Off-axis two-aperture interferometric distortion phase system and method

Abstract

This invention relates to an off-axis dual-aperture interferometric measurement system and method for twisted phase, comprising: a laser emitting component generating linearly polarized light; a beam splitter decomposing the linearly polarized light into reflected and transmitted light; a spatial light modulation component including a first computer and a spatial light modulator, wherein the first computer loads a hologram of a dynamically twisted Gaussian Sherman mode beam passing through the off-axis dual aperture onto the spatial light modulator; a filtering component filtering the twisted Gaussian Sherman mode beam from the off-axis dual aperture to obtain a first-order light spot; a light detection component including a photodetector and a second computer, wherein the photodetector acquires an image of the first-order light spot, and the second computer acquires an image of the first-order light spot at preset time intervals, and multiple first-order light spot images are superimposed to synthesize a far-field interferogram; and the second computer performs a Fourier transform on the far-field interferogram to obtain a Fourier spectrum. Its experimental optical path is relatively simple, easy to adjust and test, time-efficient, and has high measurement accuracy.

Description

Technical Field

[0001] This invention relates to the field of optical technology, and in particular to an off-axis dual-aperture interferometry system and method for measuring distorted phase. Background Technology

[0002] Compared to fully coherent light, partially coherent beams have unique applications in certain fields. For example, they offer better stability in laser communication; they can overcome speckle effects in laser nuclear fusion; they can achieve ghost imaging and ghost interference in optical imaging; and they also have unique applications in atom cooling, particle trapping, and image scanning.

[0003] In partially coherent beams, phase is a crucial and tunable parameter, which can be categorized into three types based on its form: conventional phase, twisted phase, and vortex phase. Twisted phase is a function related to the positions of two points in space and cannot be separated into the product of two independent one-dimensional coordinate parameters. Furthermore, the intensity of twisted phase is limited by the inverse square of the beam's transverse coherence width, causing it to vanish within the fully coherent limit. Therefore, twisted phase does not exist in fully coherent light and is a phase unique to partially coherent beams. Twisted phase also exhibits hand-like characteristics; its inherent asymmetry causes the beam to rotate along the optical axis during propagation. Beams carrying twisted phase, such as twisted Gaussian Sherman mode beams, have potential applications in super-resolution imaging, optical trapping, free-space optical communication, and beam self-reconstruction enhancement. Twisted phase imparts orbital angular momentum to partially coherent beams, which has unique applications in super-resolution imaging. The twist factor is a key factor in twisted phase and orbital angular momentum; the detection and control of twisted phase hold promise for applications in coherent and orbital angular momentum-based ghosting imaging.

[0004] Numerous methods exist for generating distorted Gaussian Sherman mode beams, such as the conversion system consisting of three cylindrical lenses, the eigenmode method, the randommode method, and the pseudomode method. However, methods for measuring the distorted phase are still scarce. Therefore, having a method for measuring the distorted phase with a simple experimental optical path and small experimental error is particularly important.

[0005] Currently, two experimental methods for measuring the tortuous phase have been reported. The first method is based on the generalized Humberley-Brown and Tevez method, which causes interference between the reference beam and the tortuous Gaussian Sher mode beam being measured; the second method is based on double-slit interference.

[0006] The first method involves Wang Haiyun and others splitting the light beam into two beams, a reflected beam and a transmitted beam, using a beam splitter. The reflected beam is then directed onto a spatial light modulator, which outputs a distorted Gaussian Sher mode beam using a random mode superposition method. The transmitted beam is defined as the reference beam. After passing through a 4f system to remove the first diffraction order, the distorted Gaussian Sher mode beam is directed onto a second beam splitter placed in front of the CCD. The transmitted beam is also directed onto the second beam splitter after passing through two mirrors. The distorted Gaussian Sher mode beam to be measured and the reference beam interfere with each other after passing through the second beam splitter, producing interference fringes. The real part of the twisted phase can be obtained using the generalized Humberley-Brown and Tevis method. By determining r2 as the reference point, the period of the cosine function can be calculated. An equation exists between the period and the twist factor, allowing the twist factor to be obtained, and thus the twisted phase. The second method, used by G. Canas et al., involves generating a twisted Gaussian Sher mode beam using the pseudo-mode method. This beam passes through a 4f system and strikes a double slit, then is focused by a lens and transmitted. Finally, an interferogram is obtained on a CCD. The twist factor is altered by changing the coherence width of the twisted Gaussian Sher mode beam. Multiple experiments were conducted, and an equation exists between the position of the central peak of the interferogram and the twist factor. Knowing the offset of the central peak, the value of the twist factor can be derived, thus obtaining the twisted phase.

