Commit e17950bd authored by Sean Leavey's avatar Sean Leavey

Initial commit

parent 4acc3a49
# dielectric-thermal-noise
Dielectric mirror thermal noise
# Ditherm: Dielectric Thermal Noise Calculator
This is a tool to calculate Brownian thermal noise in dielectric mirror stacks. In theory, it supports noise calculations for n-layer stacks of any material, but it has only been tested with two-material stacks using data from the [Advanced LIGO](https://www.advancedligo.mit.edu/) noise calculator, [GWINC](https://awiki.ligo-wa.caltech.edu/aLIGO/GWINC) (that link requires albert.einstein style credentials, available to members of the LIGO Scientific Community only).
## Notes ##
I provide this software without any kind of guarantee that it provides the correct answer. This software is in no way affiliated with or endorsed by any university or organisation - it is purely the work of a private individual.
In particular, the extension from the two-material Brownian noise calculation (mostly based on Harry et al., 2002) to an n-material calculation was performed simply by inspecting the formulae. I don't know if this is reasonable or not. I suspect that for coatings with more than a few (~3) materials and with extremely small or large (outwith the range wavelength * 0.15 to wavelength * 0.35) optical thicknesses per layer, the results will diverge from reality. Use at your own risk!
## Testing ##
To test the software against precomputed values from GWINC, run:
`python ditherm test`
from the root Ditherm directory (the same directory as this readme).
## Future Work ##
- Implement phase correction to Brownian calculation as per the functions on [this page](https://awiki.ligo-wa.caltech.edu/aLIGO/GWINC)
- Look at proper way to combine multiple materials by reading these papers:
- http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.042002
- http://journals.aps.org/prd/abstract/10.1103/PhysRevD.87.082001
- http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.042001
## Credits ##
This implementation was written by Sean Leavey, but the calculations are based on a number of sources:
- http://dx.doi.org/10.1088/0264-9381/19/5/305
- http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=851432 (for the correction to perpendicular component of the loss angle from Harry et al. 2002)
- http://dx.doi.org/10.1088/0264-9381/24/2/008
- GWINC (for the simplified version of the parallel component of Poisson's ratio)
- Personal discussion with colleagues
Sean Leavey
https://github.com/SeanDS/
\ No newline at end of file
import sys
if len(sys.argv) > 1:
if sys.argv[1] == 'test':
import unittest
loader = unittest.TestLoader()
suite = loader.discover('.')
runner = unittest.runner.TextTestRunner()
runner.run(suite)
\ No newline at end of file
from __future__ import division
import materials
class Layer(object):
def __init__(self, material, d):
self.material = material
self.d = d
@property
def material(self):
return self.__material
@material.setter
def material(self, material):
self.__material = material
@property
def d(self):
"""
Layer physical thickness.
"""
return self.__d
@d.setter
def d(self, d):
self.__d = d
class Bilayer(object):
def __init__(self, layerA, layerB):
self.layerA = layerA
self.layerB = layerB
@property
def layerA(self):
return self.__layerA
@layerA.setter
def layerA(self, layerA):
self.__layerA = layerA
@property
def layerB(self):
return self.__layerB
@layerB.setter
def layerB(self, layerB):
self.__layerB = layerB
def d(self):
"""
Total bilayer physical thickness.
"""
return self.layerA.d + self.layerB.d
def yPara(self):
"""
Parallel component of Young's modulus.
"""
return 1 / self.d() * (self.layerA.d * self.layerA.material.Y + self.layerB.d * self.layerB.material.Y)
def yPerp(self):
"""
Perpendicular component of Young's modulus.
"""
return self.d() / (self.layerA.d / self.layerA.material.Y + self.layerB.d / self.layerB.material.Y)
def phiPara(self):
"""
Parallel component of loss angle.
"""
return 1 / (self.d() * self.yPara()) * (self.layerA.material.Y * self.layerA.material.phi * self.layerA.d + self.layerB.material.Y * self.layerB.material.phi * self.layerB.d)
def phiPerp(self):
"""
Perpendicular component of loss angle.
"""
return self.yPerp() / self.d() * (self.layerA.d * self.layerA.material.phi / self.layerA.material.Y + self.layerB.d * self.layerB.material.phi / self.layerB.material.Y)
def sigmaPara(self):
"""
Parallel component of Poisson ratio.
