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Ideal Etalon Transmission Formula

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The transmission of etalon, also known as a Fabry–Pérot interferometer, is a result of interference between the multiple reflections of light between the two reflecting surfaces of the etalon. Check FAQs

T E = {(1 + \frac{4 \cdot ρ}{{(1 - ρ)}^{2}} \cdot {\sin (\frac{Φ}{2})}^{2})}^{- 1}

T_E - Transmission of Etalon?ρ - Reflectivity?Φ - Single-Pass Phase Shift?

Ideal Etalon Transmission Example

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Here is how the Ideal Etalon Transmission equation looks like with Values.

Here is how the Ideal Etalon Transmission equation looks like with Units.

Here is how the Ideal Etalon Transmission equation looks like.

0.9459 = {(1 + \frac{4 \cdot 0.035}{{(1 - 0.035)}^{2}} \cdot {\sin (\frac{45.3114}{2})}^{2})}^{- 1}

0.9459 = {(1 + \frac{4 \cdot 0.035}{{(1 - 0.035)}^{2}} \cdot {\sin (\frac{45.3114rad}{2})}^{2})}^{- 1}

0.9459 = {(1 + \frac{4 \cdot 0.035}{{(1 - 0.035)}^{2}} \cdot {\sin (\frac{45.3114}{2})}^{2})}^{- 1}

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Ideal Etalon Transmission Solution

Follow our step by step solution on how to calculate Ideal Etalon Transmission?

FIRST Step Consider the formula

T E = {(1 + \frac{4 \cdot ρ}{{(1 - ρ)}^{2}} \cdot {\sin (\frac{Φ}{2})}^{2})}^{- 1}

Next Step Substitute values of Variables

∴

T E = {(1 + \frac{4 \cdot 0.035}{{(1 - 0.035)}^{2}} \cdot {\sin (\frac{45.3114rad}{2})}^{2})}^{- 1}

Next Step Prepare to Evaluate

∴

T E = {(1 + \frac{4 \cdot 0.035}{{(1 - 0.035)}^{2}} \cdot {\sin (\frac{45.3114}{2})}^{2})}^{- 1}

Next Step Evaluate

∴

T E = 0.945912434615237

LAST Step Rounding Answer

∴

T E = 0.9459

Ideal Etalon Transmission Formula Elements

Variables

Functions

Transmission of Etalon

The transmission of etalon, also known as a Fabry–Pérot interferometer, is a result of interference between the multiple reflections of light between the two reflecting surfaces of the etalon.

Symbol: T_E

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Transmission of Etalon

Reflectivity

Reflectivity is a measure of the effectiveness of a surface or material in reflecting radiant energy.

Symbol: ρ

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Reflectivity

Single-Pass Phase Shift

The single-pass phase shift refers to the phase change that light undergoes when it propagates from one mirror to the other in a single pass.

Symbol: Φ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Single-Pass Phase Shift

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other formulas in Transmission Measurements category

Go Optical Attenuation

α dB = \frac{10}{L 1 - L 2} \cdot \log 10 (\frac{V 2}{V 1})

Go Absorption Loss

α abs = \frac{C \cdot T ∞}{P opt \cdot t c}

Go Time Constant of Calorimeter

t c = \frac{t 2 - t 1}{\ln (T ∞ - T t1) - \ln (T ∞ - T t2)}

Go Scattering Loss

α sc = (\frac{4.343 \cdot 10^{5}}{l}) \cdot (\frac{V sc}{V opt})

How to Evaluate Ideal Etalon Transmission?

Ideal Etalon Transmission evaluator uses Transmission of Etalon = (1+(4*Reflectivity)/(1-Reflectivity)^2*sin(Single-Pass Phase Shift/2)^2)^-1 to evaluate the Transmission of Etalon, The ideal etalon transmission refers to the optimal transmission of light through the etalon, which results in a transmission profile with peaks at specific points. This transmission is influenced by multiple factors, including the reflectance R of both surfaces of the cavity and the phase Φ acquired by light passing through the cavity once. Transmission of Etalon is denoted by T_E symbol.

How to evaluate Ideal Etalon Transmission using this online evaluator? To use this online evaluator for Ideal Etalon Transmission, enter Reflectivity (ρ) & Single-Pass Phase Shift (Φ) and hit the calculate button.

FAQs on Ideal Etalon Transmission

What is the formula to find Ideal Etalon Transmission?

The formula of Ideal Etalon Transmission is expressed as Transmission of Etalon = (1+(4*Reflectivity)/(1-Reflectivity)^2*sin(Single-Pass Phase Shift/2)^2)^-1. Here is an example- 0.945912 = (1+(4*0.035)/(1-0.035)^2*sin(45.31143/2)^2)^-1.

How to calculate Ideal Etalon Transmission?

With Reflectivity (ρ) & Single-Pass Phase Shift (Φ) we can find Ideal Etalon Transmission using the formula - Transmission of Etalon = (1+(4*Reflectivity)/(1-Reflectivity)^2*sin(Single-Pass Phase Shift/2)^2)^-1. This formula also uses Sine (sin) function(s).

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