4f system Fourier plane imaging method and device based on cross phase modulation

Abstract

The invention relates to the technical field of optical imaging, in particular to a 4f system Fourier plane imaging method and device based on cross phase modulation, and the method comprises the steps: setting a cross phase intensity factor candidate value set, and generating a Gaussian beam carrying cross phase modulation; coding an object to be measured as an equivalent representation and positioning the object to be measured on the Fourier plane of the 4f system and near the Fourier plane to traverse longitudinal displacement; traversing the cross phase intensity factor and the longitudinal displacement, and obtaining image surface light field distribution through twice Fourier transform of a 4f system; and screening an optimal parameter and an effective displacement interval based on the similarity index to realize depth-of-field extension and distortion suppression. On the premise of not increasing the complexity of the system, the tolerance to the longitudinal offset of the object is remarkably improved, the imaging distortion is inhibited, the structure is simple, the imaging is stable, and the system is suitable for the fields of optical metrology, biomedical imaging and the like.

Description

Technical Field

[0001] This invention relates to the field of optical imaging technology, and in particular to a 4f system Fourier plane imaging method and apparatus based on cross-phase modulation. Background Technology

[0002] Optical imaging technology, with its advantages of high resolution, non-contact operation, wide spectral response, and ability to acquire multi-dimensional spatial-spectral-temporal information, has become a core technology in fields such as biomedical imaging, remote sensing, industrial monitoring, and astronomical observation. To meet the demands of different scenarios for imaging quality, speed, and dimensionality, related technologies are constantly evolving, including structured light imaging, interferometric and phase imaging, coded and computational imaging, and single-photon imaging. Among these, the classic 4f Fourier optical system, due to its simple structure, ability to achieve a strict correspondence between the object and image planes, and precise spatial frequency filtering in the Fourier plane, plays a crucial role in traditional optical imaging and information processing.

[0003] However, existing imaging technologies still have significant shortcomings: on the one hand, advanced methods such as coded imaging and single-photon imaging typically rely on complex optical path layouts and multi-device collaboration, resulting in cumbersome system structures and high alignment accuracy requirements, which affect system stability and practicality; on the other hand, these methods often require large-scale numerical reconstruction and optimization, leading to high computational costs and making them difficult to apply in dynamic scenarios with high real-time requirements. While traditional 4f systems are structurally simple, their design is primarily focused on object-plane imaging and spectral filtering, making them extremely sensitive to changes in the object's position along the optical axis (longitudinal direction), resulting in limited depth of field and poor axial tolerance. In practical applications, especially in scenarios where objects need to be placed directly on the Fourier plane (spectral plane) for high-quality imaging and information extraction (such as certain spectral modulation and frequency domain sensing), classic 4f systems struggle to maintain good imaging fidelity when objects deviate from the strictly Fourier plane.

[0004] It is worth noting that cross-phase modulation, as an effective wavefront manipulation technique, has been applied in related optical technologies. For example, patent CN113916792A proposes a far-field imaging method based on the joint manipulation of coherent structure and cross-phase modulation. It utilizes the coherent structure of a partially coherent beam as an information carrier and enhances its information recovery capability under obstacle obstruction through cross-phase modulation, achieving robust imaging in complex environments. Furthermore, patent CN114485967A discloses a method and apparatus for measuring the topological charge of a vortex beam under extremely low coherence conditions. By introducing cross-phase modulation, the coherence distribution of a partially coherent vortex beam is controllably separated, thereby achieving highly flexible detection of the magnitude and sign of the topological charge. These existing technologies demonstrate that cross-phase structures have significant potential in improving system robustness and expanding the degrees of freedom of manipulation.

[0005] However, how to introduce cross-phase modulation, an effective tool, into the classic 4f imaging architecture to achieve stable imaging of objects in the Fourier plane in a simple and direct manner, and significantly improve the system's tolerance to axial positional shifts of the object (i.e., extend the depth of field), while suppressing image distortion caused by defocusing, remains an unresolved technical problem in this field. Existing solutions either rely on complex system modifications or require cumbersome computational reconstruction, failing to balance system simplicity, real-time performance, and imaging robustness. Summary of the Invention

