Star test and mirror defects

Star test and mirror defects

A Newtonian whose defects you choose: its collimation (the primary’s focus off the focuser’s axis, which gives coma) and its mirror’s figure (astigmatism, the trefoil of a pinched mirror, under- or over-corrected spherical aberration, a turned edge). Each defect is given in nanometres RMS of the wavefront, at 550 nm (the edge peak to valley): λ/14 RMS, 39 nm, is Maréchal’s criterion, the limit of a diffraction-limited instrument (Strehl 0.8). Rayleigh’s often quoted quarter wave peak to valley is about the same: for spherical aberration, 41 nm RMS.

Where the coma comes from: the collimation and the star’s place in the field. A paraboloid has none on its axis, and more and more away from it. In a collimated Newtonian the axis falls at the eyepiece’s centre; miscollimated it falls beside it, and a star in the middle of the field shows the coma it would have that far off axis: the focus offset over the focal length. A star away from the centre has its own offset’s coma too (the slider under the star’s views), the two adding up like arrows. Coma figured into the mirror comes to the same (a paraboloid seen slightly from the side) and collimating on the star takes it out, so it has no slider of its own.

The image of a star is computed by diffraction: the light through the mirror (less the secondary’s shadow and the spider) with its distorted wavefront, Fourier-transformed, in white light. Before and after focus a perfect mirror gives two identical images (turned over); a defect makes them differ: that is the star test. Spherical brightens the edge on one side and the centre on the other, astigmatism stretches the image in two crossed directions, collimation coma shifts it to the same side.

Jupiter: a Hubble photograph, blurred as this telescope would show it, colour by colour (red, green and blue each at its own wavelength), what the defects and the collimation take away from it. Jupiter is shown 40″ across, about its average (30″ near conjunction, 50″ at the closest oppositions).

A mirror measured with the Foucault test: the link under its profile brings it here, its spherical and its turned edge set on their sliders, the rest added as it is. The figures differ a little from the Foucault test’s: that test, like Foucault2 and Texereau’s method, gives each zone a single value, the average of its two edges, and ignores what the surface does inside a zone; here the profile is followed from one measured point to the next across the whole mirror. The Foucault test’s RMS is therefore a little optimistic, the more so with few zones; with 10 to 15 zones the gap becomes small. To compare a mirror whose secondary hides the centre, tick “Leave out the centre hidden by the secondary” in the Foucault test.

The turbulence, on demand: a layer of turbulent air (Kolmogorov, 20 m outer scale) carried across the mirror by the wind at 3 m/s, its wavefront added to the mirror’s, for the star and for Jupiter. Its strength is in arcseconds, the width of a star in a long exposure (the seeing of professional astronomers and forecasts); it sets r₀, the size of the air’s cells (7.4 cm for 1.5″). Each image sums what the eye sees in 0.1 s; forty images make a 4 s loop. Smaller than r₀, a mirror mostly sees the image dance; larger, it boils.

Image: NASA, ESA, STScI.