This article discusses general methodologies for realizing a model-reference molecular beam epitaxy control system for binary AlAs/GaAs distributed Bragg reflector (DBR) structures using single wavelength pyrometric interferometry monitoring. A least-square (LS) phase estimation method for end point detection is described. Experimental results on DBR structures grown with closed-loop control show evidence of a self-compensating mechanism that tends to preserve the periodicity of each DBR pair. The potentials for applying the LS phase estimation method for iterative adaptive control and spectral reflectance monitoring are also discussed.