[0006] Therefore, this invention aims to solve the above-mentioned technical problems and provides a method and apparatus for Fourier plane imaging in a 4f system based on cross-phase modulation. In a classic 4f system, this method effectively suppresses image geometric distortion caused by object deviation from the Fourier plane by introducing a controllable cross-phase distribution into the illumination field, significantly extending the effective depth of field of the system and improving the tolerance to longitudinal positioning errors of the object, thereby achieving high-quality and robust direct imaging of objects in the Fourier plane. The 4f system Fourier plane imaging method based on cross-phase modulation includes the following steps: Step S1: Set the cross-phase intensity factor according to the expected depth of field range and imaging quality requirements. A set of candidate values; using computer-generated holographic technology, each of the candidate values ​​in the set... The cross phases corresponding to the values ​​are respectively encoded into phase diagrams. The phase diagrams are used to phase-modulate the incident Gaussian beam to generate a Gaussian beam carrying cross-phase modulation. Step S2: Encode the two-dimensional image of the object to be tested into a hologram using computer generation to form an object representation equivalent to having a transmission function; adjust the position of the object representation along the optical axis so that it is initially positioned at the Fourier plane position of the 4f optical system, and traverse a preset longitudinal displacement around this position. scope; Step S3: Traverse each cross phase intensity factor according to the candidate value set. In each At this value, a first-order diffracted beam is selected from the corresponding cross-phase modulated Gaussian beam as the illumination beam to illuminate the object representation and traverse the longitudinal displacement. Range; each corresponding group Value and The value, after undergoing two Fourier transforms by the 4f optical system, yields the corresponding image plane light field distribution on the imaging plane. ; Step S4: Use the image plane light field distribution at the Fourier plane as the reference image. Calculate the current With the reference image The degree of similarity is used to select the optimal cross-phase intensity factor. and effective longitudinal displacement This range enables depth-of-field expansion and distortion suppression.

[0007] In one embodiment of the present invention, in step S1, the mathematical expression for the cross phase is: ,in , These are the spatial coordinate parameters of the light field.

[0008] In one embodiment of the present invention, in step S1, the incident Gaussian beam satisfies the expression: ,in, This indicates the size of the beam waist.

[0009] In one embodiment of the present invention, in step S1, the candidate value set is a discrete value set set according to a preset gradient, and the cross-phase intensity factor... The value is positive.

[0010] In one embodiment of the present invention, the 4f optical system includes a first lens and a second lens, the first lens and the second lens having the same focal length and the distance between the two lenses being twice the focal length; The first lens performs a Fourier transform on the Gaussian beam carrying cross-phase modulation, and the second lens performs an inverse Fourier transform on the spectrum modulated by the object representation.

[0011] In one embodiment of the present invention, in step S4, the current... With the reference image The method for determining similarity is as follows: ,in, Represents the similarity index. These are the image space coordinate parameters.

[0012] In one embodiment of the present invention, the optimal cross-phase intensity factor is selected based on the similarity. and effective longitudinal displacement The interval method is as follows: Set the similarity index The determination threshold is set for each cross-phase intensity factor. The effective longitudinal displacement z-interval is defined according to the following rules: Traverse the All longitudinal displacements corresponding to the value Get each The similarity index SDI corresponding to the value, the similarity index Not lower than the determination threshold The continuous range of values ​​is determined as the effective longitudinal displacement. interval; If there exists a discrete similarity index Not lower than the determination threshold The value is determined by taking only the longest continuous segment as the effective longitudinal displacement. interval; All candidates are processed according to a preset priority. The values ​​are sorted, and the optimal cross-phase intensity factor is selected. : Compare each The effective longitudinal displacement corresponding to the value For interval length, prioritize the longest interval. The value is used as the optimal cross phase intensity factor; If multiple The effective longitudinal displacement of the value With intervals of equal length, compare each The average of all similarity indices (SDI) within the valid range is used, and the index with the highest average SDI is selected. The value is used as the optimal cross-phase intensity factor.

[0013] The present invention also provides a 4f system Fourier plane imaging device based on cross-phase modulation, for implementing the 4f system Fourier plane imaging method, the device comprising: a light source module, a 4f Fourier imaging module and a detection module arranged sequentially along the optical axis; The light source module is used to generate and output a Gaussian beam carrying cross-phase modulation; The 4f Fourier imaging module includes a first lens and a second lens arranged sequentially along the optical path. The back focal plane of the first lens is defined as the Fourier plane and is used to set the object to be imaged. The back focal plane of the second lens is defined as the imaging plane. The detection module is disposed on the imaging surface and is used to collect the light field distribution of the imaging surface.

[0014] In one embodiment of the present invention, the light source module includes: Laser source; A beam shaping unit is used to shape the beam emitted by the laser source into a Gaussian beam; And a first spatial light modulator, disposed at the front focal plane of the first lens, for applying cross-phase modulation to the Gaussian beam.

