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The smectic-A/air interface of liquid-crystal droplets with antagonistic boundary conditions is studied by atomic force microscopy (AFM). The droplets are prepared on coated silicon wafers on which a planar alignment is preferred in contrast to the homeotropic alignment at the air interface. As a result, focal conic defects appear in the smectic-A phase causing a characteristic pattern of depressions in the droplet surface. The dimensions of the defect-induced depressions are measured by AFM as a function of temperature for two different compounds possessing a smectic-A−isotropic and a smectic-A−nematic transition. Whereas the results are independent of temperature in the smectic-A−isotropic case, reflecting the first-order nature of the transition, a pronounced temperature dependence is observed for the second compound, where the depth of the defect-induced depressions decreases continuously with …