"""
return (self.layerA.d * self.layerA.material.sigma * self.layerA.material.Y * (1 - self.layerA.material.sigma ** 2) + self.layerB.d * self.layerB.material.sigma * self.layerB.material.Y * (1 - self.layerB.material.sigma ** 2)) / (self.layerA.d * self.layerA.material.Y * (1 - self.layerB.material.sigma ** 2) + self.layerB.d * self.layerB.material.Y * (1 - self.layerA.material.sigma ** 2))
def sigmaPerp(self):
"""
Perpendicular component of Poisson ratio.
"""
return (self.layerA.material.sigma * self.layerA.material.Y * self.layerA.d + self.layerB.material.sigma * self.layerB.material.Y * self.layerB.d) / (self.layerA.material.Y * self.layerA.d + self.layerB.material.Y * self.layerB.d)
\ No newline at end of file
from __future__ import division
class Material(object):
def __init__(self, name, Y, sigma, phi, n):
self.name = name
self.Y = Y
self.sigma = sigma
self.phi = phi
self.n = n
@property
def name(self):
return self.__name
@name.setter
def name(self, name):
self.__name = name
@property
def Y(self):
return self.__Y
@Y.setter
def Y(self, Y):
self.__Y = Y
@property
def sigma(self):
return self.__sigma
@sigma.setter
def sigma(self, sigma):
self.__sigma = sigma
@property
def phi(self):
return self.__phi
@phi.setter
def phi(self, phi):
self.__phi = phi
@property
def n(self):
return self.__n
@n.setter
def n(self, n):
self.__n = n
class SilicaCoating(Material):
def __init__(self, *args, **kwargs):
super(SilicaCoating, self).__init__("Silica", 72e9, 0.17, 4e-5, 1.45)
class TantalaCoating(Material):
def __init__(self, *args, **kwargs):
super(TantalaCoating, self).__init__("Tantala", 140e9, 0.23, 3.8e-4, 2.06)
class TitaniumTantalaCoating(Material):
def __init__(self, *args, **kwargs):
super(TitaniumTantalaCoating, self).__init__("Titanium doped Tantala", 140e9, 0.23, 3e-4, 2.06)
class SilicaSubstrate(Material):
def __init__(self, *args, **kwargs):
super(SilicaSubstrate, self).__init__("Silica", 72e9, 0.17, 5e-9, 1.45)
\ No newline at end of file
from __future__ import division
import numpy as np
import layers
import materials
class Stack(object):
def __init__(self, layers, substrate):
self.layers = layers
self.substrate = substrate
@property
def layers(self):
return self.__layers
@layers.setter
def layers(self, layers):
self.__layers = layers
@property
def substrate(self):
return self.__substrate
@substrate.setter
def substrate(self, substrate):
self.__substrate = substrate
def d(self):
"""
Total thickness.
"""
return sum(layer.d for layer in self.layers)
def yPara(self):
"""
Total parallel Young's modulus.
"""
return 1 / self.d() * sum([layer.d * layer.material.Y for layer in self.layers])
def yPerp(self):
"""
Total perpendicular Young's modulus.
"""
return self.d() / sum([layer.d / layer.material.Y for layer in self.layers])
def phiPara(self):
"""
Total parallel loss angle.
"""
return 1 / (self.d() * self.yPara()) * sum([layer.material.Y * layer.material.phi * layer.d for layer in self.layers])
def phiPerp(self):
"""
Total perpendicular loss angle.
"""
return self.yPerp() / self.d() * sum([layer.d * layer.material.phi / layer.material.Y for layer in self.layers])
def sigmaPara(self):
"""
Total stack parallel Poisson ratio.
"""
return np.mean([layer.material.sigma for layer in self.layers])
def sigmaPerp(self):
"""
Total perpendicular Poisson ratio.
"""
return sum([layer.material.sigma * layer.material.Y * layer.d for layer in self.layers]) / sum([layer.material.Y * layer.d for layer in self.layers])
def phi(self, beamSize):
"""
Effective loss angle.
