If A Microscopes Resolution Is Limited By The Wavelength Of The Light It Uses, ?
The numerical aperture (NA) is related to the refractive index (n) of a medium through which light passes as well as the angular aperture (α) of a given objective (NA = n sinα). The resolution of an optical microscope is not solely dependent on the NA of an objective, but the NA of the whole system, taking into account the NA of the microscope condenser. More image detail will be resolved in a microscope system in which all of the optical components are correctly aligned, have a relatively high NA value and are working harmoniously with each other. Resolution is also related to the wavelength of light which is used to image a specimen; light of shorter wavelengths are capable of resolving greater detail than longer wavelengths.
If a microscope’s resolution is limited by the wavelength of the light it uses, …
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An Airy disc is the optimally focused point of light which can be determined by a circular aperture in a perfectly aligned system limited by diffraction. Viewed from above (Figure 1), this appears as a bright point of light around which are concentric rings or ripples (more correctly known as an Airy Pattern).
In order to increase the resolution, d = λ/(2NA), the specimen must be viewed using either a shorter wavelength (λ) of light or through an imaging medium with a relatively high refractive index or with optical components which have a high NA (or, indeed, a combination of all of these factors).
However, even taking all of these factors into consideration, the possibilities with a real microscope are still somewhat limited due to the complexity of the whole system, transmission characteristics of glass at wavelengths below 400 nm, and the challenge to achieve a high NA in the complete microscope system. Lateral resolution in an ideal optical microscope is limited to around 200 nm, whereas axial resolution is around 500 nm (examples of resolution limits are given below).
These theoretical resolution values, derived from physical and mathematical assumptions, are estimates. They assume perfect imaging systems and a point light source in a vacuum or a completely homogeneous material as the sample or specimen. Of course, this assumption is almost never the case in real life, as many samples or specimens are heterogeneous. Because there is only a finite amount of light transmitting through the sample or reflecting from its surface, the measurable resolution depends significantly on the signal-to-noise ratio (SNR).
As already mentioned, the FWHM can be measured directly from the PSF or calculated using: RFWHM = 0.51λ/(NA). Again using a light wavelength of 514 nm and an objective with an NA of 1.45, then theoretical resolution will be 181 nm. This value is very close to the lateral resolution calculated just above from the Abbe diffraction limit.
As stated above, the shorter the wavelength of light used to image a specimen, then the more the fine details are resolved. So, if using the shortest wavelength of visible light, 400 nm, with an oil-immersion objective having an NA of 1.45 and a condenser with an NA of 0.95, then R would equal 203 nm.
To achieve the maximum theoretical resolution of a microscope system, each of the optical components should be of the highest NA available (taking into consideration the angular aperture). In addition, using a shorter wavelength of light to view the specimen will increase the resolution. Finally, the whole microscope system should be correctly aligned.
The optical microscope has played a central role in helping to untangle the complex mysteries of biology ever since the seventeenth century when Dutch inventor Antoni van Leeuwenhoek and English scientist Robert Hooke first reported observations using single-lens and compound microscopes, respectively. Over the past three centuries, a vast number of technological developments and manufacturing breakthroughs have led to significantly advanced microscope designs featuring dramatically improved image quality with minimal aberration. However, despite the computer-aided optical design and automated grinding methodology utilized to fabricate modern lens components, glass-based microscopes are still hampered by an ultimate limit in optical resolution that is imposed by the diffraction of visible light wavefronts as they pass through the circular aperture at the rear focal plane of the objective. As a result, the highest achievable point-to-point resolution that can be obtained with an optical microscope is governed by a fundamental set of physical laws that cannot be easily overcome by rational alternations in objective lens or aperture design. These resolution limitations are often referred to as the diffraction barrier, which restricts the ability of optical instruments to distinguish between two objects separated by a lateral distance less than approximately half the wavelength of light used to image the specimen.
The process of diffraction involves the spreading of light waves when they interact with the intricate structures that compose a typical specimen. Due to the fact that most specimens observed in the microscope are composed of highly overlapping features that are best represented by multiple point sources of light, discussions of the microscope diffraction barrier center on describing the passage of wavefronts representing a single point source of light through the various optical elements and aperture diaphragms. As will be discussed below, the transmitted light or fluorescence emission wavefronts emanating from a point in the specimen plane of the microscope become diffracted at the edges of the objective aperture, effectively spreading the wavefronts to produce an image of the point source that is broadened into a diffraction pattern having a central disk of finite, but larger size than the original point. Therefore, due to diffraction of light, the image of a specimen never perfectly represents the real details present in the specimen because there is a lower limit below which the microscope optical system cannot resolve structural details.
Both interference and diffraction, which are actually manifestations of the same process, are responsible for creating a real image of the specimen at the intermediate image plane in a microscope. In brief, interference between two wavefronts occurs with addition to double the amplitude if the waves are perfectly in phase (constructive interference), but the waves cancel each other completely when out of phase by 180 degrees (termed destructiveinterference; however, most interference occurs somewhere in between). The photon energy inherent in a light wave is not itself doubled or annihilated when two waves interfere; rather this energy is channeled during diffraction and interference in directions that permit constructive interference. Therefore, interference and diffraction should be considered as phenomena involving the redistribution of light waves and photon energy.
A point object in a microscope, such as a fluorescent protein single molecule, generates an image at the intermediate plane that consists of a diffraction pattern created by the action of interference. When highly magnified, the diffraction pattern of the point object is observed to consist of a central spot (diffraction disk) surrounded by a series of diffraction rings (see Figure 1). In the nomenclature associated with diffraction theory, the bright central region is referred to as the zeroth-order diffraction spot while the rings are called the first, second, third, etc., order diffraction rings. When the microscope is properly focused, the intensity of light at the minima between the rings is zero. Combined, this point source diffraction pattern is referred to as an Airy disk (after Sir George B. Airy, a nineteenth century English astronomer). The size of the central spot in the Airy pattern is related to the wavelength of light and the aperture angle of the objective. For a microscope objective, the aperture angle is described by the numerical aperture (NA), which includes the term sin θ, the half angle over which the objective can gather light from the specimen. In terms of resolution, the radius of the diffraction Airy disk in the lateral (x,y) image plane is defined by the following formula:
According to Abbe's theory, images are composed from an array of diffraction-limited spots having varying intensity that overlap to produce the final result, as described above. Thus, the only mechanism for optimizing spatial resolution and image contrast is to minimize the size of the diffraction-limited spots by decreasing the imaging wavelength, increasing numerical aperture, or using an imaging medium having a larger refractive index. However, under ideal conditions with the most powerful objectives, lateral resolution is still limited to relatively modest levels approaching 200 to 250 nanometers (see Equation (1)) due to transmission characterics of glass at wavelengths beneath 400 nanometers and the physical constraints on numerical aperture. In contrast, the axial dimension of the Airy disk forms an elliptical pattern that often referred to as the point-spread function (PSF). The elongated geometry of the point-spread function along the optical axis arises from the nature of the non-symmetrical wavefront that emerges from the microscope objective. Axial resolution in optical microscopy is even worse than lateral resolution (as outlined in Equation (2)), on the order of 500 nanometers. When attempting to image highly convoluted features, such as cellular organelles, diffraction-limited resolution is manifested as poor axial sectioning capability and lowered contrast in the imaging plane. Furthermore, overall specimen contrast achieved in three-dimensional specimens is generally dominated by the relatively poor axial resolution that occurs due to out-of-focus light interference with the point-spread function.