time-of-flight measurement of ion energy tim freegarde dipartimento di fisica università di trento...
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Time-of-flight measurement of ion energy
Tim Freegarde
Dipartimento di FisicaUniversità di Trento
Italy
2
Time-of-flight measurement of ion energy
•basic principles•simple time-of-flight measurements and limitations
•spread-spectrum modulation•linearity and nonlinearity•pseudo-random sequences•transient (dynamical) problems
3
• retarding field analysis
Techniques for ion energy measurement
• Doppler spectroscopy
• time-of-flight
tdd
Vr
ramp generator
ions
ion signal
derivative
ions lens
spectrometer
ions
chopper
4
Principles of time-of-flight analysis
ions
chopper
detector
FAST
SLOW
TOTAL
time
MODULATION
• take care to transform distributions correctly
t
Lv
tt
Lv dd
2
221 mvE
vmvE dd t
N
mL
t
E
N
d
d
d
d2
3
t
N
L
t
v
N
d
d
d
d 2
5
Modulation mechanisms
• mechanical chopper
• electrostatic deflector / lens
• product generation• laser, eg photolysis• pulsed source
balance hole
trigger slit
Vin
6
Single pulse modulation
• transmit short pulse of ions modulation
distribution
distributiontime-of-flight
true
observed
=
• narrow pulse for good temporal resolution low signal: ions divided across distribution
• observed distribution is convolution of true distribution with modulating function
• modulation may be de-convoluted, but tends to amplify high-frequency noise
CONVOLUTION
7
Mathematical definitions
dtttgtftgtftI
• convolution (blurring)
dtttgtftC
• correlation
dtetfF ti
2
1• Fourier transform
tgtftgtf FTFTFT
• convolution theorem
tg
tgtftf
FT
FTFT 1
8
Frequency-domain analysis
• measure {a(),()} as functions of modulation frequency
ionsdetector
modulator
a
• time-of-flight distribution is given by
ieatN FT
time
9
Acquisition time
• variance of measured signal is - ie S/N = N N N
t
t
• to measure time-of-flight distributionwith
resolutionat S/N ratioand incident ion flux
we must run experiment for time
ttS
tN dd
tNttST dd22
of duration
PULSED MODULATION
• to measure single component at single frequencywe must run the experiment for time
SINUSOIDAL MODULATION
tNST dd2 2• for resolution over duration we must measure
components• we must therefore run the experiment for a total time
tNttST dd2 2
t t tt
10
Spread-spectrum modulation
• all frequencies present simultaneously in modulation function
SPREAD-SPECTRUM MODULATION
tNttST dd22
• phases adjusted so that components add in quadrature
• we therefore need only run the experiment for
tttN 2dd
5.02 a
flux at each frequency is
• truly random phases cause excursions out of range use pseudo-random functions
20 frequenciesrandom phases
11
Spread-spectrum history
http://www.ncafe.com/chris/pat2/index.html
• Hedy Lamarr (1913-2000), George Antheil (1900-
1959) patented submarine communication device• synchronized frequency hopping to evade jamming
• original mechanical action based upon pianolas
• used today in GPS, cellphones, digital radio
12
Spread-spectrum implementation
• We COULD implement our spread-spectrum measurement by
msi
m
s ea
atN FT
• modulating the ion beam with a spread-spectrum function• analyzing both modulation and signal for frequency components• deriving the time-of-flight distribution from
tM tM
tS
• However, if the modulating function is random – with -function autocorrelation – then the time-of-flight distribution may be extracted more directly from
dtttStMtN
• Autocorrelation of random modulating function of finite duration not quite zero
• We therefore use ideal, ‘pseudo-random’ functions
13
Linearity and saturation
• nonlinearity generates harmonics of frequencies present
tta
tbtayb
2cos1sin
sinsin
2
2
= +
2bxaxy • nonlinearity
• in deflector/modulator
• due to saturation
• spread-spectrum techniques use simultaneous detection at different frequencies harmonics introduce false signals nonlinearity should be avoided…
• … or exploited: •
•
• binary modulation can’t distinguish nonlinearity
14
Binary pseudo-random sequences
1 2 3 4 5 6 7 8
D
Clock
SHIFT REGISTER
time
clock input
output• sequence length bits
with n bit shift register12 n
=
AUTOCORRELATION
121 n
1
15
Dynamically-induced effects
electrostatic lens
detector
aperture
voltage
signal
pseudo-random sequence
V
•
•
V
• ions within lens element during transient see field-free change in potential lose or gain
Vq
• two new velocity classes:
• faster from 0-1 transition
• slower from 1-0 transition
16
Analysis of transient-induced signal
pseudo-random
sequence
fast ion transient signal
transient signal
moved left
transient signal
moved right
• negative correlation
• positive correlation
• contribution to ‘time-of-flight’ distribution:
time• additional correlations possible…
17
Time-of-flight measurement of ion energy
•pseudo-random time-of-flight measurement reduces data accumulation time by factor over pulse modulation
•simple pulse sequence generation•simple analysis by correlation•sensitive to nonlinearities and dynamic, transient effects
•offers high resolution at lowest energies to complement retarding field energy analysis
23
tt
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