Context. The protoplanetary disk around the F-type star HD 135344B (SAO 206462) is in a transition stage and shows many intriguing structures both in scattered light and thermal (sub-)millimeter emission which are possibly related to planet formation processes. Aims. We aim to study the morphology and surface brightness of the disk in scattered light to gain insight into the innermost disk regions, the formation of protoplanets, planet-disk interactions traced in the surface and midplane layers, and the dust grain properties of the disk surface. Methods. We have carried out high-contrast polarimetric differential imaging (PDI) observations with VLT/SPHERE and obtained polarized scattered light images with ZIMPOL in the R and...