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Chapter 7:
Optical Design Metrics
Abstract

There are numerous genres of computer-aided design (CAD) tools. They offer a variety of metrics in a range from simple illumination calculations to complex wave propagation. It is important to remember that every tool has its limitations. Mastery of these tools requires education and practice.

Various CAD tools are demonstrated in Secs. 7.2—7.9 through application to a doublet with a 40-mm focal length. The doublet functions as a 5X objective in combination with a 200-mm tube lens. The object field height at 1.2 mm translates into a 6.0-mm image height, which accommodates the 11.3-μm diagonal of a 1000 × 1000 array of 8-μm pixels. The projected pixel at the object is 0.8 μm.

The ensuing metrics employ the object side of the lens as the image. The effective object distance (or tube length) is infinite. The entrance pupil is 10 mm. The image NA is 0.0125. The Airy radii are 2.37 μm for the F line (486 nm), 2.86 μm for the d line (588 nm), and 3.20 μm for the C line (656 nm).

Some metrics require sampling of the image. Sampling normally occurs at 2N × 2N, where N is an integer. Errors due to insufficient sampling must be considered. The shape of the ray-intercept plot should predict any calculations based on sampling.

7.2 Wavefront Error

The wavefront error is probably the most physically significant metric of a CAD tool. A convergent wavefront should be spherical. A collimated wavefront should be flat. A reflecting telescope with 0.05 NA can easily maintain a wavefront error at λ/10. Unfortunately, such quality is not easily achieved in a refractor at 0.12 NA or higher.

Figure 7.1 displays the wavefront of the 5X doublet. The optical path difference indicates the optical path length from a perfect sphere around the image. The optical path length is specified in the wavelengths. The abscissa indicates the position within the pupil or lens stop. The wavefront error is independent of the direction of travel through the lens. On reversal of the direction of travel, the optical path difference indicates the optical path length in wavelengths from a perfectly flat wave in collimation. The wavefront error is an effective measure of collimated wavefronts.