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The familiar tools of Fourier analysis and Fisher matrices are applied to derive the uncertainties on photometric, astrometric, and weak-lensing measurements of stars and galaxies in real astronomical images. Many effects or functions that are ignored in basic exposure-time calculators can be included in this framework: pixels of size comparable to the stellar image; undersampled and dithered exposures; cosmic-ray hits; intrapixel sensitivity variations; positional and ellipticity errors as well as photometric errors. I present a formalism and a C++ implementation of these methods. As examples of their use, I answer some commonly arising questions about imaging strategies: What amount of dithering is ideal? What pixel size optimizes the productivity of a camera? Which is more efficient—space-based or ground-based observing? Subject headings: methods: data analysis—space vehicles: instruments

Advanced Exposure‐Time Calculations: Undersampling, Dithering, Cosmic Rays, Astrometry, and Ellipticities