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In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no ...
Memorial in Jena, Germany to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as = , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture).
The near-field optical (NFO) microscope involved a sub-wavelength aperture at the apex of a metal coated sharply pointed transparent tip, and a feedback mechanism to maintain a constant distance of a few nanometers between the sample and the probe. Lewis et al. were also aware of the potential of an NFO microscope at this time. [14]
It is NA that determines optical resolution, in combination with the NA of the objective. Different condensers vary in their maximum and minimum numerical aperture, and the numerical aperture of a single condenser varies depending on the diameter setting of the condenser aperture. In order for the maximum numerical aperture (and therefore ...
State of the art objectives can have a numerical aperture of up to 0.95. Because sin α 0 is always less than or equal to unity (the number "1"), the numerical aperture can never be greater than unity for an objective lens in air. If the space between the objective lens and the specimen is filled with oil however, the numerical aperture can ...
where D is the diffraction limit, λ is the wavelength of the light, and NA is the numerical aperture, or the refractive index of the medium multiplied by the sine of the angle of incidence. n describes the refractive index of the specimen, α measures the solid half‐angle from which light is gathered by an objective, λ is the wavelength of ...
The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality of the system.
Ball lenses are often used in fiber optics. Due to their short focal lengths and the subsequently small waist diameters they produce in a laser beam, they are ideally suited to focus nearly all of the light from a laser into an optical fiber core. The numerical apertures of the fiber and lens need to match. The fiber can usually be placed in ...