the ltp interferometer and phasemeter - european space agency
TRANSCRIPT
The LTP interferometer and Phasemeter
Gerhard Heinzel
on behalf of the Optical Bench team:
Albert-Einstein-Institut Hannover,
University of Glasgow,
EADS Astrium Immenstaadt,
Rutherford Appleton Laboratories Chilton,
TNO TPD Delft,
ESTEC Noordwijk
5th International LISA Symposium,ESTEC, July 12, 2004.
1
2
3
4
Heterodyne Mach-Zehnder interferometer
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PD2
PD1
∆φ
LaserAOM
AOM
f0
f0+f2
f0+f1
f1−f2 = fhet
f2
f1
00.10.20.30.40.50.60.70.80.9
1
0 2 4 6 8 10
Phot
ocur
rent
time
∆φ
It has constant sensitivity over a range of > ±100µm. The heterodyne frequency fhet is a few kHz
(1.6 kHz in the EM).
5
Interferometer budget
10-12
10-11
10-10
10-9
10-3 10-2 10-1
10-5
10-4
10-3
10-2
optic
al p
athl
engt
h no
ise
[m/√
Hz]
inte
rfer
omet
er p
hase
noi
se [r
ad/√
Hz]
frequency [Hz]
SMART2 mission goal
interferometer budget
each interferometer contrib.
170 pm/√Hz
9 pm/√Hz
1 pm/√Hz
µrad/√Hz
1000
54
6
Note the new interpretation. As compared to some earlier versions, nothing has changed for theinterferometer budget, which is, however, now a factor of nearly 20 below the mission goal.
The frequency dependence of all interferometer-related budgets is
y(f) = y(30mHz) ·
√√√√1 +
(3mHz
f
)4
,
and all budgets in the following are given at 30mHz (such as 9 pm/√
Hz for the interferometer).
6
FiberInputs
x1−x2
x1
Reference
Frequency
4 interferometers:
x1 − x2 provides the main measurement: the distance
between the two test masses and their differential
alignment.
x1 provides as auxiliary measurement the distance be-
tween one test mass and the optical bench and the
alignment of that test mass.
Reference provides the reference phase for
x1 − x2 and x1.
Frequency measures laser frequency fluctuations with
intentionally unequal pathlengths.
7
x1 − x2
−0.1
0−0
.05
0.00
0.05
0.10
−0.2
0
−0.1
5
−0.1
0
−0.0
5
0.00
0.05
0.10
0.15
0.20
BS
1
BS
4
BS
3
BS
6
BS
2
BS
9
Test
mas
s 1
GH
H A
EI H
anno
ver <
>24.
2.20
03 1
3:20
:54<
BS
16
PD
A1
WIN
1
BS
7
M11
M12
M14
BS
5
M1
BS
8
M4
WIN
2
M5
BS
10
BS
11
PD
A2
M6
PD
FA
PD
FB
PD
RA
PD
RB
PD
1A
PD
1B
M10
M8
PD
12B
M15
PD
12A
with an extra pathlength of 356.7mm in the reference fiber, the pathlength difference is 0.000 mm.
8
x1
−0.1
0−0
.05
0.00
0.05
0.10
−0.2
0
−0.1
5
−0.1
0
−0.0
5
0.00
0.05
0.10
0.15
0.20
BS
1
BS
4
BS
3
BS
6
BS
2
BS
9
Test
mas
s 1
GH
H A
EI H
anno
ver <
>24.
2.20
03 1
3:20
:54<
BS
16
PD
A1
WIN
1
BS
7
M11
M12
M14
BS
5
M1
BS
8
M4
WIN
2
M5
BS
10
BS
11
PD
A2
M6
PD
FA
PD
FB
PD
RA
PD
RB
PD
1A
PD
1B
M10
M8
PD
12B
M15
PD
12A
with an extra pathlength of 356.7mm in the reference fiber, the pathlength difference is 0.02 mm.
9
Reference
−0.1
0−0
.05
0.00
0.05
0.10
−0.2
0
−0.1
5
−0.1
0
−0.0
5
0.00
0.05
0.10
0.15
0.20
BS
1
BS
4
BS
3
BS
6
BS
2
BS
9
Test
mas
s 1
GH
H A
EI H
anno
ver <
>24.
