Method for measuring position of point light source using spatial mode decomposition multiplexing

Abstract

The application discloses a method for measuring position of a point light source by using spatial mode decomposition multiplexing, and the principle of the method is based on orthogonal projection measurement in quantum detection theory. The method converts direct measurement of distribution of light intensity of the point light source in a coordinate space into measurement of weights of each Hermite-Gaussian mode. In the specific operation, only the complex conjugate of the complex amplitude of each Hermite-Gaussian mode needs to be encoded into a computer hologram. By replacing different computer holograms, the photon number at the optical axis of the first-order diffraction light is recorded, and then the weights of the to-be-measured light field in each Hermite-Gaussian mode can be obtained after normalization. Compared with the traditional measurement, only one pixel is needed to achieve optimal measurement.

Description

Technical Field

[0001] This invention relates to the field of quantum imaging technology, specifically to a method for measuring the position of a point light source using Spatial Pattern Decomposition and Reuse (SPADE). Background Technology

[0002] In the theory of quantum parameter estimation, the Cramer-Rao error lower bound is often used to evaluate the performance of measurement schemes, i.e. in This is used to characterize the mean square error between the measured value and the true value. C represents classical Fisher information, and Q represents quantum Fisher information. Classical Fisher information depends on the chosen measurement, while quantum Fisher information is independent of the measurement. When the chosen measurement is the optimal measurement, that is, when the ideal situation is achieved, classical Fisher information equals quantum Fisher information.

[0003] Traditional imaging involves aggregating the light intensity information collected by each pixel on a CCD camera to obtain the intensity distribution of the target light field. While this method is optimal for measuring the position of a point light source, it requires information from all pixels on the CCD. However, in practical applications, since the image spot is no longer a single point, accurate measurement of a point light source requires the light intensity information from all pixels on the CCD camera. This results in a very large amount of data being collected, leading to measurement difficulties and low efficiency. Consequently, the obtained intensity distribution of the target light field is prone to deviation, causing measurement errors and affecting accuracy, making it difficult to achieve the theoretically optimal measurement. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for measuring the position of a point light source using Spatial Pattern Decomposition and Reuse (SPADE). This method requires only one pixel to accurately measure the position, making it simpler and faster.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A method for measuring the position of a point light source using spatial pattern decomposition and multiplexing includes the following steps:

[0007] S1. Construct an optical path, which includes, in order of light transmission, a laser, a DMD, an aperture, a first lens, and an SLM;

[0008] S2. Obtain a computational hologram by simulating a point light source through the constructed optical path and load it onto the SLM;

[0009] S3. The acquired computational hologram is imaged onto a CCD camera;

[0010] S4. Replace the computational hologram with different Hermigaussian modes, repeat S2 and S3, and read the number of photons at the first diffraction optical axis of each mode by the CCD camera.

[0011] S5. Normalize the number of recorded photons to obtain the weights of each mode;

[0012] S6. Then, the measurement results are obtained based on the theoretical relationship between the weight and the position of the point light source.

[0013] Preferably, the distance between the reflection point of the DMD and the transmission point of the first lens, and the distance between the imaging point of the SLM and the transmission point of the first lens, is twice the focal length of the first lens.

[0014] Preferably, in step S2, the method for obtaining the computational hologram is as follows:

[0015] S2-1: The laser outputs a laser beam to the DMD, which modulates the beam to simulate a point light source.

[0016] S2-2, The modulated point light source is imaged by adjusting the numerical aperture of the aperture and then by the lens;

[0017] S2-3. Calculate the characteristic width of the light to be measured based on the numerical aperture, and then encode the complex conjugate of the Hermigasaurus mode complex amplitude into a computational hologram, which is then loaded onto the SLM.

[0018] Preferably, a second lens is provided between the CCD camera and the SLM, and the acquired computational hologram is imaged on the CCD camera located in the Fourier plane. The Fourier plane refers to the Fourier plane of the second lens. The distances from the CCD camera and the SLM to the transmission point of the second lens are the same as the focal length of the second lens.

[0019] Preferably, in steps S2-3, the method for encoding into a hologram is as follows:

[0020] Assuming the hologram to be used is The complex amplitude information on the hologram is calculated as v(x,y)=Ae iθ The complex amplitude of the incident light field is φ in Given (x, y), the encoding method for calculating the hologram is to load the complex amplitude information onto a sinusoidal phase grating, as shown in the following expression:

[0021]

[0022] J1(f(x,y))=A ②

[0023] Where J1 is a first-order Bessel function of the first kind, and f1 and f2 are non-zero carrier frequencies.

