Computationally-assisted multi-heterodyne spectroscopy

Patent metadata

Field	Value
Publication number	US-10126170-B2
Application number	US-201615259687-A
Country	US
Kind code	B2
Filing date	Sep 8, 2016
Priority date	Sep 10, 2015
Publication date	Nov 13, 2018
Grant date	Nov 13, 2018

Abstract

According to one aspect, a multi-heterodyne system is disclosed, which comprises a first laser source for generating multi-mode radiation having a frequency spectrum characterized by a first plurality of phase coherent frequencies, and a second laser source for generating multi-mode radiation having a frequency spectrum characterized by a second plurality of phase coherent frequencies. The system further comprises at least one detector for detecting a combination of the multi-mode radiation generated by the first and second laser sources so as to provide a multi-heterodyne signal having a frequency spectrum characterized by a plurality of beat frequencies, each beat frequency corresponding to a pairwise difference in the first and second plurality of phase coherent frequencies. The system further comprises an analyzer for receiving said multi-heterodyne signal and configured to employ a predictive model of the multi-heterodyne signal to provide estimates of any of phase error and timing error associated with the beat frequencies.

First claim

What is claimed is:

1. A multi-heterodyne system, comprising:
a first laser source for generating multi-mode radiation having a frequency spectrum characterized by a first plurality of phase coherent frequencies,
a second laser source for generating multi-mode radiation having a frequency spectrum characterized by a second plurality of phase coherent frequencies,
at least one detector for detecting a combination of said multi-mode radiation generated by said first and second laser sources so as to provide a multi-heterodyne signal having a frequency spectrum characterized by a plurality of beat frequencies each beat frequency corresponding to a pairwise difference in said first and second plurality of phase coherent frequencies,
an analyzer for receiving said multi-heterodyne signal and configured to employ a predictive model of said multi-heterodyne signal to provide estimates of any of phase error and timing error associated with said beat frequencies.

2. The system of claim 1 , wherein said analyzer corrects any of said phase error and timing error of said detected multi-heterodyne signal based on said estimates so as to generate a corrected multi-heterodyne signal.

3. The multi-heterodyne system of claim 2 , wherein said predictive model of said multi-heterodyne signal (y(t)) is defined as:

y
⁡

(
t
)

=

∑
n

⁢

A
n

⁢

e

i
⁢

⁢
2
⁢
π
⁢

∫

f
n

⁢
d
⁢

⁢
t

=

∑
n

⁢

r
n

⁢

e

i
⁢

⁢

φ
n

⁢

e

i
⁢

⁢
2
⁢
π
⁢

∫

f
n

⁢
dt

wherein,
A n denotes a complex amplitude associated with n th beat frequency characterized by a real amplitude r n and a phase φ n ,
ƒ n denotes the frequency of the n th beat frequency.

4. The multi-heterodyne system of claim 3 , wherein said analyzer minimizes an error function defined as:

J
⁡

(
x
)

=

∑
k

⁢



y
k

-

h
⁡

(

x
k

)



R

-
1

2

+



x
k

-

f
⁡

(

x

k
-
1

)



Q

-
1

2

wherein,
x k denotes a state of the system at time k,
y k denotes measurement of the multi-heterodyne signal at time k,
h(x k ) denotes the measurement function h evaluated at state x k and defined as follows:
h(x k )=Σ n A nk e i2πϕ nk =Σ n r nk e iφ nk e iϕ nk , wherein A nk , r nk , φ nk , ϕ nk denote, respectively, A n , r n , φ n and ϕ n evaluated at time k,

ƒ(x k ) denotes the time evolution function ƒ evaluated at state x k such that:
r n(k+1) =r nk
φ n(k+1) =φ nk

ϕ n(k+1) =ϕ nk +2πΔ t ƒ nk

wherein r n(k+1) , φ n(k+1) , ϕ n(k+1) , denote, respectively, r n , φ n , and ϕ n evaluated at time k+1,
R is said measurement noise covariance, and
Q is said process noise covariance.

5. The multi-heterodyne system of claim 1 , wherein said analyzer is further configured to minimize an error function associated with a difference between said detected and sa

Assignees

• Massachusetts Inst Technology

Inventors

• Burghoff David
• Yang Yang
• Hu Qing

Classifications

• G01J9/04

  by beating two waves of a same source but of different frequency and measuring the phase shift of the lower frequency obtained · CPC title

• G01J3/4531

  Devices without moving parts · CPC title

• G01J3/42

  Absorption spectrometry; Double beam spectrometry; Flicker spectrometry; Reflection spectrometry (beam switching arrangements G01J3/08) · CPC title

• G01J3/28 Primary

  Investigating the spectrum (using colour filters G01J3/51) · CPC title

• G01J3/10

  Arrangements of light sources specially adapted for spectrometry or colorimetry · CPC title