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4.4.2 Aberrations of a Thin Lens

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We extend the treatment already outlined to analyse a thin lens. A thin lens can be considered as combination of two refractive surfaces, where the distance between the two surfaces is ignored. In practice, this is a reasonable assumption, provided the thickness is much less than the radii of the surfaces in question. Of course, the wavefront error produced by the two surfaces is simply the sum of the aberrations of the individual surfaces. A schematic for the analysis is shown in Figure 4.8.

The wavefront error contribution for the first surface is very easy to compute; it is simply that set out in Eqs. (4.5a)(4.5d). To compute the contribution for the second surface, one can analyse this using the same methodology as in Section 4.2, but exploiting natural symmetry. That is to say, one can analyse the second surface by rotating the whole surface about the y axis, such that z → −z and x → −x. In this event, for the second surface, R → −R2, uv, θ → −θ. It is then simply a case of substituting these values into the formulae in Eqs. (4.5a)(4.5d) and adding the wavefront error contribution of the first surface. The total wavefront error for the thin lens is then:


Figure 4.8 Aberration analysis for thin lens.

(4.25a)

(4.25b)

(4.25c)

(4.25d)

Optical Engineering Science

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