2.20
03 1
3:20
:54<
BS
16
PD
A1
WIN
1
BS
7
M11
M12
M14
BS
5
M1
BS
8
M4
WIN
2
M5
BS
10
BS
11
PD
A2
M6
PD
FA
PD
FB
PD
RA
PD
RB
PD
1A
PD
1B
M10
M8
PD
12B
M15
PD
12A
with an extra pathlength of 356.7mm in the reference fiber, the pathlength difference is 0.016mm.
10
Frequency
−0.1
0−0
.05
0.00
0.05
0.10
−0.2
0
−0.1
5
−0.1
0
−0.0
5
0.00
0.05
0.10
0.15
0.20
BS
1
BS
4
BS
3
BS
6
BS
2
BS
9
Test
mas
s 1
GH
H A
EI H
anno
ver <
>24.
2.20
03 1
3:20
:54<
BS
16
PD
A1
WIN
1
BS
7
M11
M12
M14
BS
5
M1
BS
8
M4
WIN
2
M5
BS
10
BS
11
PD
A2
M6
PD
FA
PD
FB
PD
RA
PD
RB
PD
1A
PD
1B
M10
M8
PD
12B
M15
PD
12A
with an extra pathlength of 356.7mm in the reference fiber, the pathlength difference is −380mm.
11
−0.1
0−0
.05
0.00
0.05
0.10
−0.2
0
−0.1
5
−0.1
0
−0.0
5
0.00
0.05
0.10
0.15
0.20
Test
mas
s 1
GH
H A
EI H
anno
v
BS
16
PD
A1
WIN
1
BS
1B
S2
BS
7
M11
M12
M14
BS
5
BS
3
M1
BS
8
M4
WIN
2
M5
BS
10
BS
11
PD
A2
BS
4B
S9
M6
PD
FA
PD
FB
PD
RA
PD
RB
BS
6
PD
1A
PD
1B
M10
M8
PD
12B
M15
PD
12A
12
Optical bench manufacturing
The OB was manufactured by RAL from a Zerodur baseplate and fused silica optical components,
using hydroxycatalysis bonding from U Glasgow and the optical design from AEI.
13
Recovery from accident
A handling mistake caused 4 components to break at a late assembly stage. They could be repaired
with interface plates (‘bridges’).
14
Remaining assembly problems
One bond is incomplete:
Refinement of the bonding procedure is needed.
The alignment procedure of the fiber injectors needs some refinement (≈ 100µrad vertical error).
More components need to be aligned with the ‘jig’ (horizontal template accuracy insufficient for long
lever arms).
15
Laser source
The laser (by Tesat) is already space qualified and delivers 25 mW at the end of an optical fiber.
It will be included in a larger box together with the Acousto optical modulators and associated
electronics.16
AOM Prototype (Contraves)
needs further development.
17
Functional overview
benchModulation
MasterOscillator
f het
pum
p lig
ht
Pump module
Laser head1064 nm light PD signals
PhasemeterLaser Box
DMU processingFPGA preprocessingA/D converterPD Front end
BenchOptical
1064 nm light
ControlLight power
Amp. Stab.
Spacecraft
Con
trol
Pow
er Out
put
sam
plin
g cl
ock
OPD stabilization
Frequency stabilization
18
MagnetometerSolar Power meterparticle counterthermometers
Pre−ampantialiasingA/D convertersFPGA preprocessing
Bias
�� � �� �
Laser Head
AOM driver
AOM opto−mech.
Amplitude Control
Phasemeterback end
2*setpoint 2*errsig
2*dig.out
2 * 32 kByte/sserial
1 clock
n sensor outputs
power analog ?
power analog ?
heater
Magnetic Coil
f_het
S/C data bus
1 clock
6*monitor(2*error, 4*feedback)
2 digital flags
sensor control and power ?
2*PDA1/PDA2single−element diode output
2 analog
digital flags
2*Laser IN2 fibers2*RF
S/C master oscillator
2*Amp Control(2 chann.)
2 ana.
