Method for measuring complex degree of coherence of random optical field by using mutual intensity-intensity correlation

Abstract

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.

Claims

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.sub.S.sup.(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.sub.S.sup.(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.sub.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.sub.S.sup.(1,2)(r.sub.1,r.sub.2) between the light intensity distribution information I.sub.S.sup.(1)(r) of the first combined light and the light intensity distribution information I.sub.S.sup.(2)(r) of the second combined light; S62: calculating a mutual correlation G.sub.B.sup.(1,2)(r.sub.1,r.sub.2) obtained by adding the reference light and the to-be-tested light; S63: calculating a difference value ΔG.sup.(1,2)(r.sub.1,r.sub.2,Δϕ) between the two mutual correlations G.sub.S.sup.(1,2)(r.sub.1,r.sub.2) and G.sub.B.sup.(1,2)(r.sub.1,r.sub.2); and S64: analyzing the difference value ΔG.sup.(1,2)(r.sub.1,r.sub.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.sub.1,r.sub.2)=E*(r.sub.1)E(r.sub.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.sub.1 and r.sub.2 in the space may be defined as: $\begin{array}{cc}\mu \left(r_1,r_2\right)=\frac{W\left(r_1,r_2\right)}{\sqrt{S\left(r_1\right)S\left(r_2\right)}},& \left(2\right)\end{array}$ 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.sub.r.sup.(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.sub.r.sup.(2)(r), and an electrical field of the to-be-tested light is denoted as E(r); there is a phase difference of $\frac{\pi }{2}$ between the electrical fields E.sub.r.sup.(1)(r) and E.sub.r.sup.(2)(r), that is: $\begin{array}{cc}\mathrm{\Delta \varphi }=\mathrm{Arg}\left[E_r^{\left(1\right)}\left(r\right)\right]-\mathrm{Arg}\left[E_r^{\left(2\right)}\left(r\right)\right]=\frac{\pi }{2},& \left(3\right)\end{array}$ wherein Arg represents calculating the phase of a complex function; an electrical field E.sub.S.sup.(1)(r) of the first combined light and an electrical field E.sub.S.sup.(2)(r) of the second combined light are represented as follows:
E.sub.S.sup.(1)(r)=E(r)+E.sub.r.sup.(1)(r)  (4),
E.sub.S.sup.(2)(r)=E(r)+E.sub.r.sup.(2)(r)  (5), the mutual correlation between the light intensity distribution information I.sub.S.sup.(1)(r) of the first combined light and the light intensity distribution information I.sub.S.sup.(2)(r) of the second combined light is:
G.sub.S.sup.(1,2)(r.sub.1,r.sub.2)=I.sub.S.sup.(1)(r.sub.1)I.sub.S.sup.(2)(r.sub.2)  (6), and according to theorem of Gaussian statistics, Formula (1) to Formula (5) are substituted into Formula (6), to obtain:
G.sub.S.sup.(1,2)(r.sub.1,r.sub.2)=G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)=S.sub.S.sup.(1)(r.sub.1)S.sub.S.sup.(2)(r.sub.2)+|W(r.sub.1,r.sub.2)|.sup.2+2√{square root over (S.sub.r.sup.(1)(r.sub.1)S.sub.r.sup.(2)(r.sub.2))}Re[e.sup.iΔϕW(r.sub.1,r.sub.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: $\begin{array}{cc}\begin{array}{c}{G}_B^{\left(1,2\right)}\left(r_1,r_2\right)=.Math.\left[S_r^{\left(1\right)}\left(r_1\right)+I\left(r_1\right)\right]\left[S_r^{\left(2\right)}\left(r_2\right)+I\left(r_2\right)\right].Math.\\ =S_S^{\left(1\right)}\left(r_1\right)S_S^{\left(2\right)}\left(r_2\right)+|W\left(r_1,r_2\right){|}^2.\end{array}& \left(8\right)\end{array}$

