We propose a new algorithm based on the Fourier transform with matched non-linear frequency modulation for processing femtosecond laser ranging data. The algorithm allows us to compensate for both the influence of the third-order dispersion in the fiber-based dispersive Fourier spectrometer and the influence of imbalanced second- and third-order dispersions in the interferometer. Computer simulations and experimental results show that the proposed algorithm significantly increases the accuracy of measuring the position of an object at larger displacements than the well-established non-linear time stretching.

1.
D. H.
Dolan
, “
Extreme measurements with photonic Doppler velocimetry (PDV)
,”
Rev. Sci. Instrum.
91
(
5
),
051501
(
2020
).
2.
A. V.
Andriyash
,
S. M.
Ismailov
,
V. G.
Kamenev
,
G. V.
Kaplukov
,
A. N.
Kondratev
,
P. V.
Kubasov
,
S. E.
Kuratov
,
D. B.
Rogozkin
,
A. A.
Tikhov
,
I. V.
Tur
,
A. S.
Shubin
,
S. A.
Shubin
, and
P. N.
Yaroschuk
, “
Simultaneous application of photon Doppler velocimetry and coherent backscattering for probing ejecta from shock-loaded samples
,”
J. Appl. Phys.
132
,
123103
(
2022
).
3.
S.
Bovid
,
A.
Clauer
,
M.
Kattoura
,
A.
Vivek
,
G.
Daehn
, and
S.
Niezgoda
, “
Measurement and characterization of nanosecond laser driven shockwaves utilizing photon Doppler velocimetry
,”
J. Appl. Phys.
129
(
20
),
205101
(
2021
).
4.
V. A.
Ogorodnikov
,
S. V.
Erunov
,
K. N.
Panov
,
E. A.
Chudakov
,
I. A.
Blinov
,
A. B.
Georgievskaya
,
D. N.
Zamyslov
, and
I. R.
Farin
, “
Characteristics of “dust” fluxes from the surface of copper and lead liners exposed to one or two successive shock waves
,”
JETP Lett.
117
(
10
),
747
754
(
2023
).
5.
M.
Rhodes
,
J.
Catenacci
,
M.
Howard
,
B.
La Lone
,
N.
Kostinski
,
D.
Perry
,
C.
Bennett
, and
J.
Patterson
, “
Validating data analysis of broadband laser ranging
,”
Rev. Sci. Instrum.
89
,
035111
(
2018
).
6.
L.
Zhao
,
C.
Zhao
,
C.
Xia
,
Z.
Zhang
,
T.
Wu
, and
H.
Xia
, “
Nanometer precision time-stretch femtosecond laser metrology using phase delay retrieval
,”
J. Lightwave Technol.
39
(
15
),
5156
5162
(
2021
).
7.
B. M.
La Lone
,
B. R.
Marshall
,
E. K.
Miller
,
G. D.
Stevens
,
W. D.
Turley
, and
L. R.
Veeser
, “
Simultaneous broadband laser ranging and photonic Doppler velocimetry for dynamic compression experiments
,”
Rev. Sci. Instrum.
86
,
023112
(
2015
).
8.
J.
Wang
,
S.
Liu
,
S.
Tao
,
J.
Li
, and
Q.
Peng
, “
A hybrid system for simultaneous velocity and distance measurements in dynamic experiments
,”
Rev. Sci. Instrum.
94
,
085117
(
2023
).
9.
J.
Wang
,
S.
Liu
,
J.
Li
,
S.
Tao
,
G.
Chen
,
X.
Deng
, and
Q.
Peng
, “
Multi-reference broadband laser ranging to increase the measuring range
,”
Rev. Sci. Instrum.
90
,
033108
(
2019
).
10.
L.
Zhao
,
H.
Xia
,
Y.
Hu
,
T.
Wu
,
Z.
Zhang
,
J.
Han
,
Y.
Wu
, and
T.
Luo
, “
Time-stretched femtosecond lidar using microwave photonic signal processing
,”
J. Lightwave Technol.
38
(
22
),
6265
6271
(
2020
).
11.
H.
Xia
and
C.
Zhang
, “
Ultrafast ranging lidar based on real-time Fourier transformation
,”
Opt. Lett.
34
(
14
),
2108
2110
(
2009
).
12.
T.
Jannson
, “
Real-time Fourier transformation in dispersive optical fibers
,”
Opt. Lett.
8
(
4
),
232
234
(
1983
).
13.
K.
Goda
,
D. R.
Solli
,
K. K.
Tsia
, and
B.
Jalali
, “
Theory of amplified dispersive Fourier transformation
,”
Phys. Rev. A
80
,
043821
(
2009
).
14.
T.
Godin
,
L.
Sader
,
A.
Khodadad Kashi
,
P.-H.
Hanzard
,
A.
Hideur
,
D. J.
Moss
,
R.
Morandotti
,
G.
Genty
,
J. M.
Dudley
,
A.
Pasquazi
,
M.
Kues
, and
B.
Wetzel
, “
Recent advances on time-stretch dispersive Fourier transform and its applications
,”
Adv. Phys.: X
7
(
1
),
2067487
(
2022
).
15.
H.
Xia
and
C.
Zhang
, “
Ultrafast and Doppler-free femtosecond-optical ranging based on dispersive-frequency-modulated interferometry
,”
Opt. Express
18
(
5
),
4118
(
2010
).
16.
X.
Li
,
G.
Bi
,
S.
Stankovic
, and
A. M.
Zoubir
, “
Local polynomial fourier transform: A review on recent developments and applications
,”
Signal Process.
91
(
6
),
1370
1393
(
2011
).
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