Method for measuring complex degree of coherence of random optical field by using mutual intensity-intensity correlation
The invention discloses a method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation, including the steps of: building a test optical path; rotating a quarter-wave plate to enable the fast axis of the quarter-wave plate to be consistent with a polarization direction of reference light, to obtain light intensity distribution information of a first combined light; rotating the quarter-wave plate to enable the slow axis of the quarter-wave plate to be consistent with the polarization direction of the reference light, to obtain light intensity distribution information of a second combined light; blocking the reference light to obtain light intensity distribution information of to-be-tested light; blocking the to-be-tested light to obtain light intensity distribution information of the reference light; and calculating the amplitude and phase of a complex degree of coherence of the to-be-tested light.
1. A method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation, comprising steps of:
building a test optical path comprising a quarter-wave plate, a beam splitter, a condensing element, and a light detector, using a laser as reference light, wherein the reference light is modulated by the quarter-wave plate and then enters the beam splitter, and to-be-tested light enters the beam splitter at the same time, the beam splitter combines the modulated reference light and the to-be-tested light to obtain combined light, and the combined light passes through the condensing element to be imaged on the light detector;
rotating the quarter-wave plate to enable the fast axis of the quarter-wave plate to be consistent with a polarization direction of the reference light to obtain first combined light, and photographing and recording light intensity distribution information I S (1) (r) of the first combined light by using the light detector;
rotating the quarter-wave plate to enable the slow axis of the quarter-wave plate to be consistent with the polarization direction of the reference light to obtain second combined light, and photographing and recording light intensity distribution information I S (2) (r) of the second combined light by using the light detector;
blocking the reference light, and photographing and recording light intensity distribution information I(r) of the to-be-tested light by using the light detector;
blocking the to-be-tested light, and photographing and recording light intensity distribution information S r (r) of the reference light by using the light detector; and
calculating the amplitude and phase of a complex degree of coherence of the to-be-tested light.
2. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 1 , wherein calculating the amplitude and phase of a complex degree of coherence of the to-be-tested light comprises the following steps:
S61: calculating a mutual correlation G S (1,2) (r 1 ,r 2 ) between the light intensity distribution information I S (1) (r) of the first combined light and the light intensity distribution information I S (2) (r) of the second combined light;
S62: calculating a mutual correlation G B (1,2) (r 1 ,r 2 ) obtained by adding the reference light and the to-be-tested light;
S63: calculating a difference value ΔG (1,2) (r 1 ,r 2 ,Δϕ) between the two mutual correlations G S (1,2) (r 1 ,r 2 ) and G B (1,2) (r 1 ,r 2 ); and
S64: analyzing the difference value ΔG (1,2) (r 1 ,r 2 ,Δϕ) between the two mutual correlations, to obtain the amplitude and phase of the complex degree of coherence of the to-be-tested light.
3. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 1 , wherein S61 comprises:
according to a second-order coherence matrix in the space-frequency domain, representing, by using a cross-spectral density function, a second-order statistical feature of the to-be-tested light as:
W ( r 1 ,r 2 )= E *( r 1 ) E ( r 2 ) (1),
wherein E(r) represents a random electrical field at a point r in a space, a superscript asterisk represents a complex conjugate, an angle bracket represents ensemble averaging, and in this case, a complex spatial degree of coherence between two points r 1 and r 2 in the space may be defined as:
μ
(
r
1
,
r
2
)
=
W
(
r
1
,
r
2
)
S
(
r
1
)
S
(
r
2
)
,
(
2
)
wherein S(r)=W(r,r)= I(r) represents average light intensity of a random optical field at the point r in the space;
in the step of rotating the quarter-wave plate to enable the fast axis of the quarter-wave plate to be consistent with a polarization direction of the reference light, an electrical field of the reference light obtained through modulation by using the quarter-wave plate is denoted as E r (1) (r), in the step of “rotating the quarter-wave plate to enable the slow axis of the quarter-wave plate to be consistent with the polarization direction of the reference light”, an electrical field of the reference light obtained through modulation by using the quarter-wave plate is denoted as E r (2) (r), and an electrical field of the to-be-tested light is denoted as E(r);
there is a phase difference of
π
2
between the electrical fields E r (1) (r) and E r (2) (r), that is:
Δϕ
=
Arg
[
E
r
(
1
)
(
r
)
]
-
Arg
[
E
r
(
2
)
(
r
)
]
=
π
2
,
(
3
)
wherein Arg represents calculating the phase of a complex function;
an electrical field E S (1) (r) of the first combined light and an electrical field E S (2) (r) of the second combined light are represented as follows:
E S (1) ( r )= E ( r )+ E r (1) ( r ) (4),
E S (2) ( r )= E ( r )+ E r (2) ( r ) (5),
the mutual correlation between the light intensity distribution information I S (1) (r) of the first combined light and the light intensity distribution information I S (2) (r) of the second combined light is:
G S (1,2) ( r 1 ,r 2 )= I S (1) ( r 1 ) I S (2) ( r 2 ) (6), and
according to theorem of Gaussian statistics, Formula (1) to Formula (5) are substituted into Formula (6), to obtain:
G S (1,2) ( r 1 ,r 2 )= G S (1,2) ( r 1 ,r 2 ,Δϕ)= S S (1) ( r 1 ) S S (2) ( r 2 )+| W ( r 1 ,r 2 )| 2 +2√{square root over ( S r (1) ( r 1 ) S r (2) ( r 2 ))} Re [ e iΔϕ W ( r 1 ,r 2 )] (7).
4. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 3 , wherein S62 comprises:
G
B
(
1
,
2
)
(
r
1
,
r
2
)
=
〈
[
S
r
(
1
)
(
r
1
)
+
I
(
r
1
)
]
[
S
r
(
2
)
(
r
2
)
+
I
(
r
2
)
]
〉
=
S
S
(
1
)
(
r
1
)
S
S
(
2
)
(
r
2
)
+
|
W
(
r
1
,
r
2
)
|
2
.
(
8
)
5. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 4 , wherein S63 comprises:
Δ G S (1,2) ( r 1 ,r 2 ,Δϕ)= G S (1,2) ( r 1 ,r 2 ,Δϕ)− G B (1,2) ( r 1 ,r 2 )=√{square root over ( S r (1) ( r 1 ) S r (2) ( r 2 ))} Re [ e iΔϕ W ( r 1 ,r 2 )] (9).
6. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 5 , wherein S64 comprises:
for ΔG (1,2) (r 1 ,r 2 ,Δϕ), taking a distribution Δϕ to be 0 and
π
2
,
and obtaining the real part and the imaginary part of the complex degree of coherence according to Formula (2):
Re
[
μ
(
r
1
,
r
2
)
]
=
Δ
G
(
1
,
2
)
(
r
1
,
r
2
,
Δϕ
=
0
)
2
S
r
(
1
)
(
r
1
)
S
r
(
2
)
(
r
2
)
S
(
r
1
)
S
(
r
2
)
,
(
10
)
Im
[
μ
(
r
1
,
r
2
)
]
=
Δ
G
(
1
,
2
)
(
r
1
,
r
2
,
Δϕ
=
π
2
)
2
S
r
(
1
)
(
r
1
)
S
r
(
2
)
(
r
2
)
S
(
r
1
)
S
(
r
2
)
,
(
11
)
in the foregoing formulas, Im represents calculating the imaginary part of the complex function, and obtaining the amplitude and phase of the complex degree of coherence of the to-be-tested light by using Formula (10) and Formula (11).
7. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 1 , wherein the light detector is a charge-coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS).
8. The method for measuring a complex degree of coherence of a random optical field by using a mutual intensity-intensity correlation according to claim 1 , wherein the reference light is emitted by a helium-neon laser.