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:
ΔG.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)=G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)−G.sub.B.sup.(1,2)(r.sub.1,r.sub.2)=√{square root over (S.sub.r.sup.(1)(r.sub.1)S.sub.r.sup.(2)(r.sub.2))}Re[e.sup.iΔϕW(r.sub.1,r.sub.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.sup.(1,2)(r.sub.1,r.sub.2,Δϕ), taking a distribution Δϕ to be 0 and $\frac{\pi }{2},$ and obtaining the real part and the imaginary part of the complex degree of coherence according to Formula (2): $\begin{array}{cc}\mathrm{Re}\left[\mu \left(r_1,r_2\right)\right]=\frac{\Delta G^{\left(1,2\right)}\left(r_1,r_2,\mathrm{\Delta \varphi }=0\right)}{2\sqrt{S_r^{\left(1\right)}\left(r_1\right)S_r^{\left(2\right)}\left(r_2\right)S\left(r_1\right)S\left(r_2\right)}},& \left(10\right)\\ \mathrm{Im}\left[\mu \left(r_1,r_2\right)\right]=\frac{\Delta G^{\left(1,2\right)}\left(r_1,r_2,\mathrm{\Delta \varphi }=\frac{\pi }{2}\right)}{2\sqrt{S_r^{\left(1\right)}\left(r_1\right)S_r^{\left(2\right)}\left(r_2\right)S\left(r_1\right)S\left(r_2\right)}},& \left(11\right)\end{array}$ 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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of a test optical path according to the present invention; and

(2) FIG. 2 is a schematic flowchart according to the present invention.

(3) Reference numerals: 1, to-be-tested light source; 2, reference light source; 3, quarter-wave plate; 4, beam splitter; 5, condensing element; 6, light detector; 7, computer; and 8, reflector.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(4) The present invention is further described below with reference to the accompanying drawings and specific embodiments, to enable a person skilled in the art to better understand and implement the present invention. However, the embodiments are not used to limit the present invention.

(5) Referring to FIG. 1 and FIG. 2, the present 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 following steps:

(6) S1. a test optical path including a quarter-wave plate 3, a beam splitter 4, a condensing element 5, and a light detector 6 is built, a laser is used as reference light, where reference light source 2 emits the reference light, the reference light is modulated by the quarter-wave plate and then enters the beam splitter 4, at the same time a to-be-tested light source 1 emits to-be-tested light, the to-be-tested light enters the beam splitter 4, the beam splitter 4 combines the modulated reference light and the to-be-tested light to obtain combined light, and the combined light passes through the condensing element 5 to be imaged on the light detector 6. The condensing element 5 may be a thin lens. Herein, to enable the reference light and the to-be-tested light to be both emitted to the beam splitter 4, a reflector 8 may be added to an incident optical path of the reference light or the to-be-tested light, to adjust the direction of the optical path. The light detector 6 is connected to a computer 7. The computer 7 stores information collected by the light detector 6 and performs computation. Herein, the to-be-tested light is random light.

(7) S2. the quarter-wave plate 3 is rotated 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.sub.S.sup.(1)(r) of the first combined light by using the light detector.

(8) S3. the quarter-wave plate 3 is rotated 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.sub.S.sup.(2)(r) of the second combined light by using the light detector.

(9) S4. the reference light is blocked from reaching the beam splitter, and in this case, the to-be-tested light is not blocked, and light intensity distribution information I(r) of the to-be-tested light is photographed and record by using the light detector.

(10) S5. the to-be-tested light is blocked from reaching the beam splitter, and in this case, the reference light is not blocked, and light intensity distribution information S.sub.r(r) of the reference light is photographed and record by using the light detector.

(11) S6. the amplitude and phase of a complex degree of coherence of the to-be-tested light are calculated.

(12) The “calculating the amplitude and phase of a complex degree of coherence of the to-be-tested light” specifically includes the following steps:

(13) S61. a mutual correlation G.sub.S.sup.(1,2)(r.sub.1,r.sub.2) between the light intensity distribution information I.sub.S.sup.(1)(r) of the first combined light and the light intensity distribution information I.sub.S.sup.(2)(r) of the second combined light is calculated.

