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Entry  Wed Jun 5 13:49:13 2013, Deep Chatterjee, Optics, General, Difference in the Levin and Liu & Thorne results for thermal noise Levin_throne_comparison.pdfLevin_throne_comparison.png
    Reply  Wed Jun 5 16:56:53 2013, Matt A., Optics, General, Difference in the Levin and Liu & Thorne results for thermal noise 
Message ID: 9     Entry time: Wed Jun 5 16:56:53 2013     In reply to: 8
Author: Matt A. 
Type: Optics 
Category: General 
Subject: Difference in the Levin and Liu & Thorne results for thermal noise 

Good Work Deep,

Can you include the equations that you used to calculated these expressions?

 

Quote:

The analytical expressions for thermal noise, as calculated by Liu & Thorne and Levin, was plotted as a function of frequency in a log - log plot using Matlab.

The value of the parameters were used from Levin's paper on  thermal noise.

phi = 1*10-7 (loss angle)

r0 = 1.56*10-2  (beam radius)

T = 300 K (temperature)

E0 = 7.18*1010   (Young's modulus)

sigma = 0.16 (Poisson ratio)

The value of Sx(100) that given in Levin's paper (8.7*10-40 m2 /Hz) while the Liu-Thorne value is 9.1*10-40 m2 /Hz.

Levin_throne_comparison.png

 The Liu Thorne expression being

S = 4*kb*T/(pi*f) * (1 - sigma^2) / (2*sqrt(pi)*E*sqrt(2)*r0) * phi

That of Levin goes as

S = 4*kb*T/f * (1 - sigma^2) / (pi^3*E*r0) *I*phi

sigma : Poisson ratio

phi : loss angle

r0 : Beam spot radius

E : Young's modulus

I : This is a sum the value of which is approx. 1.873.22 [Eqn.(A6) of Levin - Internal Thermal Noise]

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