High-resolution x-ray diffraction studies have been performed on the polar liquid-crystal binary mixture of octyl- and decyl-oxyphenyl nitrobenxoyloxy benzoate (47.4 mole % DB8ONO2 + 52.6% DB10ONO2). At temperatures below 127 degreesC this mixture exhibits the phase sequence (with decreasing temperature) smectic-Ad - reentrant nematic N-d - reentrant nematic N-I -smectic-A(1) - tilted smectic antiphase smectic- (C) over tilde -smectic-A(2) - smectic-C-2. The development of lateral fluid antiphase fluctuations from the partial bilayer fluctuations in the smectic-A(1) phase have been probed and analyzed as well as the transition from the tilted smectic antiphase to the tilted bilayer smectic-C-2 phase that is accompanied by the occurrence of an intermediate smectic-A(2) phase.