Absorption coefficient - Revision history

GervaisChapuis at 18:51, 24 October 2026

2026-10-24T18:51:59Z

← Older revision		Revision as of 18:51, 24 October 2026
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	The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{PE}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that		The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{PE}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that

	<math>I(t) = I_0 \exp({-\Big[{\mu\over\rho}\Big]\rho t})</math>		<center><math>I(t) = I_0 \exp({-\Big[{\mu\over\rho}\Big]\rho t})</math></center>

	where <math>t</math> is the thickness of a uniform sample and the density <math>\rho</math> is usually given in (g/cm<sup>3</sup>). The mass absorption coefficient is labeled as such because the absorption exponent is linear in the mass per unit area <math>\rho t</math>, otherwise known as the integrated column density through a sample. Use of <math>\mu</math> for this term is not recommended because it is highly ambiguous and dimensionally inconsistent. The subscript ''PE'' emphasizes that this is the photo-electric mass absorption coefficient rather than the [[mass attenuation coefficient]], which of course does not obey the Beer-Lambert law. Note also that it is rare for SI units to be used in texts on absorption spectroscopy.		where <math>t</math> is the thickness of a uniform sample and the density <math>\rho</math> is usually given in (g/cm<sup>3</sup>). The mass absorption coefficient is labeled as such because the absorption exponent is linear in the mass per unit area <math>\rho t</math>, otherwise known as the integrated column density through a sample. Use of <math>\mu</math> for this term is not recommended because it is highly ambiguous and dimensionally inconsistent. The subscript ''PE'' emphasizes that this is the photo-electric mass absorption coefficient rather than the [[mass attenuation coefficient]], which of course does not obey the Beer-Lambert law. Note also that it is rare for SI units to be used in texts on absorption spectroscopy.

BrianMcMahon: Tidied translations.

2017-11-08T17:35:15Z

Tidied translations.

← Older revision		Revision as of 17:35, 8 November 2017
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	<font color="orange">معامل الامتصاص</font> (''Ar''). <font color="blue">Coefficient d'abosrption</font> (''Fr''). <font color="red">Absorptionskoeffizient</font> (''Ge''). <font color="black">Coefficiente di assorbiment</font> (''It''). <font color="~~brown~~">~~Коэффициент поглощения~~</font> (''Ru''). <font color="~~purple~~">~~吸収係数~~</font> (''Ja''). <font color="green">Coeficiente de absorción</font> (''Sp'').		<font color="orange">معامل الامتصاص</font> (''Ar''). <font color="blue">Coefficient d'abosrption</font> (''Fr''). <font color="red">Absorptionskoeffizient</font> (''Ge''). <font color="black">Coefficiente di assorbiment</font> (''It''). <font color="purple">吸収係数</font> (''Ja''). <font color="brown">Коэффициент поглощения</font> (''Ru''). <font color="green">Coeficiente de absorción</font> (''Sp'').

	== Definition ==		== Definition ==

BrianMcMahon: Tidied translations.

2017-11-08T17:34:18Z

Tidied translations.

← Older revision		Revision as of 17:34, 8 November 2017
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	<font color="~~blue~~">~~Coefficient d'abosrption~~</font> (''Fr''); <font color="~~red~~">~~Absorptionskoeffizient~~</font> (''Ge''); <font color="~~green~~">~~Coeficiente de absorción~~</font> (''Sp''); <font color="black">Coefficiente di assorbiment</font> (''It''); <font color="brown">Коэффициент поглощения</font> (''Ru''); <font color="purple">吸収係数</font> (''Ja''); <font color="~~orange~~">~~معامل الامتصاص~~</font> (''Ar'').		<font color="orange">معامل الامتصاص</font> (''Ar''). <font color="blue">Coefficient d'abosrption</font> (''Fr''). <font color="red">Absorptionskoeffizient</font> (''Ge''). <font color="black">Coefficiente di assorbiment</font> (''It''). <font color="brown">Коэффициент поглощения</font> (''Ru''). <font color="purple">吸収係数</font> (''Ja''). <font color="green">Coeficiente de absorción</font> (''Sp'').

