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 Light RADAR (LiDAR)
 Laser Doppler velocimetry (LDV)
Wind speed measurement

Doppler frequency shift  due to scattering from   2VLOS 
the aerosols: .
VLOS
www.mitsubishielectric.com
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Single frequency (SF) LDV

Emit single beam with single frequency.

Homodyne detection of single Doppler frequency shift.
Mirror
reference beam
SF light source
f1’
f1
BS
target beam
PD
Laser Dynamics Lab., NTHU
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Speckle noise

Speckle: When a coherent light is scattered back from a target with rough surface, the wavelets interfere constructively and destructively, 
random distribution of bright and dark spots.
Laser Dynamics Lab., NTHU
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Impact of speckle noise

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Transversal motion of moving target,  time‐
varying speckle pattern,  random AM/PM.
transverse velocity
Single-Frequency, f
axial velocity
diffuser
I d , speckle (t )  I 0 cos[2kx(t )  S (t )]
1 dS (t )
2 dt
Roughness profile of laser
2 ( pt , t ) projected area
S (t )  2

f d ,speckle 
1 d
2k ( vt )  S (t )  f d  1 dS (t )
2 dt
2 dt
Laser Dynamics Lab., NTHU
fd
Double frequency (DF) LDV

Emit single beam with two frequencies.

The uncertainties of 2 Doppler frequency shifts will cancel with each other in homodyne detection.
Mirror
reference beam
DF light source
f1
f1’
f2 BS
f2’
target beam
PD
Laser Dynamics Lab., NTHU
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Homodyne detection of DF LDV
Mixing
Electrical beating Optical beating
Transmit (signal processing) (PD BW < 1GHz)
(f1,2)
f12-fd,2 f12 f1’2’ f12+fd,1 f2 f2’
fd,2 fd,1
fd,12 = fd,1-fd,2
= 2v(f1-f2)/c
fd,2
= 2vf12/c
Hz

kHz
fd,12
GHz
Received Doppler‐shifted signals (SF‐LDV)
I1 (t )  I 0 cos[2f d ,1t  S ,1 (t )   P ,1 (t )],
I 2 (t )  I 0 cos[2f d , 2t  S , 2 (t )  P , 2 (t )],

THz
where S ,1( 2 ) (t )  2
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Received (f‘1,2)
f 1 f1 ’
fd,1
f12
2 ( pt , t )
.
1( 2) ~1.3 m
(f1,2)
Mixed signal (DF‐LDV)
I12 (t )  I12 cos[2f d ,12t   S (t )   P (t )],
I12 (t )  I12 cos(2f d ,12t ),
2 ( pt , t )
2 ( pt , t )
if  ( pt , t )  eff ,  P  const.
where  S (t )  2
 2
,
eff
(c / f12 )
 P (t )  P ,1 (t )  P , 2 (t )
~2.7 cm (f12)
Experimental results

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Axial velocity 4 cm/s, optical path difference ~ 0.
Single-Frequency LDV
Dual-Frequency LDV
0.42 mm/s
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folds
0.36 mm/s
Increasing speckle noise
Increasing speckle noise
Laser Dynamics Lab., NTHU
A2
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 Optical oscilloscope
 Time lens
What is optical oscilloscope?
Frequency
Frequency
Intensity
Intensity
Phase
Phase
in real time!
in real time!
Electric signal
Electric oscilloscope (bandwidth < 60 GHz)
Frequency
Frequency
Intensity
Intensity
Phase
Phase
in real time!
in real time!
Ultrafast optical signal (carrier ~100s THz, bandwidth ~10 THz)
Optical oscilloscope
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Waveform modulation due to GVD

According to the time domain formula:

e0 (t )  Re u0 (t )  e j0t
u1 (t )   u0 ( )  e
j ( t  ) 2 ( 2 Dg )
u1 (t )
e1 (t )


e1 (t )  Re u1 (t )  e j0t
d  e
t2
j
2 Dg
  u0 ( )  e
j

 2  2 t
2 Dg
1 (t )  u1 (t )
d
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Extra temporal phase modulation
j
12
0t 2
2 fT
e
 Introducing a quadratic temporal phase on u1(t), where fT is the “focal time”; the output temporal envelope becomes:
u2 (t )  e

t 2  0 1
j

2  f T Dg




 u0 ( )  e
j
if fT = -Dg0
 2  2 t
2 Dg
d 
  u0 ( )  e
j
 2  2 t
2 Dg
d
The spectral envelope U2() = F{u2(t)} is: 
U 2 ( )    u0 ( )  e
j ( 2  2 t ) ( 2 Dg )
 U 2 ( )  u0 ( Dg  )
2
2

jt
d  e dt  u0 (t )  e
j t 2 ( 2 Dg )
t   Dg 
Acquire |u0(t)|2 by measuring |U2()|2



The above formula shows that the ultrafast temporal intensity profile |u0(t)|2 is a scaled power spectrum |U2()|2 of the (first spectrally & then temporally) phase modulated signal.
Since a spectrometer can acquire |U2()|2 in real time (can be as fast as 1 ns), so is |u0(t)|2!
The quadratic temporal phase modulation acts like a lens in diffraction (causing quadratic spatial phase modulation). That’s why it is called “time lens”.
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Setup

A grating pair provides tunable GDD (Dg).

A sinusoidally driven EO modulator gives a temporal phase Acosmt,  fT  0 ( Am2 ) near an extreme.
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Experimental results

Parameters: A = 51 rad, m= 25.2 GHz, 0 =1.064
m,  fT = 32 ns, Dg = -18 ps2, scaling = 30.3 ps/nm.

The width and shape of the 11.8 ps pulse are successfully retrieved in real time.
Appl. Phys. Lett., 64, 270 (1994)
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Performance issues


Time resolution: An over‐short pulse is stretched (by Dg) longer than the modulation aperture (1/m).
Temporal field of view: An over‐long pulse will be modulated non‐quadratically.
Input: 1.9 ps
Input: 63 ps
Appl. Phys. Lett., 64, 270 (1994)
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