"""
return (self.d() / (np.sqrt(np.pi) * beamSize * self.yPerp()) *
(self.phiPerp() *
(self.substrate.Y / (1 - self.substrate.sigma ** 2) -
2 * self.sigmaPerp() ** 2 * self.substrate.Y * self.yPara() /
(self.yPerp() * (1 - self.substrate.sigma ** 2) * (1 - self.sigmaPara()))) +
self.yPara() * self.sigmaPerp() * (1 - 2 * self.substrate.sigma) /
((1 - self.sigmaPara()) * (1 - self.substrate.sigma)) *
(self.phiPara() - self.phiPerp()) +
self.yPara() * self.yPerp() * (1 + self.substrate.sigma) *
(self.phiPara() * (1 - 2 * self.substrate.sigma) ** 2) /
(self.substrate.Y * (1 - self.sigmaPara() ** 2) * (1 - self.substrate.sigma))))
def brownianNoise(self, freq, beamSize, temperature):
k = 1.3806503e-23;
return 2 * k * temperature / (np.sqrt(np.pi ** 3) * freq * beamSize * self.substrate.Y) * (1 - self.substrate.sigma ** 2) * self.phi(beamSize)
# GWINC version, which does the same thing
#c = self.d()*(1-self.substrate.sigma**2)/(np.pi*beamSize**2)*((1/(self.yPerp()*(1-self.substrate.sigma**2))-2*self.sigmaPerp()**2*self.yPara()/(self.yPerp()**2*(1-self.substrate.sigma**2)*(1-self.sigmaPara())))*self.phiPerp() + self.yPara()*self.sigmaPerp()*(1-2*self.substrate.sigma)/(self.yPerp()*self.substrate.Y*(1-self.sigmaPara())*(1-self.substrate.sigma))*(self.phiPara()-self.phiPerp())+self.yPara()*(1+self.substrate.sigma)*(1-2*self.substrate.sigma)**2/(self.substrate.Y**2*(1-self.sigmaPara()**2)*(1-self.substrate.sigma))*self.phiPara())
#return 4 * k * temperature * c / (2 * np.pi * freq)
\ No newline at end of file
0.01,1.6682e-37,3.3897e-37
0.010163,1.6415e-37,3.3354e-37
0.010328,1.6153e-37,3.2821e-37
0.010496,1.5894e-37,3.2295e-37
0.010667,1.564e-37,3.1778e-37
0.01084,1.5389e-37,3.127e-37
0.011016,1.5143e-37,3.0769e-37
0.011196,1.4901e-37,3.0277e-37
0.011378,1.4662e-37,2.9792e-37
0.011563,1.4428e-37,2.9316e-37
0.011751,1.4197e-37,2.8846e-37
0.011942,1.3969e-37,2.8385e-37
0.012136,1.3746e-37,2.793e-37
0.012334,1.3526e-37,2.7483e-37
0.012534,1.3309e-37,2.7043e-37
0.012738,1.3096e-37,2.6611e-37
0.012945,1.2887e-37,2.6185e-37
0.013156,1.2681e-37,2.5766e-37
0.01337,1.2478e-37,2.5353e-37
0.013587,1.2278e-37,2.4948e-37
0.013808,1.2081e-37,2.4548e-37
0.014033,1.1888e-37,2.4155e-37
0.014261,1.1698e-37,2.3769e-37
0.014493,1.1511e-37,2.3388e-37
0.014729,1.1326e-37,2.3014e-37
0.014968,1.1145e-37,2.2646e-37
0.015212,1.0967e-37,2.2283e-37
0.015459,1.0791e-37,2.1927e-37
0.015711,1.0618e-37,2.1576e-37
0.015966,1.0448e-37,2.123e-37
0.016226,1.0281e-37,2.0891e-37
0.01649,1.0117e-37,2.0556e-37
0.016758,9.9548e-38,2.0227e-37
0.017031,9.7955e-38,1.9904e-37
0.017308,9.6387e-38,1.9585e-37
0.017589,9.4844e-38,1.9272e-37
0.017875,9.3326e-38,1.8963e-37
0.018166,9.1833e-38,1.866e-37
