Method and system for measuring random light field coherence structure based on poisson bright spot experiment

Abstract

The application provides a measurement method and system of optical spatial coherent structure based on Poisson bright spot experiment. The method does not have requirements on statistical characteristics of random light field, and can accurately calculate the coherent structure in real time only by shooting three groups of light intensity. In addition, the system does not need additional reference light path, and can cope with severe environmental conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the related technical field, and particularly relates to a measurement method and system of a random light field coherent structure based on a Poisson bright spot experiment. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] Unlike optical parameters such as light intensity, phase, polarization state, etc., optical spatial coherence structure is one of the unique properties of partially coherent light beams, which is described by the second-order statistical properties of random electric field. Partially coherent light fields with specific optical coherence structures have been widely used in optical coherence tomography, optical communication, ghost imaging, super-resolution optical imaging and other research fields. The spatial coherence structure is a complex-valued parameter about four-dimensional spatial coordinates, containing amplitude and phase (real and imaginary parts), and its absolute value is greater than 0 and less than 1. For a Schell model partially coherent light beam, its spatial coherence structure is a two-dimensional structure about the position difference, and for a non-Schell model partially coherent light beam (non-uniform correlation), its two-dimensional spatial coherence structure is related to the selection of the reference point. In recent years, the spatial coherence structure of random light field has been used as an information carrier to realize high-security encryption of optical images and robust imaging in the far field. These research progresses all rely on the accurate measurement technology of the coherence structure. The most original coherence structure measurement method is to use the visibility and displacement of the interference fringes between two points in the Young's interference experiment to determine the amplitude and phase, respectively. To completely characterize the two-dimensional structure of the coherence structure, each position point needs to be independently scanned at the light source, which undoubtedly consumes a lot of time. Later, Y-shaped grating based on diffraction method, non-redundant aperture array and wavefront folding interferometer based on interference method, self-reference method and other measurement technologies were also proposed. However, these measurement methods require specific approximation conditions and have the disadvantages of complex device, high requirement for light collimation and experimental environment, wavelength sensitivity, etc. The recently proposed measurement of spatial coherence structure based on Hanbury Brown-Twiss experiment and generalized Hanbury Brown-Twiss experiment can perfectly overcome the above-mentioned shortcomings, but this method is only suitable for the case that the random light field to be measured satisfies Gaussian statistics, and this method needs to take a large number of random speckles for statistical calculation, and the measurement period is long, which is not suitable for high-speed changing random light field. Therefore, how to quickly and accurately measure the spatial coherence structure of a partially coherent light field with arbitrary statistical properties is still a challenging technology. SUMMARY

[0004] To address the aforementioned issues, this invention provides a method and system for measuring the coherent structure of a random light field based on a Poisson spot experiment. This method does not require statistical characteristics of the random light field; it only requires capturing three sets of light intensities to accurately calculate the coherent structure in real time. Furthermore, this system does not require an additional reference optical path and can cope with harsh environmental conditions.

[0005] To achieve the above objectives, the first aspect of the present invention provides a measurement system for a random optical field coherence structure based on a Poisson spot experiment, employing the following technical solution:

[0006] A laser used to emit linearly polarized beams;

[0007] A beam expander is used to expand the linearly polarized beam emitted by the laser.

[0008] A first reflective phase-type spatial light modulator is used to modulate the light beam passing through the beam expander;

[0009] An optical imaging system for imaging modulated light reflected by a first reflective phase-type spatial light modulator onto a second spatial light modulator;

[0010] A beam splitter is used to image the modulated light reflected by the first reflective phase-type spatial light modulator onto the first camera.

[0011] The second spatial light modulator and the second camera are located on the front and rear focal planes of the third convex lens, respectively.

[0012] One or more embodiments provide a method for measuring the coherent structure of a random optical field based on a Poisson spot experiment, and the measurement system for the coherent structure of a random optical field based on the above-mentioned Poisson spot experiment includes:

[0013] Obtain the light intensity distribution of the beam under test in the far field after the light source surface is blocked by an obstacle;

[0014] Choose different transmittance functions for obstacles;

[0015] Different far-field light intensities of the beam under test are obtained based on different obstacle transmission functions;

[0016] The intensity difference is obtained by subtracting different far-field light intensities;

[0017] The spatial coherence structure is calculated based on the obtained light intensity difference.

