Shot noise limits on binary detection in multiphoton imaging

Much of fluorescence-based microscopy involves detection of if an object is present or absent (i.e., binary detection). The imaging depth of three-dimensionally resolved imaging, such as multiphoton imaging, is fundamentally limited by out-of-focus background fluorescence, which when compared to the in-focus fluorescence makes detecting objects in the presence of noise difficult. Here, we use detection theory to present a statistical framework and metric to quantify the quality of an image when binary detection is of interest. Our treatment does not require acquired or reference images, and thus allows for a theoretical comparison of different imaging modalities and systems.