Defining the Noise-limited-resolution for Stimulated Emission Depletion Microscopy

With recent developments in microscopy, such as stimulated emission deletion (STED) microscopy, far-field imaging at resolutions better than the diffraction limit is now a commercially available technique. Here, we analyse how the interplay between shot noise, thermal noise, the saturation intensity of a fluorescent label, and the damage threshold of the sample changes the maximum resolution of STED microscopy. We find that there is indeed a shot-noise resolution limit that depends on the fundamental physical parameters of the label. Thermal noise limits the signal integration time, which, for a given resolution, requires labels with a higher saturation intensity to obtain sufficient signal. Consequently, we find that, contrary to expectation, lower saturation intensities do not always result in better resolution. Modern microscopy is one of a number of techniques that has driven the modern biology revolution, revealing important physiological details at systemic, cellular and sub-cellular levels. One of the key limitations of optical microscopy is the diffraction limit, which hides details on scales smaller than the wavelength of the illuminating light. The drive to overcome this limit has led to several notable techniques, such as STED microscopy and stochastic optical reconstruction microscopy (STORM). These techniques are able to achieve quite astonishing resolutions. Examples include imaging frozen cells with a lateral 20-30 nm resolution using STORM [1], live cell imaging with a lateral resolution of 60 nm using STED [2] and solid state imaging of nitrogen vacancy colour centres in diamond with a resolution of 6 nm (and a centroid positional resolution of 0.1 nm) [3]. STED microscopy simultaneously illuminates the sample with two laser beams, both focused to diffraction-limited spot-sizes. One beam is Gaussian shaped and tuned to the absorption band of the fluorescent labels. The second, called the STED laser, possesses a node at the centre of the beam and is tuned to the emission wavelength of the fluorescent labels. The interplay between the label’s electronic structure and the two lasers effectively prevents excitation occurring outside of the small volume located at the node of the STED laser beam. As a result, spontaneous emission only occurs from within this smaller volume, which is defined by where the STED laser intensity is lower than the saturation intensity of the label. This means that the volume can be reduced to arbitrarily small values simply by increasing the intensity of the STED laser, which, in turn, implies that there is no limit to the achievable spatial resolution. 1 ar X iv :0 90 8. 16 78 v1 [ ph ys ic s. op tic s] 1 2 A ug 2 00 9 2 CHRIS J. LEE∗ AND KLAUS J. BOLLER This leads to the question of what might be the resolution limit of these new imaging techniques. However, research has focused on how the resolution scales with STED laser intensity. [4] To our knowledge no previous work has investigated under what conditions the resolution scaling law might fail. Although the diffraction limit no longer applies, fundamental sources of noise, such as shot noise and thermal noise must, at some point, play a role in limiting the resolution of all sub-diffraction-limited resolution microscopy techniques. In this paper, we analyse the behaviour of the signal-to-noise ratio of STED microscopy. In particular we examine the limits of thermal noise (in the form of Brownian motion of the sample), detector shot noise, and sample damage threshold on resolution. The shot noise limit is found to be strongly dependent on the saturation intensity of the emitter, while thermal noise limits the signal integration time to a few milliseconds. Taking into account the optical damage threshold of the sample, we show that there exists an optimum emitter saturation intensity that gives the best resolution.