Aberration Balancing
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To improve system performance, optical designers make sure that the total
aberration contribution from all surfaces taken together sums to nearly zero.
Normally, such a process requires computerized analysis and optimization.
However, there are some simple guidelines that can be used to achieve this
with lenses available in this catalog. This approach can yield systems that
operate at a much lower f-number than can usually be achieved with simple lenses. The figure below shows the third-order longitudinal spherical aberration coefficients (k) for four of the most common positive and negative lens shapes when used with parallel, monochromatic incident light. The plano-convex and plano-concave lenses both show minimum spherical aberration when oriented with their curved surface facing the incident parallel beam. All other configurations exhibit larger amounts of spherical a berration. With these lens types, it is now possible to show how various systems can be corrected for spherical aberration. |
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| Third-order longitudinal spherical aberration of typical lens shapes |
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The contribution to longitudinal spherical aberration (LSA) for a lens is
the -factor multiplied by the focal length and
divided by the square of the f-number. The LSA for a complete lens system is the
sum of the LSAs for the individual components. Since the sign of the aberration is
the same as focal length, to null out the effects of spherical aberrations the
system requires both positive and negative focal length elements. A two-element laser beam expander is a good starting example. In this case, two lenses are separated by a distance that is the sum of their focal lengths, so that the overall system focal length is infinite. This system will not focus incoming collimated light, but it will change the beam diameter. By definition, each of the lenses is operating at the same f-number. The equation for longitudinal spherical aberration shows that for two lenses with the same f-number, aberration varies directly with the focal lengths of the lenses. The sign of the aberration is the same as focal length. Thus, it should be possible to correct the spherical aberration of this Galilean-type beam expander, which consists of a positive focal length objective and a negative diverging lens. If a plano-convex lens of focal length f1 oriented in the normal direction is combined with a plano-concave lens of focal length f2 oriented in its reverse direction, the total spherical aberration of the system is |
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after setting this equal to zero, we obtain |
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To make the magnitude of aberration contributions of the two elements equal so
they will cancel out, and thus correct the system, select the focal length of the
positive element to be 3.93 times that of the negative element. |
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| Optics Guide Copyright 2002 Melles Griot Inc. |