We present a new technique to quantify the light contribution coming from the faint high redshift ( z \sim 6 ) galaxies below the detection threshold of imaging data , set conventionally at S / N = 4.5 .
We illustrate the technique with an application to Hubble Space Telescope Advanced Camera for Surveys images in the F775W and F850LP filters of the Ultra Deep Field parallel field NICP12 .
The aim of this analysis is to extend by a few magnitudes the faint end of the luminosity function at z \sim 6 .
After masking all the detected sources in the field we apply a Fast Fourier Transform to obtain the spatial power spectrum of the background signal .
The power spectrum permits us to separate the background noise signal , the residuals due to the data reduction of the wide field , and the overall signal produced by faint galaxies .
The ratio of the signal in the i _ { 775 } and z _ { 850 } bands is used to estimate the contribution of the faint i -dropout objects .
We rely on extensive Monte Carlo simulations to characterize various sources of uncertainty and quantify the number of faint i -dropout galaxies in the field .
The analysis allows us to put constraints on the luminosity function at z \sim 6 down to z _ { 850 } = 30 mag , 2.5 mag fainter than with standard techniques on the same data .
The data are consistent with a faint end slope of the luminosity function of \alpha = -1.9 .
Assuming a specific set of values for the clumping factor , escape fraction , and spectral energy distribution , we find that the z \sim 6 undetected galaxies down to z _ { 850 } = 30 mag could have driven cosmic reionization .