Optimization of Michelson Interferometer Signals in Crackle Noise - - PowerPoint PPT Presentation

Optimization of Michelson Interferometer Signals in Crackle Noise Detection

Horng Sheng Chia, Gabriele Vajente

LIGO SURF Project

August 20, 2014

Crackle Noise

• Crackle noise may affect LIGO detection
• Impulsive release of energy or acoustic pressure
• Changes in geometry
• Question: is crackle noise a problem to LIGO?

Figure : Dahmen, Benzion, and Uhl, Phys. Rev. Lett. (2009)

Crackle Setup

• Output: Difference between symmetric and antisymmetric

port readings

Motivation

• Crackle experiment is prone to noises:
• 1. Laser frequency noise
• 2. Laser intensity noise
• Mirror misalignment also affects signal output
• Coupling of noises can be minimized by adjusting parameters
• f setup
• Before (Crackle 1 experiment):
• trial and error
• ideal parameters drift away due to environmental factors
• Now (Crackle 2 experiment):
• Goal: automatically adjust these parameters to optimize
• utput
• Simulation - MIST optical toolbox

Laser Frequency Noise

• Variation of laser frequency
• Laser Frequency Noise Coupling, gfreq = ∆L/ν
• Aim: equalize macroscopic length difference, O(1mm)
• Piezo-translation stage controls length of one arm

0.5 1 1.5 1 2 3 4 5 6

Gain of Frequency Noise Coupled × 10−18 [m/Hz] Macroscopic Length Difference, [mm]

Simulation Expected

Laser Frequency Noise (Algorithm)

0.31 0.315 0.32 0.325 0.33 0.335 0.34 −1 1 2 3 4 x 10

−17

Macroscopic Length of movable arm [m] Laser frequency noise gain [10−17 m/Hz]

Theoretical Iteration Initial Final

• 100 measurements with random measurement uncertainties
• Average of 5 steps to complete algorithm

Laser Intensity Noise

• Variation of laser power
• RIN = δP

P

• Aim: adjust microscopic length difference, O(1 nm)
• Strategy: Locking (negative feedback) =

⇒ half fringe condition

−4 −3 −2 −1 1 2 3 4 −0.5 0.5 1 1.5 2 2.5 3 3.5

Phase of movable arm [rad] Power [W]

SP AP ABS(SP−AP)

Mirror Misalignment

• Effects of misalignment: (i) additional phase added by mirror

misalignment (ii) shifted beam center = ⇒ reduced fringe contrast

• Aim: align mirrors so fringe contrast is close to unity
• Fringe contrast = Pmax−Pmin

Pmax+Pmin =

Re[ψ1ψ∗

2]dxdy

Mirror Misalignment (Model)

Re[ψrψ∗

• ]dxdy = e−

2L2 2α2 w2

− k2w2α2

2

+ k2w2L2α2

R

−

k2L2 2w2α2 2R2

• L2 = length of arm, w = beam radius, k = wavenumber, α =

misalignment angle, R = radius of curvature of wavefront

−3 −2 −1 1 2 3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Angular misalignment of one mirror [mrad] Fringe contrast

Simulation Expected

Gradient Ascent Optimization

• Crucial parameter: step size
• Divide fringe contrast pattern into approximate linear regimes
• δ = δmax

gradlocal gradmax , where gradlocal =

    gradx1 grady1 gradx2 grady2    

−3 −2 −1 1 2 3 x 10

−3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Angular misalignment of one mirror [rad] Fringe contrast

Simulation

(0.662, 0.50) (1.21, 0.10) II I III (0.256, 0.90) V IV (0.177, 0.95)

Alignment Plots

5 10 15 20 25 30 35 −0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Steps Angular displacement [mrad]

X1 Y1 X2 Y2 5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Steps Fringe Contrast

Conclusion

• All 3 algorithms have been tested rigorously
• Next step: implement in real crackle experiment
• Acknowledge: Gabriele Vajente, Xiaoyue Ni, Alan Weinstein,

LIGO SURF students, NSF

• Thank You!

Alignment Plots

5 10 15 20 25 −0.4 −0.2 0.2 0.4 0.6 0.8 1

Steps Angular displacement [m rad]

X1 Y1 X2 Y2 5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Steps Fringe Contrast