Noise from stray light in interferometric GWs detectors

Supervisor:
Phd thesis defence by:
Jose.gonzalez@for.unipi.it

Outline
1. The quest for GWs detection
2. Low frequency noise: Stray light issues
3. Ray tracing
1. General ray tracing
2. Ray tracing improvements/development
4. A ray tracing application
5. Stray light issues during AdVirgo commissioning
6. Conclusions and future developments
Jose M. Gonzalez Castro - Noise from SL in GW 2

Jose M. Gonzalez Castro - Noise from SL in GW
GW170814 First triple detection
4

Motivation: develop a new
tool to help improve the
detection in the low
frequency range

Virgo, an instrument to measure gravitational waves
North Arm
WestArm Detection
Bench
Recycling
mirrors

Advanced Virgo: design sensitivity Vs real

Stray light: A technical noise
9
If the laser one day will supply
about 100 W and only few mW
arrive to the detection bench…
where all the light
is lost?

Stray light II: Generation methods
• Generation methods:
• Secondary beams (ghost beams)
• Diffraction
• Rough surfaces
• Point defects
• Types:
• Wide angle scattering
• Narrow angle scattering

Stray light III
● Phase change due to a moving element:
𝜙 𝑡 =
4 𝜋
𝜆
𝑥0 + 𝛿𝑥 𝑠𝑐 𝑡 = 𝜙0 + 𝛿𝜙𝑠𝑐(𝑡)
• Which can recouple as:
ℎ 𝑠𝑐 = 𝐺 ⋅ sin 𝛿𝜙𝑠𝑐
• If 𝛿𝑠𝑐 ≰ 𝜆/4𝜋 the coupling is highly non linear creating noise up to
𝑓 =
2𝐴 𝑥
𝜆
2𝜋𝑓𝑠𝑐

What was expected?
12
The sea waves produce
micro seismicity with a
frequency of approximately
0.35 Hz

Ray tracing: The rendering equation
• First works done before the 70s, but not focused on physics
• The physical principle is the Rendering equation, also called Light
Transport Equation
• Expresses the conservation of the Radiance (= conservation of the energy)
𝐿𝑖(𝑝, 𝜔𝑖) = 𝐿 𝑟 𝑝, 𝜔𝑖 +
𝑆
𝑓 𝑝, 𝜔𝑖, 𝜔𝑠 𝐿 𝑝, 𝜔𝑖 cos 𝜃𝑗 𝑑𝜔𝑗

Ray tracing: basic algorithm
• Algorithm made of
building boxes that can
be used for complex
problems
• Two different
classifications:
• Backward (rendering) or
Forward (science case) RT
• Sequential or Non-
sequential RT

Light-matter interaction: shading

Light-matter interaction: shading
What happens when the light reaches a
surface?
This is the most physical block of a ray tracing
code
𝐵𝑅𝐷𝐹 𝑝, 𝜔𝑖, 𝜔 𝑜 =
𝑑 𝐿0 (𝑝, 𝜔 𝑜)
𝐿𝑖 𝑝, 𝜔𝑖 cos 𝜃𝑖 𝑑𝜔𝑖
Different types:
• Specular
• Lambertian
Scattering mainly generated
by surface topography
Introduces phase deviations both
in transmission and reflection

RT improvements: The light model
After choosing the basic model, we make the following improvements:
• The light model used
• Include phase information into the model
• Coupling between stray light and the main beam
• We consider various options for implementation: CPU or GPU+CPU.

RT improvements: The light model
And applying the Huygens principle a wavefront is recovered
𝜓 𝑥, 𝑥𝑖 = 𝑎𝑖 𝛿 𝑥 − 𝑥𝑖 𝑒−𝑖(𝑘 𝑖∙ 𝑥+𝜙 𝑖)

RT improvements: The phase modulation
Phase split in 2 types
• Static phase  Possibility to perform modulo operation
• Time dependent phase  Not advisable to perform modulo operation
Phase modulated due to the bounces on vibrating elements
20
2 ways to simulate the displacement:
• Selecting a discrete set of frequencies and amplitudes
𝑋 𝑡 =
𝑖=1
𝑁
𝐴𝑖 sin(2 𝜋𝑓𝑖 𝑡 + 𝜙𝑖)
• Using the measured displacement from bench local controls
𝑋(𝑡)
Can be a good approach since some frequencies are
predominant!

