Is the structure on the bottom side of the X-37 in this photo a launch fairing or a transport jig? In either case, what are the arrays of transparent-looking round things on it?
That's the launch fairing (the other half is visible on the right). The silvery panels are used for noise reduction; they contain Helmholz absorbers, cavities tuned to absorb a single frequency. Each round object contains the opening of a cavity.
Without protection, the noise level during launch is loud enough to damage the payload. The absorbers reduce the noise in the fairing just enough to make sure there's no damage.
A Helmholz resonator has a single resonance frequency. If sound at that exact frequency enters the resonator, you can get the cavity to absorb some of that energy (up to 60%) as heat. So a Helmholz absorber is a resonator modified to create a high viscous resistance at the neck.
According to a BBC research paper on the subject:
...Under ideal conditions, (infinite rigidity of container etc. ), absorption of energy can be considered to take place entirely in the resistance at the neck. This resistance has two components, the viscous resistance of the air in the neck, and the radiation resistance, the latter being much the smaller component in the case of narrow necks. The viscous resistance is dependent on the dimensions of the neck and is influenced by the presence of resistive material.