Frequencies of solar acoustic oscillations can be analyzed asymptotically in terms of a function determined by the sound speed in the bulk of the sun and a function determined predominantly by conditions near the solar surface. The latter depends mainly on the frequency and is related to the phase shift induced by the reflection at the solar surface; it has been shown to be a useful diagnostic of conditions in the second helium ionization zone, providing information about the composition and equation of state of that region. However, uncertainties in the treatment of the layers immediately below the solar photosphere and the solar atmosphere introduce a contribution to the phase function which is mainly a slowly varying function of frequency. Here we demonstrate how this uncertain component can be eliminated through suitable filtering, and relate the filtered phase function to the structure of the near-surface region of the sun through similarly filtered kernels. The procedure leads to a clean isolation of the signal associated with the helium ionization zone and layers below it, permitting the detection of even quite subtle features in the frequencies.