[0007] In the generalized Humberley-Brown and Tevez method, the experimental optical path is relatively complex, and the collimation requirements for the reference light and the twisted Gaussian Sher mode beam are extremely high, making the experimental optical path difficult to construct. In the double-slit interference method, changing the coherence width requires changing the hologram loaded onto the spatial light modulator, which is a relatively troublesome process. Summary of the Invention

[0008] Therefore, the technical problem to be solved by the present invention is to overcome the technical defects of the prior art, such as the difficulty in building the experimental optical path of the distorted Gaussian Sher mode beam and the complexity of the experiment.

[0009] To solve the above-mentioned technical problems, the present invention provides an off-axis dual-aperture interferometric measurement tortuous phase system, comprising:

[0010] A laser emitting component that generates linearly polarized light;

[0011] A beam splitter that separates linearly polarized light into reflected and transmitted light;

[0012] A spatial light modulation assembly, comprising a first computer and a spatial light modulator, wherein the first computer loads a hologram of a dynamically twisted Gaussian Sher mode beam passing through an off-axis double aperture onto the spatial light modulator, and the reflected light passes through the spatial light modulator to obtain an off-axis double aperture twisted Gaussian Sher mode beam.

[0013] A filtering assembly filters an off-axis dual-aperture twisted Gaussian Shear mode beam to obtain a first-order beam spot;

[0014] The optical detection component includes a photodetector and a second computer. The photodetector acquires a first-level light spot image, and the second computer acquires the first-level light spot image at preset time intervals. Multiple first-level light spot images are superimposed to form a far-field interferogram.

[0015] The second computer performs a Fourier transform on the far-field interferogram to obtain a Fourier spectrum. The phase at the peak point of the Fourier spectrum is the twisted phase that needs to be measured.

[0016] Preferably, the filtering assembly includes a first lens, an aperture stop, and a second lens, wherein the distance between the first lens and the spatial light modulator is f, the distance between the first lens and the aperture stop is f, and the distance between the aperture stop and the second lens is f, where f is the focal length of the first lens and the second lens.

[0017] Preferably, the spatial light modulator and the first lens are located on opposite sides of the beam splitter.

[0018] Preferably, a third lens is provided between the filtering component and the photodetector component, and the third lens focuses the first-stage light spot onto the photodetector.

[0019] Preferably, the laser emitting assembly includes a laser, a polarizer, and a half-wave plate, wherein the laser emits laser light, and the laser light is polarized to form linearly polarized light.

[0020] Preferably, the laser emitting assembly includes a half-wave plate for adjusting the rotation angle of the linearly polarized light.

[0021] Preferably, the photodetector is a charge-coupled device.

[0022] Preferably, a beam expander is provided between the laser emitting component and the beam splitter.

[0023] Preferably, holograms are loaded onto the spatial light modulator at preset time intervals, and each hologram contains a random phase.

[0024] This invention discloses an off-axis dual-aperture interferometry method for distorted phase measurement, based on the aforementioned off-axis dual-aperture interferometry distorted phase measurement system.

[0025] The technical solution of the present invention has the following advantages compared with the prior art:

[0026] 1. This invention proposes a method for measuring the distorted phase using off-axis dual-aperture interferometry. This method directly loads the off-axis dual apertures into the hologram on the spatial light modulator, reducing experimental errors and simplifying the experimental optical path. Only one set of superimposed far-field interferograms corresponding to one set of holograms is needed. By performing a Fourier transform on the far-field interferograms, the distorted phase and distortion factor can be analyzed from the amplitude and phase spectra of the Fourier spectrum.

[0027] 2. The experimental optical path of this invention is relatively simple, easy to adjust, easy to test, short in time, and has high measurement accuracy. Attached Figure Description

[0028] Figure 1 A schematic diagram of an off-axis dual-aperture interferometry tortuous phase system.