	== Definition ==		== Definition ==

MassimoNespolo: Languages

2017-09-14T09:10:19Z

Languages

← Older revision		Revision as of 09:10, 14 September 2017
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			<font color="blue">Coefficient d'abosrption</font> (''Fr''); <font color="red">Absorptionskoeffizient</font> (''Ge''); <font color="green">Coeficiente de absorción</font> (''Sp''); <font color="black">Coefficiente di assorbiment</font> (''It''); <font color="brown">Коэффициент поглощения</font> (''Ru''); <font color="purple">吸収係数</font> (''Ja''); <font color="orange">معامل الامتصاص</font> (''Ar'').

	== Definition ==		== Definition ==
	The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{PE}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that		The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{PE}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that

BrianMcMahon: Style edits to align with printed edition

2017-05-19T09:42:21Z

Style edits to align with printed edition

← Older revision		Revision as of 09:42, 19 May 2017
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	== Definition ==		== Definition ==
	The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{pe}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that		The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{PE}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that

	<math>I(t) = I_0 e^{-\Big[{\mu\over\rho}\Big]\rho t}</math>		<math>I(t) = I_0 \exp({-\Big[{\mu\over\rho}\Big]\rho t})</math>

	where<math>t</math> is the thickness of a uniform sample and the density <math>\rho</math> is usually given in (g/cm<sup>3</sup>). The mass absorption coefficient is labeled as such because the absorption exponent is linear in the mass per unit area <math>\rho t</math>, otherwise known as the integrated column density through a sample. Use of <math>\mu</math> for this term is not recommended because it is highly ambiguous and dimensionally inconsistent. The subscript ''pe'' emphasizes that this is the photo-electric mass absorption coefficient rather than the [[mass attenuation coefficient]] ~~(''q.v.'')~~, which of course does not obey the Beer-Lambert law. Note also that it is rare for SI units to be used in texts on absorption spectroscopy.		where <math>t</math> is the thickness of a uniform sample and the density <math>\rho</math> is usually given in (g/cm<sup>3</sup>). The mass absorption coefficient is labeled as such because the absorption exponent is linear in the mass per unit area <math>\rho t</math>, otherwise known as the integrated column density through a sample. Use of <math>\mu</math> for this term is not recommended because it is highly ambiguous and dimensionally inconsistent. The subscript ''PE'' emphasizes that this is the photo-electric mass absorption coefficient rather than the [[mass attenuation coefficient]], which of course does not obey the Beer-Lambert law. Note also that it is rare for SI units to be used in texts on absorption spectroscopy.

	The X-ray linear absorption coefficient, <math>\mu(E)</math> or <math>\mu_{pe}(E)</math> follows <math>I(t) = I_0 e^{-\mu t}</math>, with units of length<sup>-1</sup> (conventionally cm<sup>-1</sup>). <math>\mu</math> is the product of density <math>\rho</math> (g/cm<sup>3</sup>) and the mass absorption coefficient <math>\Big[{\mu\over\rho}\Big]</math> (cm<sup>2</sup>/g).		The X-ray linear absorption coefficient, <math>\mu(E)</math> or <math>\mu_{PE}(E)</math> follows <math>I(t) = I_0 \exp({-\mu t})</math>, with units of length<sup>−1</sup> (conventionally cm<sup>−1</sup>). <math>\mu</math> is the product of density <math>\rho</math> (g/cm<sup>3</sup>) and the mass absorption coefficient <math>\Big[{\mu\over\rho}\Big]</math> (cm<sup>2</sup>/g).

	It is sometimes convenient to describe the decrease in the beam intensity in terms of the absorption length: the thickness of the material in question at which the beam intensity has fallen to <math>(1/e)</math> of the incident beam intensity: that is when <math>\mu t=1</math>, or when 63% of the flux is absorbed. In soft X-ray spectroscopy one absorption length can be some tens of nm while typical values in hard X-ray spectroscopy are microns or millimetres.		It is sometimes convenient to describe the decrease in the beam intensity in terms of the absorption length: the thickness of the material in question at which the beam intensity has fallen to <math>(1/e)</math> of the incident beam intensity; that is, when <math>\mu t=1</math>, or when 63% of the flux is absorbed. In soft X-ray spectroscopy one absorption length can be some tens of nm while typical values in hard X-ray spectroscopy are microns or millimetres.

