Lenses

Chapter 4 Overview

After a discussion of the basic optics used in the creation of lenses, this chapter looks at basic types of lenses and how lenses control exposure, angle of view, and focus.

Basic Optics

In order to form an image, light must be transmitted from the subject to the sensor. Optics accomplishes this task. The principles of optics describe how light is modulated and directed. In the study of optics, absorption, transmission, reflection, and refraction constitute major areas. These effects change the direction of light and determine how lenses and image capture work within digital imaging systems.

Optics The physical study of light and how it reacts to and with other materials.

Absorption Capturing energy when light strikes a surface and the energy enters the material that does not pass through.

Transmission Movement of radiant energy through lenses or other materials.

Reflection Change of direction of energy as it returns from a surface.

Refraction Physical effect on light; as it passes from one medium to another, it bends.

In photography, absorption is what makes the system work. Absorption can be viewed as the opposite of reflection. With an optics system, the concern is to control how the light arrives at the point in the system where absorption can occur. In the digital camera, absorption occurs twice. Initially, light absorption allows the transmission of light through the lens; then when the light enters the gate of the sensor it is absorbed again. Most materials will absorb light energy. This can be demonstrated by an object that sits in the sun and warms up above the ambient air temperature.

Reflection is often considered more important for lighting than capture, as it affects the digital system’s ability to capture an image. Briefly, the law of reflection states that the angle of incidence equals the angle of reflection. When a beam of light strikes a surface, the angle is measured between the beam and a line extending perpendicular (the normal) to that surface at the point of incidence. The light will be reflected from the surface at the same angle as measured from the normal. When the surface is curvilinear, the law still holds. In this case, the normal is a line that extends from the surface along the radius of the curved surface at the point of incidence. This means that the angle of incidence is measured from the extended radius, as is the angle of reflection.

Any surface will reflect light. The material, color, and finish of the surface will determine how the light reflects and how much of the light is absorbed—the smoother the surface, the greater the reflection. Glass and transparent materials reflect on the outside and on the inside. Internal reflections are major factors in creating camera flare. The generation of flare is a major problem for photographers. Flare occurs whenever light enters a lens system. Because of the number of elements and surfaces in modern lenses, the potential is greater for increased reflection and refraction within the lens system. Whenever light strikes a surface, some of the light can be reflected as well as transmitted and focused. When the light reflects internally in a lens, it can take a new path to the sensor. The stronger the light entering the lens and taking this nondirect path, the greater the disruption that will be seen in the captured image.

Flare Unwanted reflection within an optical system that is seen as fogging or bright spots on an image.

While it is easy to see flare when it is caused by a bright light source such as the sun, it also occurs with overcast light. There are two ways to reduce the effect of flare. First, a lens hood or shade can be used. Shading the front element of the lens system reduces the amount of non-image light entering the lens that can become flare. Second, most modern lenses are manufactured with multicoatings to reduce internal reflections.

Multicoatings Multiple optical enhancing and protective layers used on and between lenses and lens elements.

Reflection plays a part in the imaging process, but refraction is crucial to proper operation of digital systems. Refraction is the bending of light as it passes from one material (medium) to another. Light travels at slightly different speeds in different media. When light moves at an angle from one medium to another and transmits through the second medium, it bends. If the light is viewed as a short line traveling perpendicular to the light beam, as one end of this short line moves from one medium into another it slows down or speeds up, and this speed change pivots the line, changing the direction of the beam slightly.

Three variables change the amount of refraction that takes place with regard to a sensor: the angle of incidence of the focused light on the sensor, the absolute index of refraction for the gate material, and the wavelength of the light striking the sensor surface. There is a specific range of angles at which refraction can effectively take place. As the angles of incidence increase, more of the light reflects from the surface of the sensor. This means that the amount of light available for absorption into the site is reduced when the angle of incidence increases. While sensor gates are primarily transparent, indium tin oxide (ITO) is more transparent than silicon oxide, but both reflect the light as well. They absorb the maximum amount if the light striking the sensor is close to perpendicular to the surface.

Wavelengths Distance between successive crests (the high points) of a wave of light—the shorter the wavelength, the greater the refraction. Violet is the shortest visible wavelength; red, the longest.

