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Message ID: 1986     Entry time: Wed Nov 15 17:33:10 2017
 Author: Craig Type: DailyProgress Category: PD Subject: PD Dark Noise and Shot Noise calculation

Craig response to RXA:  I had forgotten to take into account the reduced power on the reflection PDs when the cavity is locked.  What I called "light noise" is in fact just shot noise, no need to confuse things.

Shot noise goes like

$S_e(f) = \sqrt{\frac{2hc}{\lambda}P}$

where S_e(f) is shot noise in watts/rtHz, h is Planck's constant, c is speed of light, lambda is the laser wavelength, and P is the power on the photodiode.

When we use PDH to lock a Fabry Perot cavity, we modulate the laser light at frequency $\Omega$.  This splits the laser power into parts:

$E_{total} = E_c(\omega_0) + E_s(\omega_0+\Omega) + E_s(\omega_0-\Omega) + E_{junk}$

where $\omega_0$ is the original laser frequency, $\Omega$ is the modulation sideband frequency, and $E_{junk}$ is higher order modes.  When the cavity is locked, all of the carrier light $E_c(\omega_0)$ is transmitted through the cavity, and does not reach the reflection PD and does not contribute to shot noise.  My previous plot neglected to account for this.

I made some measurements of the DC voltage of the reflection RFPD when the cavity was both unlocked and locked.  This way I can estimate the amount of power on the PD when the cavity is locked:

 South RFPD DC Voltage North RFPD DC Voltage South RFPD Power North RFPD Power Unlocked 1.87 V 1.05 V 1220 µW 650 µW Locked 0.590 V 0.760 V No measurement No measurement

South Power ratio: 0.316

North Power ratio: 0.724

Attached in Plot 2 is a new plot of the old shot noise data scaled by these new ratios.

RXA: Most of this ELOG is bogus. Future readers should ignore. I think Craig was going to fix it...

Yesterday I spent a bunch of time thinking about shot noise.

I found our shot noise should be about 6 mHz/rtHz.  This should be correct in order of magnitude... I think this should be multiplied by a factor of root two because we have two cavities.  Attached is a zipped Mathematica notebook with my calculations.

I also measured and plotted the REFL PD dark noise and what I call "light noise".  The dark noise is just blocking the light on the PD and measuring the electronics noise at the PD error point (Common Path Test Point 1 in the FSS Box).  The light noise measurement is measuring the PD error signal without the light blocked, but with the FSS loop open.

The approximate calibration I used in these plots is 6 MHz/Vrms.  This should definitely taken as a rough calculation, a full calibrated FSS analysis is on the way.

We are not shot noise limited with our PDs.

With the light noise measurements, we see some of the same creepy-crawly peaks at 300-2000 Hz that we saw in the Transmission Beatnote spectrum for high Fast gain.  In particular, the South light noise measurement features the broad 350 Hz peak.

awade found that when we are making the light noise PD measurements, if you tap the optics table, those creepy-crawly peaks jump up.  This is definite confirmation of scattering coming from our tabletop optics.  We need to buzz all of our optics posthaste!

 Attachment 1: PSLShotNoiseCalculation.zip  2 kB
 Attachment 2: StitchedSpectrum_NorthFSSBox_DarkNoise_Span_102p4kHz_15-11-2017_152453_Spectra.pdf  133 kB
 Attachment 3: StitchedSpectrum_NorthFSSBox_DarkNoise_Span_102p4kHz_15-11-2017_152453.tgz  75 kB
 Attachment 4: StitchedSpectrum_NorthFSSBox_DarkNoise_Span_102p4kHz_15-11-2017_152453_Spectra.pdf  162 kB  Uploaded Wed Nov 29 20:44:30 2017
 Attachment 5: StitchedSpectrum_NorthFSSBox_DarkNoise_Span_102p4kHz_15-11-2017_152453.tgz  79 kB  Uploaded Wed Nov 29 20:44:58 2017
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