11.0 Lens Bending &amp; Aberration Balancing

# 11.0 Lens Bending & Aberration Balancing - THE...

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FALL Semester 2010 THE UNIVERSITY OF CENTRAL FLORIDA OSE 6265 11.0 Lens Bending and Aberration Balancing James E. Harvey, Instructor 11.0

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11.1 Introduction 11.1 In the last chapter we learned how to calculate W 040 by summing surface contributions. This was applied to a singlet. The thin lens form (structural aberration coefficients) was also introduced and used on the same singlet. In the latter case, the formula was provided without any justification. In this chapter we will see how that thin lens form is derived from the summation procedure. The thin lens form lends itself directly to demonstrating the effects of lens bending. For a singlet with spherical surfaces, bending cannot remove all of the spherical aberration. However, by shifting the image plane, a smaller RMS spot size was achieved. What happened was that some of the spherical aberration was offset by defocus. This illustrates an important optical design principle called aberration balancing , and will be examined in more detail in this chapter.
11.2 The Thin Lens Form We begin by writing out the Seidel summation for the paraxial biconvex lens shown below. = Δ + = + = Δ = n u n u n u yC n u n nyC nu A n u y A S i i i I and where 2 As usual the primes represent quantities after refraction, and the unprimed quantities are before refraction. Substituting A into Eq.(11.1), and noting that for a thin lens y 1 = y 2 Figure 11.1 Parameter illustration for deriving thin lens form. Letting n 1 = n 2 = 1 , and n 2 = n 1 = n (11.1) (11.3) (11.2) 11.2

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11.2 The Thin Lens Form (cont.) The next step is to replace the factors within brackets with expressions containing the shape factor ( X ), the magnification factor ( Y ), and the optical power ( φ ). These details are found in Section 11.10 of the text. When everything is said and done, we have the thin lens form for the Seidel coefficient for spherical aberration where the quantity in the bracket is called the structural aberration coefficient for spherical aberration ( σ I ). See Section 10.4 or Table 10.1 on page 111 for the definition of parameter quantities. Making the substitution in the second term and rearranging, (11.4) [ ] d cY bXY aX y S I + + = 2 2 3 4 4 1 (11.5) 11.3
Lens Shape Factor and Magnification Factor It is possible to have a set of lenses with the same power and the same thickness but with different shapes. These lenses can be characterized by a lens shape factor defined by H. H. Hopkins as: 2 1 2 1 2 1 2 1 φ + = + = C C C C X >1 1 0 -1 <-1 Similarly, it is possible to use a given lens with a variety different conjugate planes or magnifications. These different conjugates can be characterized by a magnification factor defined as: m m Y + = 1 1 >1 1 0 -1 <-1 11.4

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11.3 Thin Lens Bending Assuming that Y is constant (as it is for a given set of imaging conjugates), a plot of σ I ( X ) would yield an offset parabola as illustrated in Figure 11.2. Note that there is a low point where σ I is a minimum.
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## This note was uploaded on 02/04/2012 for the course ECON 101 taught by Professor Gulipektunc during the Spring '11 term at Middle East Technical University.

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11.0 Lens Bending & Aberration Balancing - THE...

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