberration, vignetting, etc.) at the edges of the field of view when used at the widest aperture. This has led to the rule of thumb that you mentioned. As an examples of exceptions, my Sony 50mm and 100mm macro lenses provide the sharpest and best quality results at their widest aperture, f/2.8. On the other hand, my 16-80mm Zeiss shows vignetting and softness in the corners at the widest aperture, which clears up about a one stop smaller.

Getting to know the strengths and weaknesses of your lenses is very important but dont get stuck using only the 'sweet spot.'

[alhazen]

John C,

Your experience of having sweet spot at smallest aperture or largest aperture with certain lens is something new for me. Thanks for the information.

As you said "...don't get stuck using only the sweet spot" - I agree with you. I actually never really care about using the lens at it's sweet spot. I just want to know the reason technically because somebody asked me this question and I don't really know the answer.

Thanks again for sharing

[alhazen]

Inkanyezi,

Your answer really made sense for me.

But, somebody said that the reason is also because of light bent at largest or smallest aperture. In middle aperture, light move in straight line, so highest quality image or sweet spot can be attained. Is this true?

[Inkanyezi]

Inkanyezi,

Your answer really made sense for me.

But, somebody said that the reason is also because of light bent at largest or smallest aperture. In middle aperture, light move in straight line, so highest quality image or sweet spot can be attained. Is this true?

No, it is not true. Light generally is considered to travel in a straight line, and it is deviated when it passes the boundary between different optical media, such as glass and air or different kinds of glass. This principle is used when designing lenses, using different types of glass, as well as air, to correct aberrations. Light can also be physically "bent" around an edge, and that is the reason why the image will soften when the aperture is very small.

When the aperture is very small, a significant part of the light that passes through the aperture (diaphragm) will be "bent" around the edge of the orifice and soften the image. The extent of softening depends on the size of the aperture compared to the wavelength of light, and it can also be described as related to the relatively large edgeline compared to the small area of the aperture. The edge of the aperture is a linear function, while the area is a square function. This bending of light is what we call diffraction.

At large apertures, the same thing happens, light bends at the edge of the aperture, but the amount of light thus bent is very small, compared to the massive amount of light that passes in a straight line through the large aperture and is not bent at the edge. Contrast will be higher than at very small apertures, because there is a large difference between the size of the aperture and the wavelength (or a larger area compared to the length of the edge of the aperture).

[rpcrowe]

All lenses do not have a distinct quality dividing line regarding the aperture at which they are shot. Perhaps pixel peepers might see a difference but, in real-life photography the imagery some lenses produce wide open is quite remarkable.

My Canon 400mm f/5.6L seems to be as sharp from the widest to the smallest aperture. This somewhat negates the problem of this lens not having IS because I readily shoot wide open in order to attain the fastest shutter speed. It also negates the narrow DOF you produce with a 400mm lens because I can shoot at f/16 with no worry about diffraction.

And, while perhaps my 17-55mm f/2.8 IS and 70-200mm f/4L IS lenses "might" have a sweet spot at 2-stops below maximum, I will readily use either lens at its maximum aperture without any worries.

However, with lenses like the 18-55mm f/3.5-5.6 IS and 55-250mm f/3.5-5.6 IS there seems to be a definite difference in quality between wide open and stopped down 2-stops. Many photographers are surprised at the excellent quality these lenses can produce when shot on a tripod and stopped down 2-stops.

[alhazen]

Inkanyezi, thanks again. Crystal clear!
Richard, thanks for the additional information. Really appreciate it.

[Inkanyezi]

It might be added, that for a lens as long as 400 mm, f/16 is an inch wide, or quite as large as f/2 for a 50 mm lens. Compared to the wavelength of light, this is a very large aperture, and diffraction is negligible. Diffraction rarely is a problem in lenses for SLR cameras; it is the short focal lengths of compact cameras or video cameras that suffer when stopped down too much. Compact cameras often limit stopping down to f/8 in order to avoid softening due to diffraction. Only with some short focal length lenses that can be stopped down to very small apertures will you notice significant softening due to diffraction.

Some macro lenses may be stopped down to very small apertures, but as they also have rather long focal length, the DOF gain is more significant than the diffraction loss.

[alhazen]

Made sense again. Thanks Inkanyezi, you manage to lay out everything nicely related to each other.

[Glenn NK]

Alhazen - a bit more technical.

Light passing through a lens is bent when it passes from air to glass and from glass to air. This bending is called refraction.

Light passing through the dead centre of a lens is not bent at all. Light rays that are off the centre are bent (refracted) and the farther they are from the centre of the lens, the more they must be bent or refracted.

Different colours of light have different wavelengths and different wavelengths of light are bent (refracted) differing amounts. So the farther from the centre of the lens, the more the bending (refraction) and the more the difference between different colours. The difference in the refraction of different colours causes imperfect resolution.

On the other hand, light passing near an edge is diffused a bit - it is deflected and changes direction slightly. This is called diffraction. Light rays near the edge of the lens opening are diffracted slightly causing some loss in resolution (focus).

