Computational techniques for image reconstruction in terahertz microscopy using Josephson cantilevers

The terahertz microscope is a measurement system designed primarily for imaging of spatial distributions of high-frequency electromagnetic fields in the microwave and terahertz bands. It relies on a Josephson junction as a sensor, which makes it possible to demodulate the signal for low frequency readout while also retaining information about its original frequencies. The junction is located on the tip of a cantilever that can be brought into the near field of the examined sample, allowing the microscope to achieve higher image resolutions then what would be otherwise possible due to the Rayleigh criterion at these wavelengths. This work focuses on the algorithms designed for reconstruction of the irradiating spectra and the images from the sensor's responses, as well as discussing the electronics required for the measurement itself.

The data is acquired through sampling of the current-voltage characteristics of the junction for each of the target pixels individually. After a brief overview of the terahertz microscopy setup, the different Josephson junction readout schemes used throughout the literature are discussed and the solution designed for this setup is presented. Due to the short measurement times required for imaging, there are tradeoffs to be made in terms of the accuracy and noise of this readout. Therefore, a set of preprocessing steps is employed, including automated offset correction and noise-tolerant reconstruction of the differential resistance of the characteristic, latter required by other processing algorithms.

For small signal powers, spectra can be reconstructed based on closed-form approximations of the small-signal response of the junction. Alternative to the well-known Hilbert spectroscopy, a direct deconvolution method has proven to be well suited for the employed measurement scheme. For larger signal amplitudes, the expected response can be calculated using a number of numerical methods. To facilitate curve fitting for a large number of pixel measurements based on these methods, graphics processing units (GPUs) are employed to accelerate such computations through parallelization.

Finally, a set of exemplary measurements is presented, highlighting the cases where the proposed reconstruction techniques prove superior to the ones used in previous works