Building on his work designing and operating his one-�ngstr�m microscope ( O�M ), O'Keefe produced the design for the LBNL TEAM ( transmission electron aspheric microscope ) able to resolve atoms in the deep sub-�ngstr�m resolution region ( less than 0.5 ?) using a hardware electron-wave phase-corrector ( Cs corrector ) in combination with a coherence-enhancing electron-beam monochromator.
22.
Here k = \ sqrt { 2m E } / \ hbar and \ delta _ s =-k \ cdot r _ 0 is the s-wave phase shift ( the phase difference between incoming and outgoing wave ), which is fixed by the boundary condition u ( r _ 0 ) = 0; A is an arbitrary normalization constant.
23.
Because of the assumption of slow variations in the wave train as well as in a possible inhomogeneous medium and mean motion the quantities A, a, \ omega, \ boldsymbol { k } and \ alpha all vary slowly in space \ boldsymbol { x } and time t but the wave phase \ theta itself does not vary slowly.
24.
As a last step, this averaging result \ overline { L } can be expressed as the " averaged Lagrangian " density \ mathcal { L } ( \ omega, \ boldsymbol { k }, a ) which is a function of the slowly varying parameters \ omega, \ boldsymbol { k } and a and independent of the wave phase \ theta itself.
25.
Or, the installer can increase the height of either one or both the transmitting and receiving antenna so that the object ( roof ) that is deflecting the signal is in the 2nd region rather than the 1st ( the inverted signal would behave as if it was right side up by the time it reached the receiver due to the half-wave phase shift in region 2 ).
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