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We develop in detail a recently proposed optical-path modification ofastronomical intensity interferometers. Extended-Path Intensity Correlation(EPIC) introduces a tunable path extension, enabling differential astrometry ofmultiple compact sources such as stars and quasars at separations of up to afew arcseconds. Combined with other recent technological advances inspectroscopy and fast single-photon detection, a ground-based intensityinterferometer array can achieve microarcsecond resolution and even betterlight-centroiding accuracy on bright sources of magnitude $m \lesssim 15$. Welay out the theory and technical requirements of EPIC, and discuss thescientific potential. Promising applications include astrometric lensing ofstars and quasar images, binary-orbit characterization, exoplanet detection,Galactic acceleration measurements and calibration of the cosmic distanceladder. The introduction of the path extension thus significantly increases thescope of intensity interferometry while reaching unprecedented levels ofrelative astrometric precision.

Extended-Path Intensity Correlation: Microarcsecond Astrometry with an Arcsecond Field of View