A comprehensive understanding of spin-polarized photoemission is crucial for accessing the electronic structure of spin-orbit coupled materials. Yet, the impact of the final state in the photoemission process on the photoelectron spin has been difficult to assess in these systems. We present experiments for the spin-orbit split states in a Bi-Ag surface alloy showing that the alteration of the final state with energy may cause a complete reversal of the photoelectron spin polarization. We explain the effect on the basis of ab initio one-step photoemission theory and describe how it originates from linear dichroism in the angular distribution of photoelectrons. Our analysis shows that the modulated photoelectron spin polarization reflects the intrinsic spin density of the surface state being sampled differently depending on the final state, and it indicates linear dichroism as a natural probe of spin-orbit coupling at surfaces.The creation and manipulation of spin-polarized electronic states in crystalline solids, low-dimensional systems, and heterostructures through strong spin-orbit interaction is a central topic in contemporary condensed matter physics [1][2][3][4][5]. Among the most vivid examples are the surface states of topological insulators in which the coupling of the spin and momentum degrees of freedom gives rise to helical spin textures in momentum space [6]. Moreover, spin-orbit split band structures, in general, attract attention in a broad range of materials, including Weyl semimetals [7], with unconventional spin-polarized states in the bulk and at the surface, stronglycorrelated topological Kondo insulators [8,9], as well as twodimensional systems, such as metallic oxide interfaces [5] and transition-metal dichalcogenide layers [3]. Thus, given the tremendous interest in spin-orbit coupled materials, it is of critical importance to probe their electronic structure with spin sensitivity and to reliably verify the anticipated spin dependences, see, e.g., Refs. [10-13].The most versatile tool to spectroscopically address the momentum-dependent spin polarization of electronic band structures in condensed matter physics has been spin-and angle-resolved photoemission spectroscopy (spin-ARPES). In recent years it has been successfully applied to a variety of materials [14][15][16]. At the same time, the efficiency of stateof-the-art photoelectron spin detectors has been improved tremendously [11,16,17], making it now possible to measure the photoelectron spin polarization over wide regions of momentum space with varying energy and polarization of the exciting light. Despite these encouraging developments fundamental issues remain debated, namely to which degree, under which conditions, and in which way the measured photoelectron spin polarization actually reflects the intrinsic spin properties of spin-orbit split states [11,[18][19][20][21][22][23][24][25][26].Within the one-step theory of photoemission the spindependent photocurrent is determined by the photoemission matrix element which involves the ...