The experience of target fabrication with low-density and cluster heterogeneity is presented. Cluster plasma research is strongly dependent on target fabrication development and target structure characterization. Ten more target parameters should be measured for experiment interpreting in case of micro-heterogeneous plasma. Foam and foil targets, high-Z doped also, are produced and irradiated on the existing laser facilities. The density of 4.5 mg/cc cellulose triacetate in the form of regular three-dimensional polymer networks are achieved which is as low as plasma critical density for the third harmonic of iodine laser light. The possibilities of varying important target parameters, methods of their monitoring are discussed. Experiments with underdense foam targets with or without clusters irradiated on Prague Asterix Laser System (PALS) laser facility are analyzed preliminary for target optimization. Under-critical foams of varying structure (closed-cell foam or three-dimensional networks) and densities are reported for plasma experiments. Thermal and radiation transport in such targets are considered.