New formulae for constructing the pion photoproduction amplitude J from experimental data are presented. The phase of J is expressed in terms of its zeroes in the energy plane, the particle poles and a dispersion integral over the modulus of J , the latter being given, except for a finite unphysical interval, in terms of differential cross sections and recoil nucleon polarizations. For γ p→ π + n at t ≈−0.870 μ 2 , where the unphysical-region contribution vanishes, the zeroes are found approximately, so that the phase of J can be uniquely determined from the experimental data.
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