Lens Sharpness -- Part I

Article and Photography by Ron Bigelow

www.ronbigelow.com

Image sharpness is often a prime topic of discussion in photographic circles. Run a search on any popular, photography, discussion forum and you will, likely, be inundated with postings on the subject.

Of course, we all want our images to be sharp. However, sharpness is determined by a number of factors. In order to maximize sharpness, each of the factors needs to be optimized. One of the major factors that determines image sharpness is the lens. Of course, more expensive lenses tend to have better materials and designs that lead to better sharpness. So, one recommendation could be to break out your wallet and buy some expensive lenses. On the other hand, most of us are not really interested in parting with some more of our hard earned cash. Thus, the question becomes, "Is there some way to optimize the sharpness of the lenses that I already have?" The answer to that question is yes!

The key to optimizing the sharpness of a lens resides in the fact that, in general, lenses are not equally sharp at all apertures. In addition, zooms are sometimes not equally sharp at all focal lengths. By selecting the best combination of lens, focal length, and aperture, a photographer can increase image sharpness. All that is required is a little testing. Of course, few of us have access to an optical lab that will allow us to conduct exacting tests on our lenses. No need to worry! Your house will work just fine as an optical lab for this testing.

To better understand lens sharpness and how to maximize it, this series of articles will concentrate on three subjects: 1) how lenses function, 2) factors that reduce the sharpness of a lens (aberrations and diffraction), and 3) how to test a lens.

How Lenses Function

Figure 1: Single Element Lens

In the simplest sense, the purpose of a lens is to bend light. By bending the light, the lens forces the light to go where we want it to go. Of course, being photographers, we want the light to go to the plane of the sensor or film in such a way that the light focuses on that plane. This is shown in Figure 1. Light from an object or scene passes through the lens, and the lens bends the light so that it focuses on the sensor/film plane.

While such a simplistic lens might be okay for a child's magnifying glass, photographic lenses today are far more complex and require many lens elements. Figure 2 shows how multiple elements are used in a lens to focus the light. However, even this figure is an oversimplification compared to modern lenses. For instance, one of my zoom lenses has twenty-three elements arranged in eighteen groups.

Figure 2: Multiple Element Lens

Regardless of the complexity of a lens, its primary purpose is to focus the light onto the sensor or film. That may sound like a fairly simple task, however, Mother Nature has a way of making things a bit more difficult due to lens aberrations and diffraction.

Both aberrations and diffraction degrade the quality of the images that a lens can produce. Luckily, photographers actually have some control over some of the aberrations as well as diffraction. Understanding how these work, and how photographers can minimize them, is an important part of producing sharp images.

Spherical Aberration

Figure 3: Spherical Aberration

Spherical aberration occurs because the shape of a lens is such that not all light is focused at the same point. This is shown in Figure 3. As can be seen in the figure, the problem is that light that does not strike the lens along the center axis is focused at a different point than light that does strike along the axis. The farther away from the center axis that the light strikes the lens, the more the focus point changes.

The reason that this occurs is that most lenses are spherical lenses. That means that the surfaces of the lenses are spherical shaped. Unfortunately, spherical shaped lenses are shaped such that light striking at different distances from the lens axis will be focused at different points. When light toward the edges of the lens is focused closer to the lens than the light along the axis, the lens has undercorrected spherical aberration. When light toward the edges of the lens is focused farther from the lens than the light along the axis, the lens has overcorrected spherical aberration. The result of spherical aberration is that the light that hits the sensor/film plane forms a halo instead of a point. This causes a blurring of the image, a reduction in local contrast, and a loss of image detail.

Spherical aberration can be eliminated by the use of aspheric lenses. Aspheric lenses have more complex surfaces that focus the light at a point regardless of how far from the lens axis the light strikes.

So, how does one deal with spherical aberration? Of course, the first thought is that the lens designers should stop creating spherical lenses. The problem is that spherical lenses are less expensive to produce than aspheric lenses. So, one way to deal with spherical aberration is to buy more expensive lenses. However, there is another method that can significantly reduce spherical aberration, and the best part is that this method is free. The key to this method is that spherical aberration increases as light moves farther from the lens axis. If the light is restricted so that it does not strike toward the edges of the lens, the spherical aberration problem will decrease. This can be managed by the proper selection of the aperture. In short, spherical aberration is greatest when the lens is wide open (at maximum aperture). As the lens is stopped down, spherical aberration decreases because the light is restricted to the more central portion of the lens. This is demonstrated in Figures 4 and 5.
Figure 4: Spherical Aberration at Large Aperture
Figure 4 shows that, when a lens is shot at larger apertures, there is nothing to limit the spherical aberration of the lens.
Figure 5: Spherical Aberration at Small Aperture

However, when the lens is stopped down, the aperture prevents the light from striking the outer parts of the lens (see Figure 5). This reduces the problem of spherical aberration. The more the lens is stopped down to smaller apertures, the less spherical aberration will be a problem.

We often hear or read advice that a lens should be stopped down a couple of stops to increase the sharpness of the image. This is because stopping down the lens will reduce the spherical aberration.

Coma Aberration

Figure 6: Coma Aberration

Like spherical aberration, coma aberration occurs because the shape of the lens is such that not all light is focused at the same point. However, coma aberration occurs when light that is angled to the lens axis strikes the lens. This is shown in Figure 6. As can be seen in the figure, the focus point of the light changes depending on where the light strikes the lens. This results in a blurring of the image, a reduction in local contrast, and a loss of image detail.

