Введение
Свойство дисперсии материала
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
В оптике и проектировании линз число Аббе, также известное как число V или констрингенция прозрачного материала, является приблизительной мерой дисперсии материала (изменение показателя преломления в зависимости от длины волны), при этом высокие значения V указывают на низкую дисперсию. Оно названо в честь Эрнста Аббе (1840–1905), немецкого физика, который его определил. Термин «число V» не следует путать с нормированной частотой в волокнах. Число Аббе материала определяется как
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
,
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
где и – показатели преломления материала на длинах волн спектральных линий Фраунгофера C, d и F (656,3 нм, 587,56 нм и 486,1 нм соответственно). Эта формулировка применима только к человеческому зрению. За пределами этого диапазона требуется использование других спектральных линий. Для невидимых спектральных линий термин «число V» используется чаще. Более общая формулировка определяется как
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
,
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
где и – показатели преломления материала при трех различных длинах волн. Показатель преломления для самой короткой длины волны – , а для самой длинной – .
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
Числа Аббе используются для классификации стекла и других оптических материалов по их хроматичности. Например, стекла с высокой дисперсией (флинты) имеют относительно небольшие числа Аббе, в то время как стекла с низкой дисперсией (кроны) имеют большие числа Аббе. Значения варьируются от менее 25 для очень плотных флинтов, около 34 для поликарбонатных пластиков, до 65 для обычных крон и от 75 до 85 для некоторых фтористых и фосфатных крон. Числа Аббе используются при проектировании ахроматических линз, поскольку их величина, обратная дисперсии (наклон показателя преломления в зависимости от длины волны), пропорциональна дисперсии в области длины волны, где человеческий глаз наиболее чувствителен (см. график). Для различных диапазонов длин волн или для более точной характеристики хроматичности системы (например, при проектировании апохроматических линз) используется полное соотношение дисперсии (зависимость показателя преломления от длины волны).
Material dispersion property
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
In optics and lens design, the Abbe number, also known as the V number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V number should not be confused with the normalized frequency in fibers. The Abbe number, of a material is defined as
,
where and are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non visible spectral lines the term "V number" is more commonly used. The more general formulation defined as,
,
where and are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is , and the longest's is
Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers whereas the lower dispersion crown glasses have larger Abbe numbers. Values of range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.
Диаграмма Аббе
Диаграмма Аббе, также называемая «стеклянной завесой», строится путем нанесения числа Аббе материала на график в зависимости от его показателя преломления. Стекла затем можно классифицировать и выбирать в соответствии с их положением на диаграмме. Это может быть буквенно-цифровой код, как в каталоге Schott Glass, или 6-значный код стекла. Числа Аббе стекол, наряду с их средними показателями преломления, используются при расчете требуемых рефракционных сил элементов ахроматических линз для компенсации хроматической аберрации первого порядка. Именно эти два параметра, входящие в уравнения для проектирования ахроматических дублетов, отображаются на диаграмме Аббе. В связи с трудностями и неудобствами при получении натриевых и водородных линий часто используются альтернативные определения числа Аббе (ISO 7944). Например, вместо стандартного определения, приведенного выше, которое использует изменение показателя преломления между водородными линиями F и C, одна альтернативная мера использует индекс «e» для e-линии ртути по сравнению с линиями F′ и C′ кадмия. Эта альтернатива берет разность между синим (C′) и красным (F′) показателями преломления кадмия при длинах волн 480,0 нм и 643,8 нм относительно для e-линии ртути при 546,073 нм, все из которых расположены близко друг к другу и несколько легче в получении, чем линии C, F и e. Могут использоваться и другие определения; в следующей таблице перечислены стандартные длины волн, при которых обычно определяется , включая стандартные индексы. λ(нм) Символ Фраунгофера Источник света Цвет 365,01 i Hg УФ A 404,66 h Hg фиолетовый 435,84 g Hg синий 479,99 F′ Cd синий 486,13 F H синий 546,07 e Hg зеленый 587,56 d He желтый 589,3 D Na желтый 643,85 C′ Cd красный 656,27 C H красный 706,52 r He красный 768,2 A′ K ИК A 852,11 s Cs ИК A 1013,98 t Hg ИК A
An Abbe diagram, also called 'the glass veil', is produced by plotting the Abbe number of a material versus its refractive index Glasses can then be categorised and selected according to their positions on the diagram. This can be a letter number code, as used in the Schott Glass catalogue, or a 6 digit glass code. Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required refractive powers of the elements of achromatic lenses in order to cancel chromatic aberration to first order. These two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe diagram. Due to the difficulty and inconvenience in producing sodium and hydrogen lines, alternate definitions of the Abbe number are often substituted (ISO 7944). For example, rather than the standard definition given above, that uses the refractive index variation between the F and C hydrogen lines, one alternative measure using the subscript "e" for mercury's e line compared to cadmium's F′ and C′ lines is
This alternate takes the difference between cadmium's blue (C′) and red (F′) refractive indices at wavelengths 480.0 nm and 643.8 nm, relative to for mercury's e line at 546.073 nm, all of which are close by, and somewhat easier to produce than the C, F, and e lines. Other definitions can similarly be employed; the following table lists standard wavelengths at which is commonly determined, including the standard subscripts used. λ(nm) Fraunhofer’ssymbol Lightsource Color 365.01 i Hg UV A 404.66 h Hg violet 435.84 g Hg blue 479.99 F′ Cd blue 486.13 F H blue 546.07 e Hg green 587.56 d He yellow 589.3 D Na yellow 643.85 C′ Cd red 656.27 C H red 706.52 r He red 768.2 A′ K IR A 852.11 s Cs IR A 1013.98 t Hg IR A
This alternate takes the difference between cadmium's blue (C′) and red (F′) refractive indices at wavelengths 480.0 nm and 643.8 nm, relative to for mercury's e line at 546.073 nm, all of which are close by, and somewhat easier to produce than the C, F, and e lines. Other definitions can similarly be employed; the following table lists standard wavelengths at which is commonly determined, including the standard subscripts used. λ(nm) Fraunhofer’ssymbol Lightsource Color 365.01 i Hg UV A 404.66 h Hg violet 435.84 g Hg blue 479.99 F′ Cd blue 486.13 F H blue 546.07 e Hg green 587.56 d He yellow 589.3 D Na yellow 643.85 C′ Cd red 656.27 C H red 706.52 r He red 768.2 A′ K IR A 852.11 s Cs IR A 1013.98 t Hg IR A