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-Zeldovich 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.
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