Reflection also plays a role in effective light absorption. As the angle of incident increases, the percentage of the light that can be absorbed decreases, which means that light absorption at the extremes of the cone of illumination of the lens is less effective. The operation of the sensor requires the light to be perpendicular for maximum effect. The angular spread of the light, particularly with films based wideangle lenses, also reduces the use of these lenses where the sensor is expected to capture light on the extremes of the cone of illumination. Very-wide-angle lenses and view cameras with large amounts of camera movement particularly experience problems with fall-off. Lenses designed to function optimally for digital capture must condense or collimate the light to eliminate the possibility of light striking the sensor at an ineffective angle. For a wide-angle lens, when light spreads across the sensor, the angle of incidence increases as the light approaches the edge of the sensor along with natural fall-off of the light’s strength.

To address this issue, some manufacturers are adopting the Four-Thirds standard (4/3rds), which originated with video and suggests that the center portion of the cone of illumination be used for digital imaging. The standard specifies an aspect ratio for the sensor’s size in relation to the cone of light and allows for interchangeable lenses with particular design specifications. Other manufacturers have altered the structure of the angle and light-gathering potentials of the micro-lenses to concentrate the light to the photodiodes. Also, some lens manufacturers, as is discussed at the end of this chapter, use additional lens elements to restructure the light to bring it into the sensor as parallel rays.

Four-Thirds standard (4/3rds) A standard for digital camera lenses that allows optimal performance in these digital systems. Sensors do not respond well to light striking at a high angle of incidence, so the four-thirds standard uses only the light projected from the lens.

The second variable that controls the amount of refraction is the absolute index of refraction. This index relates the amount of divergence that is expected to occur as the light passes from a vacuum into the medium. For example, the average index for water is 1.333, while crown glass has an average index of 1.524. The difference in indexes shows that the two different media bend light at different rates.

Crown glass A type of glass used for making fine optics that consists mostly of lime and silicate of soda or potash, with no lead.

These indexes change, however, due to the third variable—the difference in wavelengths. Crown glass has indexes of refraction of 1.519 for red light and 1.538 for violet light, which means that short wavelengths (blue–violet) will bend more than long wavelengths (red–yellow). This difference in bending based on wavelengths creates chromatic aberrations that can be seen within lenses that have large internal angles focusing on the sensor. This differential bending of portions of the image creates problems. Because the sensor is acquiring the image with color-specific photodiodes, this problem is exaggerated. These effects are seen as color shifts on edges as boundary lines that appear away from the image center or with high angles of incidence on the sensor’s surface. These colored lines will tend to be seen in complementary color pairs of one long and one short wavelength—for example, red–cyan or blue–yellow. Apochromatic lenses reduce chromatic aberration by using compound lenses and special coatings.

Chromatic aberrations Caused by lights of different wavelengths focusing at different points. Aberrations can be reduced by the use of multicoatings and compound lens elements.

Apochromatic lenses Compound lenses with higher curvature elements that reduce chromatic aberration. They often have special coatings to further reduce chromatic aberrations.

Diffraction happens when waveform light passes an edge or through a narrow opening. Part of the light is deflected as it moves past the edge. When part of the light is deflected it slightly softens the image of the edge where the light has been bent. Smaller apertures of most lenses create diffraction, which has a major effect on the ability of a particular lens to be used at smaller apertures with sensors. When light diffraction occurs, it is likely that the light arriving at the sensor’s gate has lost part of the intensity. This restricts the effective use of smaller apertures with small gates.

Diffraction Changes in the direction and intensity of light as the lightwaves pass by an edge or through a small aperture.

Lens Basics

The two basic types of lenses are positive and negative. Positive lenses converge and focus the light, and negative lenses diverge and spread the light. In simple lenses, positive lenses are primarily convex lenses; the thickest part of the lens is at the center. At least one surface must be convex, but the other side can be convex, planar, or concave. If the center of the lens is the thinnest part, then the lens is negative. As opposed to positive lenses, negative lenses have at least one concave surface with the other side being planar, convex, or concave. Positive lenses have a point of focus while negative lenses do not bring the light to a focal point but instead spread the light as though it were emanating from a point (a virtual focus) on the lit side of the lens.

