In this work, we extend the classical analysis of concentration fluctuations in polymer solutions under shear flow to consider the same phenomenology under extensional flow. Experimental work by van Egmond and Fuller [Macromolecules 26, 7182-7188 (1993)] revealed a four-lobe scattering pattern for a polystyrene solution in a planar extensional flow field. Similar to earlier results found in shear, they find the existence of finite-wavelength peak intensity locations. To investigate this phenomenon, we couple stress and concentration using a two-fluid model with fluctuations driven by thermal noise incorporated through a canonical Langevin approach. The polymer stress is governed by the Rolie-Poly model augmented with finite extensibility to account for large stretching of chains at high Weissenberg numbers. Perturbing the equations about homogeneous planar extensional flow for weak amplitude inhomogeneities, but arbitrary flow strength, we solve for the steady correlations. The resulting structure factor undergoes a pattern transition for increased strain rates. At small Weissenberg numbers, we predict fluctuation enhancement along the stretching axis (abnormal butterfly pattern). At Wi similar to O(1), a four-lobe substructure emerges accompanied by finite-wavelength scattering peaks located along the 45 degrees axis, as observed in experiment. However, these peaks rotate toward the compression axis under the increasing effect of advection as the flow strength increases, and, at very large stretching rates, fluctuation enhancement occurs along the compression axis (normal butterfly pattern). These latter changes were not seen experimentally. In addition, the peak intensity varies nonmonotonically with Weissenberg number exhibiting two local maxima at extension rates corresponding to the inverse reptation and Rouse times, respectively, providing a clear relationship between the extensional rheology and the concentration fluctuation spectrum. (C) 2013 The Society of Rheology.