Transmittance

Transmittance
Transmittance
Dimension	dimensionless
Notes
	scalar value

The transmittance coefficient is a dimensionless physical quantity equal to the ratio of the radiation flux $\Phi$ ${\ displaystyle \ Phi}$ $\ Phi$ passed through the medium to the radiation flux $\Phi _{0}$ ${\ displaystyle \ Phi _ {0}}$ $\ Phi _ {0}$ that fell on its surface ^[1] :

An example of the transmission spectrum of a ruby single crystal 1 cm thick in the visible and near infrared parts of the spectrum. The figure shows absorption bands in the blue and green parts of the spectrum and a narrow absorption line at a wavelength of 694 nm — the wavelength of a ruby laser.

T={\frac {\Phi }{\Phi _{0}}}.

{\ displaystyle T = {\ frac {\ Phi} {\ Phi _ {0}}}.}

T = {\ frac {\ Phi} {\ Phi _ {0}}}.

In general, the transmittance value $T$ ${\ displaystyle T}$ $T$ ^{[2] of the} body depends both on the properties of the body itself and on the angle of incidence, spectral composition and polarization of the radiation.

Numerical transmittance is expressed in shares or as a percentage.

The transmittance of inactive media is always less than 1. In active media, the transmittance is greater than or equal to 1; as radiation passes through such media, it is amplified. Active media are used as laser working media ^[3] ^[4] ^[5] ^[6] .

The transmittance is related to optical density. $D$ ${\ displaystyle D}$ $D$ ratio:

T=10^{-D}.

{\ displaystyle T = 10 ^ {- D}.}

T = 10 ^ {{- D}}.

The sum of the transmittance and the coefficients of reflection , absorption and scattering is equal to unity. This statement follows from the law of conservation of energy .

Content

Derivative, related and related concepts

Together with the concept of "transmittance" are widely used and other concepts based on it. Some of them are presented below.

Directional transmittance $T_{r}$ ${\ displaystyle T_ {r}}$

The coefficient of directional transmission is equal to the ratio of the radiation flux transmitted through the medium, without scattering, to the flux of incident radiation.

Diffuse transmittance $T_{d}$ ${\ displaystyle T_ {d}}$

The diffuse transmittance is equal to the ratio of the flux transmitted through the medium and scattered by it to the flux of incident radiation.

In the absence of absorption and reflections, the relationship is:

T=T_{r}+T_{d}.

{\ displaystyle T = T_ {r} + T_ {d}.}

Spectral transmittance $T_{\lambda }$ ${\ displaystyle T _ {\ lambda}}$

The transmittance of monochromatic radiation is called spectral transmittance. The expression for it is:

T_{\lambda }={\frac {\Phi _{\lambda }}{\Phi _{\lambda 0}}},

{\ displaystyle T _ {\ lambda} = {\ frac {\ Phi _ {\ lambda}} {\ Phi _ {\ lambda 0}}},}

Where $\Phi _{\lambda 0}$ ${\ displaystyle \ Phi _ {\ lambda 0}}$ and $\Phi _{\lambda }$ ${\ displaystyle \ Phi _ {\ lambda}}$ - streams of monochromatic radiation incident on the medium and transmitted through it, respectively.

Internal transmittance $T_{i}$ ${\ displaystyle T_ {i}}$

The internal transmittance reflects only those changes in the radiation intensity that occur inside the medium, that is, the losses due to reflections on the input and output surfaces of the medium are not taken into account.

Thus, by definition:

T_{i}={\frac {\Phi _{out}}{\Phi _{in}}},

{\ displaystyle T_ {i} = {\ frac {\ Phi _ {out}} {\ Phi _ {in}}},}

Where

\Phi _{in}

{\ displaystyle \ Phi _ {in}}

- the flux of radiation entering the medium, and

\Phi _{out}

{\ displaystyle \ Phi _ {out}}

- radiation flux reaching the output surface.

Taking into account the reflection of radiation on the input surface, the ratio between the radiation flux $\Phi _{in}$ ${\ displaystyle \ Phi _ {in}}$ entered environment and radiation flux $\Phi _{0}$ ${\ displaystyle \ Phi _ {0}}$ falling on the entrance surface has the form:

\Phi _{in}=(1-R_{in})\Phi _{0},

{\ displaystyle \ Phi _ {in} = (1-R_ {in}) \ Phi _ {0},}

Where

R_{in}

{\ displaystyle R_ {in}}

- reflection coefficient from the input surface.