[0018] The beneficial effects of this invention are:

[0019] The system and method proposed in this invention do not require statistical characteristics of random light fields. Only three sets of light intensities need to be captured to accurately calculate the coherent structure in real time. In addition, the system does not require an additional reference optical path and can cope with harsh environmental conditions. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0021] Figure 1 This is a schematic diagram of the measurement system for the random optical field coherence structure based on the Poisson spot experiment in Embodiment 1 of the present invention;

[0022] Figure 2(a) is a schematic diagram of a random light field taken in the experiment of a partially coherent Shear mode source with Gaussian statistical characteristics in Embodiment 2 of the present invention;

[0023] Figure 2(b) is a schematic diagram of the probability density function curve of a partially coherent Shear mode source with Gaussian statistical characteristics in Embodiment 2 of the present invention.

[0024] Figure 2(c) shows the real part of the spatial coherence structure of the partially coherent Shear mode source with Gaussian statistical characteristics as measured in Embodiment 2 of the present invention.

[0025] Figure 2(d) shows the imaginary part of the spatial coherence structure measured by the partially coherent Shear mode source with Gaussian statistical characteristics in Embodiment 2 of the present invention;

[0026] Figure 2(e) is a schematic diagram of a random light field taken in an experiment with a partially coherent Shear mode source with non-Gaussian statistical characteristics in Embodiment 2 of the present invention.

[0027] Figure 2(f) is a schematic diagram of the probability density function curve of a partially coherent Shear mode source with non-Gaussian statistical characteristics in Embodiment 2 of the present invention.

[0028] Figure 2(g) shows the real part of the spatial coherence structure of the partially coherent Shear mode source with non-Gaussian statistical characteristics as measured in Embodiment 2 of the present invention.

[0029] Figure 2(h) shows the imaginary part of the spatial coherence structure measured by the partially coherent Shear mode source with non-Gaussian statistical characteristics in Embodiment 2 of the present invention;

[0030] Figure 3(a) is a schematic diagram of the real part of the position of the obstacle in the simulation of r0 = (0mm, 0mm) in Embodiment 2 of the present invention;

[0031] Figure 3(b) is a schematic diagram of the imaginary part of the position of the obstacle in the simulation of r0 = (0mm, 0mm) in Embodiment 2 of the present invention;

[0032] Figure 3(c) is a schematic diagram of the real part of the position of the obstacle in the experiment where the obstacle is located at r0 = (0mm, 0mm) in Embodiment 2 of the present invention;

[0033] Figure 3(d) is a schematic diagram of the imaginary part in the experiment where the obstacle is located at the position r0 = (0mm, 0mm) in Embodiment 2 of the present invention;

[0034] Figure 3(e) is a schematic diagram of the real part of the position of the obstacle in the simulation of r0 = (1mm, 0mm) in Embodiment 2 of the present invention.

[0035] Figure 3(f) Schematic diagram of the imaginary part of the position of the obstacle in the simulation of r0 = (1mm, 0mm) in Embodiment 2 of the present invention;

[0036] Figure 3(g) Schematic diagram of the real part of the position of the obstacle in the experiment where r0 = (1mm, 0mm) in Embodiment 2 of the present invention;

[0037] Figure 3(h) is a schematic diagram of the imaginary part of the position of the obstacle in the experiment where the obstacle is located at r0 = (1mm, 0mm) in Embodiment 2 of the present invention. Detailed Implementation

[0038] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0039] Example 1

[0040] Example 1

[0041] like Figure 1 As shown, this embodiment provides a measurement system for the coherent structure of a random optical field based on a Poisson spot experiment, comprising:

[0042] A laser used to emit linearly polarized beams;

[0043] A beam expander is used to expand the linearly polarized beam emitted by a laser.

[0044] The first reflective phase-type spatial light modulator is used to modulate the beam passing through the beam expander;

[0045] An optical imaging system for imaging modulated light reflected by a first reflective phase-type spatial light modulator onto a second spatial light modulator;

[0046] A beam splitter is used to image the modulated light reflected by the first reflective phase-type spatial light modulator onto the first camera.

[0047] The second spatial light modulator and the second camera are located on the front and rear focal planes of the third convex lens, respectively.

[0048] In this embodiment, as Figure 1 As shown, it includes the experimental generation of partially coherent light fields with a specific spatial coherent structure, i.e., Part 1, and the experimental measurement, i.e., Part 2.