2*on/off2*on/off
(fast/slow)
2*OUT
*
*Frequencydivider
DMU
optical benchPhasemeter front end
(4 * RS−422)
(2*16 quadrant + 2 single channels)
Laser Box(es)
digital signal
optical fiberanalog signal
one box
* : digital status/control/reset signals TBD
clock signal28V Power
Photodiodes:8*5 + 2*2 = 44
plus screens44 wires
28V S/C Power
PCU
PCU
Some on optical bench?
high power DAC
high power DACplus interface ?
n * ADC
2*digital control
digitalcommands
Status
2 dig, 2 ADC
2 analog
thermometers? coils? heaters?
2 analog
MIL−STD−1553 TBD
2*Freq. control
2*DAC
2* power DAC
1*IN1 fiber
2 Fiber actuators+2 thermometers
2 clocksclockclock
2 digital
Laser status
2*DAC2*ADC
phasedata
PCU
2 power RFfastslow
1 analog
1*DAC6*ADC6 analog
2*Amp Control
SMART−2 Optical metrology avionics DRAFT 0.727.04.2004
19
Laser power stabilization
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-3 10-2 10-1 1 101 102 103 104
rela
tive
pow
erfl
uctu
atio
ns [1
/√H
z]
frequency [Hz]
requirement fromradiation pressure
req. fromphase measurement
filtered voltage reference(AD587/OP177)
shot noise(0.5mA photocurrent)
radiation pressure:
δ̃P
P<
m c ω2
2Pδ̃y at 1 mHz
phase measurement:
δ̃P
P<
c
2√
2δ̃ϕ at fhet
Stabilization via split feedback to Laser pump module (common mode)and AOM RF power (differential mode, BW>50 kHz).
20
AOM driver
A laboratory prototype of the AOM driver was built and characterized. It consists of two independent
TCVCXO’s, which are frequency-locked by a PLL to give a constant difference frequency (e.g.
1.6 kHz).
TCVCXO80 MHz − 250 Hz
∆
500 HzInput
Comp
∆ f∆φ
BP
BP
∆ f∆φ
10 MHzInput
10 MHzOutput
LF
TCVCXO80 MHz + 250 Hz
Σ
LP ∆ f∆φ
LF
−1
Comp
BP
Com
p
Comp = comparator to generate logic level signalsDiv = digital frequency dividerDBM = double balanced mixer
f = digital phase/frequency detector∆φ∆
ΑΟΜ1
ΑΟΜ2
Sign
5 M
Hz
−ε5
MH
z+ε
+ε
500 Hz
LP = lowpass filterBP = bandpass filterLF = loop filter
DBM DBM
TCVCXO = temperature compensated voltage controlled crystal oscillator
−ε
Div
Div
/16
/16
5 MHz
5 MHz10
MH
z
Both the difference frequency (≈ 1.6kHz) and
the average frequency (80MHz) are controlled by
phase-locked loops (PLL).
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
10-1 1 101 102 1k 10k 100k
rad r
ms/
√Hz
Fourier frequency [Hz]
The phase noise of each oscillator is
< 10−6 rad/√
Hz at 1 kHz.
21
80 MHzTCVCXO
BP Det LP LF
2 W out
DBM 2 W PA 20 dB DC
AM input10VRef
DBM = double balanced mixer (used as attenuator)TCVCXO = Temp. compens. VCXO
PA = Power AmplifierDC = Directional Coupler
Det = Schottky DetectorLP = 10 MHz LowpassLF = Loop Filter
BP = 80 MHz Bandpass
1e-10
1e-09
1e-08
1e-07
1e-06
1e-05
0.0001
0.1 1 10 100 1000
1/sq
rt(H
z)
�
Hz
free
outloop
inloop
preamp
The RF amplitude of each oscillator is stabilized to ≈ 10−8 /√
Hz at 1 kHz and has a fast input
(BW > 100kHz) to compensate light power fluctuations that are measured at the fiber end.
22
Laser Frequency noise
Laser frequency fluctuations δν = δω/(2π) cause spurious phase fluctuations δϕ via a pathlength
difference ∆l between the arms.
Conversion factor δω [rad/s] −→ δϕ :
τ = ∆l/c, the differential time delay.