Reflection also occurs on the output surface, so the radiation flux $\Phi _{out}$ ${\ displaystyle \ Phi _ {out}}$ falling on this surface and flow $\Phi$ ${\ displaystyle \ Phi}$ leaving the environment are related by the relation:

\Phi =(1-R_{out})\Phi _{out},

{\ displaystyle \ Phi = (1-R_ {out}) \ Phi _ {out},}

Where

R_{out}

{\ displaystyle R_ {out}}

- reflection coefficient from the output surface. Accordingly, it is performed:

\Phi _{out}={\frac {\Phi }{(1-R_{out})}}.

{\ displaystyle \ Phi _ {out} = {\ frac {\ Phi} {(1-R_ {out})}}.}

As a result, for communication $T_{i}$ ${\ displaystyle T_ {i}}$ and $T$ ${\ displaystyle T}$ it turns out:

T_{i}={\frac {T}{(1-R_{in})(1-R_{out})}}.

{\ displaystyle T_ {i} = {\ frac {T} {(1-R_ {in}) (1-R_ {out})}}.}

The internal transmittance is usually used not in describing the properties of bodies as such, but as a characteristic of materials, mainly optical ^[7] .

Spectral internal transmittance $T_{i,\lambda }$ ${\ displaystyle T_ {i, \ lambda}}$

The spectral internal transmittance is the internal transmittance for monochromatic light.

Integral internal transmittance $T_{A}$ ${\ displaystyle T_ {A}}$

Integral internal transmittance $T_{A}$ ${\ displaystyle T_ {A}}$ for white light of a standard source A (with correlated color temperature of radiation T = 2856 K) is calculated by the formula ^[7] ^[8] :

T_{A}={\frac {\int \limits _{380}^{760}\Phi _{in,\lambda }(\lambda )V(\lambda )T_{i,\lambda }(\lambda )d\lambda }{\int \limits _{380}^{760}\Phi _{in,\lambda }(\lambda )V(\lambda )d\lambda }},

{\ displaystyle T_ {A} = {\ frac {\ int \ limits _ {380} ^ {760} \ Phi _ {in, \ lambda} (\ lambda) V (\ lambda) T_ {i, \ lambda} ( \ lambda) d \ lambda} {\ int \ limits _ {380} ^ {760} \ Phi _ {in, \ lambda} (\ lambda) V (\ lambda) d \ lambda}},}

or following from it:

T_{A}={\frac {\int \limits _{380}^{760}\Phi _{out,\lambda }(\lambda )V(\lambda )d\lambda }{\int \limits _{380}^{760}\Phi _{in,\lambda }(\lambda )V(\lambda )d\lambda }},

{\ displaystyle T_ {A} = {\ frac {\ int \ limits _ {380} ^ {760} \ Phi _ {out, \ lambda} (\ lambda) v (\ lambda) d \ lambda} {\ int \ limits _ {380} ^ {760} \ Phi _ {in, \ lambda} (\ lambda) V (\ lambda) d \ lambda}},}

Where

\Phi _{in,\lambda }(\lambda )

{\ displaystyle \ Phi _ {in, \ lambda} (\ lambda)}

- spectral density of the radiation flux entering the medium,

\Phi _{out,\lambda }(\lambda )

{\ displaystyle \ Phi _ {out, \ lambda} (\ lambda)}

- spectral density of the radiation flux reaching the output surface, and

V(\lambda )

{\ displaystyle V (\ lambda)}

- relative spectral light efficiency of monochromatic radiation for day vision ^[9] .

The integral transmittances for other light sources are determined in a similar way.

The integral internal transmittance characterizes the ability of a material to transmit light perceived by the human eye, and is therefore an important characteristic of optical materials ^[7] .

Transmission Spectrum

The transmission spectrum is the dependence of the transmission coefficient on the wavelength or frequency (wavenumber, quantum energy, etc.) of the radiation. For light, such spectra are also called light transmission spectra.

The transmission spectra are the primary experimental material obtained in studies performed by absorption spectroscopy methods. Such spectra are also of independent interest, for example, as one of the main characteristics of optical materials ^[10] .

Notes

↑ Transmission coefficient // Physical encyclopedia / Ch. ed. A. M. Prokhorov . - M .: Great Russian Encyclopedia , 1994. - T. 4. - P. 149. - 704 p. - 40 000 copies - ISBN 5-85270-087-8 .
↑ Designations correspond to those recommended in GOST 26148-84. Greek is also allowed. $\tau .$ ${\ displaystyle \ tau.}$
↑ INTERSTATE STANDARD. LASERS AND MANAGEMENT DEVICES FOR LASER RADIATION. Terms and Definitions. [one]
↑ Handbook of lasers. Per. from English by ed. A. M. Prokhorov, t. 1-2, M .: 1978.
↑ Zvelto O. Physics of lasers. Per. from English, 2 ed., M .: 1984.
↑ Karlov N.V. Lectures on quantum electronics. M .: 1983. M.N. Andreeva.
↑ ¹ ² ³ Colorless optical glass of the USSR. Catalog. Ed. Petrovsky G. T. - M: House of Optics, 1990. - 131 p. - 3000 copies
↑ Zverev V. A., Krivopustova E. V., Tochilina T. V. Optical materials. Part 1 . - St. Petersburg: ITMO, 2009. - p. 95. - 244 p.
↑ GOST 8.332-78. Light measurements. The values of the relative spectral luminous efficiency of monochromatic radiation for daytime vision. - M: Publishing house of standards, 1979. - 6 p. - 2000 copies
↑ Colored optical glass and special glass. Catalog. Ed. Petrovsky G. T. - M: House of Optics, 1990. - 229 p. - 1500 copies

