  Kinetic Inductance Detectors (KIDs) are superconductive low$-$temperature
detectors useful for astrophysics and particle physics. We have developed
arrays of lumped elements KIDs (LEKIDs) sensitive to microwave photons,
optimized for the four horn-coupled focal planes of the OLIMPO balloon-borne
telescope, working in the spectral bands centered at 150 GHz, 250 GHz, 350 GHz,
and 460 GHz. This is aimed at measuring the spectrum of the Sunyaev-Zel'dovich
effect for a number of galaxy clusters, and will validate LEKIDs technology in
a space-like environment. Our detectors are optimized for an intermediate
background level, due to the presence of residual atmosphere and
room--temperature optical system and they operate at a temperature of 0.3 K.
The LEKID planar superconducting circuits are designed to resonate between 100
and 600 MHz, and to match the impedance of the feeding waveguides; the measured
quality factors of the resonators are in the $10^{4}-10^{5}$ range, and they
have been tuned to obtain the needed dynamic range. The readout electronics is
composed of a $cold$ $part$, which includes a low noise amplifier, a
dc$-$block, coaxial cables, and power attenuators; and a $room-temperature$
$part$, FPGA$-$based, including up and down-conversion microwave components (IQ
modulator, IQ demodulator, amplifiers, bias tees, attenuators). In this
contribution, we describe the optimization, fabrication, characterization and
validation of the OLIMPO detector system.
