The newly discovered topological crystalline insulators feature a complex band structure involving multiple Dirac cones [1][2][3][4][5][6] , and are potentially highly tunable by external electric field, temperature or strain. Theoretically, it has been predicted that the various Dirac cones, which are o set in energy and momentum, might harbour vastly di erent orbital character 7 . However, their orbital texture, which is of immense importance in determining a variety of a material's properties [8][9][10] remains elusive. Here, we unveil the orbital texture of Pb 1−x Sn x Se, a prototypical topological crystalline insulator. By using Fourier-transform scanning tunnelling spectroscopy we measure the interference patterns produced by the scattering of surface-state electrons. We discover that the intensity and energy dependences of the Fourier transforms show distinct characteristics, which can be directly attributed to orbital e ects. Our experiments reveal a complex band topology involving two Lifshitz transitions 11 and establish the orbital nature of the Dirac bands, which could provide an alternative pathway towards future quantum applications.A counterpart to charge and spin, electron orbitals are of great importance in the underlying physical processes of a variety of systems. The orbital degrees of freedom, for example, play a crucial role in the colossal magnetoresistance effect in manganese oxides, and contribute to the anisotropic electronic and magnetic properties in many other transition-metal oxide systems 8 . More recently, orbital ordering within the superconducting FeAs layer has been thought to govern structural phase transitions and 'stripe'-like antiferromagnetism in Fe-based high-temperature superconductors 9,10 . Similarly, topological materials host complex orbital arrangements often strongly coupled to other electronic degrees of freedom [12][13][14][15][16][17][18] . Topological crystalline insulators (TCIs) in particular are predicted to exhibit intricate band, spin and orbital textures, potentially relevant for interactions in the quantum Hall regime. Although previous experiments provided a glimpse into the complex band topology present in TCIs (refs 3-5,19,20), these experimental efforts have not been able to shed light onto its orbital texture. Here we use Fourier-transform (FT) scanning tunnelling spectroscopy (STS) to reveal the distinct orbital nature of the Dirac bands in the TCI, Pb 1−x Sn x Se.In its stoichiometric state, Pb 1−x Sn x Se with x = 0 is a trivial insulator under the Z 2 topological classification of materials owing to the absence of band inversion. The process of adding Sn, which substitutes for Pb, leads to band inversion at an even number of time-reversal points, and the solutions remain Z 2 trivial. However, for a particular region of the composition-temperature parameter space, such as x > ∼0.23 and room temperature, or x > ∼0.18 and 4 K, topologically protected surface states emerge owing to the non-trivial band topology classified by crystalline symmetries 3...