  We show that an intensity speckle can be directly interpreted as the
properties of incident light - amplitude, phase, polarization, and coherency
over spatial positions. Revisiting the speckle-correlation scattering matrix
(SSM) method [Lee and Park, Nat. Comm. 7, 13359 (2016)], we successfully
extract the intact information of incident light from an intensity speckle
snapshot as the form of coherency matrix. The idea is verified experimentally
by introducing the peculiar states of light that exhibit uneven amplitude,
phase, polarization, and coherency features. We also find substantial practical
advantage of the proposed method compared to the conventional coherency matrix
measuring techniques such as Stokes polarimetry. We believe this physical
interpretation of an intensity speckle could open a new avenue to study and to
utilize the speckle phenomenon in vast subfields of wave physics.