0.018461,9.0363e-38,1.8361e-37
0.018762,8.8917e-38,1.8067e-37
0.019067,8.7494e-38,1.7778e-37
0.019377,8.6093e-38,1.7493e-37
0.019692,8.4715e-38,1.7213e-37
0.020012,8.336e-38,1.6938e-37
0.020338,8.2025e-38,1.6667e-37
0.020669,8.0713e-38,1.64e-37
0.021005,7.9421e-38,1.6138e-37
0.021347,7.815e-38,1.5879e-37
0.021694,7.6899e-38,1.5625e-37
0.022047,7.5668e-38,1.5375e-37
0.022405,7.4457e-38,1.5129e-37
0.02277,7.3265e-38,1.4887e-37
0.02314,7.2093e-38,1.4649e-37
0.023516,7.0939e-38,1.4414e-37
0.023899,6.9804e-38,1.4183e-37
0.024288,6.8687e-38,1.3956e-37
0.024683,6.7587e-38,1.3733e-37
0.025084,6.6505e-38,1.3513e-37
0.025492,6.5441e-38,1.3297e-37
0.025907,6.4394e-38,1.3084e-37
0.026328,6.3363e-38,1.2875e-37
0.026756,6.2349e-38,1.2669e-37
0.027192,6.1351e-38,1.2466e-37
0.027634,6.0369e-38,1.2266e-37
0.028083,5.9403e-38,1.207e-37
0.02854,5.8452e-38,1.1877e-37
0.029004,5.7517e-38,1.1687e-37
0.029476,5.6596e-38,1.15e-37
0.029955,5.569e-38,1.1316e-37
0.030443,5.4799e-38,1.1135e-37
0.030938,5.3922e-38,1.0956e-37
0.031441,5.3059e-38,1.0781e-37
0.031952,5.221e-38,1.0609e-37
0.032472,5.1374e-38,1.0439e-37
0.033,5.0552e-38,1.0272e-37
0.033537,4.9743e-38,1.0107e-37
0.034083,4.8947e-38,9.9455e-38
0.034637,4.8163e-38,9.7864e-38
0.0352,4.7393e-38,9.6297e-38
0.035773,4.6634e-38,9.4756e-38
0.036355,4.5888e-38,9.324e-38
0.036946,4.5153e-38,9.1747e-38
0.037547,4.4431e-38,9.0279e-38
0.038158,4.372e-38,8.8834e-38
0.038778,4.302e-38,8.7412e-38
0.039409,4.2331e-38,8.6013e-38
0.04005,4.1654e-38,8.4637e-38
0.040701,4.0987e-38,8.3282e-38
0.041363,4.0331e-38,8.1949e-38
0.042036,3.9686e-38,8.0638e-38
0.04272,3.905e-38,7.9347e-38
0.043415,3.8425e-38,7.8077e-38
0.044121,3.781e-38,7.6827e-38
0.044839,3.7205e-38,7.5598e-38
0.045568,3.661e-38,7.4388e-38
0.046309,3.6024e-38,7.3197e-38
0.047062,3.5447e-38,7.2026e-38
0.047828,3.488e-38,7.0873e-38
0.048606,3.4322e-38,6.9739e-38
0.049396,3.3772e-38,6.8623e-38
0.0502,3.3232e-38,6.7524e-38
0.051016,3.27e-38,6.6444e-38
0.051846,3.2177e-38,6.538e-38
0.052689,3.1662e-38,6.4334e-38
0.053546,3.1155e-38,6.3304e-38
0.054417,3.0656e-38,6.2291e-38
0.055302,3.0166e-38,6.1294e-38
0.056202,2.9683e-38,6.0313e-38
0.057116,2.9208e-38,5.9348e-38
0.058045,2.874e-38,5.8398e-38
0.058989,2.828e-38,5.7463e-38
0.059948,2.7828e-38,5.6544e-38
0.060923,2.7382e-38,5.5639e-38
0.061914,2.6944e-38,5.4748e-38
0.062921,2.6513e-38,5.3872e-38
0.063945,2.6089e-38,5.301e-38
0.064985,2.5671e-38,5.2161e-38
0.066042,2.526e-38,5.1326e-38
0.067116,2.4856e-38,5.0505e-38
0.068208,2.4458e-38,4.9697e-38
0.069317,2.4067e-38,4.8901e-38
0.070445,2.3681e-38,4.8119e-38
0.07159,2.3302e-38,4.7348e-38
0.072755,2.293e-38,4.6591e-38
0.073938,2.2563e-38,4.5845e-38
0.075141,2.2201e-38,4.5111e-38
