A system for guiding a first repositionable object with respect to a second object , comprising: a first radiation emitting element , a second radiation emitting element , and a third radiation emitting element , each located at the second object configured to emit, respectively, modulated optical radiation, each of the first, second, and third radiation emitting elements being one of a transmitter and a retro-reflector; a first electro-optical sensor on the repositionable object including (i) a first signal-modifying optical element having a first transmission function, (ii) a first detector configured to detect modulated optical radiation transmitted through the first signal-modifying electro-optical element , and (iii) a first demodulator configured to generate, from the modulated optical radiation detected by the first detector , a respective demodulated electrical signal; a second electro-optical sensor on the repositionable object including (i) a second signal-modifying optical element having a second transmission function differing from the first transmission function in at least one of spatially-varying phase transmission and spatially-varying amplitude transmission, (ii) a second detector configured to detect the modulated optical radiation transmitted through the second signal-modifying optical element , and (iii) a second demodulator configured to generate, from the modulated optical radiation detected by the second detector , a respective demodulated electrical signal; and a processor for determining, from the demodulated electrical signals, a three-dimensional location and a three-dimensional orientation of the second object relative to the detectors . a first radiation emitting element , a second radiation emitting element , and a third radiation emitting element , each located at the second object configured to emit, respectively, modulated optical radiation, each of the first, second, and third radiation emitting elements being one of a transmitter and a retro-reflector; a first electro-optical sensor on the repositionable object including (i) a first signal-modifying optical element having a first transmission function, (ii) a first detector configured to detect modulated optical radiation transmitted through the first signal-modifying electro-optical element , and (iii) a first demodulator configured to generate, from the modulated optical radiation detected by the first detector , a respective demodulated electrical signal; a second electro-optical sensor on the repositionable object including (i) a second signal-modifying optical element having a second transmission function differing from the first transmission function in at least one of spatially-varying phase transmission and spatially-varying amplitude transmission, (ii) a second detector configured to detect the modulated optical radiation transmitted through the second signal-modifying optical element , and (iii) a second demodulator configured to generate, from the modulated optical radiation detected by the second detector , a respective demodulated electrical signal; and a processor for determining, from the demodulated electrical signals, a three-dimensional location and a three-dimensional orientation of the second object relative to the detectors . <EOS>