The limiting separation at which two objects appear distinct—the socalled limit of resolution—depends on both the wavelength of the light and the numerical aperture of the lens system used. The numerical aperture affects the lightgathering ability of the lens and is related both to the angle of the cone of light that can enter it and to the refractive index of the medium the lens is operating in; the wider the microscope opens its eye, so to speak, the more sharply it can see (Figure 9–6). The refractive index is the ratio of the speed of light in a vacuum to the speed of light in a particular transparent medium. For example, for water this is 1.33, meaning that light travels 1.33 times slower in water than in a vacuum. Under the best conditions, with violet light (wavelength = 0.4 μm) and a numerical aperture of 1.4, the basic light microscope can theoretically achieve a limit of resolution of about 0.2 μm, or 200 nm. Some microscope makers at the end of the nineteenth century achieved this resolution, but it is routinely matched in contemporary, factoryproduced microscopes. Although it is possible to enlarge an image as much as we want—for example, by projecting it onto a screen—it is not possible, in a conventional light microscope, to resolve two objects in the light microscope that are separated by less than about 0.2 μm; they will appear as a single object. It is important, however, to distinguish between resolution and detection. If a small object, below the resolution limit, itself emits light, then we may still be able to see or detect it. Thus, we can see a single fluorescently labeled microtubule even though it is about ten times thinner than the resolution limit of the light microscope. Diffraction effects, however, will cause it to appear blurred and at least 0.2 μm thick (see Figure 9–16). In a similar way, we can see the stars in the night sky, even though their diameters are far below the angular resolution of our unaided eyes: they all appear as similar, slightly blurred points of light, differing only in their color and brightness.
photon noise Creates additional Limits to resolution When Light Levels are Low
Any image, whether produced by an electron microscope or by an optical microscope, is made by particles—electrons or photons—striking a detector of some sort. But these particles are governed by quantum mechanics, so the numbers reaching the detector are predictable only in a statistical sense. Finite samples, collected by imaging for a limited period of time (that is, by taking a snapshot), will show random variation: successive snapshots of the same scene will not be exactly identical. Moreover, every detection method has some level of background signal or noise, adding to the statistical uncertainty. With bright illumination, corresponding to very large numbers of photons or electrons, the features of the imaged
Figure 9–4 Interference between light waves. When two light waves combine in phase, the amplitude of the resultant wave is larger and the brightness is increased. two light waves that are out of phase cancel each other partly and produce a wave whose amplitude, and therefore brightness, is decreased.
Figure 9–5 Images of an edge and of a point of light. (a) the interference effects, or fringes, seen at high magnification when light of a specific wavelength passes the edge of a solid object placed between the light source and the observer. (B) the image of a point source of light. Diffraction spreads this out into a complex, circular pattern, whose width depends on the numerical aperture of the optical system: the smaller the aperture, the bigger (more blurred) the diffracted image. two point sources can be just resolved when the center of the image of one lies on the first dark ring in the image of the other: this is used to define the limit of resolution.
Figure 9–6 Numerical aperture. the path of light rays passing through a transparent specimen in a microscope illustrates the concept of numerical aperture and its relation to the limit of resolution.