Again, as with spherical aberration, coma aberration is due to the shape of the lens and can be corrected by adjusting the lens shape.

Since coma aberration increases the farther from the lens axis that the light strikes, one way to reduce coma aberration is to use a smaller aperture that restricts the light to the more central portion of the lens. This is demonstrated in Figures 7 and 8.

Figure 7: Coma Aberration at Large Aperture
Figure 7 shows that there is nothing to limit the coma aberration of a lens when a large aperture is used.
Figure 8: Coma Aberration at Small Aperture
Figure 8 shows that, when a lens is stopped down, the aperture prevents the light from striking the outer parts of the lens -- reducing coma aberration.

Chromatic Aberration

Figure 9: Longitudinal Chromatic Aberration

Chromatic aberration is different than the previous types of aberration in that it is not caused by the shape of the lens. Rather, chromatic aberration is caused by the material of which the lens is made. Specifically, chromatic aberration occurs when the refractive index of the lens material varies with the wavelength of the light. What this means is that the lens bends the different colors of light by different amounts. This results in two types of chromatic aberration. Longitudinal chromatic aberration results when the different colors of light are focused at different points (see Figure 9). Lateral chromatic aberration results when the different colors of light are magnified different amounts (see Figure 10).

Figure 10: Lateral Chromatic Aberration
Longitudinal chromatic aberration is improved by using smaller apertures. However, changing the aperture has no effect on lateral chromatic aberration.

Diffraction

Figure 11: Little Diffraction at Large Aperture

Up until now, most of the aberrations could be reduced by using smaller apertures. This might lead one to conclude that photographers can improve image quality by stopping their lenses down to the smallest aperture possible. Unfortunately, it is not as simple as that due to a phenomenon called diffraction.

Under normal circumstances, light travels in straight lines. However, when light travels through a small hole, diffraction causes the light to bend. The problem for photographers is that the aperture functions as a hole that the light passes through as it travels through the lens. As the aperture becomes smaller, diffraction becomes more pronounced.

As can be seen in Figure 11, when large apertures are used, light passes through the aperture in a fairly straight line and little, if any, noticeable diffraction occurs.

Figure 12: Moderate Diffraction at Medium Aperture
When medium apertures are used, some diffraction occurs as seen in Figure 12.
Figure 13: Major Diffraction at Small Aperture
At very small apertures, the diffraction becomes significant as shown in Figure 13.
Figure 14: Constructive Interference (Perfectly in Phase)
To understand why diffraction is a problem, it is necessary to understand a little bit about light and wave theory. From a scientific point of view, light is essentially a wave. This wave is composed of electromagnetic radiation. Waves have what is called a phase. In simplistic terms, the phase of a wave refers to the position of the wave. When two waves are of the same wavelength, we can compare the phases (i.e., the positions) of the two waves. Figure 14 shows two waves that are perfectly in phase. When the waves are in phase, the crests and troughs of the two waves align with each other. When this happens, the two waves reinforce each other to produce a new wave which has higher crests and lower troughs. In other words, the two waves add together to produce a new wave that is twice as tall as the original waves. Thus, the new wave is bigger. In the case of light waves, the color from the new wave is brighter. This is called constructive interference -- the two waves constructively interfere with each other to produce a new wave of light that is brighter.
Figure 15: Destructive Interference (Perfectly Out of Phase).

Figure 15 shows two waves that are perfectly out of phase. When the waves are out of phase, the crests of one wave are aligned with the troughs of the other. When this happens, the two waves cancel each other. This destroys the two waves. In the case of light waves, there will be no light from the waves. This is called destructive interference -- the two waves destroy each other so that there is no light.

Figures 14 and 15 show waves that are perfectly in phase and perfectly out of phase. In the real word, waves can be in between these two situations so that the waves either partly reinforce or partly destroy each other.

Figure 16: Interference's Effect on Distance Light Travels
The problem with diffraction is that light that travels through the aperture travels different distances to get to the sensor depending on how much it diffracts. This is shown in Figure 16. Light that does not diffract travels the shortest distance. Light that diffracts the most travels the greatest distance. Since the waves travel different distances to get to the sensor, the phases of the waves change relative to each other. When the waves arrive at the sensor, some are in phase. This results in constructive interference and causes the light to be very bright at that point. Some waves are out of phase. This results in destructive interference and causes the light to be very dark at that point. Consequently, a pattern of light/dark rings is produced as shown in Figure 17. This pattern is referred to as the airy disk.
Figure 17: Airy disk
Now, the airy disk is actually very small. However, so are the details that a lens is trying to resolve. Thus, not surprisingly, the airy disk degrades the quality of the image. The smaller the aperture, the greater the degradation becomes.

Diffraction Limited

In some lenses, the aberrations have been reduced to the point were the quality of the image is limited mostly by diffraction. These lenses are referred to as diffraction limited.

The Sharpest Aperture

We often hear that one should use the middle apertures for the greatest sharpness. That is because large apertures degrade image quality through the various aberrations, and small apertures degrade image quality through diffraction. However, the aperture is often chosen for reasons other than just image quality. For instance, the amount of available light and the desired depth of field also affect the choice of aperture. Thus, one may want to use a large aperture for low light situations or a small one for a wider depth of field. The question becomes, "How large or small of an aperture can be used with a particular lens before the image quality starts suffers?" This can be determined by testing and is the subject of Part II of this series.

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