[0049] In the first part of this embodiment, a linearly polarized beam with wavelength λ = 632.8 nm is emitted from a He-Ne laser, expanded by a beam expander, and uniformly illuminates a first reflective phase-type spatial light modulator. Since the phase-type spatial light modulator only modulates incident horizontally polarized light, the incident beam on the spatial light modulator is ensured to have a horizontal polarization direction by rotating a half-wave plate.

[0050] In the experimental setup of this embodiment, the principle of superposition of random modes and pseudo-modes is used to generate a random light field with specific spatial coherence structure and statistical characteristics. As shown in Figure 2(a), each mode can be loaded onto a first reflective phase-type spatial light modulator in the form of a hologram. The modulated light reflected by the first reflective phase-type spatial light modulator is imaged onto a second spatial light modulator and a first camera after passing through a 4f optical imaging system composed of a first convex lens and a second convex lens and a beam splitter. The slit located between the first and second convex lenses is used to select the first-order diffracted light. In this optical system, the random light fields at the locations of the second spatial light modulator and the first camera are identical.

[0051] like Figure 1 As shown, the planes where the second spatial light modulator and the first camera are located are both the light source planes of the random light field to be measured. Figure 1 The small image labeled b shows the light intensity of the instantaneous random light field captured by camera 1, and the shaded area is an obstacle loaded on the second spatial light modulator.

[0052] In the second part of this embodiment, a Poisson spot experiment is performed on the random light field. An obstacle hologram is loaded onto the second spatial light modulator. The modulated random light field to be measured passes through a beam splitter and a third convex lens to reach the second camera. The second spatial light modulator and the second camera are located at the front and rear focal planes of the third convex lens, respectively, and the focal length of the third convex lens is 25 cm. The slit before the second camera, close to the second camera, is sufficient to filter out the first-order diffraction spot, used to select the intensity of the first-order diffraction light modulated by the second spatial light modulator. Therefore, the response function of this measurement system satisfies:

[0053] h(r,u)=exp(-i2πu·r / λf) (1)

[0054] Where r and u are the plane vector position coordinates of the second spatial light modulator and the second camera, respectively, λ is the wavelength, and f is the focal length of the third convex lens.

[0055] By refreshing the obstacle O on the second spatial light modulation i (r)(i=1,2,3) can respectively obtain three far-field light intensities I i(u)(i=1,2,3), and then the spatial coherence structure distribution of the measurement is calculated.

[0056] Example 2

[0057] This embodiment provides a method for measuring the optical spatial coherence structure based on the Poisson spot experiment, including:

[0058] Obtain the light intensity distribution of the beam under test in the far field after the light source surface is blocked by an obstacle;

[0059] Choose different transmittance functions for obstacles;

[0060] Different far-field light intensities of the beam under test are obtained based on different obstacle transmission functions;

[0061] The intensity difference is obtained by subtracting different far-field light intensities;

[0062] The spatial coherence structure is calculated based on the obtained light intensity difference.

[0063] In this embodiment, in the space-frequency domain, the second-order statistical properties of a quasi-monochromatic, statistically stable scalar random electric field E(r) can be described by the cross-spectral density function:

[0064] W(r1,r2)= <E(r1)E * (r2)> (2)

[0065] Where r j (j=1,2) is an arbitrary spatial position vector at the plane where the light source to be measured is located. The asterisk and angle brackets represent the complex conjugate and the covariant mean, respectively. Formula (2) can be written in the following form:

[0066] W(r1,r2)=τ(r1)τ * (r1)γ(r1,r2) (3)

[0067] Where τ(r) and γ(r) 1, r2) represents the amplitude and spatial coherence structure of the coherent beam to be measured, respectively.

[0068] In this embodiment, a modified Poisson spot experiment is used, wherein the beam to be tested is blocked by an obstacle at the light source surface, and the intensity distribution of the blocked beam in the far field can be represented by the Huygens-Fresnel diffraction integral:

[0069] I(u)=∫∫γ(r1,r2)O(r1)O * (r2)h(r1,u)h * (r2,u)d 2 r1d 2 r2 (4)

[0070] Where u is the position coordinate of the far-field observation surface. O(r) and h(r,u) represent the transmission function of the obstacle and the response function of the optical system, respectively.

[0071] To accurately recover the spatial coherence structure γ(r1,r2) of the beam under test, the transmittance functions of the obstacles are selected as O1(r)=1-q(r-r0), O2(r)=exp(iπ)-q(r-r0) and O3(r)=exp(iπ / 2)-q(r-r0), respectively, where q(r-r0) represents the shape of the obstacle whose center is located at r0.

