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Considering the spatially separated polarization radiation and Faradayrotation regions to simulate complex interstellar media, we study synchrotronpolarization gradient techniques' measurement capabilities. We explore how totrace the direction of projected magnetic field of emitting-source region atthe multi-frequency bands, using the gradient technique compared with thetraditional polarization vector method. Furthermore, we study how Faradayrotation density in the foreground region, i.e., a product of electron numberdensity and parallel component of magnetic fields along the line of sight,affects the measurement of projected magnetic field. Numerical results showthat synchrotron polarization gradient technique could successfully traceprojected magnetic field within emitting-source region independent of radiofrequency. Accordingly, the gradient technique can measure the magnetic fieldproperties for a complex astrophysical environment.

Gradient measurement of synchrotron polarization diagnostic: Application to spatially separated emission and Faraday rotation regions