Budget: δϕ < 6µrad/√
Hz
between 3 mHz and 30mHz
Frequency stability requirement:
δ̃ν =c
2π ∆lδ̃ϕ = 28
kHz√Hz
/[∆l
1cm
]103
104
105
106
107
108
10-4 10-3 10-2 0.1 1
Freq
uenc
y no
ise
[Hz/
√Hz]
Frequency [Hz]
measured
requirement
noise of aux. ifo
23
Frequency stabilization
We use the extra interferometer with ∆L = 38cm as sensor with sufficiently low noise. Two options
are:
• Use that signal in a feedback loop to actively stabilize the laser (the baseline):
Required loop gain : ≈ 100 at 30mHz.
With a 1/f simple integrator as loop filter we need unity gain frequency > 3Hz.
Allowing an extra phase delay of 45◦ in the loop gain at 3 Hz, the permissible processing time
delay is 40ms (achievable).
Small complication with DC feedback: laser is forced to follow drifts of auxiliary interferometer
(solvable).
• Do not stabilize the laser but use that signal to correct the main output signals for the
frequency flucuations thus measured (fallback option). The actual pathlength differences ∆l
must be known to relatively high precision: δl = 0.1mm and δL = 4mm. Manufacturing to such
accuracy is difficult, but measurement during operation is possible.
24
Phasemeter using SBDFT (Single-Bin Discrete Fourier Transform)
Inputs from one quadrant diode: xi = UA(ti), same for UB(t), UC(t), UD(t).First step: SBDFT achieves data reduction by a factor of ≈ 100:
DC components: DCA,DCB,DCC,DCD (real) : DCA =n−1∑i=0
xi,
fhet components: FA,FB,FC,FD : <(FA) =n−1∑i=0
xi · ci, =(FA) =n−1∑i=0
xi · si.
The constants si and ci are pre-computed: ci = cos(2π i k
n
), si = sin
(2π i k
n
).
At the moment, our prototype uses PC software.
Prototypes close to the LTP phasemeter
(using FPGAs for this step) are under construction
in Hannover and Birmingham:
seroutserclk
stateclkadclk
CONTROL
SERIAL
seroutserclk
stateclkadclk
CONTROL
SERIAL
� ��
� ��
��
��
�
�
ADCclock
databusy adbusy
addata
DATA
SIN/COSTable
FPGA
ADCclockdatabusy adbusy
addata
DATA
SIN/COSTable
FPGA
Central Controller
adclk
stateclk
16*serin
16*serclk
master clock
serout
16 channels per phasemeter
To DMU/PC
(only 2 are drawn)
25
Phasemeter EM/FM concept
– for redundancy, there are 2 separate phasemeters, each processing 4 photodiodes (one from each
interferometer) = 16 channels.
– Data rate from ADC: 100kHz× 16bit× 16channels = 3.2MByte/sec.
– Early concepts needed high-speed DSP for DFT.
– New concept: Initial data processing stage (SBDFT) is done in hardware (FPGA).
Reduced data rate 100Hz× 20bytes× 16channels = 32kByte/sec, i.e. data reduction by factor 100.
FPGA also handles ADC timing and control.
– DSP is still needed for final processing stages, but with 1/100 of the data rate and no critical
timing any more.
– FPGAs exist in rad-tolerant and rad-hard versions, e.g. by Actel.
– Prototype FPGA phasemeters are under construction in Birmingham and Hannover.
26
Further processing in DMU
Longitudinal Signal:
F(1)Σ = FA + FB + FC + FD the total fhet amplitude on the first quadrant diode, and
F(2)Σ for the second (reference) quadrant diode equivalently.
ϕlong = arg(F(1)Σ )− arg(F(2)
Σ ) + n · 2π, (integer n from phasetracking algorithm).
Alignment signals, independently on each diode:
FLeft = FA + FD: amplitude in left half, DCLeft = DCA + DCD: average in left half,
FRight, FUpper, FLower, DCRight, DCUpper, DCLower equivalently.
The DC (center of gravity) signals:
∆x =DCLeft −DCRight
DCΣ, ∆y =
DCUpper −DCLower
DCΣ,
The DWS (differential wavefront sensing) signals:
Φx = arg
(FLeft
FRight
), Φy = arg
(FUpper
FLower
),
Alignment signals are obtained from each quadrant diode individually (no reference needed)
−→ Rejection of several common mode noise sources.
27
Optical windows
There will be 4 transmissions through an optical window of approx. 5mm thickness in the main x1−x2
measurement path:
28
Pathlength effects
Four major disturbing effects on the optical pathlength are expected:
Thermal variation of optical pathlength.
