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

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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

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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

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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

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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

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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

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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

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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…

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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

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