Initial commit

README.md

-# 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

ditherm/__init__.py

+ 

ditherm/__main__.py

+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

ditherm/layers.py

+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

ditherm/materials.py

+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

ditherm/stacks.py

+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

ditherm/tests/gwinc/aligo.csv

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