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The cold dark matter (CDM) structure formation model predicts that about 5-10percent of a typical galactic halo of mass $\sim 10^{12} \ms$ is insubstructures with masses $\lesssim 10^8 \ms$. To directly detect suchsubstructures, we propose to observe dust continuum emission from a stronglylensed QSO-host galaxy using a large submillimeter interferometer array with ahigh angular resolution of $\sim 0.01$arcsec such as the planned Atacama LargeSubmillimeter Array (ALMA). To assess their observational feasibility, wenumerically simulate millilensing of an extended circular source by a CDMsubstructure modeled as a tidally truncated singular isothermal sphere (SIS)embedded in a typical QSO-galaxy lens system, B1422+231, modeled as a singularisothermal ellipsoid (SIE) with an external constant shear and a constantconvergence. Assuming an angular resolution of 0.01arcsec, we find that theangular positions of $\sim 10^8 \ms$ substructures at several kpc from thecenter of the macrolens halo can be directly measured if the size of the dustcontinuum emission region and the gradient of the surface brightness at theposition of the perturber are sufficiently large. From the astrometric shift ona scale of a few times $10~$mas of an image perturbed by a subhalo with respectto an unperturbed macrolensed image, we can break the degeneracy betweensubhalo mass and distance provided that macrolensing parameters are determinedfrom positions and fluxes of multiple images.Comment: 7 pages, 7 EPS files. An assessment of our assumption of constancy in  shear and convergence has been included. Version accepted for publication in  Ap

Three‐dimensional Mapping of CDM Substructure at Submillimeter Wavelengths