  It is demonstrated that the use of a Micrometric Thin $^{39}$K vapor Cell
(MTC) and Saturated Absorption spectroscopy (SA) allows to form narrow atomic
lines in transmission spectrum without unwanted Cross-Over (CO) resonances.
Another important feature is the small characteristic magnetic field value $B_0
= A_{hf}/\mu_B$ of $^{39}$K, significantly smaller than for Rb and Cs. As a
consequence, decoupling of $J$ and $I$ can be observed at relatively low
magnetic fields $\sim$300 G, which results in the formation of two groups of
four well-spectrally-resolved and equidistantly-positioned atomic transitions
having the same amplitude (each group corresponds to a given circular
polarization $\sigma^\pm$) which we record using a simple experimental setup
with a linearly polarized tunable diode-laser and a longitudinal magnetic field
obtained with two permanent magnets. Fabrication of a MTC is much easier than
the fabrication of the $^{39}$K nanocells used in our previous works. A simple
method to determine the magnitude of a wide range of B-fields with a spatial
resolution of 30 $\mu$m is presented, which is intrinsically calibrated and
does not require a frequency reference.
