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Optical Engineering Science. Stephen RoltЧитать онлайн книгу.

Optical Engineering Science - Stephen Rolt


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      As previously outlined, the uncompensated rms wavefront error may be calculated from the RSS sum of all the four Zernike terms. Naturally, for the compensated system, we need only consider the first term.

      (5.24)equation

      In the optimisation of an optical design it is important to understand the form of the OPD fan displayed in Figure 5.5 in order recognise the desired endpoint of the optimisation process. It displays three minima and two maxima (or vice versa), whereas the unoptimised OPD fan has one fewer maximum and minimum. Thus, although the design optimisation process itself might be computer based, nevertheless, understanding and recognising the how the process works and its end goal will be of great practical use. That is to say, as the computer-based optimisation proceeds, on might expect the OPD fan to acquire a greater number of maxima and minima.

Graphical illustration of the profile of an optimised OPD based on fifth order Zernike polynomial and aberration balancing.

      (5.25c)equation

       θ represents the field angle

      Worked Example 5.2 A plano-convex lens, with a focal length of 100 mm is used to focus a collimated beam; the refractive index of the lens material is 1.52. It is assumed that the curved surface faces the infinite conjugate. The pupil diameter is 12.5 mm and the aperture is situated at the lens. What is the rms spherical aberration produced by this lens – (i) at the paraxial focus; (ii) at the compensated focus? What is the rms coma for a similar collimated beam with a field angle of one degree?

      Firstly, we calculate the spherical aberration of the single lens. With the object at infinity and the image at the first focal point, the conjugate parameter, t, is equal to −1. The shape parameter, s, for the plano convex lens is equal to 1 since the curved surface is facing the object. From Eq. (4.30a) the spherical aberration of the lens is given by:

equation

      rmax = 6.25 mm (12.5/2); f = 100 mm; n = 1.52; s = 1; t = −1

      By substituting these values into the above equation, the spherical aberration may be directly calculated:

equation

      where A = 4.13 × 10−4 mm ρ = r/rmax

       Φ rms (paraxial) = 185 nm; Φ rms (compensated) = 30.8 nm

      Secondly, we calculate the coma. From (4.30b), the coma of the lens is given by:

equation

      Again, substituting the relevant values for f, n, rmax, s, and t, we get:

equation

      where A = 3.24 × 10−3 mm ρ = r/rmax ry = r sin ϕ

      We are told that θ = 1° or 0.0174 rad. Therefore, Φrms = 6.66 × 10−6or 6.66 nm

      5.3.4 General Representation of Wavefront Error


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