(14) Specifically, according to the definition of a second-order coherence matrix in the space-frequency domain proposed by Wolf et al., a second-order statistical feature (including the coherence) of the to-be-tested light can be represented, by using a cross-spectral density function, as:
W(r.sub.1,r.sub.2)=E*(r.sub.1)E(r.sub.2)  (1),

(15) where 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.sub.1 and r.sub.2 in the space may be defined as:

(16) $\begin{array}{cc}\mu \left(r_1,r_2\right)=\frac{W\left(r_1,r_2\right)}{\sqrt{S\left(r_1\right)S\left(r_2\right)}},& \left(2\right)\end{array}$

(17) where S(r)=W(r,r)=I(r) represents average light intensity of a random optical field at the point r in the space;

(18) 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.sub.r.sup.(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.sub.r.sup.(2)(r), and an electrical field of the to-be-tested light is denoted as E(r);

(19) because E.sub.r.sup.(1)(r) is an electrical field of the reference light obtained when the fast axis of the quarter-wave plate coincides with the polarization direction and E.sub.r.sup.(2)(r) is an electrical field of the reference light obtained when the slow axis of the quarter-wave plate coincides with the polarization direction, there is a phase difference of

(20) $\frac{\pi }{2}$
between the electrical fields E.sub.r.sup.(1)(r) and E.sub.r.sup.(2)(r), that is:

(21) $\begin{array}{cc}\mathrm{\Delta \varphi }=\mathrm{Arg}\left[E_r^{\left(1\right)}\left(r\right)\right]-\mathrm{Arg}\left[E_r^{\left(2\right)}\left(r\right)\right]=\frac{\pi }{2},& \left(3\right)\end{array}$

(22) where Arg represents calculating the phase of a complex function;

(23) an electrical field E.sub.S.sup.(1)(r) of the first combined light and an electrical field E.sub.S.sup.(2)(r) of the second combined light are represented as follows:
E.sub.S.sup.(1)(r)=E(r)+E.sub.r.sup.(1)(r)  (4),
E.sub.S.sup.(2)(r)=E(r)+E.sub.r.sup.(2)(r)  (5),

(24) the mutual correlation between the light intensity distribution information I.sub.S.sup.(1)(r) of the first combined light and the light intensity distribution information I.sub.S.sup.(2)(r) of the second combined light is:
G.sub.S.sup.(1,2)(r.sub.1,r.sub.2)=I.sub.S.sup.(1)(r.sub.1)I.sub.S.sup.(2)(r.sub.2)  (6), and

(25) according to theorem of Gaussian statistics, Formula (1) to Formula (5) are substituted into Formula (6), to obtain:
G.sub.S.sup.(1,2)(r.sub.1,r.sub.2)=G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)=S.sub.S.sup.(1)(r.sub.1)S.sub.S.sup.(2)(r.sub.2)+|W(r.sub.1,r.sub.2)|.sup.2+2√{square root over (S.sub.r.sup.(1)(r.sub.1)S.sub.r.sup.(2)(r.sub.2))}Re[e.sup.iΔϕW(r.sub.1,r.sub.2)]  (7).

(26) Re represents calculating the real part of the complex function. It is found that the mutual intensity-intensity correlation G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ) is correlated to a phase difference Δϕ between reference optical paths, and the amplitude information and phase information of the degree of coherence of the to-be-tested light are also included in G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ). For example: when Δϕ=0, the last term in Formula (7) includes the real part information of the complex degree of coherence; and when

(27) 0$\mathrm{\Delta \varphi }=\frac{}{2},$
the last term in Formula (7) includes the imaginary part information of the complex degree of coherence. The phase difference between the two reference optical paths can be controlled to obtain the real part information and the imaginary part information of the complex degree of coherence, so as to obtain the amplitude and phase of the complex degree of coherence of a random light field. In addition, it is found from Formula (7) that the mutual intensity-intensity correlation function includes background terms.

(28) To remove background terms, the mutual intensity-intensity correlation of incoherent superposition of the reference light and the to-be-tested light, that is, S62, is introduced.

(29) S62. a mutual correlation G.sub.B.sup.(1,2)(r.sub.1,r.sub.2) between the reference light and the to-be-tested light is calculated.

