Add instrumental noises

lisainstrument/noises.py

@@ -65,3 +65,114 @@ def infrared(fs, size, psd):
         return 0
     red_noise = red(fs, size, psd)
     return numpy.cumsum(red_noise) * (2 * pi / fs)
+
+
+def laser(fs, size, asd=28.2):
+    """Generate laser noise [Hz].
+
+    This is a white noise,
+
+        S_p(f) = asd^2.
+
+    Args:
+        asd: amplitude spectral density [Hz/sqrt(Hz)]
+    """
+    logging.debug("Generating laser noise (fs=%s Hz, size=%s, asd=%s Hz/sqrt(Hz))", fs, size, asd)
+    return white(fs, size, asd**2)
+
+
+def clock(fs, size, asd=6.32E-14):
+    """Generate clock noise fluctuations [ffd].
+
+    The power spectral density in fractional frequency deviations is a pink noise,
+
+        S_q(f) [ffd] = (asd)^2 f^(-1)
+
+    Args:
+        asd: amplitude spectral density [/sqrt(Hz)]
+    """
+    logging.debug("Generating clock noise fluctuations (fs=%s Hz, size=%s, asd=%s /sqrt(Hz))", fs, size, asd)
+    return pink(fs, size, asd**2)
+
+
+def modulation(fs, size, asd=1E-14, fknee=1.5E-2):
+    """Generate modulation noise [ffd].
+
+    The power spectral density in timing jitter reads
+
+        S_M(f) [s] = (asd)^2 [ 1 + (fknee / f)^2 ].
+
+    Multiplying by (2π f)^2 to express it as fractional frequency deviations,
+
+        S_M(f) [ffd] = (2π asd)^2 [ f^2 + fknee^2 ]
+                     = (2π asd fknee)^2 + (2π asd)^2 f^2.
+
+    Args:
+        asd: amplitude spectral density [s/sqrt(Hz)]
+        fknee: cutoff frequency [Hz]
+    """
+    logging.debug("Generating modulation noise (fs=%s Hz, size=%s, asd=%s s/sqrt(Hz), fknee=%s Hz)",
+        fs, size, asd, fknee)
+    return white(fs, size, (2 * pi * asd * fknee)**2) \
+        + violet(fs, size, (2 * pi * asd)**2)
+
+
+def backlink(fs, size, asd=3E-12, fknee=2E-3):
+    """Generate backlink noise as fractional frequency deviation [ffd].
+
+    The power spectral density in displacement is given by
+
+        S_bl(f) [m] = asd^2 [ 1 + (fknee / f)^4 ].
+
+    Multiplying by (2πf / c)^2 to express it as fractional frequency deviations,
+
+        S_bl(f) [ffd] = (2π asd / c)^2 [ f^2 + (fknee^4 / f^2) ]
+                      = (2π asd / c)^2 (f)^2 + (2π asd fknee^2 / c)^2 f^(-2)
+
+    Because this is a optical pathlength noise expressed as fractional frequency deviation, it should
+    be multiplied by the beam frequency to obtain the beam frequency fluctuations.
+
+    Args:
+        asd: amplitude spectral density [m/sqrt(Hz)]
+        fknee: cutoff frequency [Hz]
+    """
+    logging.debug("Generating modulation noise (fs=%s Hz, size=%s, asd=%s m/sqrt(Hz), fknee=%s Hz)",
+        fs, size, asd, fknee)
+    return violet(fs, size, (2 * pi * asd / c)**2) \
+        + red(fs, size, (2 * pi * asd * fknee**2 / c)**2)
+
+
+def ranging(fs, size, asd=3E-9):
+    """Generate stochastic ranging noise [s].
+
+    This is a white noise as a timing jitter,
+
+        S_R(f) [s] = asd.
+
+    Args:
+        asd: amplitude spectral density [s/sqrt(Hz)]
+    """
+    logging.debug("Generating ranging noise (fs=%s Hz, size=%s, asd=%s s/sqrt(Hz))", fs, size, asd)
+    return white(fs, size, asd**2)
+
+
+def testmass(fs, size, asd=2.4E-15, fknee=0.4E-3):
+    """Generate test-mass acceleration noise [ffd].
+
+    Expressed in acceleration, the noise power spectrum reads
+
+        S_delta(f) [ms^(-2)] = (asd)^2 [ 1 + (fknee / f)^2 ].
+
+    Multiplying by 1 / (2π f c)^2 yields the noise as a fractional frequency deviations,
+
+        S_delta(f) [ms^(-2)] = (asd / (2π c))^2 [ f^(-2) + (fknee^2 / f^4) ]
+                             = (asd / (2π c))^2 f^(-2) + (asd fknee / (2π c))^2 f^(-4) ].
+
+    Args:
+        asd: amplitude spectral density [ms^(-2)/sqrt(Hz)]
+        fknee: cutoff frequency [Hz]
+    """
+    logging.debug("Generating test-mass noise (fs=%s Hz, size=%s, asd=%s ms^(-2)/sqrt(Hz), fknee=%s Hz)",
+        fs, size, asd, fknee)
+    return red(fs, size, (asd / (2 * pi * c))**2) \
+        + infrared(fs, size, (asd * fknee / (2 * pi * c))**2)