Image quality assessment (IQA) is crucial in the evaluation stage of novel algorithms operating on images, including traditional and machine learning based methods. Due to the lack of available quality-rated medical images, most commonly used full-reference IQA measures have been developed and tested for natural images. Reported pitfalls and inconsistencies arising when applying such measures for medical images are not surprising, as they rely on different properties than natural images. In photoacoustic imaging (PAI), especially, standard benchmarking approaches for assessing the quality of image reconstructions are lacking. PAI is a multi-physics imaging modality, in which two inverse problems have to be solved, which makes the application of IQA measures uniquely challenging due to both, acoustic and optical, artifacts. To support the development and testing of IQA measures we assembled PhotIQA, a data set consisting of 1134 photoacoustic images. The images were rated by five experts across five quality properties in a full-reference setting, where the detailed rating enables usage beyond PAI. The data set with the images and corresponding ratings is publicly available on Zenodo.