There is an ongoing discussion in the visualization community about the relevant factors that render a visualization effective, expressive, memorable, aesthetically pleasing, etc. These factors lead to a large design space for visualizations. To explore this design space, qualitative research methods based on observations and interviews are often necessary. We describe an interview method that allows us to systematically acquire and assess important factors from subjective answers by interviewees. To this end, we adopt the repertory grid methodology in the context of visualization. It is based on the personal construct theory: each personality interprets a topic based on a set of personal, basic constructs expressed as contrasts. For the individual interpretation of visualizations, this means that these personal terms can be very different, depending on numerous influences, such as the prior experiences of the interviewed person. We present an interviewing process, visual interface, and qualitative and quantitative analysis procedures that are specifically devised to fit the needs of visualization applications. A showcase interview with 15 typical static information visualizations and 10 participants demonstrates that our approach is effective in identifying common constructs as well as individual differences. In particular, we investigate differences between expert and nonexpert interviewees. Finally, we discuss the differences to other qualitative methods and how the repertory grid can be embedded in existing theoretical frameworks of visualization research for the design process.