This chapter provides a brief overview of essential imaging concepts used in lens design. Whether classical imaging, which is congruent with first-order optics, is required in a lens system, or any other type of imaging, depends on system application. Therefore, a clear understanding of what imaging is and of departures from such imaging, called aberrations, is essential for a lens design practice.

There are a variety of lens design computer programs. Some of them are CODE V, OpTaliX, OpticStudio, Oslo, and Synopsys. The costs of these programs are two-fold, one for the license to use them, the other for the time the engineer must spend learning to use them, which can be substantial.

By moving groups of lenses along the optical axis of a lens system, it is possible to continuously vary the focal length of the system, which results in a varifocal system. A zoom lens results whenever the position of the image plane remains stationary. As the focal length of the lens changes, the field of view also changes. The focal length is varied by moving axially at least one group of lenses, called the variator. To maintain the image plane position as stationary, another group of lenses is required, which is called the compensator. The axial movement of the variator and the compensator are usually different in nature. The variator might be moved in a linear manner, and the compensator in a non-linear manner by using a mechanical cam. As shown in Figure 18.1, zoom lenses that maintain the image position by moving the variator and the compensator equally are referred to as having optical compensation. Zoom lenses that require different movements for the variator and the compensator are referred to as mechanically compensated. The variator and the compensator constitute the lens kernel of the zoom lens. Mechanically compensated lenses have more optical design freedom than optically compensated lenses, and most modern zoom lenses are of the former class.

An important class of optical systems are those that use mirrors. For a mirror, the ray angle of incidence equals the ray angle of reflection, and there is no light dispersion. Using mirrors for imaging has the advantages of allowing for large element diameters, no intrinsic chromatic aberrations, lesser surface curvature for a given optical power, and potential compactness as the beam of light can be folded. The disadvantages are a central obscuration, more sensitivity to surface errors, the need to include baffles to control stray light, and sometimes fewer degrees of freedom to control aberration. Mirror systems, however, use aspheric surfaces to help control aberration. Lenses can be used in conjunction with mirrors to enhance performance. Optical systems that use both mirrors and lenses are known as catadioptric. This chapter discusses some basic mirror systems. The discussion uses aberration coefficients to determine primary aberrations and to find solutions that can later be optimized with real ray tracing.

The quality of a lens system for a given application depends on several factors. Among them are the choice of lens form that best suits the application, the image quality provided by the lens, and how well the image quality can be maintained under actual lens fabrication and assembly errors, environmental conditions, and actual lens use. A starting point for a lens design is the lens specifications, which includes first-order requirements, packaging constraints, optical power-efficiency, and image quality requirements. Ultimately, lens cost is often a major design driver.

Fabrication of a lens system may take several weeks or months. This can be objectionable in a project. Sometimes it is possible to design a lens system out of off-the-shelf single lens elements. For sharp imaging, this might be possible if the lens system is slower than about F/6 and the field of view is less than about ±12°.

Optical systems comprise lenses and mirrors made with precise surfaces. Optical surfaces can be divided into spherical and nonspherical surfaces; the latter are called aspheric surfaces. For a given image quality, the choice of optical surfaces has a major impact on the packaging and cost of a lens system. Therefore, familiarity with types of optical surfaces, with how they can correct aberration, and with their manufacturing and testing methods is important in lens design. This chapter provides an overview of several useful surface types, some of their optical properties, and how they introduce and mitigate aberrations.

The index of refraction of glass depends on the wavelength of light. For N-BK7 glass from Schott Company, the index of refraction is shown in Figure 7.1 for wavelengths ranging from 0.4 to 0.8 µm; shorter wavelengths have a higher index of refraction than longer wavelengths. Since the angle of refraction depends on the index of refraction, then the angle of refraction varies as the wavelength changes. This results in chromatic aberration. Similarly, the index of refraction and the radii of curvature and thickness of a lens vary with changes in lens temperature. This results in thermal aberrations; thermal change of focus, and thermal change of magnification. This chapter discusses both types of aberrations and their correction.

A lens manufacturer requires tolerances in the dimensions of a lens to be able to provide a cost estimate and be able to manufacture the lens. Further, for the lens to meet the lens specifications after it is built, it is necessary that the actual lens dimensions do not depart from the nominal design ones by some amounts known as fabrication and assembly tolerances. Thus, the task of the lens designer is not only to provide a lens design that meets image quality requirements, but to also provide tolerances, so that the as-built lens actually meets the specifications and satisfies the needs of the application. Critical goals of the lens tolerancing process are to provide tolerances to each of the constructional parameters of the lens, and to find out the statistics of the as-built lens so that the fabrication yield, and final cost, can be estimated. This chapter provides a primer into the lens tolerancing process. Commercial lens design software allows for the lens tolerancing analyses discussed below.

Ray tracing originated in optics to determine the path of light. However, ray tracing is used in modern technology by many fields, such as acoustics and computer graphics. Ray tracing is at the heart of optical design. Most optical calculations are done by tracing rays of light and, therefore, for competent lens design, it is important to have an understanding about how ray tracing is performed. This chapter provides an introduction to ray tracing, to ray tracing pitfalls, and to some useful ray tracing techniques.

An optical engineer is not only concerned with the design of a single lens system, but also in combining several lens systems. An optical system may comprise several individual lens systems. These lens systems must be combined to meet the overall optical system specifications. Often each lens system serves to relay an image or a pupil of the previous system to a new location. In combining lens systems, several effects can take place due to image and/or pupil aberrations. Being aware of such effects is key to design, analyze, or debug a combination of lens systems. For example, a telescope can be considered as the combination of an objective lens, an image erecting system, an eyepiece, and the human eye. To properly form an image on the eye’s retina, these subsystems must be properly combined. In this chapter we discuss combining lens systems, pupil aberrations, and optical relays.

Lens systems produce images by transferring radiant energy. At any plane transverse to the optical axis in an optical system there is a light distribution that may be subject to specifications. The light distribution is modeled with the laws of radiometry. To have a broader understanding about how optical systems work it is relevant to discuss how radiometric aspects impact the design of a lens system. In particular, we are concerned with the light distribution at the exit pupil and image planes. This chapter discusses basic and useful radiometric concepts in a lens system.

There are a number of technological applications that use miniature lenses in which the lens diameter is a few millimeters, and typically smaller than 10 mm. For lens systems that employ such miniature lenses, several advantages result because of the scale. For a given lens form and, except for distortion, the aberrations scale down, while the wavelength of light remains the same. Given that lens volume is small, a wider possibility of lens materials becomes possible due to cost or material limitations. Lens weight is reduced, as well as dimensional changes due to temperature. Further, very thick lenses can be used in some applications. However, lens tolerances for lens thickness and decenter become tighter. Many microscope objectives, lenses for endoscopes, and lenses for mobile phones are in the category of miniature lenses. This chapter provides a discussion about lens design for mobile phones lenses.

Lens systems are designed to form an image according to an ideal model. Light that passes through the stop aperture forms the image. However, some light may not contribute to the formation of the intended image, and reaches the image plane to degrade the image. This light is known as stray light, flare, veiling glare, and ghost images.