This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f (a) and certain n-intensity measurements |〈f,Ea1⋯an〉|, where a, ⋯, a∈ D, and Ea1⋯an is the n-th term of the Gram-Schmidt orthogonalization of the Szegö kernels ka1,⋯,kan, or their multiple forms. Three schemes are presented. The first two schemes each directly obtain all the function values f (z). In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus |f (z)|. In the second scheme we do not use deep complex analysis, but require some 2- and 3-intensity measurements. The third scheme, as an application of AFD, gives sparse representation of f (z) converging quickly in the energy sense, depending on consecutively selected maximal n-intensity measurements |〈f,Ea1⋯an〉|.