substrate thermorefractive noise simplification

substrate_thermorefractive() function updated to calculate thermal
noise of a single suspended optic.

ifo ITMThermoRefractive Noise class modified to handle specific case
of Fabry-Perot Michelson.

gwinc/ifo/noises.py

@@ -164,7 +164,12 @@ class ITMThermoRefractive(nb.Noise):
     )
 
     def calc(self):
-        return noise.substratethermal.thermorefractiveITM(self.freq, self.ifo)
+        L = self.ifo.Infrastructure.Length
+        gPhase = self.ifo.gwinc.finesse * 2/np.pi
+        n = noise.substratethermal.substrate_thermorefractive(
+            self.freq, self.ifo.Materials, self.ifo.Optics.ITM.BeamRadius)
+        # 2 ITMS
+        return n * 2 / (gPhase*L)**2
 
 
 class ITMCarrierDensity(nb.Noise):

gwinc/noise/substratethermal.py

@@ -53,71 +53,51 @@ def substrate_carrierdensity(f, materials, wBeam, exact=False):
         psdElec = psdCD(gammaElec, mElec, integralElec)
         psdHole = psdCD(gammaHole, mHole, integralHole)
 
-def thermorefractiveITM_adiabatic(f, ifo):
-    """strain noise psd arising from thermorefractive
-    fluctuations in ITM substrate (for semiconductor substrates)."""
-
-    Omega = 2*pi*f
-    H = ifo.Materials.MassThickness
-    beta = ifo.Materials.Substrate.dndT
-    kappa = ifo.Materials.Substrate.MassKappa
-    rho = ifo.Materials.Substrate.MassDensity
-    C = ifo.Materials.Substrate.MassCM
-    Temp = ifo.Materials.Substrate.Temp
-    kBT = const.kB * Temp
-    r0 = ifo.Optics.ITM.BeamRadius/np.sqrt(2)
-    L = ifo.Infrastructure.Length
-    gPhase = ifo.gwinc.finesse*2/pi
+    else:
+        psdElec = 4*H*gammaElec**2*cdDens*diffElec/(pi*r0**4*omega**2)
+        psdHole = 4*H*gammaHole**2*cdDens*diffHole/(pi*r0**4*omega**2)
 
-    psd = 4*H*beta**2*kappa*kBT*Temp/(pi*r0**4*Omega**2*(rho*C)**2) # units are meters
-    psdMeters = 2*psd # two ITMs
-    n = psdMeters / (gPhase*L)**2
-    return n
+    return psdElec + psdHole
 
 
-def thermorefractiveITM_exact(f, ifo):
-    """Strain noise from thermorefractive fluctuations in ITM substrate
+def substrate_thermorefractive(f, materials, wBeam, exact=False):
+    """Substrate thermal displacement noise spectrum from thermorefractive fluctuations
 
     For semiconductor substrates.
 
-    """
-    
-    w = ifo.Optics.ITM.BeamRadius
-    L = ifo.Infrastructure.Length
-    H = ifo.Materials.MassThickness
-    kBT = const.kB * ifo.Materials.Substrate.Temp
-    Temp = ifo.Materials.Substrate.Temp
-    c = const.c
-    
-    rho = ifo.Materials.Substrate.MassDensity
-    beta = ifo.Materials.Substrate.dndT
-    C = ifo.Materials.Substrate.MassCM
-    kappa = ifo.Materials.Substrate.MassKappa
+    :f: frequency array in Hz
+    :materials: gwinc optic materials structure
+    :wBeam: beam radius (at 1 / e^2 power)
+    :exact: whether to use adiabatic approximation or exact calculation (False)
 
-    gPhase = ifo.gwinc.finesse*2/pi
+    :returns: displacement noise power spectrum at :f:, in meters
 
+    """
+    H = materials.MassThickness
+    kBT = const.kB * materials.Substrate.Temp
+    Temp = materials.Substrate.Temp
+    rho = materials.Substrate.MassDensity
+    beta = materials.Substrate.dndT
+    C = materials.Substrate.MassCM
+    kappa = materials.Substrate.MassKappa
+    r0 = wBeam/np.sqrt(2)
     omega = 2*pi*f
-    
-    def integrand(k,om,D):
-        return D * k**3 * exp(-k**2 * w**2/4) / (D**2 * k**4 + om**2)
-    
-    inte = np.array([scipy.integrate.quad(lambda k: integrand(k, om, kappa/(rho*C)), 0, inf)[0] for om in omega])
-    
-    # From P1400084 Heinert et al. Eq. 15 
-    #psdCD = @(gamma,m,int) 2*(3/pi^7)^(1/3)*kBT*H*gamma^2*m/hbar^2*cdDens^(1/3)*int; %units are meters
-    psdTR = lambda int_: 2/pi * H * beta**2 * kBT * Temp / (rho*C) * int_; #units are meters
-    
-    
-    psd = psdTR(inte)
-    
-    psdMeters = 2*psd # two itms
-    
-    n = psdMeters / (gPhase*L)**2
 
-    return n
+    if exact:
+        def integrand(k, om, D):
+            return D * k**3 * exp(-k**2 * wBeam**2/4) / (D**2 * k**4 + om**2)
+
+        inte = np.array([scipy.integrate.quad(lambda k: integrand(k, om, kappa/(rho*C)), 0, inf)[0] for om in omega])
+
+        # From P1400084 Heinert et al. Eq. 15
+        #psdCD = @(gamma,m,int) 2*(3/pi^7)^(1/3)*kBT*H*gamma^2*m/hbar^2*cdDens^(1/3)*int; %units are meters
+        psdTR = lambda int_: 2/pi * H * beta**2 * kBT * Temp / (rho*C) * int_;
 
-thermorefractiveITM = thermorefractiveITM_adiabatic
+        psd = psdTR(inte)
+        psd = 2/pi * H * beta**2 * kBT * Temp / (rho*C) * inte
 
+    else:
+        psd = 4*H*beta**2*kappa*kBT*Temp/(pi*r0**4*omega**2*(rho*C)**2)
 
 def subbrownian(f, ifo):
     """Strain noise from the Brownian thermal noise due to substrate mechanical loss