In biomedical photoacoustic imaging the images are proportional to the absorbed optical energy density, and not the optical absorption, which makes it difficult to obtain a quantitatively accurate image showing the concentration of a particular absorbing chromophore from photoacoustic measurements alone. Here it is shown that the spatially varying concentration of a chromophore whose absorption becomes zero above a threshold light fluence can be estimated from photoacoustic images obtained at increasing illumination strengths. This technique provides an alternative to model-based multiwavelength approaches to quantitative photoacoustic imaging, and a new approach to photoacoustic molecular and functional imaging.