(30) $\begin{array}{cc}\begin{array}{c}{G}_B^{\left(1,2\right)}\left(r_1,r_2\right)=.Math.\left[S_r^{\left(1\right)}\left(r_1\right)+I\left(r_1\right)\right]\left[S_r^{\left(2\right)}\left(r_2\right)+I\left(r_2\right)\right].Math.\\ =S_S^{\left(1\right)}\left(r_1\right)S_S^{\left(2\right)}\left(r_2\right)+|W\left(r_1,r_2\right){|}^2.\end{array}& \left(8\right)\end{array}$

(31) S63. a difference value ΔG.sup.(1,2)(r.sub.1,r.sub.2,Δϕ) between the two mutual correlations G.sub.S.sup.(1,2)(r.sub.1,r.sub.2) and G.sub.B.sup.(1,2)(r.sub.1,r.sub.2) is calculated.
ΔG.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)=G.sub.S.sup.(1,2)(r.sub.1,r.sub.2,Δϕ)−G.sub.B.sup.(1,2)(r.sub.1,r.sub.2)=√{square root over (S.sub.r.sup.(1)(r.sub.1)S.sub.r.sup.(2)(r.sub.2))}Re[e.sup.iΔϕW(r.sub.1,r.sub.2)]  (9).

(32) S64. the difference value ΔG.sup.(1,2)(r.sub.1,r.sub.2,Δϕ) between the two mutual correlations is analyzed, to obtain the amplitude and phase of the complex degree of coherence of the to-be-tested light.

(33) For ΔG.sup.(1,2)(r.sub.1,r.sub.2,Δϕ), a distribution Δϕ is taken to be 0 and

(34) $\frac{\pi }{2},$
and at the same time the real part and the imaginary part of the complex degree of coherence are obtained according to Formula (2):

(35) $\begin{array}{cc}\mathrm{Re}\left[\mu \left(r_1,r_2\right)\right]=\frac{\Delta G^{\left(1,2\right)}\left(r_1,r_2,\mathrm{\Delta \varphi }=0\right)}{2\sqrt{S_r^{\left(1\right)}\left(r_1\right)S_r^{\left(2\right)}\left(r_2\right)S\left(r_1\right)S\left(r_2\right)}},& \left(10\right)\\ \mathrm{and}& \\ \mathrm{Im}\left[\mu \left(r_1,r_2\right)\right]=\frac{\Delta G^{\left(1,2\right)}\left(r_1,r_2,\mathrm{\Delta \varphi }=\frac{\pi }{2}\right)}{2\sqrt{S_r^{\left(1\right)}\left(r_1\right)S_r^{\left(2\right)}\left(r_2\right)S\left(r_1\right)S\left(r_2\right)}},& \left(11\right)\end{array}$

(36) in the foregoing formulas, Im represents calculating the imaginary part of the complex function, and the amplitude and phase of the complex degree of coherence of the to-be-tested light are obtained by using Formula (10) and Formula (11).

(37) In the invention, the light detector is a CCD or a CMOS. In this embodiment, the used CCD is the professional camera of the model Grasshopper GRAS-20S4M developed by the Point Grey Company. For specific parameters, the horizontal resolution is 1624, the vertical resolution is 1224, and the frame frequency/row frequency is 30 fps. The CCD is connected to a computer installed with software named Point Grey provided by the Point Grey Company. The foregoing software is used for observing and saving image information received by the CCD. After the CCD is connected to the computer, the software Point Grey is opened to record and save the image information received by the CCD.

(38) In the present invention, the reference light is emitted by a helium-neon laser. The helium-neon laser generates fully coherent line polarized light with a wavelength of 632.8 nanometers.

(39) The to-be-tested light may be produced by using the solution in Patent No. CN201410399805.8.

(40) The foregoing embodiments are merely preferred embodiments used to fully describe the present invention, and the protection scope of the present invention is not limited thereto. Equivalent replacements or variations made by a person skilled in the art to the present invention all fall within the protection scope of the present invention. The protection scope of the present invention is as defined in the claims.