Optical aberrations limit resolution in biological tissues, and their influence is particularly large for promising techniques such as light-sheet microscopy. In principle, image quality might be improved by adaptive optics (AO), in which aberrations are corrected by using a deformable mirror (DM). To implement AO in microscopy, one requires a method to measure wavefront aberrations, but the most commonly used methods have limitations for samples lacking point-source emitters. Here we implement an image-based wavefront-sensing technique, a variant of generalized phase-diverse imaging called multiframe blind deconvolution, and exploit it to calibrate a DM in a light-sheet microscope. We describe two methods of parameterizing the influence of the DM on aberrations: a traditional Zernike expansion requiring 1040 parameters, and a direct physical model of the DM requiring just 8 or 110 parameters. By randomizing voltages on all actuators, we show that the Zernike expansion successfully predicts wavefronts to an accuracy of approximately $30\mathrm{nm}$ (rms) even for large aberrations. We thus show that image-based wavefront sensing, which requires no additional optical equipment, allows a simple but powerful method to calibrate a deformable optical element in a microscope setting.