Table 2 Summary of software and libraries.

From: Dynamic caustics by ultrasonically modulated liquid surface

Software/library

Description

OpenCV

Used for camera calibration, image processing, and perspective transformation

TensorFlow

Used for numerical optimization of acoustic holograms and implementation of the Digital Twin framework

NumPy

Used for numerical computations and array manipulation

Pillow (PIL)

Used for image loading and manipulation

PySerial

Used for serial communication with the FPGA board controlling the PAT

SciPy

Used for loading transducer array data

Matplotlib

Used for generating plots