[0029] Figure 2 In the image, (a) the theoretical far-field interferogram intensity distribution, (b) the theoretical one-dimensional intensity distribution in the x-direction, (c) the one-dimensional amplitude spectrum distribution of the theoretical Fourier spectrum in the x-direction, (d) the one-dimensional phase spectrum distribution of the theoretical Fourier spectrum in the x-direction, (e) the experimentally generated far-field interferogram intensity distribution, (f) the experimental one-dimensional intensity distribution in the x-direction, (g) the one-dimensional amplitude spectrum distribution of the experimental Fourier spectrum in the x-direction, and (h) the one-dimensional phase spectrum distribution of the experimental Fourier spectrum in the x-direction.

[0030] Figure 3 The figure shows the fitting of theory and experiment in the x-direction, where (a) is the light intensity, (b) is the amplitude spectrum of the Fourier spectrum, (c) is the phase spectrum of the Fourier spectrum, and the black solid line in (ac) is generated by theory, and the circle is generated by experiment.

[0031] Explanation of reference numerals in the accompanying drawings: 1. Laser; 2. Polarizer; 3. Half-wave plate; 4. Beam expander; 5. Spatial light modulator; 6. Beam splitter; 7. First lens; 8. Aperture; 9. Second lens; 10. Third lens; 11. Photodetector; 12. Second computer; 13. First computer. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0033] Reference Figure 1 As shown, the present invention discloses an off-axis dual-aperture interferometric distortion phase measurement system, including a laser emitting component, a beam splitter 6, a spatial light modulation component, a filtering component, and a light detection component.

[0034] Laser emitting components can generate linearly polarized light.

[0035] Beam splitter 6 separates linearly polarized light into reflected light and transmitted light.

[0036] The spatial light modulation assembly includes a first computer 13 and a spatial light modulator 5. The first computer 13 loads a hologram of a dynamically twisted Gaussian Sher mode beam passing through an off-axis double aperture onto the spatial light modulator 5. The reflected light passes through the spatial light modulator 5 to obtain an off-axis double aperture twisted Gaussian Sher mode beam.

[0037] The filtering assembly filters the off-axis dual-aperture twisted Gaussian Shear mode beam to obtain the first-order beam spot.

[0038] The optical detection component includes a photodetector 11 and a second computer 12. The photodetector 11 acquires a first-level light spot image, and the second computer 12 acquires the first-level light spot image at preset time intervals. Multiple first-level light spot images are superimposed to form a far-field interferogram. The second computer 12 performs a Fourier transform on the far-field interferogram to obtain a Fourier spectrum. The phase at the peak point corresponding to the Fourier spectrum is the twisted phase to be measured.

[0039] The working principle of this invention is as follows: This invention directly loads the off-axis dual apertures into the hologram on the spatial light modulator 5, which reduces the generation of experimental errors and simplifies the experimental optical path. Only a set of superimposed and synthesized far-field interferograms corresponding to a set of holograms are needed. By performing Fourier transform on the far-field interferograms, the twisted phase and twist factor can be analyzed from the amplitude spectrum and phase spectrum of the Fourier spectrum.

[0040] The filtering assembly includes a first lens 7, an aperture stop 8, and a second lens 9. The distance between the first lens 7 and the spatial light modulator 5 is f, the distance between the first lens 7 and the aperture stop 8 is f, and the distance between the aperture stop 8 and the second lens 9 is f, where f is the focal length of the first lens 7 and the second lens 9. The desired first-order light spot can be filtered out using the 4f system.

[0041] The spatial light modulator 5 and the first lens 7 are located on opposite sides of the beam splitter 6. This reduces the size of the optical system.

[0042] A third lens 10 is provided between the filtering component and the photodetector component, and the third lens 10 focuses the first-stage light spot onto the photodetector 11.

[0043] The laser emitting assembly includes a laser 1, a polarizer 2, and a half-wave plate 3. The laser 1 emits laser light, which is polarized to form linearly polarized light. The half-wave plate 3 is used to adjust the rotation angle of the linearly polarized light. The combination of polarizer 2 and half-wave plate 3 can eliminate the influence of background light.

