Introduction to Achromatic Lenses
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Basic Design Concept
The optical performance of compound lenses (two or more single elements designed to work together) is superior to that of single lens elements working alone. Achromatic doublets and triplets are compound lenses composed of two and three singlets. Designers often abbreviate their reference to achromatic doublets and triplets by simply calling them achromats.
The origin of the technical term “achromatic” is in the color-corrected performance of compound lenses. They are designed to outperform singlets by all measures, but designers give special attention to the reduction of color effects in their images. “Achromatic” literally means “without color,” and in lens design, the term refers to minimal difference of focal length between two specific wavelengths. Achromats are the simplest of the multi-element or compound lens designs. Aberrations inherent in a single lens element limit imaging performance. By carefully combining complementary singlets and assembling them into a compound lens, designers can reduce the net aberration of the image. Aberrations induced by one singlet can be canceled by the opposing aberrations of other singlets.
The two most important principles guiding designers in their efforts to balance the aberrations of an achromat are:
1. Glasses of different refractive index can be used to reduce aberrations in a single color (monochromatic aberrations).
2. Glasses of different Abbe number, a measure of the prismatic power or dispersion of glass, can be used to reduce aberrations of color (chromatic aberrations).
Achromatic doublets generally demonstrate these principles: one element is made of crown glass (low refractive index and low dispersion); the other is made of flint glass (high refractive index and high dispersion). The ultimate quality of an image often can be related to the number of elements within the lens. A rule of thumb states, “The more elements, the better the quality.” This rule is usually valid because more elements give the designer more degrees of freedom to control aberrations in the image. Achromatic doublets and triplets deliver about the same image quality; the advantage of the triplet over the doublet lies in its ability to work at lower f-numbers (higher speed) and larger fields of view.
Blur Circle or Spot Size
Dramatic improvement in image quality can result when a singlet is replaced by an achromat. One measure of image quality is the size of the blur circle or spot size created by the lens. The smaller the blur circle, the higher the quality of the image; the blur circle of an achromat is much smaller than that of a singlet. There are two components to the axial blur circle of a lens: spherical aberration and longitudinal color. They are modeled separately in the following diagrams because they are fundamentally different. Spherical aberration is measured in the light of one single color and is defined as the change in focus of the lens as a function of aperture. Longitudinal color is measured in the light of many colors and is defined as the change in focus as a function of wavelength.
The size of the blur circle varies along the optical axis. This is a characteristic of every lens and is the reason that a lens must be focused: the act of focusing is the act of finding the smallest blur circle. When attention is limited to performance along the axis, the point of geometric best focus is the location of the circle of least confusion. This is the point at which an observer would identify the smallest spot size and in the laboratory represents the location at which the blur circle or spot size is usually measured.
Spherical Aberration and Spot Size
A singlet suffers from significant spherical aberration; hence, its spot size is rather large (Figure 1). Spherical aberration, inherent in the performance of the spherical singlet, causes rays of light near the edge of the lens to focus at a different location than the more centrally located rays will focus. Its magnitude is measured in the paraxial image plane, and its effect is to displace the location of best focus toward the lens.
Figure 1
In an achromat, such as a cemented doublet, spherical aberration can be reduced and the separation between the point of best focus and the paraxial image plane becomes smaller. As shown in the diagram (Figure 2), the spot size also shrinks. An achromat can produce a small, high-quality focal spot on axis but, for points off axis, spot quality deteriorates significantly. Historically, this limitation in an achromat’s field of view led to the development of more sophisticated compound lenses.
Figure 2
Longitudinal Color and Spot Size
Another major criterion by which lenses are measured is the quality of color correction. Chromatic aberrations arise from the variation of focus with wavelength. Poor correction of longitudinal color causes a large axial spot size as well as halos of color in the image plane. Achromatic doublets and triplets exhibit superior color performance when compared to singlets. A singlet cannot be corrected for color because to do so requires more than one type of glass. Engineers model the color performance of a singlet as shown below.
The lens will focus blue wavelengths at a point closer to itself than the point at which it will focus red wavelengths. In other words, the focal length of the lens is shorter for blue light than it is for red light. The difference in focal lengths is approximately f/n, where f is the focal length in green light and n is the Abbe number of the lens’ glass. Yellow, rather than green, light is often used as the reference wavelength. The design of an achromat reduces the chromatic difference in focus and thereby reduces the chromatic blur as well (Figure 4).
Figure 3
Figure 4
The red and blue wavelengths focus at the same plane while intermediate green wavelengths focus in a plane just a bit closer to the lens. In fact, the distance between the green focal point and the red-blue focal point of an achromat is typically 1/2000 of the red focal length.
