Resolution - resolving power

Japanese: 分解能 - ぶんかいのう（英語表記）resolving power

The ability to separate and distinguish two points or lines that are close together. In a telescope, the objective lens has a finite size, so the bundle of light rays is limited, and the image of a point or line becomes blurred and spreads due to the phenomenon of light diffraction. As a result, when two points or lines get closer than a certain point, the image becomes a single peak instead of two peaks, and they cannot be separated. Resolution is given as θ = 1.22(λ/ D ) (λ is the wavelength of light , D is the diameter of the objective lens), where θ (radian) is the limit angle at which two points (lines) at infinity can be separated, as shown in the figure. In a microscope, in order for the image to reproduce the structure of an object, it is necessary for the light diffracted by the object (first-order diffracted light) to enter the objective lens, and from this condition, resolution is given as d = λ/ NA , where d is the minimum distance that can be separated. Here, NA is a quantity called the numerical aperture, and NA = n sinθ, where 2θ is the spread of light entering the objective lens from an object on the optical axis, and n is the refractive index of the medium between the object and the objective lens. The resolution of a normal eye is approximately 1' for two points and 10" for two lines, in terms of visual angle.

The resolution of a spectrometer is the ability to separate two spectral lines with wavelengths λ and λ + Δ λ, and is given by λ/ Δ λ. In prism and grating spectrometers, the finite size of the prism or grating limits the resolution due to broadening of the spectral lines caused by diffraction, and is given by h Δ n / Δ λ ( h is the length of the base of the prism, and Δ n / Δ λ is the change in the refractive index n of the prism material with wavelength λ, i.e., dispersion) in the former and mN ( m is the order of diffraction, and N is the number of grating lines) in the latter.

[Tanaka Shunichi]

[Reference item] | Spectrometer

Resolution (figure)
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Resolution (figure)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

接近した二つの点や線を分離して見分ける能力。望遠鏡では対物レンズが有限の大きさであるので光線束が制限され、光の回折現象によって点や線の像がぼけて広がる。この結果、二つの点や線がある程度以上接近すると、像は二つの山でなく一つの山になってしまって分離できなくなる。分解能は図のように無限遠の2点（2線）が分離できる極限の角度をθ（ラジアン）としてθ=1.22(λ/D)（λは光の波長、Dは対物レンズの直径）で与えられる。顕微鏡では、像が物体の構造を再現するためには、物体で回折した光（一次回折光）が対物レンズに入射することが必要で、この条件から分解能は、分離できる最小の距離をdとしてd=λ/NAで与えられる。ここでNAは開口数とよばれる量で、光軸上の物体から対物レンズに入射する光の広がりを2θ、物体と対物レンズの間の媒質の屈折率をnとしたときNA=nsinθである。正常な目の分解能は、視角でいって、2点のとき1′、2線のとき10″程度である。

　分光器の分解能は、接近した波長λとλ+Δλの2本のスペクトル線を分離する能力で表され、λ/Δλで与えられる。プリズム分光器や回折格子分光器では、プリズムや回折格子の大きさが有限であることから、回折によるスペクトル線の広がりが生じて分解能が制限され、前者ではhΔn/Δλ（hはプリズム底辺の長さ、Δn/Δλはプリズム材料の屈折率nの波長λによる変化、すなわち分散）、後者ではmN（mは回折の次数、Nは格子線の本数）で与えられる。