Most cameras today have lens systems comprised of multiple lens elements, or compound lenses. Compound lenses use both positive and negative lenses in combinations that can be constructed to correct a variety of lens problems. Also, these compound lenses have coatings on and between the lens elements that attenuate color aberrations and reduce internal reflections and flare. The requirement for light to be brought to the sensor collimated or with low angular variation requires the use of compound lenses.

Lenses control how light reaches the sensor. This includes focusing the image and controlling how much light arrives at the sensor. Focus is defined by the lens equation. The equation says that the inverse of the object distance (1/o) plus the inverse of the image distance (1/i) equals the inverse of the focal length (1/f_L). If the object distance is infinity (∞) such that 1/∞ equals zero, then the image distance will be equal to the focal length. When focusing a lens at infinity, the lens distance has its smallest value and the lens is at its most compact. Due to the inverse nature of the equation, as the object distance gets shorter the distance from the lens to the sensor increases. While photographers often discuss focal length as the angle of view, the focal length relates the distance between the lens and the sensor only when the camera is focused at infinity.

Aperture

The amount of light reaching the sensor is controlled by the aperture and shutter speed. The f-stop defines the size of the aperture opening in the lens compared to its focal length. The diameter of the lens aperture divided into the focal length equals the f-number. The standard full-stop numbers are f1, f1.4, f2, f2.8, f4, f5.6, f8, f11, f16, f22. The f-numbers continue doubling every other number. More important, each successive higher full f-stop number allows half as much light to reach the sensor. Changing from f11 to f16 (one full stop) cuts the light in half. The reverse is true for descending f-numbers—twice the amount of light enters the lens with each full stop that is opened up.

Aperture Size of the opening in a lens that allows the light through—larger apertures allow more light to reach the sensor. The aperture is commonly described by the ratio of the f-number.

f-stop The ratio for a lens or lens system computed by dividing the effective diameter or aperture by its focal length; used to define lens aperture for exposure calculation.

The aperture not only determines the amount of light that reaches the sensor but also changes the amount of acceptable focus of the image. The depth of field is the range of acceptable focus from close to the camera to the most distant within the scene, although the notion of “acceptable focus” is subjective. Each point of light in the image focuses a cone of light, with the perfect focus making a circle of light on the sensor surface. When the cone of focused light contacts the sensor, the size of the circle formed on the sensor surface changes because of the focus of the lens and the width of the aperture defining the widest part of the cone of focused light. This concept of defining focus by the size of a circle projected from a point is known as the circle of confusion. Our willingness to accept a certain size circle of confusion defines acceptable focus. With a smaller aperture, a larger f-stop number means that the lens produces a narrower cone of light with a greater depth of field and close to far image sharpness.

Circle of confusion Circle of light created when light from a point source is focused on the surface of the sensor. The size is determined by the size of the aperture and the fineness of the focus. If the circle is acceptably small to the viewer, then the image is considered to be in focus.

For each f-stop on a lens there is a maximum depth of field that can be acquired. When a lens is focused, the depth of focus is divided such that one-third of the depth of field is in front of the point of focus and two-thirds behind the point of focus. For example, if you focus on an object 10 feet away and have a 3-foot depth of field, then the image will be in focus 9 (i.e., 10 – 1) to 12 (i.e., 10 + 2) feet from the camera. To maximize the depth of field and include infinity (∞), the lens is focused at the hyperfocal distance for the given f-stop. This is done manually by placing the ∞ setting on the lens focus at the f-stop number on the lens’s depth of field indicator. In this way, the hyperfocal point of the lens at that f-stop is used for the point of focus. When the lens is focused at infinity, two-thirds of the potential depth of field is lost; however, diffraction at small apertures spreads the light off of the active sensor sites, thus reducing their effectiveness at high f-numbers. Depending on the sensor’s architecture, the smallest apertures may lose effectiveness and limit the ability of these stops to hold exposure and sharpness.

Hyperfocal distance Focusing distance that provides the maximum focus that includes infinity at any given aperture.

Shutter speed constitutes the other control of how much light reaches the sensor. The speeds increase by nominally half or double the preceding shutter speed and thus change the light admitted. Standard shutter speeds are expressed in seconds or fractions of seconds. In this way one-half second is 1/2 where the 2 is the denominator. The denominator of the shutter speed fraction (the lower number) will normally define the shutter speed as a full number. The full shutter stops increase the denominator by doubling: 1, 2, 4, 8, 15, 30, 60, 125, 250, 500, 1000,…. Because the shutter stops are doubling in the denominator, each full shutter stop cuts the light in half.