RT improvements: The phase modulation
Phase split in 2 types
• Static phase  Possibility to perform modulo operation
• Time dependent phase  Not advisable to perform modulo operation
Phase modulated due to the bounces on vibrating elements
In magenta: High
microseismic period
In blue: Quiet period
21

RT improvements: The coupling
• As expressed by A.Vinet et.al. 1997, the coupling is:
[The coupling of a wave with the main beam] “ is given by the projection of the
scattered wave onto the main transverse electromagnetic wave”
𝛾 𝑡 = ∫ 𝜙0 𝑦 𝜓 𝑠𝑐𝑎𝑡 𝑦, 𝑡 𝑑 𝑦
And the most important effect on the main beam is that it changes the
phase as:
Δ𝜙 𝑟𝑒𝑐 =
𝕀𝕞 𝛾(𝑡)
𝑃

RT improvements II:
An implementation algorithm
• The parallel implementation can
be done as:
• CPU
• Heterogeneous programming (CPU+
GPU)
23
Read the
displacement of
the mechanical
components
Modulate the ray
Implemented
inside light-matter
interaction

Coupling light with optomechanical elements
• A phase change in the FP cavity generates a noise as
ℎ 𝑓 =
𝜆
4 𝜋𝐿
Δ𝜙 𝑟𝑒𝑐 𝑓
ℎ 𝑓 =
𝜆 𝕀𝕞 𝛾(𝑡)
4 𝜋𝐿 𝑃

Simulating the End benches

Simulating the End benches: data
• The microseismic day and the wave noise and the real data
RMS displacement
Quiet period:
• SNEB: 0.14 µm
• SWEB: 0.13 µm
High microseismic
activity:
• SNEB: 1.25 µm
• SWEB: 2.83 µm

We observe a
upconversion shoulder
due to large oscillations
at slow frequencies

End Benches Results

AdVirgo commisioning
How is previous work done experimentally?
1. Tapping the interferometer to find the most
sensible location
2. Use a shaker and analyse the data

How to do a noise projection?
1 - Perform a
noise injection
2 - Compute
transfer
function
3- Apply
transfer
function to a
quiet period
Get the
noise
projection

Sensitivity was limited by B4Ghost
on:
• f < 25Hz
• f ∈ (90 − 170)Hz
A bafle was installed on October
2017 and now the stray light from
B4Ghost is no longer limiting the
sensitivity

Conclusions
• First development of a non-sequential ray tracing method with phase
information
• Development of a novel method to estimate phase noise with a ray tracing
simulation, including upconversion shoulders
• Noise projections are a powerful tool to experimentally analyse sources of
noise, including stray light
Future work
• Experimental testing of the developed model can be exploited
• Is forward scattering a non negligible source of SL?

Backend slides

Preprocessing and ray creation
• Preprocessing involves the definition of all the elements,
from primitives to complex objects
let centre = Point(0.,0.,0.)
let ball = sphere(centre,1.0<m>,"material")
From simple elements
let l_U200 =
U200(Point(0.,0.,0.),UnitVector(0.,1.,0.),UnitVector(0.,0.,1.),
"Material__27",'L',([||],[||]))
To a complex element

Ray Tracing: Intersection tests
• It’s the core of a Ray tracing code
• Must be well optimized and one of the places
that can be better parallelized
let intersect_sphere_simp(ray:Ray,centre:Point,rad:float<m>, material:string) =
// Intersction of a ray with a sphere comming from a cylinder
let s = ray.from - centre
let sv = s*ray.uvec
let ss = s*s
let adRad = float rad // Adimensional Radius
let discr = sv*sv - ss + adRad*adRad
if discr < 0.0 then [||]
else
let t1 , t2 = (-sv + sqrt(discr))|> LanguagePrimitives.FloatWithMeasure<m>,
(-sv - sqrt(discr)) |> LanguagePrimitives.FloatWithMeasure<m>
let travel1, travel2 = ray.OpticalPathTravelled + ray.IndexOfRefraction*t1,
ray.OpticalPathTravelled + ray.IndexOfRefraction*t2
let ray1, ray2 = {ray with OpticalPathTravelled = travel1}, {ray with OpticalPathTravelled = travel2}
let point1, point2 = (ray.from + float(t1)*ray.uvec), (ray.from + float(t2)*ray.uvec)
let dnormal1, dnormal2 = point1-centre, point2 - centre
[|{normal = dnormal1.ToUnitVector();point= point1; ray= ray1; MatName = material; t= t1} ;
{normal = dnormal2.ToUnitVector();point= point2; ray= ray2; MatName = material; t= t2} |]

Sensor
Defined depending on the need:
• Rendering? -> It needs a camera model
• Beam profile?
Rendered image of the lens holder from Newport corporation

How to do a noise projection?
ℎ(𝑓) = 𝐹𝑇[
𝜆
4𝜋
β(𝑓) ⋅ sin
4𝜋
𝜆
𝑧 𝑡 ]
1. Use the data of the injection to find out β(f) as the ratio between
the desired target channel and the injection channel
2. Use β(f) on the quiet time to project quiet noise on the target
channel

Gravitational Waves
• Gravitational waves are radiated from
accelerated non-symmetrical masses
• Gravitational waves alternately
stretch and squeeze space-time both
vertically and horizontally as they
propagate
Jose M. Gonzalez Castro Noise from SL in GW 41
Credits: M. Pössel

Expected sources of
gravitational waves
The presented sensitivity expects to detect the next
candidates
• Compact binaries objects: BBH, BNS , BHNS
• Continuous waves
• Supernovae
• Stochastic background
Already detected!

Noise from stray light in interferometric GWs detectors

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