  This paper reports on the design and characteristics of a compact module
integrating an optical displacement sensor and an electromagnetic actuator for
use with vibration-isolation systems installed in KAGRA, the 3-km baseline
gravitational-wave detector in Japan. In technical concept, the module belongs
to a family tree of similar modules called OSEMs, used in other interferometric
gravitational-wave detector projects. After the initial test run of KAGRA in
2016, the sensor part, which is a type of slot sensor, was modified by
increasing the spacing of the slot from 5 mm to 15 mm to avoid the risk of
mechanical interference with the sensor flag. We confirm the sensor performance
is comparable to that of the previous design despite the modification. We also
confirm the sensor noise is consistent with the theoretical noise budget. The
noise level is 0.5 nm/rtHz at 1 Hz and 0.1 nm/rtHz at 10 Hz, and the linear
range of the sensor is 0.7 mm or more. We measured the response of the actuator
to be 1 N/A, and also measured the resistances and inductances of coils of the
actuators to confirm consistency with theory. Coupling coefficients among the
different degrees of freedom were also measured and shown to be negligible,
varying little between designs. A potential concern about thermal noise
contribution due to eddy current loss is discussed. As of 2020, 42 of the
modules are in operation at the site.
