# Why is a flower shaped diffraction occluder the best solution for controlling diffraction?

According to this TED talk by Jeremy Kasdin, Nasa is planning to spend 1bn on a "Starshade" project, where a giant flower shaped metal eclipser 20 meters wide is placed 50k kilometers in front of a space telescope, to fit the telescope diameter. The idea is to occlude a star and photograph it's exoplanets. The above solution is surreal. Why can't they control the diffraction of the light around the occlusion circle with a refractive material, to direct it outwards? I suggest that they can design a round black occluder with soft edges overlaid with a refractive material that deflects the light away from the centre, similar to a lense. Why do the angles and shapes at the edge of the flower shaped occluder have to be very precise in order to control diffraction? • Would light diffract around the edges of your refractive material? – BMS May 1 '14 at 7:16 • A higher-resolution zone plate would likely take more material. The transparent zones would need to be made of refractive material, and/or the opaque zones would need to be thicker to withstand space weathering. They probably optimized for size given a constant mass and construction from a single material. Space radiation would probably cause warping/disintegration of a heterogeneous structure. – Blackbody Blacklight May 1 '14 at 7:20 • A bit OT, but if 50k kilometers doesn't sound too far (just a few oil changes, right?), that's still 4 Earth diameters. Sometimes NASA makes weird "like looking at a baseball in San Fransisco…" analogies, but such a shade would literally be aligning something the size of a tennis court at the circumference of the earth plus change. – Blackbody Blacklight May 1 '14 at 7:29 • That's precisely what i was thinking. Why do they have to place the starshade 50k kilometers away from the telescope, as the star is a tiny speck in the sky? couldnt they make the occluder smaller? The light from the star would fill the telescope mirrors and lenses with so much light, many artefacts would exist that bounce inside the telescope and any occluder that could be inside it, so it has to be in front, and if the telescope is 10 meters diameter, they have to place it 50k away. mm accurate spaceship positioning in space is possible, it's just a disproportionately difficult task. – DeltaEnfieldWaid May 1 '14 at 9:56 • Somehow I suspect the optical design engineers at NASA actually know more than all of us and have worked out the diffraction patterns for the telescope & stars of interest :-) – Carl Witthoft May 1 '14 at 11:44 ## 1 Answer Whatever the shape of the shield is, at the telescope you're going to see the Fourier transform of it. With a simple disk shaped shield you'll see ringing artefacts at the edges and these will cause the light from the star to spill round the shield potentially hiding the planets. Generally speaking Gaussian profiles are good for this, because the Fourier transform of a Gaussian is just another Gaussian and there is no ringing. The petals at the edge of the disk are designed to cut the transmitted intensity in an approximately Gaussian curve. I don't have the kit to hand to calculate 2D Fourier transforms, but I can show you how this works in 1D. Suppose our shield is a simple disk, i.e. a top hat function in 1D, then the Fourier transform looks like this: The blue line,f(x)$, is the profile of the shield and the magenta line,$g(k)\$, is the Fourier transform. Note how the ringing spreads the light well outside the shield. Now suppose use a Gaussian edge to the shield. If I make the half width of the Gaussian 0.05 (in the arbitrary coordinates I've used) then the transform changes to:

Note how the ringing is reduced, and if I increase the Gaussian width to 0.1 the first maximum is almost completely eliminated:

Now, be a little cautious about taking the above graphs too literally as a guide to the performance of the shield. These are 1D plots remember, and to calculate the performance of the shield you'd need to do a 2D Fourier transform. Nevertheless it does show the basic principle of how feathering the edges of the shield improves its performance.

You ask about the precise shape of the petals. To be honest I don't know to what extent the width of the petals matters. Their shape matters because it will control the profile at the edge of the shield, and the length determines the overall width of the feathered area. I don't think it makes a lot of difference if you use lots of narrow petals of fewer wider ones. I would guess fewer wider ones is technically easier given that you've got to deploy this thing automatically in space.

• Thanks. that's such a good demonstration and explanation. here is a pic of the fourrier transform of a starshield with what seems to be the first pic of an exoplanet, quite some time prior to the NASA managing with their project. images.gizmag.com/hero/gemini_planet_imager.jpg – DeltaEnfieldWaid May 4 '14 at 20:39