Spherical Aberration
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Spherical aberration, shown below in a computer-generated mesh, is a deviation of the laser wavefront from an ideal spherical shape. If the wavefront of a laser has spherical aberration, then a focused spot made from the wavefront will be bright spot surrounded by a faint halo. In imaging systems, spherical aberration tends to blur the image and reduce the contrast. |
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Wavefront showing spherical aberration |
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The figure below illustrates how an aberration-free lens focuses incoming collimated light. |
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Focusing with aberration-free lens |
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All rays pass through the focal point F". The next figure shows the situation more typically encountered in single
lenses. |
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Focusing with a lens exhibiting spherical aberration |
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The farther from the optical axis the ray enters the lens, the nearer to the lens it focuses (crosses the optical axis). The distance along the optical axis between the intercept of the rays that are nearly on the optical axis (paraxial rays) and the rays that go through the edge of the lens (marginal rays) is called longitudi- nal spherical aberration (LSA). The height at which these rays intercept the paraxial focal plane is called transverse spherical aberration (TSA). These quantities are related by |
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Spherical aberration is dependent on lens shape, orientation, and conjugate ratio, as well as on the index of refraction of the materials present. Parameters for choosing the best lens shape and orientation for a given task are presented later in this chapter. However, the third-order, monochromatic, spherical aberration of a plano-convex lens used at infinite conjugate ratio can be estimated by |
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Theoretically, the simplest way to eliminate or reduce spherical aberration is to make the lens surface(s) with a varying radius of curvature (i.e., an aspheric surface) designed to exactly compensate for the fact that sinq is not equal to q at larger angles. In practice, however, most lenses with high surface quality are manufactured by grinding and polishing techniques that naturally produce spherical or cylindrical surfaces. The manufacture of aspheric surfaces is more complex, and it is difficult to produce a lens of sufficient surface accuracy to eliminate spherical aberration completely. Fortunately, these aberrations can be virtually eliminated, for a chosen set of conditions, by combining the effects of two or more spherical (or cylindrical) surfaces. In general, simple positive lenses have undercorrected spherical aberration, and negative lenses usually have overcorrected spherical aberration. By combining a positive lens made from low-index glass with a negative lens made from high-index glass, it is possible to produce a combination in which the spherical aberrations cancel but the focusing powers do not. The simplest examples of this are cemented doublets, such as the 01 LAO series, which produce minimal spherical aberration when properly used. |
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| Optics Guide Copyright 2002 Melles Griot Inc. |