0.076363,2.1846e-38,4.4389e-38
0.077605,2.1496e-38,4.3679e-38
0.078867,2.1152e-38,4.298e-38
0.08015,2.0814e-38,4.2292e-38
0.081454,2.0481e-38,4.1615e-38
0.082779,2.0153e-38,4.0949e-38
0.084125,1.983e-38,4.0294e-38
0.085493,1.9513e-38,3.9649e-38
0.086884,1.9201e-38,3.9014e-38
0.088297,1.8893e-38,3.839e-38
0.089733,1.8591e-38,3.7775e-38
0.091193,1.8294e-38,3.7171e-38
0.092676,1.8001e-38,3.6576e-38
0.094183,1.7713e-38,3.599e-38
0.095715,1.7429e-38,3.5414e-38
0.097272,1.715e-38,3.4848e-38
0.098854,1.6876e-38,3.429e-38
0.10046,1.6606e-38,3.3741e-38
0.1021,1.634e-38,3.3201e-38
0.10376,1.6078e-38,3.267e-38
0.10544,1.5821e-38,3.2147e-38
0.10716,1.5568e-38,3.1632e-38
0.1089,1.5319e-38,3.1126e-38
0.11067,1.5073e-38,3.0628e-38
0.11247,1.4832e-38,3.0138e-38
0.1143,1.4595e-38,2.9655e-38
0.11616,1.4361e-38,2.9181e-38
0.11805,1.4131e-38,2.8714e-38
0.11997,1.3905e-38,2.8254e-38
0.12192,1.3683e-38,2.7802e-38
0.12391,1.3464e-38,2.7357e-38
0.12592,1.3248e-38,2.6919e-38
0.12797,1.3036e-38,2.6488e-38
0.13005,1.2828e-38,2.6064e-38
0.13217,1.2622e-38,2.5647e-38
0.13432,1.242e-38,2.5237e-38
0.1365,1.2221e-38,2.4833e-38
0.13872,1.2026e-38,2.4435e-38
0.14098,1.1833e-38,2.4044e-38
0.14327,1.1644e-38,2.3659e-38
0.1456,1.1458e-38,2.3281e-38
0.14797,1.1274e-38,2.2908e-38
0.15038,1.1094e-38,2.2542e-38
0.15282,1.0916e-38,2.2181e-38
0.15531,1.0742e-38,2.1826e-38
0.15783,1.057e-38,2.1476e-38
0.1604,1.04e-38,2.1133e-38
0.16301,1.0234e-38,2.0795e-38
0.16566,1.007e-38,2.0462e-38
0.16836,9.909e-39,2.0134e-38
0.17109,9.7504e-39,1.9812e-38
0.17388,9.5944e-39,1.9495e-38
0.1767,9.4408e-39,1.9183e-38
0.17958,9.2897e-39,1.8876e-38
0.1825,9.141e-39,1.8574e-38
0.18547,8.9947e-39,1.8276e-38
0.18848,8.8508e-39,1.7984e-38
0.19155,8.7091e-39,1.7696e-38
0.19467,8.5697e-39,1.7413e-38
0.19783,8.4326e-39,1.7134e-38
0.20105,8.2976e-39,1.686e-38
0.20432,8.1648e-39,1.659e-38
0.20764,8.0341e-39,1.6325e-38
0.21102,7.9056e-39,1.6063e-38
0.21445,7.779e-39,1.5806e-38
0.21794,7.6545e-39,1.5553e-38
0.22149,7.532e-39,1.5304e-38
0.22509,7.4115e-39,1.5059e-38
0.22875,7.2929e-39,1.4818e-38
0.23247,7.1761e-39,1.4581e-38
0.23625,7.0613e-39,1.4348e-38
0.24009,6.9483e-39,1.4118e-38
0.244,6.8371e-39,1.3892e-38
0.24797,6.7276e-39,1.367e-38
0.252,6.62e-39,1.3451e-38
0.2561,6.514e-39,1.3236e-38
0.26026,6.4098e-39,1.3024e-38
0.2645,6.3072e-39,1.2816e-38
0.2688,6.2062e-39,1.261e-38
0.27317,6.1069e-39,1.2409e-38
0.27762,6.0092e-39,1.221e-38
0.28213,5.913e-39,1.2015e-38
0.28672,5.8183e-39,1.1822e-38
0.29138,5.7252e-39,1.1633e-38
0.29612,5.6336e-39,1.1447e-38
0.30094,5.5434e-39,1.1264e-38
0.30583,5.4547e-39,1.1083e-38
0.31081,5.3674e-39,1.0906e-38
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