  We perform scanning tunneling microscopy/spectroscopy study on the layered
iron based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ with a critical temperature
of about 33.5 K. Two types of terminated surfaces are generally observed after
cleaving the samples in vacuum. On one commonly obtained surface, we observe a
full gap feature with energy gap values close to 4.6 meV. This type of spectrum
shows a clean and uniform full gap in space, which indicates the absence of gap
nodes in this superconductor. Quasiparticle interference patterns have also
been measured, which show no scattering patterns between the hole and tiny
electron pockets, but rather an intra-band scattering pattern is observed
possibly due to the hole-like $\alpha$ pocket. The Fermi energy of this band is
only about $24\pm6$ meV as derived from the energy dispersion result.
Meanwhile, impurity induced bound-state peaks can be observed at about $\pm2.2$
meV on some spectra, and the peak value seems to be independent to magnetic
field. On the second type of surface which is rarely obtained, the fully gapped
feature can still be observed on the tunneling spectra, although multiple gaps
are obtained either from a single spectrum or separate ones, and the gap values
determined from coherence peaks locate mainly in the range from 4 to 8 meV. Our
results clearly indicate multiple and nodeless superconducting gap nature in
this layered superconductor KCa$_2$Fe$_4$As$_4$F$_2$, and the superfluid is
mainly contributed by the hole-like Fermi surfaces near $\Gamma$ point. This
would inspire further consideration on the effect of the shallow and incipient
bands near M point, and help to understand the pairing mechanism in this highly
layered iron-based superconductor.
