Development of a forward model for Bayesian analysis of a single crystal dispersion interferometer

The Single Crystal Dispersion Interferometer (SCDI) is a newly developed dispersion interferometer (DI) system installed on KSTAR and has obtained the first data successfully in January 2020. Unlike conventional heterodyne DI systems, which use two nonlinear crystals, only one nonlinear crystal is used to eliminate the difficulty in overlapping the first and second harmonic beams, aligning and focusing the beams to a small aperture of the second nonlinear crystal, and resolving a problem of significant efforts to maintain the beam alignment to the second nonlinear crystal after a long beam transmission. The second nonlinear crystal is replaced by a frequency doubler, a simple electronic component. To infer a line integrated electron density with its associated uncertainty consistent with the measured data, we develop a forward model of the KSTAR SCDI that can be used as a likelihood within a Bayesian-based data analysis routine. The forward model consists of two main parts, which are an optical system and an electronics system, and it takes into account noises by modeling the mechanical vibrations and the electronic noises as Gaussian distributions, while the photon noise is modeled with a Poisson distribution. The developed forward model can be used for designing and improving the SCDI system.