We have completed a feasibility study for the measurement of weak distortion of distant galaxy images by intervening large-scale structure by using the 5-m Hale reflector to acquire a very deep, r ~ 26, exposure of a single field. The error budget of our observations is dominated by the effects of atmospheric seeing (which strongly degrades this signal because the faintest images are under-resolved) and telescope effects. After performing a correction for telescope aberrations and possible guiding errors, the observed mean ‘polarization’ of the images of 4363 galaxies with magnitudes 23 ≤ r ≤ 26 within a circle of radius 4.8 arcmin was found to be p̄ =0.01 ± 0.01. The associated two-point polarization correlation function has a constant value of C_(pp) = (1.4 ± 3.0) x 10^(−5) over the angular range 1 to 6 arcmin. It is predicted that the cosmological polarization should be in the range p = 0.03 ± 0.01 for a standard CDM universe normalized by a bias parameter, b, of unity (p scales inversely with b and approximately linearly with Ω_0). For the atmospheric seeing and sky noise conditions associated with our data, Monte Carlo simulations suggest that the efficiency of measuring the mean cosmological polarization is on the order of 40 ± 10 per cent. Thus our preliminary analysis suggests an upper limit on the cosmological mean polarization in the field of p̄_(max) ∼ 0.04. Deep wide-field imaging in 0.5 arcsec seeing to study this polarization signal should provide limits that constrain current cosmological models
