The excitation and collection of optical signals using lenses form the basis for many applications in imaging, nephelometry, fluorometry, and spectroscopy. While lenses are needed for imaging systems, their use is not so obvious for volume sensing applications. Here, we study the excitation and collection of fluorescence signals to show that lensless systems generally provide a stronger signal compared to lensed systems for the case of extended Lambertian-like sources, such as LEDs. To elucidate this result, we provide a foundational framework to analyze the signal collection efficiency from an arbitrary detection volume with and without lenses when extended sources and detectors are used. A combination of factors, including the limited numerical aperture, the use of extended sources/detectors, and the requirement of a finite imaging distance between the source/detector, lenses, and the sample, limits the performance of the lensed system compared to the lensless system. Our theoretical and experimental results indicate that conventional wisdom based on the assumption of point-like sources and detectors should not always be followed. We provide a systematic approach for analyzing and simplifying the design of low-cost, lensless fluorometers and nephelometers without sacrificing their performance, reporting a sub-ppb level detection limit for measuring tryptophan-like-fluorescence in drinking water.
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