2023ApJ...958...27P

In this series of papers, we present new methods of frequency- and time-dependent instrumental polarization calibration for very long baseline interferometry (VLBI). In most existing calibration tools and pipelines, it has been assumed that instrumental polarization is constant over frequency within the instrument bandwidth and over time. The assumption is not always true and may prevent an accurate calibration, which can result in degradation of the quality of linear polarization images. In this paper, we present a method of frequency-dependent instrumental polarization calibration that is implemented in GPCAL, a recently developed polarization calibration pipeline. The method is tested using simulated data sets generated from real Very Long Baseline Array (VLBA) data. We present the results of applying the method to real VLBA data sets observed at 15 and 43 GHz. We were able to eliminate significant variability in cross-hand visibilities over frequency that is caused by frequency-dependent instrumental polarization. As a result of the calibration, linear polarization images were slightly to modestly improved as compared to those obtained without frequency-dependent instrumental polarization calibration. We discuss the reason for the minor impact of frequency-dependent instrumental polarization calibration on existing VLBA data sets and prospects for applying the method to future VLBI data sets, which are expected to provide very large bandwidths.