(abridged) NML Cyg is a highly evolved OH/IR supergiant and supposed to be among the most luminous supergiants in the galaxy. We present the first diffraction limited 2.13micron observations of NML Cyg with 73mas resolution. The speckle interferograms were obtained with the SAO 6m telescope, image reconstruction is based on the bispectrum speckle interferometry method. Radiative transfer calculations have been carried out to model the spectral energy distribution, our 2.13micron visibility function, and mid-infrared visibility functions. The observed dust shell properties do not appear to be in accordance with single-shell models but seem to require multiple components. Considering previous periods of enhanced mass-loss, various density enhancements in the dust shell were taken into account. An extensive grid of models was calculated for different locations and strenghts of such superwind regions in the dust shell. To match the observations from the optical to the sub-mm domain requires at least two superwind regions embedded in the shell. The best model includes a dust shell with a temperature of 1000K at its inner radius of 6.2Rstar, a close embedded superwind shell extending from 15.5Rstar to 21.7Rstar with amplitude 10 (factor of density enhancement), and a far-out density enhancement at 186Rstar with amplitude 5. The angular diameter of the inner dust-shell rim amounts to 105mas. Within the various parts of the dust shell, 1/r^2 density distributions could be maintained differing only in their amplitude A. The present-day mass-loss rate was determined to be 1.2 10^-4 Msol/yr. The inner embedded superwind shell corresponds to a phase of enhanced mass-loss which began ~59yr ago and lasted for ~18yr, and the outer superwind region to a high mass-loss period which terminated 529yr ago.
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