A linear optical sampling apparatus, temporally samples a modulated optical signal using the amplitude of the interference of its electric field with the electric field of a laser pulse. The apparatus includes a 90 optical hybrid that combines the optical signal and laser pulse in order to generate two quadratures interference samples S_A and S_B. A processor compensates for optical and electrical signal handling imperfections in the hybrid, balanced detectors, and A/D converters used in the optical sampling apparatus. The processor numerically scales the two quadratures interference samples S_A and S_B over a large collection of samples by imposing that the average S_A=S_B=0 and S_A²=S_B² and then minimizes 2S_AS_B/(S_A²+S_B²) =cos(_B-_A)). This is done by adjusting the phase between the two quadratures (ideally either -/2 or +/2) so that cos(_B-_A)) is zero. The processor then generates a demodulated sample signal using the quadratures interference samples S_A and S_B. According to one feature, the hybrid sets the relative phase between two quadratures of their interferometric component so that the phase sensitivity inherent to linear optics is removed. A variety of hybrid arrangements is disclosed that can be implemented using integrated waveguide technology. The apparatus enables sampling of picosecond pulses up to 640 Gb/s with high sensitivity and temporal resolution.