Optogenetic systems utilize genetically-encoded proteins that change conformation in response to specific wavelengths of light to alter cellular processes. There is a need for culturing and measuring systems that incorporate programmed illumination and stimulation of optogenetic systems. We present a protocol for building and using a continuous culturing apparatus to illuminate microbial cells with programmed doses of light, and automatically acquire and analyze images of cells in the effluent. The operation of this apparatus as a chemostat allows the growth rate and the cellular environment to be tightly controlled. The effluent of the continuous cell culture is regularly sampled and the cells are imaged by multi-channel microscopy. The culturing, sampling, imaging, and image analysis are fully automated so that dynamic responses in the fluorescence intensity and cellular morphology of cells sampled from the culture effluent are measured over multiple days without user input. We demonstrate the utility of this culturing apparatus by dynamically inducing protein production in a strain of Saccharomyces cerevisiae engineered with an optogenetic system that activates transcription.