The word “lens” is ambiguous, since it may refer to a single element or to a complete objective such as that supplied with a camera. The term “system” is often used for an assembly of units such as lenses, mirrors, prisms, polarizers, and detectors. The name “element” always refers to a single piece of glass having polished surfaces, and a complete lens thus contains one or more elements. Sometimes a group of elements, cemented or closely airspaced, is referred to as a “component” of a lens. However, these usages are not standardized and the reader must judge what is meant when these terms appear in a book or article.

1.1RELATIONS BETWEEN DESIGNER AND FACTORY

The lens designer must establish good relations with the factory because, after all, the lenses that he designs must eventually be made. He should be familiar with the various manufacturing processes and work closely with the optical engineers. He must always bear in mind that lens elements cost money, and he should therefore use as few of them as possible if cost is a serious factor. Sometimes, of course, image quality is the most important consideration, in which case no limit is placed on the complexity or size of a lens. Far more often the designer is urged to economize by using fewer elements, flatter lens surfaces so that more lenses can be polished on a single block, lower-priced types of glass, and thicker lens elements since they are easier to hold by the rim in the various manufacturing operations.

1.1.1 Spherical versus Aspheric Surfaces

In almost all cases the designer is restricted to the use of spherical refracting

or reflecting surfaces, regarding the plane as a sphere of infinite radius. The standard lens manufacturing processes3,4,5,6,7 generate a spherical surface with

great accuracy, but attempts to broaden the designer’s freedom by permitting the use of nonspherical or “aspheric” surfaces historically lead to extremely difficult manufacturing problems; consequently such surfaces were used only when no other solution could be found. The aspheric plate in the Schmidt camera is a classic example. In recent years, significant effort has been expended in developing manufacturing and testing technology to fabricate, on a commercial scale,

aspheric surfaces for elements such as mirrors, infrared lenses, and glass lenses.8,9,10,11,12 New fabrication technologies such as single-point diamond

turning, reactive ion etching, and computer-controlled free-form grinding and polishing have greatly increased the design space for lens designers. Also, molded aspheric surfaces are very practical and can be used wherever the

production rate is sufficiently high to justify the cost of the mold; this applies particularly to plastic lenses made by injection molding.

In addition to the problem of generating and polishing a precise aspheric surface, there is the further matter of centering. Centered lenses with spherical surfaces have an optical axis that contains the centers of curvature of all the surfaces, but an aspheric surface has its own independent axis, which must be made to coincide with the axis containing all the other centers of curvature in the system. In the first edition of this book, it was noted that most astronomical instruments and a few photographic lenses and eyepieces have been made with aspheric surfaces, but the lens designer was advised to avoid such surfaces if at all possible.

Today, the situation has changed significantly and aspheric lenses are more commonly incorporated in designs primarily because of advances in manufacturing technologies that provide quality surfaces in a reasonable time frame and at a reasonable cost. Many of the better photographic lenses now sold by companies such as Canon and Nikon, for example, incorporate one or more aspheric surfaces. The lens designer needs to be aware of which glasses can currently be molded and aspherized by grinding or other processes. As mentioned previously, maintaining good communications with the fabricator cannot be overstressed.

1.1.2 Establishment of Thicknesses

Negative-power lens elements should have a center thickness between 6 and 10% of the lens diameter,13 but the establishment of the thickness of a positive element requires much more consideration. The glass blank from which the lens is made must have an edge thickness of at least 1 mm to enable it to be held during the grinding and polishing operations (Figure 1.1). At least 1 mm will be removed in edging the lens to its trim diameter, and we must allow at least another 1 mm in radius for support in the mount. With these allowances in mind, and knowing the surface curvatures, the minimum acceptable center thickness of a positive lens can be determined. These specific limitations refer to a lens of average size, say 12 to 3 in. in diameter; they may be somewhat reduced for small lenses, and they must be increased for large ones. A knife-edge lens is very hard to make and handle and it should be avoided wherever possible. A discussion of these matters with the glass-shop foreman can be very profitable. Remember that the space between the clear and trim diameters shown in Figure 1.1 is where the lens is held. The lens designer needs to be sure that the mounting will not vignette any rays.

As a general rule, weak lens surfaces are cheaper to make than strong surfaces because more lenses can be polished together on a block. However,

Blank

Trim

Clear

Figure 1.1 Assigning thickness to a positive element.

if only a single lens is to be made, multiple blocks will not be used, and then a strong surface is no more expensive than a weak one.

A small point but one worth noting is that a lens that is nearly equiconvex is liable to be accidentally cemented or mounted back-to-front in assembly. If possible such a lens should be made exactly equiconvex by a trifling bending, any aberrations so introduced being taken up elsewhere in the system. Another point to note is that a very small edge separation between two lenses is hard to achieve, and it is better either to let the lenses actually touch at a diameter slightly greater than the clear aperture, or to call for an edge separation of one millimeter or more, which can be achieved by a spacer ring or a rigid part of the mounting. Remember that the clearance for a shutter or an iris diaphragm must be counted from the bevel of a concave surface to the vertex of a convex surface.

Some typical forms of lens mount are shown in Figure 1.2. When designing a lens, it is wise to keep in mind what type of mounting might be employed and

Figure 1.2 Some typical lens mounts: (a) Clamp ring, (b) spinning lip, (c) spacer and screw cap, and (d) mount centering.

any required physical adjustments for alignment. This can make the overall lens

development project progress smoother. A study of optomechanics taught by Yoder can be of much benefit to the lens designer.14,15,16 In many cases, the

optomechanical structure of the lens needs to be integrated into the larger system and modeled to ensure that overall system-level performance will be realized in the actual system.17

1.1.3 Antireflection Coatings

Today practically all glass–air lens surfaces are given an antireflection coating to improve the light transmission and to eliminate ghost images. Since many lenses can be coated together in a large bell jar, the process is surprisingly inexpensive. However, for the most complete elimination of surface reflection over a wide wavelength range, a multilayer coating is required, and the cost then immediately rises. In the past few decades, great strides have been made in the design and production of high-efficiency antireflective coatings for optical material in both the visible and infrared spectrums.18,19

1.1.4 Cementing

Small lens elements are often cemented together, using either Canada balsam or some suitable organic polymer. However, in lenses of diameter over about 3 in., the differential expansion of crown and flint glasses is prone to cause warpage or even fracture if hard cement is used. Soft yielding cements or a liquid oil can be introduced between adjacent lens surfaces, but in large sizes it is more usual to separate the surfaces by small pieces of tinfoil or an actual spacer ring. The cement layer is (almost) always ignored in raytracing, the ray being refracted directly from one glass to the next.

The reasons for cementing lenses together are (a) to eliminate two-surface reflection losses, (b) to prevent total reflection at the air film, and (c) to aid in mounting by combining two strong elements into a single, much weaker cemented doublet. The relative centering of the two strong elements is accomplished during the cementing operation rather than in the lens mount, which is most generally preferred.

Cementing more than two lens elements together can be done, but it is very difficult to secure perfect centering of the entire cemented component. The designer is advised to consult with the manufacturing department before planning to use a triple or quadruple cemented component. Precise cementing of lenses is not a low-cost operation, and it is often cheaper to coat two surfaces that are airspaced in the mount rather than to cement these surfaces together.