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Paper text:
the experimental set - up used to generate and acquire the experimental data is shown in supplementary fig .
s1 . the source used was a q - switched frequency - doubled nd : yag laser ( elforlight inc .
, uk ) centred at 532 nm with pulse duration of 10 ns and coherence length of 7 mm .
the repetition rate of the laser was tuneable between 50 hz and 200 hz , and the full pulse energy was 0.6 mj . before entering the mach - zehnder interferometer ,
the light beam was collimated to a diameter of 2 mm by a beam expander .
the power injected into the system was adjustable via a half - wave plate ( hwp ) paired with a polarizing beamsplitter ( pbs ) , and further attenuated through a neutral density filter .
light was split into a probe beam and a reference beam by another pbs , the ratio between the two beams was controlled by a hwp .
the polarization of the reference beam was rotated by 90 before passing through an acousto - optic modulator ( aom ) which up - shifted its frequency by f .
the reference beam was further expanded by an afocal lens pair to a diameter of 25 mm and spatially filtered by a pinhole .
the probe beam entered a scattering cell composed of two optical diffusers ( dg10 - 600 , thorlabs , usa ) or two pieces of ex vivo chicken breast tissue .
the reference beam was combined with the scattered light from the probe by a 50:50 beamsplitter ( bs1 ) .
the path lengths of the reference and probe beams were balanced for strongest interference using two tuneable delay lines .
inside the dopc , the beams were retro - reflected by the surface of a phase - only slm ( vis - pluto , holoeye , germany ) .
the beams were further reflected by a 90:10 ( 90% transmission ) beamsplitter ( bs2 ) to form a speckle pattern on an scmos camera ( pco .
the pixels of the camera and the slm were digitally aligned with 1 ( pixel ) alignment error for optimal phase conjugation quality .
once the scattered fields were measured at two instants , a trap phase map was calculated and displayed on the slm . in the hologram reading mode , the probe beam was blocked .
reflection by the slm generated the phase - conjugated beam , which was delivered to the scattering medium after passing through bs2 and bs1 .
the light intensity distribution on the focal plane inside the two scattering media was monitored either by replacing the target with a cmos camera ( firefly mv , point grey research , canada ) , or by using a bs to reflect the focal pattern onto the camera .
the frequency difference between the probe and reference beams was set by the aom modulation frequency , which was f = 50.0000125 mhz .
the aom was triggered by a function generator ( dg4000 , rigol technologies , china ) with a sinusoidal waveform at f . a delay generator ( dg645 , stanford research systems , usa ) , sharing a global time - base with the function generator , produced two channels of pulse sequences at fs = 50 hz with a proper relative delay to externally trigger and synchronize the laser and the camera .
the reference beam , when undersampled at fs by the camera , cycled through four phases0 , /2 ,  , 3/2corresponding to four interferograms pi ( i = 1 , 2 , 3 , 4 ) . during the measurement ,
the slm was blanked by displaying a constant phase map ( phase value = 0 ) .
the complex amplitude of the field was obtained by e = ( p1  p3 ) + i(p2  p4 ) .
after the two complex amplitudes were acquired , they were subtracted to get e , and the trap phase map was calculated by  = arg [ i m ( e)/re(e ) ] ( arg[ ] denotes taking the argument ) . for applications requiring higher measurement accuracy ( e.g. , the experiment shown in fig .
i , where the perturbation was weak ) , a different signal acquisition scheme was used .
the aom was driven at f = 50.0000001 mhz , and the delay generator triggered the laser and the camera at 200 hz and 4 hz , respectively .
the sampling frequency of fs = 4 hz ensured a phase difference of /2 between neighbouring frames .
the exposure time of the camera was set to 51 ms , during which 10 laser shots were averaged to reduce the noise caused by laser shot - to - shot intensity fluctuations . in the probing mode ( fig .
1d ) , the scattered electromagnetic field distribution on a phase - only spatial light modulator ( slm ) was measured via digital phase - shifting holography .
the virtual difference field e was synthesized by subtracting the fields acquired before and after the perturbation and then optimizing the phase offset .
a phase map  was then extracted from e and subsequently conjugated to yield the trap phase map (  ) . in the focusing mode ( fig .
1e ) , an intense planar reading beam was transformed into a time - reversed beam after reflecting off the slm , and converged onto the target .
the experimental set - up used to generate and acquire the experimental data is shown in supplementary fig .
s1 . the source used was a q - switched frequency - doubled nd : yag laser ( elforlight inc .
