A first-order linear perturbation model for simulating imaging through weak turbulence is introduced and developed. It is based on a first-order approximation of the Born expansion of paraxial propagation. The model generates a random scalar field that encodes information about the imaging parameters, such as wavelength, range, Cn2, and the aperture diameter. The gradients of the field are then multiplied to the corresponding gradients of the average turbulent image of a Lambertian target. The result is a model that can rapidly generate a sequence of turbulent images. Some limitations of the model are discussed, and possible improvements are suggested.