Types of Lenses

For many photographers, an important feature of a lens is its focal length. Photographers tend to use this as a descriptor defining the angle of view, but it only defines the effective length from the lens to the sensor. For 35-mm single-lens reflex (SLR) digital cameras, the focal lengths of lenses might be used to describe angle of view in terms of the film format and will not be the same for a digital sensor unless the sensor is a “full-frame “ sensor. While using the focal length is convenient, it is misleading if the photographer expects similar lens views and effects when the lens is mounted to a camera that uses less than a full-frame sensor.

Angle of view specifies the perspective that the camera captures. The calculation of angle of view is dependent on the diagonal size of the sensor and the focal length. Simply stated, the angle of view is the angle created by lines drawn from each end of the diagonal distance of the sensor and passing through a point centered and at the focal length from the sensor. As the focal length increases, the angle becomes more acute; as the focal length decreases, the angle broadens.

Because the diagonal of the sensor is involved in determining the angle of view, smaller sensors have more acute angles of view than larger sensors when calculated with the same focal lengthened lenses. This becomes quite evident when using lenses designed for standard film sizes, such as 35-mm SLR film cameras that are used with digital cameras. When this lens is used on digital camera bodies with sensors that have smaller diagonals, than the angle of view will be more acute. This is known as the “telephoto effect” because the lens gives an angle of view typical of the longer focal length on the original-size film.

Lens denomination relates directly to the angle of view. Three primary names are used to discuss lenses: normal, telephoto, and wide-angle. Because the sensor size remains constant, the type of lens will depend on the focal length. Normal lenses give a perspective similar to that of the human eye. More technically, the focal length of these lenses is the same as the sensor diagonal.

Lenses that give a magnified view are known as telephoto lenses. While these lenses act as though they have long focal lengths (long lenses), the use of compound elements changes the focusing function of the lens such that it can be physically shorter than its nominal focal length. The telephoto’s design produces a lighter, shorter lens than if the lens was manufactured with a simple lens structure, but the lens creates a narrower angle of view than a normal lens.

Telephoto lenses Lenses that give a magnified view, making distant objects look closer by narrowing the angle of view.

Wide-angle lenses give a perspective with a greater angle of view than a normal lens. Depending on the viewing system, wide-angle lenses might need to have broad angles of view while focusing at a greater distance than the geometry used for calculating angle of view would expect. A common lens design for an SLR camera is the retrofocus lens. A retrofocus lens allows the SLR’s mirror to pivot out of the way for exposure without hitting the back of the lens.

Retrofocus lens A lens that works as though it is a longer focal length lens mounted backwards to the camera, thus allowing the lens to have a wider angle of view than normal. It is positioned far enough away from the sensor to allow the mirror in the SLR design to operate without difficulty.

To achieve a range of angles of view, photographers use zoom lenses. These lenses are a combination of positive and negative lens elements that move to change the angle of view. These lenses compensate either optically by moving elements corresponding to varying the focal lengths to change the angle of view or mechanically by moving elements differentially. While the focal length changes, the f-stop is maintained by a component at the rear of the lens that keeps the aperture and distance to the sensor constant. The zoom lens does not have any connection to “digital zoom.” A digital zoom is a reduction of the captured image to make it appear as though the angle of view has been reduced. This is a software application that groups pixels and degrades the detail captured in the image.

Zoom lenses are designed to allow exceptionally close photography; they are considered macro-lenses. A macro-lens maintains a consistent optic focusing distance and aperture relationship, thus allowing each f-stop to function effectively without losing light intensity due to expanded focusing distance.

Regardless of the type of lens, lenses can be focused either manually or automatically. Autofocus lenses use a linear pattern of sensor sites to determine when the light pattern uses the lower sites. This happens because the image goes out of focus and becomes larger both in front of and behind the point of focus. The system uses servomotors to move the lens focusing mechanism until the sites are minimized. Because of the nature of images, lines and edges become critical for autofocusing. The autofocus function uses lines and edges for focusing. For this reason, if you try to use an autofocus function to photograph through a fence, the sensor will isolate the edge of the fence and pull it into focus. If your subject is beyond the depth of field behind the fence, then the fence will be in focus but the subject will not be.

