Employing a leading-edge technology can fundamentally change the requirements on an optical design. This is true for a range of emerging technologies, including the curved electro-optical detector. Curved electro-optical detectors will enable the development of new optical design configurations that can be smaller than conventional flat-field designs, thereby benefiting many aerospace applications.

Figure 1. left to right: (A) Wide angle objective with 14 elements & 90° field angle (B) Objective with 6 elements & 28° field angle (C) Objective with 2 elements & 6° field angle

Space-borne, aerospace optical systems often require a very wide field of view, for example, in full-earth observation applications. On a satellite in a typical orbit altitude, an objective lens needs to cover about 120° to view horizon to horizon on the earth. Achieving this wide field coverage typically requires a complex and long lens. However, the cost of launching a satellite requires the size of each subsystem to be kept to a minimum.

It is often preferable to cover the entire field of interest simultaneously (i.e. in a “staring” mode), instead of in a scanning mode in which the field of view at any given instant is a subset of the full field of interest. Scanning systems also require moving parts such as rotating mirrors. Moving parts should be kept to a minimum in a space-borne system due to the risk of mission failure if the moving mechanism jams or breaks down.

Traditional Design

Optical designs are available to cover wide angles of 90° to 120° or more, but traditionally consist of numerous optical elements. An example of this is a conventional inverted telephoto lens, which needs this complexity to minimize image imperfections, or aberrations, across the field of view. The length, as a multiple of the input beam diameter, is typically 15 or more for an F/3-class lens, as in the example in Figure 1A. Disadvantages of a design with a large number of elements include greater sensitivity to manufacturing and alignment errors, cost, and length.

Figure 2. Monocentric objective with 2 elements & 120° field coverage

The image-recording surface (film or detector) in a camera is typically flat, which is the easiest shape to manufacture. However, in most image-forming lenses, the natural tendency is for the surface of best focus to be curved, not flat. This is due to an aberration known as Petzval curvature, which is the power of an element divided by its refractive index summed over all elements in the lens. The wider the field angle of a lens, the more severe the image degradation is due to Petzval curvature. Severity increases as the square of the field angle. Therefore, to create a wide-angle flat-field lens requires a complex arrangement of positive and negative elements to keep the “Petzval sum” (and other aberrations) adequately low. The complexity and length of the lens also increases with the field angle. This can be seen by comparing the design of Figure 1A (90° field angle, 14 elements) with those of Figure 1B (28°, 6 elements) and Figure 1C (6°, 2 elements).

Another factor in the complexity of Figure 1A is the asymmetry of the lens. Certain aberrations are exactly or nearly zero in a lens with front-to-back symmetry. In a non-symmetric lens, these aberrations must be corrected by the complexity of the configuration. The best-performing, flat-field wide-angle lenses have the characteristic and non-symmetrical layout of Figure 1A, specifically, a negative power front group of elements, and a positive power group toward the image plane.

Monocentric Design

A general design form that can achieve wide-angle field coverage with a simple design is known as the monocentric form, consisting of surfaces all concentric about a common point. Such de- signs have been accepted in various forms for some time. Monocentric designs can address the issues of length and complexity in a wide-angle staring lens. The following example achieves wide field coverage by symmetry rather than complexity.

Figure 3. Spot size at detector versus field angle

The enabling factor in this design is the use of a curved focal surface. Curved photographic film has been used in specialized applications for years, such as in the well-known Schmidt camera. Modern aerospace systems predominantly use electro-optical detectors like CCDs, rather than film. Curved focal surfaces, especially using electro-optical detectors, are not nearly as common as flat focal planes due to the manufacturing difficulty. Electro-optical detectors are preferable to film in aerospace applications because of the nearly instantaneous data transmission (no need to retrieve film and develop it) and the continual reusability of the detector. These are the same reasons digital cameras are becoming more popular in the consumer market and are competitive with film cameras. Likewise in the commercial filmmaking industry, digital cameras are expected to largely displace film cameras in the coming years.

When the constraint for a flat image is removed, this eliminates the need to control Petzval curvature, and therefore, the need for asymmetric layout (Figure 1A). This allows the potential to correct the remaining aberrations with a dramatically simpler layout.

This design consists of two spherical glass components: a meniscus (convex-concave) first element, and a ball-shaped second element. The ball-shaped second element may be two hemispherical plano-convex elements bonded together, with an aperture stop to limit the beam boundary deposited in the center, as shown in Figure 2. All surfaces are concentric about the central aperture stop. This concentricity results in the aberrations of coma, distortion, and lateral color (variation in image height with wavelength) to be identically zero. The other aberrations can be controlled (if not exactly zero) by appropriate choice of glass types and element thicknesses.

The length from the first surface of the lens to the focal surface is 7.5 input beam diameters, half the length of typical inverted telephoto lenses of the same field of view and f number. The f number is the ratio of the lens focal length to the input beam diameter. The design is less sensitive to fabrication and alignment errors than the flat-field design of Figure 1A, because the angles of incidence of the rays on the surfaces are lower, and there are only two components to align instead of ten or more.

The concentricity of the design causes the performance to be nearly uniform across the field, since the ray angles on the air-glass interfaces are the same at any field angle. Variation in performance across the field is due only to the change in beam angle at the aperture stop, causing a truncation of the beam in one direction according to the cosine of the incidence angle. The example in Figure 2 has a 120° total field, and in principle this could be extended to nearly 180°, although the cosine falloff of the beam area would preclude a useful signal at angles at or near 180°. The variation in performance across the field is gradual, as shown in Figure 3, which plots the spot size at the focal surface in microns versus the field angle in degrees.

This article was authored by J. Michael Rodgers, principal engineer of Optical Design, for Optical Research Associates (Pasadena, CA). For more information, contact the author at This email address is being protected from spambots. You need JavaScript enabled to view it.. Visit Optical Research Associates at www.optical-res.com. The monocentric design example included in this article is courtesy of Raytheon Company (Lexington, MA), U.S. Patent 6,320,703; C.W. Chen; Raytheon, 2001. Images created using CODE V ®.

Photonics Tech Briefs Magazine

This article first appeared in the April, 2003 issue of Photonics Tech Briefs Magazine.

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