To support the integration of Acousto-Optic Tunable Filters (AOTFs) in optical systems and lay the groundwork for further research, this report presents the development and validation of an analytical model for a noncollinear AOTF based on tellurium dioxide (TeO2). The AOTFs are compact solid-state devices that filter desired optical wavelengths by applying an appropriate RF signal. Their compactness and quick tunability make them particularly appealing for Earth observation missions, where an AOTF can be integrated into small platforms like CubeSats.

However, there is a significant gap in the availability of comprehensive optical AOTF simulations that can predict the behaviour of AOTFs, and specify the momentum-matching frequencies required for the highest diffraction efficiency (DE) to occur. This report addresses that gap by developing a detailed three-dimensional (3D) analytical model for the non-collinear AOTFs based on TeO2, the most commercially available and widely used AOTF configuration. The analytical model, developed in this report, aims to facilitate the design and optimization of AOTFs for optical systems used in various fields, particularly in space-based instruments.

The core of the AOTF’s analytical model can be broken down into three main stages: the entrance facet, the acoustic field, and the exit facet. The interaction of light with these three stages is simulated by rays, the direction of which is determined by the Directional Cosine Matrices (DCMs). The model performs calculations to describe the path of incoming rays as they enter, propagate through, and exit the AOTF crystal. Special attention is given to simulating the Acousto-Optic (AO) interaction within the crystal, where a diffracted light is produced. Furthermore, the model calculates the momentum-matching frequency and outputs the propagation
of a newly created diffracted light through the AO interaction.

The developed model is adapted to operate for both incident polarisation types, ordinary and extraordinary. Furthermore, the model can simulating the AOTF’s behaviour as it is rotated, allowing further versatility of AOTF’s placement in the optical design. The model, as well as the adaptations, were first verified with the data from the Voloshinov et al. paper, where it accurately predicted both the separation angles and the momentum-matching frequencies. Further verification was performed with known AOTF parameters at various optical wavelengths with the help of an experiment performed at Université Polytechnique Hauts-de-France (UPHF).

Furthermore, the model was validated through diffraction testing, where it successfully simulated the AOTF’s behaviour, predicting both diffracted and undiffracted ray angles with an accuracy of 0.1 degrees. Testing was conducted at various rotational angles and for both incident polarisation types, with the model’s predictions closely matching the experimental data. Based on the testing, it was possible to determine the frequency-matching method used in characterising the essential AOTF angles that dictate the AOTF’s behaviour.

The analytical model was further enhanced by incorporating an optimization algorithm, which automates the characterization of key AOTF variables for newly acquired devices. The algorithm characterises the crystallographic axis angle, tilt angle, and facet inclination angles. These parameters are typically not provided by manufacturers, leaving the AOTF’s behaviour largely unknown. However, by characterising these variables with the model created, it becomes possible to extrapolate the AOTF’s performance for any incident optical wavelength within the visible spectrum.