The method of phase distortion correction used in the Fourier telescopy imaging for laser beams in strongly inhomogeneous atmosphere implies an additional operation preceding the phase closure operation. In this additional operation, power of the radiation scattered by the object illuminated by a selected pair of laser transmitters is divided by the product of powers of radiation scattered by the object illuminated by each of the transmitters. It is proposed to measure these powers by registering radiation scattered by the object illuminated by all transmitters except one belonging to the selected pair. Thus, transmitter with short coherence length can be used. However, high level of additive noise and strongly inhomogeneous atmosphere, which leads to a considerable broadening of the laser radiation, considerably reduce the registered signal and hence, the probability of the object detection in the Fourier telescopy, The probability of detecting the object can be substantially increased by rotating the directional diagrams of the transmitters. This probability is studied as a function of the given threshold value, sizes of the transmitting and receiving apertures, standard deviations and correlation radii of the object surface roughness height distribution, and phase distortions. The suggested version of the Fourier telescopy allows one to make the object detection probability close to unity even for the noise power comparable with the power of the radiation scattered by the object. Under the condition of considerably large arrays of the laser transmitters, the method provides high accuracy of determining the object parameters.