These two photos are the top and bottom plate of the Orbiting Carbon Observatory (OCO) solar diffuser. Optical design by Brian Sutin, drafting by Tim Wagner, EDM machining and photo by Wire Cut Company. NASA has published a photo of this system installed on the satellite.

Orbiting Carbon Observatory needed a deployable solar diffuser that could be placed in front of the normally Earth-observing telescope for calibration. The diffuser had to be lightweight, well diffuse, and not pick up stray light from other parts of the satellite.

The final design consisted of small pyramids with rough surfaces. One place had pyramidal bumps, while the other had pyramidal dents. Small window frames were added on one side to prevent light from crossing to the wrong side of the pyramid at larger angles.

]]>The first summation term dominates at large *v*. This term can be summed up into a closed-form expression as

The formula for F(*v*) for large v now becomes

Applying this to both formulas for F(*v*) gives

The major difference between the before and after plots is that, for the small-*v* formula, the convergence is vastly improved for small *v*.

Unfortunately the remaining terms do not appear to have convenient closed-form summations. One approach would be to use the logarithmic series accelerations such as methods by Herbert H. H. Homeier. Another is to subtract off similar summations, pushing the error terms off to higher orders.

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