Diffraction limited spot

The ratio F/d is the F number of the lens. For F numbers much less than unity, spherical aberration precludes reaching the ultimate diffraction-limited spot size. Therefore a practical limit for the minimum spot size obtainable is approximately the wavelength of the light. Commonly this is expressed as the statement that laser light may be focused to a spot with dimensions equal to its wavelength. 

When focussed into a diffraction limited spot (ca. 10 y in diameter) the 1 mW laser yields a power density of 10 watts per square centimeter. Readily available c.w. lasers produce 10 watts of output, whence a focussed power density of 10 w/cm can be obtained. Moderately powerful pulsed lasers may produce pulse... 

Fig. 2 Positional detection and mean-square displacement (MSD). (a) The x, y-coordinates of a particle at a certain time point are derived from its diffraction limited spot by fitting a 2D-Gaussian function to its intensity profile. In this way, a positional accuracy far below the optical resolution is obtained, (b) The figure depicts a simplified scheme for the analysis of a trajectory and the corresponding plot of the time dependency of the MSD. The average of all steps within the trajectory for each time-lag At, with At = z, At = 2z,... (where z = acquisition time interval from frame to frame) gives a point in the plot of MSD = f(t). (c) The time dependence of the MSD allows the classification of several modes of motion by evaluating the best fit of the MSD plot to one of the four formulas. A linear plot indicates normal diffusion and can be described by = ADAt (D = diffusion coefficient). A quadratic dependence of on At indicates directed motion and can be fitted by = v2At2 + ADAt (v = mean velocity). An asymptotic behavior for larger At with = [1 - exp (—AA2DAt/)] indicates confined diffusion. Anomalous diffusion is indicated by a best fit with = ADAf and a < 1 (sub-diffusive)...

The availability of laser scanning confocal fluorescence microscopy,68 first commercially offered in the 1980s, enabled a major advance in chemical microscopy imaging convenient summaries are available in the Handbook of Biological Confocal Microscopy.69 Confocal fluorescence microscopy works by focusing continuous-wave laser illumination to a diffraction-limited spot in a focal... 

Figure 6 shows a typical SCOM image of single fluorescent molecules of Dil embedded in a 20 nm PMMA film on glass. The molecules show up as bright diffraction-limited spots with peak count rates as expected from our previous analysis. The dark pixels inside the molecular spots correspond to quantum jumps of the molecule into the triplet state. They become visible since the pixel integration time is comparable to the triplet relaxation rate. 

In this case, laser light is focused with suitable lenses to a diffraction-limited spot. For reviews on instrumentation and application see [iv, v]. A typical experimental setup is depicted below... 

In the case of a bull s eye structure, the relative electromagnetic enhancement is about 100 (computed for an incoming plane wave and consistent with experiment (72)), but the structure radius and thus the laser beam focus spot are about 4 times the diffraction limit (minimum focus size). If we compare the relative intensity enhancement to the case of a diffraction-limited spot, the intensity with the bull s eye is increased by 100x(l/4) = 6.25, which is about the enhancement with a single (bare) aperture with a tightly focused beam. Of course, this argument has to be supplemented with the influence the emission rate and the directivity of the fluorescence beam, which contribute to the overall enhanced fluorescence. However,... 

Point source beam scanning microscopes provide optimal optical sectioning and lateral resolution, because the source and detector apertures are both restricted to diffraction-limited spots. However, single spot illumination with a laser can reach power densities of hundreds of mW/cm ... 

Fig. 3. Simplified diagram of the confocal components of the AC AS 570. The laser beam is expanded to provide a diffraction limited spot at the sample. A focusing lens in front of the detection system directs the fluorescence from the focal plane through an adjustable pinhole. In the bilateral laser scanning confocal microscope, a similar technique is employed with a cursor rather than a point for illumination and detection.

A molecule can also be excited by absorbing two photons simultaneously [189]. The sum of the energy of the photons must be larger than the energy gap between SI and SO. Because two photons are required to excite one molecule, the excitation efficiency increases with the square of the photon flux. Efficient two-photon excitation requires a high photon flux, which is achieved in practice only by a pulsed laser and by focusing into a diffraction-limited spot. Due to the nonlinearity of two-photon absorption, the excitation is almost entirely confined to the central part of the diffraction pattern. 

Beam shaping of the excitation beam. The beam from a laser diode has a no-tieeable astigmatism and is not focused into a diffraction limited spot. Improv-... 

Diode lasers have an extremely small cavity. Most lasers in the power range below 200 mW (CW) are single-mode lasers, i.e. the height and width are so small (a few pm) that only one transversal mode is excited. This implies that the radiation ean, in prineiple, be focused into a diffraction-limited spot. However, beeause the eavity is only a few pm long, the light is emitted over a wide angle. The general beam profile of a laser diode is shown in Fig. 7.1. 

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