Diffraction tomography is a powerful algorithm for producing high-resolution quantitative reconstructions across a wide range of applications. A major drawback of the method is that it operates on the scattered field, which cannot generally be directly measured, but must instead be calculated by subtracting the incident field, i.e. the equivalent field with no scatterer present. Unfortunately, often the incident field is not measurable and hence must be estimated, causing errors. This paper highlights an important, but not widely recognized, result: for particular widely used formulations of the algorithm, the subtraction of the incident field is unnecessary, and the algorithm can actually be applied directly to measured signals. The theory behind this is derived, showing that the incident field will vanish under far-field conditions, and the result is demonstrated in practice. Tests with subsampled arrays show that aliasing artefacts can appear, but can be removed with a filter at the expense of resolution. The incident field also has no effect for a variety of array configurations tested. Finally, the performance in the presence of both correlated and uncorrelated errors is confirmed, in all cases demonstrating that the incident field has a negligible effect on the final reconstruction.