In tomographic adaptive-optics ( AO ) systems , errors due to tomographic wave-front reconstruction limit the performance and angular size of the scientific field of view ( FoV ) , where AO correction is effective . We propose a multi time-step tomographic wave-front reconstruction method to reduce the tomographic error by using the measurements from both the current and the previous time-steps simultaneously . We further outline the method to feed the reconstructor with both wind speed and direction of each turbulence layer . An end-to-end numerical simulation , assuming a multi-object AO ( MOAO ) system on a 30 m aperture telescope , shows that the multi time-step reconstruction increases the Strehl ratio ( SR ) over a scientific FoV of 10 arcminutes in diameter by a factor of 1.5–1.8 when compared to the classical tomographic reconstructor , depending on the guide star asterism and with perfect knowledge of wind speeds and directions . We also evaluate the multi time-step reconstruction method and the wind estimation method on the RAVEN demonstrator under laboratory setting conditions . The wind speeds and directions at multiple atmospheric layers are measured successfully in the laboratory experiment by our wind estimation method with errors below 2 ms ^ { -1 } . With these wind estimates , the multi time-step reconstructor increases the SR value by a factor of 1.2–1.5 , which is consistent with a prediction from end-to-end numerical simulation .