[0044] Photodetector 11 is a charge-coupled device.

[0045] A beam expander 4 is disposed between the laser emitting component and the beam splitter 6. The linearly polarized light is broadened by passing through the beam expander 4.

[0046] Holograms are loaded onto the spatial light modulator 5 at preset time intervals, and each hologram contains a random phase. The number of holograms to be displayed is determined based on the specific parameters of the distorted Gaussian Sherman mode beam to be generated, such as the beam waist and coherence width.

[0047] This invention discloses an off-axis dual-aperture interferometry method for distorted phase measurement, based on the aforementioned off-axis dual-aperture interferometry distorted phase measurement system.

[0048] The technical solution in this invention will be explained theoretically below:

[0049] The sampled optical field at the source plane of a torsion Gaussian Sherman mode beam passing through an off-axis double aperture:

[0050]

[0051] Where ρ=(ξ,η), W(ρ) i ,ρ j )=V(ρ i V * (ρ j ) represents a distorted Gaussian Sherman mode beam, h(ρ)=circ(ρ / a) is the aperture function, a is the aperture radius, δ(ρ-ρ n () indicates the position of the nth hole. Represents convolution;

[0052] The cross spectral density function of the far-field interferogram generated by formula (1) is expressed as:

[0053]

[0054] Where υ=r / λf represents the coordinates on the focal plane, λ represents the wavelength, and f represents the focal length of the third lens.

[0055] When r1 = r2 = r, the cross spectral density of the far-field interferogram is converted into light intensity:

[0056]

[0057] in Let J1 represent the Fourier transform of the circular aperture function, where J1 represents the Bessel function of the first kind, and N represents the number of apertures.

[0058] The cross spectral density of the twisted Gaussian Sherman mode beam is expressed in terms of coherence:

[0059]

[0060] Where I(ρ)n ,ρ n ) = I n ,I(ρ m ,ρ m ) = I m μ represents the light intensity of the nth and mth circular apertures. nm This represents the coherence between the nth and mth circular holes.

[0061] Substituting formula (4) into formula (3), we obtain the light intensity of the far-field interferogram:

[0062]

[0063] The light intensity in the far-field interferogram can be expressed as the sum of interference and diffraction:

[0064]

[0065] Perform a Fourier transform on the far-field interferogram:

[0066]

[0067] Where Λ(ρ) represents the autocorrelation of the circular aperture function. The phase of the peak point of the amplitude spectrum after the Fourier transform of the far-field interferogram is the twisted phase.

[0068] Coherence derivation results:

[0069]

[0070] Derivation of the distortion factor:

[0071]

[0072] Where α represents the phase of the peak point.

[0073] The present invention will be further described and explained below with reference to specific embodiments.

[0074] According to the mode superposition method, twisted Gaussian Sher mode beams with different parameters can be generated by random mode superposition. The parameters of the twisted Gaussian Sher mode beam to be generated in this invention are: beam waist σ. x =σ y =0.6mm, coherence width δ x =δ y =0.6mm, twist factor μ0=2.778mm -2 The distance from the circular hole to the axis is y = 0.3 mm, the diameter of the circular hole is D = 0.3 mm, and the distance between the center points of the two circular holes is d = 0.5 mm. The laser generates a beam with a wavelength of λ = 532 × 10⁻⁶. -9The coherent light of m passes through a polarizer and a half-wave plate to eliminate the background light and generate linearly polarized light. The linearly polarized light is then broadened by a beam expander and hits a beam splitter. The beam splitter splits the linearly polarized light into two beams: a reflected beam and a transmitted beam. The reflected beam hits a spatial light modulator. The first computer is connected to the spatial light modulator. To ensure that the generated distorted Gaussian Shear mode beam is consistent with the theoretical value, 5000 holograms need to be loaded onto the spatial light modulator. After passing through an off-axis dual-aperture twisted Gaussian Sherman mode beam, which is output from the spatial light modulator, it passes through a beam splitter, the first lens (focal length f = 150 mm) in the 4f imaging system, and the aperture in the 4f imaging system to filter out the positive first-order light spot required for the experiment. Then it passes through the second lens (focal length f = 150 mm) in the 4f imaging system. A charge-coupled device (CCD) is placed on the focal plane of the third lens to receive the far-field interferogram. The far-field interferogram is then superimposed and synthesized by a second computer. After synthesis, a Fourier transform is performed to obtain the amplitude spectrum and phase spectrum of the Fourier spectrum, thus obtaining the twisted phase.

