Pre-existing methods for photon beam energy spectral reconstruction are reviewed. Spectral reconstruction by attenuation analysis is discussed and the Schiff analytical spectral model is introduced. An alternative reconstruction method by "scatter analysis" is proposed. The method consists in irradiating a phantom and collecting beam spectral information by measuring scatter around the phantom as a function of scatter angle. A Monte Carlo code is used to simulate the irradiation setup and determine scatter behavior as a function of angle for mono-energetic beams. Based on the mono-energetic beam data and using a parametric spectral Schiff model, the spectrum is unfolded by optimization. The method is applied to a 6MV photon beam accelerator, and the reconstructed spectrum matches the Monte Carlo calculated spectrum for the same accelerator to within 6.2% (direct comparison of spectral shapes). Depth dose values derived from the reconstructed spectrum agree with the physically measured depth dose values within 1% for depths up to 20 cm. This new method is intended as a practical one requiring few measurements under standard 100cm SSD broad beam geometry, feasible in any radiotherapy department equipped with a scattering phantom and a conventional Farmer chamber.