, uk ) centred at 532 nm with pulse duration of 10 ns and coherence length of 7 mm .
the repetition rate of the laser was tuneable between 50 hz and 200 hz , and the full pulse energy was 0.6 mj . before entering the mach - zehnder interferometer ,
the light beam was collimated to a diameter of 2 mm by a beam expander .
the power injected into the system was adjustable via a half - wave plate ( hwp ) paired with a polarizing beamsplitter ( pbs ) , and further attenuated through a neutral density filter .
light was split into a probe beam and a reference beam by another pbs , the ratio between the two beams was controlled by a hwp .
the polarization of the reference beam was rotated by 90 before passing through an acousto - optic modulator ( aom ) which up - shifted its frequency by f .
the reference beam was further expanded by an afocal lens pair to a diameter of 25 mm and spatially filtered by a pinhole .
the probe beam entered a scattering cell composed of two optical diffusers ( dg10 - 600 , thorlabs , usa ) or two pieces of ex vivo chicken breast tissue .
the reference beam was combined with the scattered light from the probe by a 50:50 beamsplitter ( bs1 ) .
the path lengths of the reference and probe beams were balanced for strongest interference using two tuneable delay lines .
inside the dopc , the beams were retro - reflected by the surface of a phase - only slm ( vis - pluto , holoeye , germany ) .
the beams were further reflected by a 90:10 ( 90% transmission ) beamsplitter ( bs2 ) to form a speckle pattern on an scmos camera ( pco .
the pixels of the camera and the slm were digitally aligned with 1 ( pixel ) alignment error for optimal phase conjugation quality .
once the scattered fields were measured at two instants , a trap phase map was calculated and displayed on the slm . in the hologram reading mode , the probe beam was blocked .
reflection by the slm generated the phase - conjugated beam , which was delivered to the scattering medium after passing through bs2 and bs1 .
the light intensity distribution on the focal plane inside the two scattering media was monitored either by replacing the target with a cmos camera ( firefly mv , point grey research , canada ) , or by using a bs to reflect the focal pattern onto the camera .
the frequency difference between the probe and reference beams was set by the aom modulation frequency , which was f = 50.0000125 mhz .
the aom was triggered by a function generator ( dg4000 , rigol technologies , china ) with a sinusoidal waveform at f . a delay generator ( dg645 , stanford research systems , usa ) , sharing a global time - base with the function generator , produced two channels of pulse sequences at fs = 50 hz with a proper relative delay to externally trigger and synchronize the laser and the camera .
the reference beam , when undersampled at fs by the camera , cycled through four phases0 , /2 ,  , 3/2corresponding to four interferograms pi ( i = 1 , 2 , 3 , 4 ) . during the measurement ,
the slm was blanked by displaying a constant phase map ( phase value = 0 ) .
the complex amplitude of the field was obtained by e = ( p1  p3 ) + i(p2  p4 ) .
after the two complex amplitudes were acquired , they were subtracted to get e , and the trap phase map was calculated by  = arg [ i m ( e)/re(e ) ] ( arg[ ] denotes taking the argument ) . for applications requiring higher measurement accuracy ( e.g. , the experiment shown in fig .
i , where the perturbation was weak ) , a different signal acquisition scheme was used .
the aom was driven at f = 50.0000001 mhz , and the delay generator triggered the laser and the camera at 200 hz and 4 hz , respectively .
the sampling frequency of fs = 4 hz ensured a phase difference of /2 between neighbouring frames .
the exposure time of the camera was set to 51 ms , during which 10 laser shots were averaged to reduce the noise caused by laser shot - to - shot intensity fluctuations .
1d ) , the scattered electromagnetic field distribution on a phase - only spatial light modulator ( slm ) was measured via digital phase - shifting holography .
the virtual difference field e was synthesized by subtracting the fields acquired before and after the perturbation and then optimizing the phase offset .
a phase map  was then extracted from e and subsequently conjugated to yield the trap phase map (  ) . in the focusing mode ( fig .
1e ) , an intense planar reading beam was transformed into a time - reversed beam after reflecting off the slm , and converged onto the target .
the ability to steer and focus light inside scattering media has long been sought for a multitude of applications . to form optical foci inside scattering media , 
 the only feasible strategy at present is to guide photons by using either implanted1 or virtual24 guide stars , which can be inconvenient and limits potential applications . here , 
 we report a scheme for focusing light inside scattering media by employing intrinsic dynamics as guide stars . by time - reversing the perturbed component of the scattered light adaptively , 
 we show that it is possible to focus light to the origin of the perturbation . using the approach , 
 we demonstrate non - invasive dynamic light focusing onto moving targets and imaging of a time - variant object obscured by highly scattering media . 
 anticipated applications include imaging and photoablation of angiogenic vessels in tumours as well as other biomedical uses .