dc and ac optical nulling bridges for sensitive transmittance measurements

We present a formal comparison between dc and ac nulling optical bridges. We consider their performance in monitoring over long periods of time (several minutes), small and slow (in a time scale of seconds) changes in transmittance of an optical component. We consider two fundamentally different ac optical bridges (OB), an amplitude modulated optical bridge (AM-OB), and a switching optical bridge (Sw-OB). For each OB, we derive a general expression for the minimum detectable change in transmittance (|ΔT|_min), taking into account all the important noises. It is found that under optimum conditions the dc- and AM-OB have similar detection limits imposed by the 1/f noise of the photodetectors. It is shown that the Sw-OB can in principle overcome the 1/f noise of the detector and approach the shot-noise limit; however, it is sensitive to switching device imperfections (to first order in smallness), which could easily prevent achieving a detection limit below the 1/f noise. It is also shown that the Sw-OB has intrinsic advantages over the dc- and AM-OB for its use in remote sensors. It can eliminate more efficiently noise induced along the propagation of light from the sensing point to the photodetector. We conclude that when using low power optics (P ≤ 1 mW) and considering a bench instrument, the dc- and AM-OB can be used for a target resolution down to |ΔT|_min≈10^-5-10^-6. The Sw-OB optical bridges should be chosen if |ΔT|_min≈10^-6-10^-8 is to be attempted. In any case, strict conditions are to be met before considering approaching the detection limits imposed by electronic noises. These conditions are discussed in detail. In particular, atmospheric isolation will be needed in general below |ΔT|_min ≈10^-4.