Stress-induced change in refractive index.
mechanical motion of the window in z-direction.
mechanical tilt fluctuations of the window.
The sum of all noise contributions of one window (in double pass) is counted as one interferometer
noise source and allocated a bufget of 1 pm/√
Hz. Hence the window effects contribute no more than
1 pm/√
Hz in the x1 measurement and no more than 2 pm/√
Hz in the x1 − x2 measurement. Each
effect is allocated 0.33 pm/√
Hz (for one window double pass).
29
Thermal variation of optical pathlength:
∆s = ∆T × L×(dndT + (n− 1)α
).
dn/dT + (n− 1)α is ≈ 5ppm/K for most glasses (e.g. BK7).
Athermal glasses (e.g. Ohara S-PHM52, Schott N-FK51 and Schott N-FK56) have 0.5 . . .1ppm/K.
The Schott glasses have a high α ≈ 15ppm/K, not well matched to Ti.
The best candidate that we identifed so far is Ohara S-PHM52.
At 1064 nm, dn/dT + (n− 1)α = 0.59ppm/K.
The linear thermal expansion coefficient α is 10.1 ppm/K, well matched to Ti.
All these athermal glasses are difficult to polish and very brittle, which may limit the mounting
options. With glueing, care must be taken to avoid high static stresses that might cause the glass to
break in thermal cycling.
30
From δ̃T = δ̃s
L×(
dndT +(n−1)α
),a pathlength error of δ̃s = 0.33pm/
√Hz
and L = 12mm,
the required thermal stability at the window is:
δ̃T < 4 · 10−5 K/√
Hz
10-5
10-4
10-3
10-2
10-4 10-3 10-2 0.1 1
LSD
(K/√
Hz)
Frequency (Hz)
Thermometer noise
AD-590: out-of-loopPT-10.000: out-of-loop
NTC: out-of-loopreq.
Ohara S-PHM52
Linear thermal expansion α = 10.1ppm/K.
at 1064 nm:
n = 1.60645,
dn/dT + (n− 1)α = 0.589ppm/K.
31
Stress-induced change in refractive index:
While in some materials the stress-induced birefringence can be made small, we have here the
absolute variation in refractive index, which is never small. The relevant material constant is:
“Photoelastic constant” β = 1.0nm/cm/105Pa.
For a pathlength error of 0.33pm/√
Hz and L = 12mm, the required stability of mechanical stress in
the window is:
δ̃σ < 30Pa/√
Hz.
We have no knowledge of the real stress fluctuation.
This error might be big.
Mounting of the optical window will be critical (In seal? Au-Sn seal?).
Measuring the thermally induced pathlength fluctuation is essential.
32
Mechanical motion:
If there is a deviation γ from parallelism and the window moves in z direction by ∆z this yields a
pathlength error (double-pass):
∆s = 2γ(n− 1)∆z.
For γ = 30′′, n− 1 = 0.6 and a pathlength error of 0.33pm/√
Hz one gets
δ̃z < 2nm/√
Hz.
If this is difficult, the obvious remedy is to improve the parallelism.
33
Mechanical tilt fluctuations:
α
d
d
βα− β
l
∆x
a
l =d
cosβ,
a = l cos(α− β),
sinα
sinβ= n ,
∆s = nl− a
∆s = d
√cos 2α + 2n2 − 1
2− cosα
With α = 2.5◦, d = 6mm, n = 1.6:
d(∆s)
dα= 0.98 · 10−4 ≈ 10−4m/rad
For a pathlength error of 0.16pm/√
Hz (0.33 pm/2 because of double-pass) one gets
δ̃α < 1.6nrad/√
Hz.
If too difficult, α might be reduced at the expense of stray light problems.
34
Functional, environmental and performance tests
The EM was tested during March and April, 2004 at TNO/TPD, Delft. The tests included:
• Functional tests before and after each other test,
• Thermal vacuum test:several cycles 0. . . 40 ◦C,
• Vibrational test (with dummy masses):8 grms sine and random,25 g at the struts.