Autofocus lenses Automatic focus. Automatic focusing lenses use a linear pattern in the sensor to determine focus by movement of lens elements to a point at which the fewest number of sites capture the light.

Collimators

Lenses designed specifically for digital sensors use an added lens element (or compound element) that is designed to bring all the light rays reaching the surface of the sensor as near to parallel and perpendicular as possible. This is known as a collimator because it forms the light into a column. Photodiodes are very susceptible to a loss of effectiveness as the light varies from being perpendicular to the sensor surface. The collimator reduces the spread of the light bringing the rays of light more perpendicular to the sensor. The column of light can reduce loss of edge exposure on the sensor and can create a larger apparent angle of view for the digital designed lenses.

Collimators Lenses used to form light into a column. Similar to a lighthouse beacon, the light has little spread. These are helpful in digital systems as they bring light into the sensor perpendicularly.

Summary

• The physics of light controls many functions of digital imaging. Most important are the concepts of refraction, the bending of light, and the reflection of light. These affect the way in which lenses focus and control the light reaching the sensor.
• Lenses for both film-based and digital capture have the same basic functions. Primarily, the way lenses focus light and control the amount of light allowed through the lens affect the quality of the image.
• The use of compound lenses adds functionality to the way images are captured.
• Control of the angle of view defines types of lenses.
• Autofocusing of lenses has always been controlled by the use of sensors, and digital capture devices can be used with programs that provide this control on specific lenses.
• The design of lenses for digital capture must take into account factors that are not considered when designing lenses for capture on film.

Glossary of Terms

Absorption Capturing energy when light strikes a surface and the energy enters the material that does not pass through.

Aperture Size of the opening in a lens that allows the light through—larger apertures allow more light to reach the sensor. The aperture is commonly described by the ratio of the fnumber.

Apochromatic lenses Compound lenses with higher curvature elements that reduce chromatic aberration. They often have special coatings to further reduce chromatic aberrations.

Autofocus lenses Automatic focus. Automatic focusing lenses use a linear pattern in the sensor to determine focus by movement of lens elements to a point at which the fewest number of sites capture the light.

Chromatic aberrations Caused by lights of different wavelengths focusing at different points. Aberrations can be reduced by the use of multicoatings and compound lens elements.

Circle of confusion Circle of light created when light from a point source is focused on the surface of the sensor. The size is determined by the size of the aperture and the fineness of the focus. If the circle is acceptably small to the viewer, then the image is considered to be in focus.

Collimators Lenses used to form light into a column. Similar to a lighthouse beacon, the light has little spread. These are helpful in digital systems as they bring light into the sensor perpendicularly.

Crown glass A type of glass used for making fine optics that consists mostly of lime and silicate of soda or potash, with no lead.

Diffraction Changes in the direction and intensity of light as the lightwaves pass by an edge or through a small aperture.

Flare Unwanted reflection within an optical system that is seen as fogging or bright spots on an image.

Four-Thirds standard (4/3rds) A standard for digital camera lenses that allows optimal performance in these digital systems. Sensors do not respond well to light striking at a high angle of incidence, so the Four-Thirds standard uses only the light projected from the lens.

f-stop The ratio for a lens or lens system computed by dividing the effective diameter or aperture by its focal length; used to define lens aperture for exposure calculation.

Hyperfocal distance Focusing distance that provides the maximum focus that includes infinity at any given aperture.

Multicoatings Multiple optical enhancing and protective layers used on and between lenses and lens elements.

Optics The physical study of light and how it reacts to and with other materials.

Reflection Change of direction of energy as it returns from a surface.

Refraction Physical effect on light; as it passes from one medium to another, it bends.

Retrofocus lens A lens that works as though it is a longer focal length lens mounted backwards to the camera, thus allowing the lens to have a wider angle of view than normal. It is positioned far enough away from the sensor to allow the mirror in the SLR design to operate without difficulty.

Telephoto lenses Lenses that give a magnified view, making distant objects look closer by narrowing the angle of view.

Transmission Movement of radiant energy through lenses or other materials.

Wavelengths Distance between successive crests (the high points) of a wave of light—the shorter the wavelength, the greater the refraction. Violet is the shortest visible wavelength; red, the longest.