Literature

GOST 26148—84. Photometry. Terms and Definitions. . - M .: Publishing house of standards, 1984. - 24 p.

GOST 7601-78. Physical optics. Terms, letter designations and definitions of basic quantities . - M .: Standards Publishing House, 1999. - 16 p.

Physical encyclopedic dictionary. - M: Soviet encyclopedia, 1984. - p. 590.

Physical Encyclopedia. - M: The Great Russian Encyclopedia, 1992. - T. 4. - P. 149. - ISBN 5-85270-087-8 ..

[1] Transmission coefficient // Physical encyclopedia / Ch. ed. A. M. Prokhorov . - M .: Great Russian Encyclopedia , 1994. - T. 4. - P. 149. - 704 p. - 40 000 copies - ISBN 5-85270-087-8 .

[ГОСТ-2] Designations correspond to those recommended in GOST 26148-84. Greek is also allowed. $\tau .$ ${\ displaystyle \ tau.}$

[3] INTERSTATE STANDARD. LASERS AND MANAGEMENT DEVICES FOR LASER RADIATION. Terms and Definitions. [one]

[4] Handbook of lasers. Per. from English by ed. A. M. Prokhorov, t. 1-2, M .: 1978.

[5] Zvelto O. Physics of lasers. Per. from English, 2 ed., M .: 1984.

[6] Karlov N.V. Lectures on quantum electronics. M .: 1983. M.N. Andreeva.

[Каталог-7] ¹ ² ³ Colorless optical glass of the USSR. Catalog. Ed. Petrovsky G. T. - M: House of Optics, 1990. - 131 p. - 3000 copies

[8] Zverev V. A., Krivopustova E. V., Tochilina T. V. Optical materials. Part 1 . - St. Petersburg: ITMO, 2009. - p. 95. - 244 p.

[9] GOST 8.332-78. Light measurements. The values of the relative spectral luminous efficiency of monochromatic radiation for daytime vision. - M: Publishing house of standards, 1979. - 6 p. - 2000 copies

[10] Colored optical glass and special glass. Catalog. Ed. Petrovsky G. T. - M: House of Optics, 1990. - 229 p. - 1500 copies

Transmittance

Content

Derivative, related and related concepts

Directional transmittance $T_{r}$ ${\ displaystyle T_ {r}}$

Diffuse transmittance $T_{d}$ ${\ displaystyle T_ {d}}$

Spectral transmittance $T_{\lambda }$ ${\ displaystyle T _ {\ lambda}}$

Internal transmittance $T_{i}$ ${\ displaystyle T_ {i}}$

Spectral internal transmittance $T_{i,\lambda }$ ${\ displaystyle T_ {i, \ lambda}}$

Integral internal transmittance $T_{A}$ ${\ displaystyle T_ {A}}$

Transmission Spectrum

See also

Notes

Literature

More articles:

Transmittance
$T,\tau$ ${\ displaystyle T, \ tau}$ $T, \ tau$
Dimension	dimensionless
Notes
scalar value

Transmittance

Content

Derivative, related and related concepts

Directional transmittanceTr {\ displaystyle T_ {r}}

Diffuse transmittanceTd {\ displaystyle T_ {d}}

Spectral transmittanceTλ {\ displaystyle T _ {\ lambda}}

Internal transmittanceTi {\ displaystyle T_ {i}}

Spectral internal transmittanceTi,λ {\ displaystyle T_ {i, \ lambda}}

Integral internal transmittanceTA {\ displaystyle T_ {A}}

Transmission Spectrum

See also

Notes

Literature

More articles:

Directional transmittance $T_{r}$ ${\ displaystyle T_ {r}}$

Diffuse transmittance $T_{d}$ ${\ displaystyle T_ {d}}$

Spectral transmittance $T_{\lambda }$ ${\ displaystyle T _ {\ lambda}}$

Internal transmittance $T_{i}$ ${\ displaystyle T_ {i}}$

Spectral internal transmittance $T_{i,\lambda }$ ${\ displaystyle T_ {i, \ lambda}}$

Integral internal transmittance $T_{A}$ ${\ displaystyle T_ {A}}$