The methods of separated or successive oscillatory fields (often calle
d Ramsey methods) are described for radio, microwave and optical coher
ent radiation. The methods are initially described qualitatively. The
quantitative theories of the methods are also given. For a two-level s
ystem at radio frequencies exact expressions for the transition probab
ility amplitudes for an arbitrary number of successive oscillatory reg
ions can be found in terms of products of successive transformation ma
trices. The expressions are greatly simplified if the oscillatory-fiel
d regions are very short. If there are only two oscillatory-field regi
ons the situation is similar to a Young's two-slit interference patter
n except that the two paths are separated in spin space rather than no
rmal space. Some results from more than two oscillatory regions are di
scussed. The extensions of the methods and the theories to optical fre
quencies are described. The advantages and disadvantages of the method
s are given as are the many extensions of the method beyond the origin
al concept.