Schlieren imaging is a widely applied optical technique for visualizing small refractive index changes in transparent media. An emerging application of schlieren is real-time monitoring and optimization of ultrasound pressure fields for acoustic levitation applications. However, the typically nonlinear relationship between the schlieren intensity and the pressure field complicates deducing the latter from the former. Here, we propose a method to remove this nonlinear relationship, thereby permitting a more quantitative analysis of the pressure variations in the levitation field. By exploiting the harmonic nature of the pressure field using phase-shifted stroboscopic schlieren images we extract the linear part of the schlieren intensity. This linear part is proportional to the instantaneous pressure gradient. The method is successfully employed experimentally and validated by comparing it to simulated acoustic levitation fields. Thereby, our work paves the way towards an improved quantitative analysis of periodic schlieren images that is easily implemented and is particularly suitable for the analysis of ultrasound pressure fields for acoustic levitation applications.