[0072] The three far-field light intensities I can be obtained from formula (4). i (u), where i = 1, 2, 3. Subtracting the light intensity I1(u) from the light intensity I2(u) yields the light intensity difference:

[0073] ΔI 21 (u)=I2(u)-I1(u)=4Re[Λ(u)] (5)

[0074] Similarly, subtracting the light intensity I1(u) from the light intensity I3(u) yields the light intensity difference:

[0075] ΔI 31 (u)=I3(u)-I1(u)=2Re[Λ(u)]-2Im[Λ(u)] (6)

[0076] in,

[0077] Λ(u)=∫∫γ(r1,r2)q(r1-r0)h(r1,u)h * (r2,u)d 2 r1d 2 r2 (7)

[0078] The symbols Re[] and Im[] represent the operations of taking the real part and the imaginary part, respectively. Through simple calculations using formulas (5) to (7), we can obtain:

[0079] Λ(u)=ΔI 21 / 4+i(ΔI 21 / 4-ΔI 31 / 2) (8)

[0080] In our optical system, the observation plane is located in the far field, so the system response function is h(r,u)=exp(-i2πu·r). Taking a Fourier transform of both sides of equation (7) yields:

[0081]

[0082] The wavy line symbol represents the two-dimensional Fourier transform operation. From formulas (8) and (9), it can be seen that the spatial coherence structure γ(r1,r2) can be calculated based on the three light intensities obtained by loading different obstacles and the obstacles.

[0083] For the Scherrer model of random light fields, its coherence structure is a function of position difference, i.e., γ(r',r+r')=γ(r). Therefore, in this case, equation (9) can be further simplified to: Furthermore, the measurement results are independent of the location, shape, and size of the obstacle.

[0084] According to the definition of a non-Sherlock model source, its spatial coherence structure is related to the location of the reference point. Therefore, if the obstacle is chosen as a Dirac point located at r0, the coherence structure of the non-Sherlock model source can be obtained by formula (9): The coherent structure was found to be related to the position r0 of the obstacle.

[0085] Figure 2 shows the experimental measurement results of the spatial coherence structure of a partially coherent Shear mode source with different statistical properties. Figures 2(a) to 2(d) Partially coherent Shear mode sources with Gaussian statistical properties Figures 2(e) to 2(h) A partially coherent Shear mode source with non-Gaussian statistical properties. Figures 2(a) and 2(e) show the random light field captured in the experiment, and Figures 2(b) and 2(f) show the probability density function curves measured in the experiment. Figures 2(c) to 2(d) and Figures 2(g) to 2(h) The real and imaginary parts of the spatial coherent structure measured experimentally.

[0086] Figure 2 shows the experimental results measured using this method and system. Figures 2(a) to 2(d) The instantaneous light intensity and corresponding probability density function of the partially coherent Sherman mode beam generated by the random mode are shown in Figure 2(a) and Figure 2(b). It can be seen that the partially coherent Sherman mode source satisfies Gaussian statistics. Figures 2(e) to 2(f) The instantaneous light intensity and corresponding probability density function of the partially coherent Sherman mode beam generated using the pseudo-mode are shown in Figures 2(e) and 2(f). It can be seen that this partially coherent Sherman mode source satisfies non-Gaussian statistics. The real and imaginary parts of the spatially coherent structure experimentally measured using this method in both cases are respectively... Figures 2(c) to 2(d) and Figures 2(g) to 2(h) As shown, although the statistical characteristics of the two are different, the measurement results are consistent, indicating that this method is applicable to partially coherent beams with different statistical characteristics.

[0087] As shown in Figure 3, a partially coherent beam with a non-uniform correlation structure was measured using this method and system. Figures 3(a) to 3(d) The obstacle is located at position r0 = (0mm, 0mm). Figures 3(e) to 3(f)The obstacle is located at r0 = (1mm, 0mm). It can be observed that both the real and imaginary parts of its spatial coherence structure are related to the selection of the reference point r0, indicating that this part of the coherence structure beam has a non-uniform spatial correlation structure.

