  We introduce a new space IDA of locally integrable functions whose integral
distance to holomorphic functions is finite, and use it to completely
characterize boundedness and compactness of Hankel operators on weighted Fock
spaces. As an application, for bounded symbols, we show that the Hankel
operator $H_f$ is compact if and only if $H_{\bar f}$ is compact, which
complements the classical compactness result of Berger and Coburn. Motivated by
recent work of Bauer, Coburn, and Hagger, we also apply our results to the
Berezin-Toeplitz quantization.
