The evolution of a cellular interface from the threshold of instability until the formation of deep cells is studied in situ during the directional solidification of thin samples of a dilute AlCu alloy by using the real-time white-beam synchrotron X-ray topography method. This means that strain visualization provides a powerful tool to access the very birth of morphological instability, even at times before classical optical methods become applicable. Indeed, elastic strains that give specific contrasts on the topographs precede visible interface destabilization. These contrasts can be attributed to the strains induced by the selective enhancement of fluctuations at the solid-liquid interface. Then, the strain contrasts and the evolution of the dislocations bound to the cellular microstructure are analysed for the different cellular patterns obtained near the threshold and somewhat above. In particular, it is shown that the cellular bodies are always strained due to the non-uniform composition field in the solid generated by the cellular shape.