• Performance tests:
– Full stroke test: each mirror moved by ±100µm,
– Noise test: mirrors not actuated
– Tilt test: each mirror tilted by ±1000µrad,
All tests were successful!35
EM Test results: high velocity full stroke test (2.9 samples/cycle)
0
50
100
150
200
0 20 40 60 80 100
0
20
40
60
80
100
optic
al p
athl
engt
h [u
m]
mir
ror 1
PZ
T m
otio
n [u
m]
time [sec]
PZT stroke
-200
-150
-100
-50
0
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
optic
al p
athl
engt
h [u
m]
cont
rast
time [sec]
LPF OB Full Stroke Test 1/2:end mirror 1 actuatedTNO/AEI 2004/03/03
measured x1measured x1-x2
contrast Refcontrast x1
contrast x1-x2
0
50
100
150
200
0 20 40 60 80 100
0
20
40
60
80
100
optic
al p
athl
engt
h [u
m]
mir
ror 2
PZ
T m
otio
n [u
m]
time [sec]
PZT stroke
0
50
100
150
200
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
optic
al p
athl
engt
h [u
m]
cont
rast
time [sec]
LPF OB Full Stroke Test 2/2:end mirror 2 actuatedTNO/AEI 2004/03/04
measured x1measured x1-x2
contrast Refcontrast x1
contrast x1-x2
36
EM Test results: Noise
10-5
10-4
10-3
10-2
0.1
10-4 10-3 10-2 0.1 1 10
1
10
100
1000
10000
phas
e [r
ad/√
Hz]
optic
al p
athl
engt
h [p
m/√
Hz]
frequency [Hz]
LPF OB performance AEI/TNO 2004/03/19
LPF mission goal
interferometer goal
LPF EM (TNO/AEI) no PZT-stab, quad diodesGlasgow/AEI best with PZT-stab, quad diodes
x1 - x2 LPF EM (TNO/AEI) with PZT-stab, quad diodesGlasgow/AEI best with PZT-stab, single-elt. diodes
37
EM Test results: Contrast
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
cont
rast
time[sec]
LPF OB performance: ContrastTNO/AEI 2004/03/19
contrast Refcontrast x1-x2
38
EM Test results: Noise sources 1
At frequencies < 3mHz, real motion of the test mirrors is dominant:
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0
20
40
60
80
100
120
140
phas
e x 1
- x 2
[rad
]
optic
al p
athl
engt
h fl
uctu
atio
n be
twee
n m
irro
rs [n
m]
time[sec]
-0.01
-0.005
0
0.005
0.01
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
-1.5
-1
-0.5
0
0.5
1
1.5
phas
e x 1
- x 2
[rad
]
optic
al p
athl
engt
h fl
uctu
atio
n be
twee
n m
irro
rs [n
m]
time[sec]
54nm/h drift subtracted
39
EM Test results: Noise sources 2
An attempt to glue the Zerodur mirrors to the Zerodur baseplate failed: Curing of the glue caused
≈ 200µrad misalignment and a contrast drop to < 0.5. This is mainly a testing problem.
40
EM Test results: Noise sources 3
f hetϕ el
ϕ R ϕ M
∆R
∆M
LaserBS
f1
f2
AOM
L2R
L1
L2
L1M
L2M
L1R
∆F Fiber
PDR PDM
ultra−stable
Fluctuations of the fibers’ Optical Pathlength Difference (OPD, ∆F ) should ideally completely cancel,
but in reality some error remains.
41
-3
-2
-1
0
1
2
3
4
0 500 1000 1500 2000 2500 3000 3500 4000
ϕ =
ϕ R -
ϕ M [
mra
d], d
rift
sub
trac
ted
time [seconds]
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
500 550 600 650 700 750 800
ϕ =
ϕ R -
ϕ M [
mra
d], d
rift
sub
trac
ted
time [seconds]
The measured pathlength x1− x2 signal has an erroneous component of ≈ mrad magnitude which is
quasi-periodic with ∆F .
42
-10
0
10
20
30
40
50
60
70
80
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
ϕ R, ϕ
M [
rad]
time [seconds]
Unless the origin of the noise will be understood, a remedy is to actively stabilize ∆F . This was done
using an analog phasemeter, analog servo and long-range PZT at TNO.
Further investigations are under way in Hannover and Glasgow.
43
Alignment measurement with quadrant photodiodes
3 ways to use a quadrant diode:
A B
C D
• Σ = A + B + C + D is used as before for the longitudinal readout.