[0088] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A measurement system for optical spatial coherence structures based on the Poisson spot experiment, characterized in that, include: A laser used to emit linearly polarized beams; A beam expander is used to expand the linearly polarized beam emitted by the laser. A first reflective phase-type spatial light modulator is used to modulate the light beam passing through the beam expander; An optical imaging system for imaging modulated light reflected by a first reflective phase-type spatial light modulator onto a second spatial light modulator; A beam splitter is used to image the modulated light reflected by the first reflective phase-type spatial light modulator onto the first camera. The second spatial light modulator and the second camera are located at the front focal plane and the rear focal plane of the third convex lens, respectively. The measurement method of the optical spatial coherence structure measurement system based on the Poisson spot experiment is as follows: obtain the light intensity distribution of the beam to be measured in the far field after the light source surface is blocked by an obstacle; select different transmittance functions of the obstacle; obtain different far field light intensities of the beam to be measured based on the different transmittance functions of the obstacle; obtain the light intensity difference by subtracting the different far field light intensities; calculate the spatial coherence structure based on the obtained light intensity difference. The intensity distribution of the beam in the far field after the light source surface is blocked by an obstacle is represented by the Huygens-Fresnel diffraction integral as follows: Where u represents the position coordinates of the far-field observation surface. and Let these represent the transfer function of the obstacle and the response function of the optical system, respectively. For the spatial coherence structure of the beam under test, r j (j=1,2) is an arbitrary spatial position vector at the plane where the light source to be measured is located, and the asterisk indicates the complex conjugate; The transmittance functions of the selected obstacles are as follows: in, This indicates the shape of the obstacle centered at r0; The intensity difference is obtained by subtracting different far-field light intensities, where the light intensity is... Subtract light intensity The light intensity difference can be obtained as follows: Light intensity Subtract light intensity The light intensity difference can be obtained as follows: in, ,symbol and These represent the operations of taking the real part and the imaginary part, respectively; For a Sher model random light field, the coherent structure is a function of the position difference, i.e. ,Right now: The wavy line symbol represents the two-dimensional Fourier transform operation; For non-Sherlock model sources, if the obstacle is selected as a Dirac point located at r0, the formula for obtaining the relevant structure is: .

2. The measurement system for optical spatial coherence structures based on the Poisson spot experiment as described in claim 1, characterized in that, A half-wave plate is disposed between the laser and the beam expander, and the half-wave plate is adjusted so that the incident beam on the first reflective phase-type spatial light modulator is horizontally polarized.

3. The measurement system for optical spatial coherence structures based on the Poisson spot experiment as described in claim 1, characterized in that, The imaging system includes a first convex lens and a second convex lens, with a slit between the first convex lens and the second convex lens for extracting first-order diffracted light.

4. The measurement system for optical spatial coherence structures based on the Poisson spot experiment as described in claim 3, characterized in that, The focal lengths of the first convex lens, the second convex lens, and the third convex lens are all 25cm.

5. A method for measuring the optical spatial coherence structure based on the Poisson spot experiment, employing the measurement system for the optical spatial coherence structure based on the Poisson spot experiment as described in any one of claims 1-4, characterized in that, include: Obtain the light intensity distribution of the beam under test in the far field after the light source surface is blocked by an obstacle; Choose different transmittance functions for obstacles; Different far-field light intensities of the beam under test are obtained based on different obstacle transmission functions; The intensity difference is obtained by subtracting different far-field light intensities; The spatial coherence structure is calculated based on the obtained light intensity difference; The intensity distribution of the beam in the far field after the light source surface is blocked by an obstacle is represented by the Huygens-Fresnel diffraction integral as follows: Where u represents the position coordinates of the far-field observation surface. and Let these represent the transfer function of the obstacle and the response function of the optical system, respectively. For the spatial coherence structure of the beam under test, r j (j=1,2) is an arbitrary spatial position vector at the plane where the light source to be measured is located, and the asterisk indicates the complex conjugate; The transmittance functions of the selected obstacles are as follows: in, This indicates the shape of the obstacle centered at r0; The intensity difference is obtained by subtracting different far-field light intensities, where the light intensity is... Subtract light intensity The light intensity difference can be obtained as follows: Light intensity Subtract light intensity The light intensity difference can be obtained as follows: in, ,symbol and These represent the operations of taking the real part and the imaginary part, respectively; For a Sher model random light field, the coherent structure is a function of the position difference, i.e. ,Right now: The wavy line symbol represents the two-dimensional Fourier transform operation; For non-Sherlock model sources, if the obstacle is selected as a Dirac point located at r0, the formula for obtaining the relevant structure is: .

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