  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. 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.
