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.

Lens design is an exciting and important field of optics. This field provides designs for a great diversity of lens and mirror systems needed in many other fields, such as consumer optics, microscope optics, telescope optics, lenses for optical lithography, and photographic optics. Lens and mirror systems are ubiquitous. The work of a lens designer is to provide the constructional data and fabrication tolerances of all the optical elements that a given lens system requires to perform the intended function. Currently many students and engineers are interested in lens design because the field by itself is of great interest, or because they have the need to analyze and design lens systems required in their engineering practice. An optical engineer should have at least some familiarity with how a lens system is designed so that he or she can effectively contribute to develop optical systems.

Three well-known and important classical lens forms are the Petzval objective, the Cooke triplet lens, and the double Gauss lens. An understanding about how these lens forms work, and how they are designed, provides a solid background to push forward the skill of lens design. Many other lens forms are derived from such classical lens forms by lens splitting and adding lens complexity.

The achromatic doublet is a fundamental building block in lens design because it is corrected for chromatic aberrations, and can also be corrected for spherical aberration and coma aberration. The early lens designers explored all combinations of two achromatic doublets. This chapter discusses some of the solutions found by those designers. In doing so, insight is gained into how simple lens combinations are designed. Emphasis is given to how the primary aberrations are controlled in doublet combinations, as this knowledge is important to become skilled in lens design. Providing degrees of freedom to correct the primary aberrations is a first step toward the optimization of a lens. In practice, the primary aberrations may not be fully corrected so that higher order aberrations might be balanced against the primary aberration residuals. Once a primary aberration solution was reached in the examples given in this chapter, then they were optimized with real rays in a lens design program by minimizing RMS spot size across the field of view. Thus, a lens design method is to find a primary aberration solution and then optimize it with real ray tracing.