[0075] To verify whether the experimental results match the theoretical results, this invention uses Matlab to simulate a tortuous Gaussian Sher mode beam passing through an off-axis double aperture in... Figure 2 The far-field interferogram, amplitude spectrum, and phase spectrum of the Fourier spectrum were obtained, and the theoretical and experimental results were fitted together.

[0076] The fitting relationship between the theoretical and experimental results is as follows:

[0077] Figure 2 The far-field interferograms, Fourier spectrum amplitude and phase spectra of the off-axis dual-aperture interferometry tortuous phase system produced in theory (ad) and experiment (eh) in a preferred embodiment of the present invention are shown.

[0078] Figure 3 This is a far-field interferogram, a fitted graph of the amplitude spectrum and the phase spectrum of the Fourier spectrum, generated in theory and experiment by the off-axis dual-aperture interferometry tortuous phase system in a preferred embodiment of the present invention. The black solid line and the red circle represent the theoretical and experimental results, respectively. The final tortuous factor value is 2.74, verifying that the experimentally measured tortuous phase is consistent with the theoretical design.

[0079] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0080] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0081] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0082] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0083] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An off-axis dual-aperture interferometric measurement system for distorted phase, characterized in that, include: A laser emitting component that generates linearly polarized light; A beam splitter that separates linearly polarized light into reflected and transmitted light; A spatial light modulation assembly includes a first computer and a spatial light modulator. The first computer loads a hologram of a dynamically twisted Gaussian Sherman mode beam passing through an off-axis double aperture onto the spatial light modulator. The reflected light passes through the spatial light modulator to obtain an off-axis double aperture twisted Gaussian Sherman mode beam. Holograms are loaded onto the spatial light modulator at preset time intervals, and each hologram contains a random phase. The off-axis double apertures in the holograms are used to enable the dynamically twisted Gaussian Sherman mode beam to form a sampling light field at the source plane. A filtering assembly includes a first lens, an aperture stop, and a second lens. The distance between the first lens and the spatial light modulator is f, the distance between the first lens and the aperture stop is f, and the distance between the aperture stop and the second lens is f, where f is the focal length of the first lens and the second lens. The filtering assembly filters the off-axis dual-aperture twisted Gaussian Shear mode beam to obtain a first-order light spot. The optical detection component includes a photodetector and a second computer. The photodetector acquires a first-level light spot image, and the second computer acquires the first-level light spot image at preset time intervals. Multiple first-level light spot images are superimposed to form a far-field interferogram. A third lens is disposed between the filtering component and the photodetector component, and focuses the first-stage light spot onto the photodetector. The second computer performs a Fourier transform on the far-field interferogram to obtain a Fourier spectrum. The phase at the peak point corresponding to the Fourier spectrum is the twisted phase that needs to be measured.

2. The off-axis dual-aperture interferometric tortuous phase measurement system according to claim 1, characterized in that, The spatial light modulator and the first lens are located on opposite sides of the beam splitter.

3. The off-axis dual-aperture interferometric tortuous phase measurement system according to claim 1, characterized in that, The laser emitting assembly includes a laser, a polarizer, and a half-wave plate. The laser emits laser light, which is then polarized by the polarizer to form linearly polarized light.

4. The off-axis dual-aperture interferometric tortuous phase measurement system according to claim 1, characterized in that, The laser emitting assembly includes a half-wave plate, which is used to adjust the rotation angle of linearly polarized light.

5. The off-axis dual-aperture interferometric tortuous phase measurement system according to claim 1, characterized in that, The photodetector is a charge-coupled device.

6. The off-axis dual-aperture interferometric tortuous phase measurement system according to claim 1, characterized in that, A beam expander is provided between the laser emitting component and the beam splitter.

7. A method for measuring distorted phase using off-axis dual-aperture interferometry, characterized in that, The off-axis dual-aperture interferometric tortuous phase measurement system according to any one of claims 1-6.

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