[0024] Preferably, in S3, imaging is performed on its Fourier plane, as expressed below:

[0025]

[0026] in, This represents the light field imaged on the SLM plane.

[0027] Preferably, the feature width of the Hermetic mode used for measurement is consistent with the feature width of the point light source.

[0028] Preferably, the position of the point light source is measured using the optical axis of the hologram as a reference.

[0029] This invention has the following characteristics and beneficial effects:

[0030] Using the above technical solution, when a point light source reaches the imaging plane after passing through the imaging system, it is no longer a single point, but a diffraction pattern (Airy disk) with a certain area. The shape and size of the diffraction pattern are determined by the numerical aperture of the imaging system. This invention, employing this method, requires only one pixel to accurately measure its position, resulting in less data acquisition, reduced measurement difficulty, greater simplicity and speed, less computational load, and avoidance of measurement errors, thus enabling precise measurement of the point light source's position. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is an optical path diagram for measuring the position of a point light source using SPADE technology in an embodiment of the present invention.

[0033] In the diagram, 1-1 is the laser, 1-2 is the DMD (Digital Microchip), 2-1 is the aperture, 2-2 is the first lens, 3-1 is the SLM (Spatial Light Modulator), 3-2 is the second lens, and 3-3 is the CCD camera. Detailed Implementation

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0035] This invention provides a method for measuring the position of a point light source using Spatial Mode Decomposition and Reuse (SPADE), based on orthogonal projection measurement in quantum detection theory. The method transforms the traditional direct measurement of the light intensity distribution of the point light source in coordinate space into measuring the weights of each Hermitian mode. Specifically, it only requires encoding the complex conjugate of the complex amplitude of each Hermitian mode into a computational hologram. By changing different computational holograms and recording the photon count at the first diffraction axis, the weights of the measured light field in each Hermitian mode can be obtained after normalization. Compared to traditional measurements, this method only requires measuring a single pixel to achieve optimal measurement.

[0036] Specifically, firstly according to Figure 1 The optical path shown is constructed as follows, and the optical path includes, in order of light transmission, a laser 1-1, a DMD 1-2, an aperture 2-1, a first lens 2-2, and an SLM 3-1.

[0037] The decomposition and multiplexing of the target light field is achieved by using a phase-type spatial light modulator (SLM) equipped with a hologram of a Hermitian transverse spatial mode. In quantum mechanics, a set of orthogonal and complete basis vectors can be used to measure quantum states, a process known as orthogonal projection measurement. In this method, the Hermitian transverse spatial mode {|E} is selected. mn >;m,n=0,1,...} is a set of orthogonal and complete basis vectors, which are used to measure the quantum state of the target light field.

[0038] In this embodiment of the invention, mode decomposition and multiplexing can be achieved by using a phase-type spatial light modulator (SLM) equipped with a CGH. However, the computational hologram is mounted on a phase-type SLM, so it is essentially still phase modulation. But we can represent the amplitude information using phase, which involves a key tool—a sinusoidal phase grating.

[0039] First, let's assume the hologram to be used is... The complex amplitude information on the hologram is calculated as v(x,y)=Ae i θ The complex amplitude of the incident light field is φ in (x,y). The encoding method for computing a hologram is to load the information of the complex amplitude onto a sinusoidal phase grating, that is...

[0040]

[0041] J1(f(x,y))=A ②

[0042] Where J1 is a first-order Bessel function of the first kind, and f1 and f2 are non-zero carrier frequencies. The sinusoidal phase grating satisfies the following identities:

[0043]

[0044] J q It is a Bessel function of the first kind.

[0045] When incident light strikes an SLM, the optical field on the SLM plane is: Then, after passing through the second lens 3-2, the image is formed on the Fourier plane by the CCD camera 3-3, which performs a Fourier transform on it.

[0046]

[0047] Using identity ③, substituting it into the equation, we can obtain...

[0048]

[0049] From equation ②, we can see that when q = 1, which is the first-order diffraction, it is the Fourier transform of the target light field. The above equation can be transformed into...

[0050]

[0051] When we take the point (f1, f2), which is the optical axis of the first-order diffraction, the above equation can be transformed into:

[0052]

[0053] Therefore, this method can be used for mode decomposition. Replace v(x,y) with the complex conjugate E of the complex amplitude of the Hermetic mode. mn * (x,y), let φ in (x-x0, y-y0) is the complex amplitude of the point light source, i.e.