Summary
Achromats are a class of lenses whose image quality is superior to that of singlets. Achromatic lenses include cemented doublets and cemented triplets. Improved performance is achieved with two different kinds of glass. Multiple elements provide added degrees of freedom for the designer to balance aberrations near the optical axis. Achromats are useful in applications requiring a lens with a narrow field of view and large to moderately small f-numbers.
The performance difference between achromatic triplets and doublets is small. Sometimes the slightly lower f-number or slightly larger field of view of a cemented triplet makes it a better candidate for an application than a cemented doublet. In addition, the symmetrical construction of most cemented triplets enhances performance for 1:1 imaging. Doublets rank high among the types of lenses available to the optical systems engineer. With just two elements, each of different glass type, designers can create one lens with excellent color correction throughout narrow fields of view. Achromatic doublets may be air spaced or cemented (Figure 5).
Achromatic doublets are used as telescope objectives, eye loupes, magnifying glasses and eyepieces. These lenses can be found in a wide variety of instruments. Since the development of the laser, achromatic doublets have also been used to focus and manipulate laser beams because their image quality is superior to that of singlets.
Figure 5
The classic structure of a doublet combines a positively powered crown element with a negatively powered flint element. The lens must be correctly oriented for it to achieve its full potential for performance. For example, the most common cemented doublet, sometimes called a “Harting Doublet,” should have its positive crown element facing the more distant conjugate. In monochromatic light this orientation will allow an appropriately designed lens to produce a diffraction-limited spot size on axis.
Field angles of up to 6 degrees are typical for applications involving white light. Typical performance for a doublet across its whole field is 40 lp/mm though performance directly on axis can be higher than 1000 lp/mm when using monochromatic sources such as lasers if the lens operates faster than f/2. Cemented achromatic doublets form a superb and durable subset of doublet lenses. They are assembled with precision alignment techniques and the use of UV setting optical cement assures that their alignment will not degrade over time. Therefore, cemented doublets are more environmentally stable than air-spaced doublets.
Since elimination of the air space reduces the number of degrees of freedom available to the designer, the inevitable tradeoff between simplicity and performance is in a slightly reduced limit of correction. Cemented achromatic doublets deliver high performance when the application involves small fields of view near the mechanical centerline of the lens. Their image quality surpasses that of singlets.
JML’s symmetrical triplets have been achromatized for the red and blue; they will perform extremely well throughout the visible spectrum and into the infrared. They perform best at 1:1 imaging, but these lenses still produce quality images at magnifications of up to 30 times for small fields of view. The optical cement used by JML assures a long, stable lifetime free of alignment degradation.
Cemented Achromats Transmission with MgF2 Coatings*
Typical Physical Properties*
• Recommended operating temperature range = -60°C to 70°C
• Coefficient of thermal expansion (cement) = 63ppm/°C
• Coefficient of thermal expansion (glass) = 10ppm/°C
• Limiting Young’s Modulus = 0.44 × 105kg/cm2
• Limiting shear strength (cement) = 5200PSI = 35N/mm2
• Resistance to weathering = High
• Resistance to scratching = High
• Resistance to acid = High
• Resistance to staining = High
• Resistance to alkaline = High
*For reference only; critical data must be confirmed.
Cemented Triplets
Achromatic triplets are ideal for many applications. Triplets are used in eyepieces for microscopes, telescopes and endoscopes. Achromatic triplets also relay images down long tubes such as those found in borescopes. They also are used in high-powered loupes. Inspectors in the textile industry use them to examine the warp and weave of fabrics; printers use them to evaluate the quality of halftone patterns; and architects use achromatic triplets to study finely detailed or reduced drawings.
An achromatic triplet is usually a symmetrical lens; it affords a modest increase in performance over that of a cemented doublet. Its plane of symmetry can be drawn through the middle of its central element (Figure 6). With an achromatic triplet, the designer has one less degree of freedom than with a cemented achromatic doublet.
Figure 6
The cemented doublet offers three independent curves for adjustment of its design. The achromatic triplet offers only two independent curves since its outer elements are identical. Nevertheless, the achromatic triplet produces a slightly wider field of view. The symmetry of an achromatic triplet allows a systems designer to take advantage of the “symmetrical principle of imaging.” This principle is a statement of three special features of 1:1 imaging with a symmetrically constructed lens, the elimination of distortion, lateral color and coma.
These aberrations are major challenges to engineers designing non-symmetrical systems. Distortion causes an image to appear compressed or expanded near its edges. Lateral color creates rainbow effects in the image and reduces its sharpness. Coma destroys quality of focus. Since symmetry automatically produces an image without these three aberrations, a lens designer can economically design a symmetrical lens for 1:1 magnification.
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