Cosmic shear measurements rely on our ability to measure and correct the Point Spread Function ( PSF ) of the observations .
This PSF is measured using stars in the field , which give a noisy measure at random points in the field .
Using Wiener filtering , we show how errors in this PSF correction process propagate into shear power spectrum errors .
This allows us to test future space-based missions , such as Euclid or JDEM , thereby allowing us to set clear engineering specifications on PSF variability .
For ground-based surveys , where the variability of the PSF is dominated by the environment , we briefly discuss how our approach can also be used to study the potential of mitigation techniques such as correlating galaxy shapes in different exposures .
To illustrate our approach we show that for a Euclid-like survey to be statistics limited , an initial pre-correction PSF ellipticity power spectrum , with a power-law slope of -3 must have an amplitude at \ell = 1000 of less than 2 \times 10 ^ { -13 } .
This is 1500 times smaller than the typical lensing signal at this scale .
We also find that the power spectrum of PSF size ( \delta _ { R ^ { 2 } } ) at this scale must be below 2 \times 10 ^ { -12 } . Public code available as part of iCosmo at http : //www.icosmo.org