  The detection and quantification of quantum coherence play significant roles
in quantum information processing. We present an efficient way of tomographic
witnessing for both theoretical and experimental detection of coherence. We
prove that a coherence witness is optimal if and only if all of its diagonal
elements are zero. Naturally, we obtain a bona fide homographic measure of
coherence given by the sum of the absolute values of the real and the imaginary
parts of the non-diagonal entries of a density matrix, together with its
interesting relations with other coherence measures like $l_1$ norm coherence
and robust of coherence.
