  Josephson junctions containing ferromagnetic layers are of considerable
interest for the development of practical cryogenic memory and superconducting
qubits. Such junctions exhibit a phase shift of $\pi$ for certain ranges of
ferromagnetic layer thickness. We present studies of Nb based micron-scale
elliptically-shaped Josephson junctions containing ferromagnetic barriers of
Ni$_{81}$Fe$_{19}$ or Ni$_{65}$Co$_{20}$Fe$_{15}$. By applying an external
magnetic field, the critical current of the junctions are found to follow
characteristic Fraunhofer patterns, and display sharp switching behavior
suggestive of single-domain magnets. The high quality of the Fraunhofer
patterns enables us to extract the maximum value of the critical current even
when the peak is shifted significantly outside the range of the data due to the
magnetic moment of the ferromagnetic layer. The maximum value of the critical
current oscillates as a function of the ferromagnetic barrier thickness,
indicating transitions in the phase difference across the junction between
values of zero and $\pi$. We compare the data to previous work and to models of
the 0-$\pi$ transitions based on existing theories.