	<math>\mu</math> depends on energy, <math>E</math>, of the incoming photon and the elemental composition of the sample. The XAFS technique measures the variations in <math>\mu(E)</math>.		<math>\mu</math> depends on energy, <math>E</math>, of the incoming photon and the elemental composition of the sample. The XAFS technique measures the variations in <math>\mu(E)</math>.

	== Historical Note ==		== Historical Note ==
	Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert~~, 1729~~); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg~~, 1760~~); A. Beer~~, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'',~~ ''Annalen der Physik''. '''86''' (1852) pp. 78-87.		Early references are P. Bouguer (1729). ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert); J. H. Lambert (1760). ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg); A. Beer (1852). ''Annalen der Physik''. '''86''' (1852) pp. 78-87. ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten''.

	Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. ~~Johnston~~(2001), CRC Press] p18: ~~‘The~~ logarithm of the quantity of light received is inversely [meaning multiplied by <math>-1</math>] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.		Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [Johnston, S. F. (2001), CRC Press] p18: 'The logarithm of the quantity of light received is inversely [meaning multiplied by <math>-1</math>] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)'.

	== See also ==		== See also ==

BrianMcMahon at 16:29, 13 April 2016

2016-04-13T16:29:43Z

← Older revision		Revision as of 16:29, 13 April 2016
Line 18:		Line 18:

	== See also ==		== See also ==
	*[[~~linear~~ attenuation coefficient]]		*[[Linear attenuation coefficient]]
	*[[~~mass~~ attenuation coefficient]]		*[[Mass attenuation coefficient]]

	[[Category: X-ray absorption spectroscopy]]		[[Category: X-ray absorption spectroscopy]]

BrianMcMahon at 16:30, 12 April 2016

2016-04-12T16:30:15Z

← Older revision		Revision as of 16:30, 12 April 2016
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	Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert, 1729); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg, 1760); A. Beer, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'', ''Annalen der Physik''. '''86''' (1852) pp. 78-87.		Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert, 1729); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg, 1760); A. Beer, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'', ''Annalen der Physik''. '''86''' (1852) pp. 78-87.

	Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. Johnston(2001), ~~Bristol: Institute of Physics~~] p18: ‘The logarithm of the quantity of light received is inversely [meaning multiplied by <math>-1</math>] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.		Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. Johnston(2001), CRC Press] p18: ‘The logarithm of the quantity of light received is inversely [meaning multiplied by <math>-1</math>] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.

	== See also ==		== See also ==

BrianMcMahon at 16:25, 12 April 2016

2016-04-12T16:25:25Z

← Older revision		Revision as of 16:25, 12 April 2016
Line 15:		Line 15:
	Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert, 1729); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg, 1760); A. Beer, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'', ''Annalen der Physik''. '''86''' (1852) pp. 78-87.		Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert, 1729); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg, 1760); A. Beer, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'', ''Annalen der Physik''. '''86''' (1852) pp. 78-87.

	Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. Johnston(2001), Bristol: Institute of Physics] p18: ‘The logarithm of the quantity of light received is inversely [meaning multiplied by -1] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.		Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. Johnston(2001), Bristol: Institute of Physics] p18: ‘The logarithm of the quantity of light received is inversely [meaning multiplied by <math>-1</math>] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.

	== See also ==		== See also ==

BrianMcMahon: Created page with "== Definition == The X-ray mass absorption coefficient, $\Big[{\mu\over\rho}\Big](E)$ or $\Big[{\mu\over\rho}\Big]_{pe}(E)$ follows the Beer-Lambert law for..."

2016-04-12T16:15:45Z

Created page with "== Definition == The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{pe}(E)</math> follows the Beer-Lambert law for..."

