The Nature of Phase and Amplitude Modulation in Heterodyne Background-Oriented Schlieren Systems

This research is the result of Austrian-German joint research project, funded by the Austrian Science Fund FWF within grant FWF-I5392-N. This project is a Lead-Agency D-A-CH project in cooperation between Graz University of Technology, Austria and Technische Universität Dresden, Germany, named "FOUR-DIMENSIONAL MEASUREMENT OF THERMOACOUSTIC OSCILLATIONS".

The underlying hypothesis of this project claims that four-dimensional detection of local thermoacoustic oscillations, based on the combination of a (camera-based) laser interferometric vibrometer with multidirectional background-oriented schlieren method, density tagging velocimetry and deep neural networks as a binding element, will reveal local and coupled information on combustion, acoustics and fluid dynamics. 

As of May 2026, this repository contains the routines and sample data from this project involved in the analysis reported in the manuscript.

Data collected during the investigation on the nature of amplitude modulation in HBOS.

In the folder "Sample shadowgraphy", there are two different folders: "Background" and "Flame". Each of these folders contains 100 .tiff images. These images are a subset of the images acquired during shadowgraphy measurements. In particular, the "Background" folder contains the images used as reference intensity, while the "Flame" folder contains the images affected by the intensity redistribution induced by the flame. 

In the folder "Sample data HBOS", there are also two different folders: "Background" and "Time signal". Each of these folders contains 100 .tiff images. These images are a subset of the ones acquired during HBOS measurements. In particular, the "Background" folder contains the reference images necessary for background-oriented schlieren, while the folder "Time signal" contains the images of the background when affected by the virtual displacements introduced by the flame.

The folder "Ray tracing code" stores the Microsoft Windows-compatible version of the BOS ray tracing code for Linux published with the following paper: "Rajendran, L. K., Bane, S., & Vlachos, P. (2019). PIV/BOS synthetic image generation in variable density environments for error analysis and experiment design. Measurement Science and Technology.". Note that the settings in config/bos_config.json need to be adjusted to match the simulated case.

Additional material is available in the Reference section.