A system for guiding a first repositionable object (120, 205, 220, 230, 260, 270, 405) with respect to a second object, comprising: a first radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), a second radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), and a third radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), each located at the second object configured to emit, respectively, modulated optical radiation, each of the first, second, and third radiation emitting elements (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711) being one of a transmitter and a retro-reflector; a first electro-optical sensor (122, 224, 401, 531, 831, 1331, 1680, 1681, 1740, 1911, 2011, 2701) on the repositionable object (120, 205, 220, 230, 260, 270, 405) including (i) a first signal-modifying optical element (534, 1334, 2014, 2702) having a first transmission function, (ii) a first detector (533, 833, 1681, 1841, 2703, 2821) configured to detect modulated optical radiation transmitted through the first signal-modifying electro-optical element (534, 1334, 2014, 2702), and (iii) a first demodulator (532, 832, 1332, 1360, 1690) configured to generate, from the modulated optical radiation detected by the first detector (533, 833, 1681, 1841, 2703, 2821), a respective demodulated electrical signal; a second electro-optical sensor (122, 224, 401, 531, 831, 1331, 1680, 1681, 1740, 1911, 2011, 2701) on the repositionable object (120, 205, 220, 230, 260, 270, 405) including (i) a second signal-modifying optical element (534, 1334, 2014, 2702) 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 (533, 833, 1681, 1841, 2703, 2821) configured to detect the modulated optical radiation transmitted through the second signal-modifying optical element (534, 1334, 2014, 2702), and (iii) a second demodulator (532, 832, 1332, 1360, 1690) configured to generate, from the modulated optical radiation detected by the second detector (533, 833, 1681, 1841, 2703, 2821), a respective demodulated electrical signal; and a processor (412, 2380) for determining, from the demodulated electrical signals, a three-dimensional location and a three-dimensional orientation of the second object relative to the detectors (533, 833, 1681, 1841, 2703, 2821). a first radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), a second radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), and a third radiation emitting element (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711), each located at the second object configured to emit, respectively, modulated optical radiation, each of the first, second, and third radiation emitting elements (106, 162, 210, 280, 215, 222, 240, 262, 272, 408, 511, 711) being one of a transmitter and a retro-reflector; a first electro-optical sensor (122, 224, 401, 531, 831, 1331, 1680, 1681, 1740, 1911, 2011, 2701) on the repositionable object (120, 205, 220, 230, 260, 270, 405) including (i) a first signal-modifying optical element (534, 1334, 2014, 2702) having a first transmission function, (ii) a first detector (533, 833, 1681, 1841, 2703, 2821) configured to detect modulated optical radiation transmitted through the first signal-modifying electro-optical element (534, 1334, 2014, 2702), and (iii) a first demodulator (532, 832, 1332, 1360, 1690) configured to generate, from the modulated optical radiation detected by the first detector (533, 833, 1681, 1841, 2703, 2821), a respective demodulated electrical signal; a second electro-optical sensor (122, 224, 401, 531, 831, 1331, 1680, 1681, 1740, 1911, 2011, 2701) on the repositionable object (120, 205, 220, 230, 260, 270, 405) including (i) a second signal-modifying optical element (534, 1334, 2014, 2702) 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 (533, 833, 1681, 1841, 2703, 2821) configured to detect the modulated optical radiation transmitted through the second signal-modifying optical element (534, 1334, 2014, 2702), and (iii) a second demodulator (532, 832, 1332, 1360, 1690) configured to generate, from the modulated optical radiation detected by the second detector (533, 833, 1681, 1841, 2703, 2821), a respective demodulated electrical signal; and a processor (412, 2380) for determining, from the demodulated electrical signals, a three-dimensional location and a three-dimensional orientation of the second object relative to the detectors (533, 833, 1681, 1841, 2703, 2821).