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== Definition ==
The X-ray mass absorption coefficient, <math>\Big[{\mu\over\rho}\Big](E)</math> or <math>\Big[{\mu\over\rho}\Big]_{pe}(E)</math> follows the Beer-Lambert law for a parallel beam of photons of energy <math>E</math> in which the transmitted photon intensity <math>I(t)</math> is related to the incoming photon intensity <math>I_0</math> such that

<math>I(t) = I_0 e^{-\Big[{\mu\over\rho}\Big]\rho t}</math>

where<math>t</math> is the thickness of a uniform sample and the density <math>\rho</math> is usually given in (g/cm3). The mass absorption coefficient is labeled as such because the absorption exponent is linear in the mass per unit area <math>\rho t</math>, otherwise known as the integrated column density through a sample. Use of <math>\mu</math> for this term is not recommended because it is highly ambiguous and dimensionally inconsistent. The subscript ''pe'' emphasizes that this is the photo-electric mass absorption coefficient rather than the [[mass attenuation coefficient]] (''q.v.''), which of course does not obey the Beer-Lambert law. Note also that it is rare for SI units to be used in texts on absorption spectroscopy.

The X-ray linear absorption coefficient, <math>\mu(E)</math> or <math>\mu_{pe}(E)</math> follows <math>I(t) = I_0 e^{-\mu t}</math>, with units of length-1 (conventionally cm-1). <math>\mu</math> is the product of density <math>\rho</math> (g/cm3) and the mass absorption coefficient <math>\Big[{\mu\over\rho}\Big]</math> (cm2/g).

It is sometimes convenient to describe the decrease in the beam intensity in terms of the absorption length: the thickness of the material in question at which the beam intensity has fallen to <math>(1/e)</math> of the incident beam intensity: that is when <math>\mu t=1</math>, or when 63% of the flux is absorbed. In soft X-ray spectroscopy one absorption length can be some tens of nm while typical values in hard X-ray spectroscopy are microns or millimetres.

<math>\mu</math> depends on energy, <math>E</math>, of the incoming photon and the elemental composition of the sample. The XAFS technique measures the variations in <math>\mu(E)</math>.

== Historical Note ==
Early references are P. Bouguer, ''Essai d’Optique sur la Graduation de la Lumière'' (Paris, Jombert, 1729); J. H. Lambert, ''Photometria sive Mensura et Gradibus Luminus, Colorum et Umbrae'' (Augsburg, 1760); A. Beer, ''Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten'', ''Annalen der Physik''. '''86''' (1852) pp. 78-87.

Note that all these preceded the discovery of X-rays, and were based on visible optics. From ''A History of Light and Colour Measurement'' [S. F. Johnston(2001), Bristol: Institute of Physics] p18: ‘The logarithm of the quantity of light received is inversely [meaning multiplied by -1] proportional to the thickness (Bouguer’s Law) and to the chemical composition (Beer’s Law) of an absorbing material, and the quantity of light to the cosine of the angle of incidence of the illuminated sample (Lambert’s Law)’.

== See also ==
*[[linear attenuation coefficient]]
*[[mass attenuation coefficient]]

[[Category: X-ray absorption spectroscopy]]

Absorption coefficient - Revision history

GervaisChapuis at 18:51, 24 October 2026

BrianMcMahon: Tidied translations.

BrianMcMahon: Tidied translations.

MassimoNespolo: Languages

BrianMcMahon: Style edits to align with printed edition

BrianMcMahon at 16:29, 13 April 2016

BrianMcMahon at 16:30, 12 April 2016

BrianMcMahon at 16:25, 12 April 2016

BrianMcMahon: Created page with "== Definition == The X-ray mass absorption coefficient, \Big[{\mu\over\rho}\Big](E) or \Big[{\mu\over\rho}\Big]_{pe}(E) follows the Beer-Lambert law for..."

BrianMcMahon: Created page with "== Definition == The X-ray mass absorption coefficient, $\Big[{\mu\over\rho}\Big](E)$ or $\Big[{\mu\over\rho}\Big]_{pe}(E)$ follows the Beer-Lambert law for..."