  Focal Ratio Degradation (FRD) in fibres is a crucial factor to control in
astronomical instruments in order to minimize light loss. As astronomical
instrumentation has advanced, the integration of large populations of fibres
has become common. However, determining FRD in multiplexed fibre systems has
become a challenging and time-consuming task. The Integral Field Unit for the
Fiber Arrayed Solar Optical Telescope (FASOT-IFU) represents the most densely
arranged fibre-based IFU in a single unit. Due to the close packing of fibres
in the V-groove of the slit end, measuring FRD is particularly challenging as
the output spots are prone to overlapping with adjacent fibres. In this paper,
a novel method based on the quasi-near field model is proposed to enable rapid
FRD measurement in highly multiplexed fibre systems like IFUs and multi-object
observation systems. The principle and uncertainties associated with the method
are investigated. The method's validity is demonstrated by applying it to
determine the FRD in FASOT-IFU, with the achieved FRD performance meeting the
acceptable requirements of FASOT-IFU, where the output focal ratio primarily
falls within the range of 5.0-7.0. The results indicate that the proposed
method offers several advantages, including the simultaneous and rapid
measurement of FRD in multiple fibres with high accuracy (error smaller than
0.35 in F-ratio). Furthermore, besides FRD, the method exhibits potential for
extensive measurements of throughput, scrambling, and spectral analysis.
