Optical projection tomography (OPT) is a three-dimensional mesoscopic imaging modality that can use absorption or fluorescence contrast, and is widely applied to fixed and live samples in the mm-cm scale. For fluorescence OPT, we present OPT implemented for accessibility and low cost, an open-source research-grade implementation of modular OPT hardware and software that has been designed to be widely accessible by using low-cost components, including light-emitting diode (LED) excitation and cooled complementary metal-oxide-semiconductor (CMOS) cameras. Both the hardware and software are modular and flexible in their implementation, enabling rapid switching between sample size scales and supporting compressive sensing to reconstruct images from undersampled sparse OPT data, e.g. to facilitate rapid imaging with low photobleaching/phototoxicity. We also explore a simple implementation of focal scanning OPT to achieve higher resolution, which entails the use of a fan-beam geometry reconstruction method to account for variation in magnification. This article is part of the Theo Murphy meeting issue 'Open, reproducible hardware for microscopy'.