• The DC signals ∆y = A + B − C −D and ∆x = A + C −B −D measure the
average lateral displacement of both beams.
• Differential wavefront sensing measures the angle between interfering wavefronts:
Phasemeter avg pathlength change
testmass longitudinal
Phasemeter wavefront angle
testmass tiltdiff
splitphotodiode
44
-4
-3
-2
-1
0
1
2
3
4
-1500 -1000 -500 0 500 1000 1500
DW
S si
gnal
[rad
]
mirror tilt [urad]
tilt test: mirror 1 x (horizontal)
x1 Phixx1 Phiy
x12 Phixx12 Phiy
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-1500 -1000 -500 0 500 1000 1500
DC
sig
nal
mirror tilt [urad]
x1 DCxx1 DCy
x12 DCxx12 DCy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-1500 -1000 -500 0 500 1000 1500
cont
rast
mirror tilt [urad]
x1 contrastx12 contrast
-4
-3
-2
-1
0
1
2
3
4
-1500 -1000 -500 0 500 1000 1500
DW
S si
gnal
[rad
]
mirror tilt [urad]
tilt test: mirror 2 x (horizontal)
x1 Phixx1 Phiy
x12 Phixx12 Phiy
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
-1500 -1000 -500 0 500 1000 1500
DC
sig
nal
mirror tilt [urad]
x1 DCxx1 DCy
x12 DCxx12 DCy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-1500 -1000 -500 0 500 1000 1500
cont
rast
mirror tilt [urad]
x1 contrastx12 contrast
45
EM Test results: DC alignment signals
The calibration factor from test mass tilt angle α to ∆x is (with several idealizations) given byd(∆x)/dα = 2
√2/π L/w, where L ≈ 25 . . .50cm is the lever arm from test mass to photodiode, and
w ≈ 0.5 . . .1mm the beam radius at the photodiode.
Rot. TM1 Rot. TM2 units
x1 ifo predicted (numerical) 759 0 1/radx1 ifo measured (x) 357 0 1/radx1 ifo measured (y) 310 0 1/rad
x1 − x2 ifo predicted (numerical) 1147 304 1/radx1 − x2 ifo measured (x) 537 180 1/radx1 − x2 ifo measured (y) 468 184 1/rad
• conversion factor depends on beam parameters and beam power ratio (unbalanced during thismeasurement).
• DC alignment signals have higher noise than DWS signals.
• DC alignment signals are used for rough alignment of test mass when DWS contrast is insufficient.
46
EM Test results: DC alignment signals
0.001
0.01
0.1
1
10
100
10-3 10-2 0.1 1 10
LSD
(µra
d/√H
z)
Frequency (Hz)
DC PDR xDC PDR yDC PD1 xDC PD1 y
DC PD12 xDC PD12 y
47
EM Test results: Differential wavefront sensing (DWS)
The conversion factor of test-mass angle α to (differential) phase readout ϕ is analytically:
ϕ/α = 2√
2πw(z)/λ ≈ 5000 rad/rad.
Rot. TM1 Rot. TM2 units
x1 ifo predicted (numerical) 5337 0 rad/radx1 ifo measured (x) 5441 0 rad/radx1 ifo measured (y) 5167 0 rad/rad
x1 − x2 ifo predicted (numerical) 4963 5994 rad/radx1 − x2 ifo measured (x) 5365 7263 rad/radx1 − x2 ifo measured (y) 5072 6940 rad/rad
• conversion factor depends on beam parameters; calibration is necessary.
• Better than the angular readout capability of the capacitive sensors; will be used to stabilize thealignment of the test masses.
• DWS works only when there are fringes (test mass absolute alignment better than 300 µrad).Otherwise, DC alignment signals are used for rough alignment of test mass.
48
EM Test results: Differential wavefront sensing (DWS)
1
10
100
1000
10000
10-3 10-2 0.1 1 10
TM
1-T
M2
diff
eren
tial m
isal
ignm
ent (
nrad
/√H
z)
Frequency (Hz)
PDR xPDR y
PD12 xPD12 y
10 nrad/sqrt(Hz)
49
Summary
• interferometry and phase measurement for LTP work as predicted.
• some minor refinements are needed in the construction procedure.
• environmental and performance testing was successful.
• further investigations will concentrate on the ‘small vector’ noise.
50