  Observations of a relation between continuum intensity and magnetic field
strength in sunspots have been made during nearly five decades. This work
presents full-Stokes measurements of the full-split (g = 3) line Fe I 1564.85
nm with spatial resolution of 0.5" obtained with the GREGOR Infrared
Spectrograph in three large sunspots. The continuum intensity is corrected for
instrumental scattered light and the brightness temperature is calculated.
Magnetic field strength and inclination are derived directly from the line
split and the ratio of Stokes components. The continuum intensity (temperature)
relations to the field strength are studied separately in the umbra, light
bridges, and penumbra. The results are consistent with previous studies and it
was found that the scatter of values in the relations increases with increasing
spatial resolution thanks to resolved fine structures. The observed relations
show trends common for the umbra, light bridges, and the inner penumbra, while
the outer penumbra has a weaker magnetic field compared to the inner penumbra
at equal continuum intensities. This fact can be interpreted in terms of the
interlocking comb magnetic structure of the penumbra. A comparison with data
obtained from numerical simulations was made. The simulated data have a
generally stronger magnetic field and a weaker continuum intensity than the
observations, which may be explained by stray light and limited spatial
resolution of the observations and by photometric inaccuracies of the
simulations.