Consider a round opening (which a lens diaphragm approximates): the circumference of a round opening varies as the diameter of the opening whereas the area varies as the square of the opening. As the diameter gets larger, the effect of the edge diffraction becomes less relative to the area. But as I noted above, as the area gets larger, the light rays are more severely bent (refracted) and the variation of refraction of different colours results in poorer focus/resolution. Thus, the largest apertures are where refraction (bending) is more significant; the smallest apertures are where diffraction is more significant.

I use a simple method to determine the best apertures at which to use a lens - I look at lens tests. Invariably, the smallest and the largest apertures have lower resolution than the ones in the mid range. A lens test shows this quite clearly. Actually I've memorized where

This is a test of one of my lenses on my camera:

http://www.photozone.de/canon_eos_ff..._28_5d?start=1

Scroll down to the MTF CHART.

It's easy to see that at f/4 and f/5.6 it's at its best

The testing procedure automatically includes the variations in diffraction and refraction resolution.

Wide open (f/2.8) refraction governs, then it gets a bit better when stopped down, but you can see that at f/11, it's falling off quickly - this is a result of diffraction. At very small openings, the effect of light rays being close to a hard edge is more significant than at large openings.

Now, having said all that, there are exceptions as others have noted. One of the seemingly strangest is this one (another lens I have):

http://www.photozone.de/canon_eos_ff...35tse2?start=2

It's best at the two widest stops, not partially stopped down. This is because the lens area is made larger than normal lenses so that when the shift feature is used, part of the image isn't lost. The next page confirms this - at full shift, the best f/stop is f/8, and the resolution is noticeably less than non-shifted. But again, in this instance the light rays are using the very edge of the lens where refraction dominates.

Zoom lenses can also deviate from the "usual" behaviour.

http://www.photozone.de/canon_eos_ff...6islff?start=1

Hope this isn't too confusing.

The bottom line as others have said is not to worry too much about this sweet spot (I rarely do), and concentrate on good composition and exposure. These will impact your photography more than will sweet spots.

Glenn

[alhazen]

Glenn NK,

Thanks for shedding some light here. I think I got your point.

P/S: I do not worry about sweet spot at all. I just want to know the technical part of it, so I will understand what other people are talking about. With your help, now I understand refraction and diffraction better!

[Inkanyezi]

I'll put another log on the fire.

There is a confusing error in post #12; the coating of lenses is in no way related to colour correction. Colour correction is achieved by combining positive and negative lenses of different glass types. The coating of lenses is done in order to maximise light transmission and minimise reflection.

Different kinds of glass have different index of refraction, so that a light ray reaching it from a certain angle will be differently refracted. Moreover, different colours refract differently as well. Red passes somewhat more straight than blue. This property is called dispersion. When a positive and a negative lens or different kinds of glass with different dispersions are combined, colours may reach a common focal point instead of a focal point that is spread out. Without correction, the focal length for red is longer than for blue, a property we name colour aberration. This error is largely alleviated by colour correction, but we never reach perfect matching for all colours.

When we want a lens to collect more light, we evidently must make it larger, with a larger surface. A larger lens will become thicker as well, having more glass, as its curvature will make it contain a larger volume of glass. Then, when a ray of white light (light of a mixture of many colours) hits the lens surface obliquely, the various colours are dispersed so that they will hit different parts of the opposite surface of the lens when they emerge at the other side. If the lens is infinitely thin, they would hit the opposite surface without being scattered over it, but as we cannot make it infinitely thin, they are always spread out by the effect of dispersion. Therefore correction of a lens is always simpler with thin lens elements than with thicker lens elements, which will always introduce larger errors than thinner lens elements. A lens with a large aperture is more difficult to correct than one with a small aperture (and thinner elements), and the one with the smaller aperture will usually be sharper, because the elements are thinner. Increasing complexity of a lens design make it increasingly more difficult to correct for all imaging flaws. To understand why thicker glass introduces errors, you may think of a light ray that hits a block of glass with parallel sides obliquely. It will be dispersed at the first surface, and then all colours will return to the original direction when they exit at the other side, but the ray will be wider and all colours of the white light will be separated, as they do not all exit from the same point.

Sweet spot is not a point considered in lens design. Sweet spot is a photographer's term, invented to more easily understand how a lens works and where it performs optimally. There are a panoply of imaging flaws in any lens, and they are different at different apertures. The opinion about where the lens has its sweet spot may also differ among different photographers. If you accept some vignetting and softness toward the corners but prefer maximum center sharpness, your sweet spot may be a larger aperture than for a photographer that abhors vignetting but accepts somewhat softer central contrast, preferring a more uniform performance over the entire area. Hence we may have different opinions about which aperture is optimal for overall image quality.

So sweet spot is a very fuzzy concept.

[alhazen]

Inkanyezi,

Thank you for the additional information. It's getting clearer to me now.
Not many photographer can really explain the theory about lens as good as you do!

[Photon Hacker]

There is more information on the physics of imaging formation in http://www.telescope-optics.net/wave.htm.

[alhazen]

Photon Hacker,
Thanks for the information

[Glenn NK]

So sweet spot is a very fuzzy concept.

Absolutely.

But would you recommend that I shoot my Canon 100 mm f/2.8 macro lens at f/32?

http://www.photozone.de/canon_eos_ff..._28_5d?start=1

I wonder what it would look like stopped down that far?