[0054]

[0055] Therefore, it can be determined that the light field to be measured is in Hermetic mode E. mn The weight on is

[0056] p mn (x0,y0)=|C mn (x0,y0)| 2

[0057] It is understandable that: 1. Different values ​​of m and n represent different Hermetic Gaussian modes, and the measured values ​​are the weights of different Hermetic Gaussian modes when performing mode decomposition. 2. The light intensity measured in the experiment is proportional to the weight under certain exposure time and gain conditions. The weights can only be obtained after normalizing the results measured by all Gaussian modes.

[0058] When the position (x0, y0) of a point light source changes, its weights in each Hermitian mode also change accordingly. Theoretically, to measure the position of a point light source, E...10 The mode measures the position of the point light source on the x-axis and uses E 01 When measuring the position of a point light source on the y-axis using the model, the optimal measurement is achieved when it is close to the optical axis. Therefore, it is only necessary to adjust E... 10 Pattern and E 01 The weights of the patterns, respectively, are related to E 00 By comparing the weights of the patterns, p can be obtained. 10 / p 00 The relationship with x0 and p 01 / p 00 The relationship between x and y0 is used to determine the position of the point light source (x0, y0).

[0059] It should be noted that the following points should be considered when using this method: 1. The feature width of the Hermetic mode used for measurement should be consistent with the feature width of the point light source; 2. The position of the point light source to be measured is based on the optical axis of the hologram; 3. This method is suitable for measuring point light sources that are relatively close to the optical axis.

[0060] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments, including components, without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method for measuring the position of a point light source using spatial pattern decomposition and multiplexing, characterized in that, Includes the following steps: S1. Construct an optical path, which includes, in order of light transmission, a laser, a DMD, an aperture, a first lens, and an SLM; S2. Simulate a point light source by constructing an optical path, obtain a computational hologram, and load it onto the SLM; S3. The acquired computational hologram is imaged onto a CCD camera; S4. Replace the computational hologram with different Hermigaussian modes, repeat S2 and S3, and read the number of photons at the first diffraction optical axis of each mode by the CCD camera. S5. Normalize the number of recorded photons to obtain the weights of each mode; S6. Then, the measurement results are obtained based on the theoretical relationship between the weight and the position of the point light source.

2. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 1, characterized in that, The distance between the reflection point of the DMD and the transmission point of the first lens, and the distance between the imaging point of the SLM and the transmission point of the first lens, is twice the focal length of the first lens.

3. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 1, characterized in that, In step S2, the method for obtaining the computational hologram is as follows: S2-1: The laser outputs a laser beam to the DMD, which modulates the beam to simulate a point light source. S2-2, The modulated point light source is imaged by adjusting the numerical aperture of the aperture and then by the lens; S2-3. Calculate the characteristic width of the light to be measured based on the numerical aperture, and then encode the complex conjugate of the Hermigasaurus mode complex amplitude into a computational hologram, which is then loaded onto the SLM.

4. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 1, characterized in that, A second lens is provided between the CCD camera and the SLM. The acquired computational hologram is imaged on the CCD camera located in the Fourier plane. The Fourier plane refers to the Fourier plane of the second lens. The distances from the CCD camera and the SLM to the transmission point of the second lens are the same as the focal length of the second lens.

5. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 3, characterized in that, In S2-3, the method for encoding into a hologram is as follows: Assuming the hologram to be used is The complex amplitude information on the hologram is calculated as v(x,y)=Ae i θ, the complex amplitude of the incident light field is φ in Given (x, y), the encoding method for calculating the hologram is to load the complex amplitude information onto a sinusoidal phase grating, as shown in the following expression: J1(f(x,y))=A ② Where J1 is a first-order Bessel function of the first kind, and f1 and f2 are non-zero carrier frequencies.

6. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 5, characterized in that, In S3, the image is formed on its Fourier plane, as expressed below: in, This represents the light field imaged on the SLM plane.

7. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 1, characterized in that, The feature width of the Hermetic mode used for measurement is the same as the feature width of the point light source.

8. The method for measuring the position of a point light source using spatial pattern decomposition and multiplexing according to claim 1, characterized in that, The position of the point light source is measured using the optical axis of the hologram as a reference.

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