[0015] In one embodiment of the present invention, the 4f Fourier imaging module further includes a second spatial light modulator disposed on the Fourier plane for loading a hologram representing the transmission function of the object to be imaged, and the position of the second spatial light modulator can be adjusted along the optical axis.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: This invention effectively improves the system's tolerance to longitudinal positional shifts of objects in the Fourier plane by introducing controllable cross-phase modulation into the input light field of a traditional 4f imaging system. Its advantages are specifically manifested in the following ways: without increasing system complexity, by adjusting a single cross-phase intensity factor, geometric distortions such as image stretching and rotation caused by object deviation from the strict Fourier plane can be significantly suppressed, thereby maintaining image sharpness and structural fidelity over a large axial range. This method achieves "extended depth-of-field" imaging of fixed planar objects, reduces the stringent requirements for object placement accuracy, enhances the system's practicality and robustness, and allows the entire modulation process to be flexibly and digitally completed through a spatial light modulator, facilitating integration with computational imaging techniques to further optimize imaging performance. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0018] Figure 1 This is a schematic diagram of the structure of the 4f system Fourier plane imaging device based on cross-phase modulation provided in an embodiment of the present invention; Figure 2 This is a schematic flowchart of the 4f system Fourier plane imaging method based on cross-phase modulation provided in an embodiment of the present invention; Figure 3 In the middle (a), it represents the theoretical model of Fourier plane direct imaging based on cross-phase modulation, and (b) is a schematic diagram of the simulation results; Figure 4 Different cross phase intensities and longitudinal displacement of the object A schematic diagram of the simulation results of the light intensity distribution on the image plane; Figure 5 This is a schematic diagram of the experimental samples and results of the Fourier plane direct imaging experiment, where (a1) represents sample 1, (a2) represents the imaging result of sample 1, (b1) represents sample 2, and (b2) represents the imaging result of sample 2. Figure 6 (a) shows the variation of the similarity index SDI with longitudinal displacement under different cross-phase intensities; (b) shows the variation of each... The effective imaging interval length corresponding to the value; Explanation of reference numerals in the accompanying drawings: 1. Light source module; 11. Laser light source; 12. Beam shaping unit; 121. Neutral density filter; 122. Beam expander; 13. First spatial light modulator; 2. 4f Fourier imaging module; 21. First lens; 22. Second spatial light modulator; 23. Second lens; 3. Detection module. Detailed Implementation

[0019] 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.

[0020] This embodiment discloses a 4f system Fourier plane imaging method and apparatus based on cross-phase modulation. The aim is to achieve direct imaging of Fourier plane objects by introducing cross-phase modulation technology into the classic 4f optical architecture, while simultaneously expanding the system's depth of field and improving tolerance to longitudinal positional shifts of the object. This embodiment combines numerical simulation and physical experiments to detail the specific implementation process of the imaging method, the parameters of the apparatus used, and the performance verification results. Those skilled in the art can replicate the technical solution of this invention based on the description of this embodiment.

[0021] The 4f system Fourier plane imaging device based on cross-phase modulation used in this embodiment, such as... Figure 1 As shown, the optical axis includes, in sequence, a light source module 1, a 4f Fourier imaging module 2, and a detector module 3. The specific structure, component selection, and parameters of each module are as follows: The light source module 1 is used to generate and output a Gaussian beam carrying cross-phase modulation. Its core function is to provide a stable and controllable illumination field for subsequent imaging. Specifically, it includes: a laser light source 11, a beam shaping unit 12, and a first spatial light modulator 13. The laser source 11 is an Nd:YAG laser with an output wavelength of 532nm. It has high output light field stability, which meets the requirements of the imaging system for the monochromaticity and coherence of the light source. The beam shaping unit 12 is disposed after the laser source 11 along the optical path, and includes a neutral density filter 121 and a beam expander 122 arranged sequentially. The neutral density filter 121 is used to precisely adjust the incident light power to avoid excessively high or low light intensity affecting image quality. The beam expander 122 is used to expand and shape the original beam output from the laser source 11 into an approximately uniform collimated Gaussian beam, wherein the beam waist radius of the Gaussian beam is... Its light field distribution satisfies the expression: ,in , These are the spatial coordinate parameters of the light field; The first spatial light modulator 13 is a high-resolution reflective spatial light modulator, positioned after the beam expander 122 and at the front focal plane of the first lens 21 in the 4f Fourier imaging module 2. It is used to load a computer-generated hologram containing the cross-phase modulation, achieving amplitude-phase encoding of the light field on the light source surface through computer-generated holography, thus obtaining a Gaussian beam in the form of… The cross-phase distribution, in which The phase intensity factor is used; after loading the hologram, a circular aperture can also be configured in the optical path to select the required first-order diffraction light as illumination light, filter out higher-order diffraction light and stray light, and ensure the purity of the illumination light field.

[0022] The 4f Fourier imaging module 2 specifically includes a first lens 21, a second spatial light modulator 22, and a second lens 23. The first lens 21 and the second lens 23 have the same focal length, preferably a long focal length. The achromatic thin lens has two collinear central axes, and the distance between the two lenses is strictly set to 2f (i.e., This constitutes a standard 4f optical architecture. The first lens 21 is used to perform a Fourier transform on the Gaussian beam carrying cross-phase modulation, converting it to the spectral domain; the second lens 23 is used to perform an inverse Fourier transform on the spectrum modulated by the object, restoring the light field from the spectral domain to the spatial domain, forming a clear image of the object behind it.

[0023] The back focal plane of the first lens 21 is defined as the Fourier plane. This plane is the equivalent placement position of the object to be imaged and is also the key region for coupling and modulating the light field spectrum and the object's transmission function. The second spatial light modulator 22 is a high-resolution reflective spatial light modulator of the same model as the first spatial light modulator 13, and is set on the back focal plane of the first lens 21. It is used to load a hologram representing the transmission function of the object under test, effectively realizing the experimental condition that the object is located in the Fourier plane. The second spatial light modulator 22 can be precisely adjusted along the optical axis with an adjustment accuracy of 0.1 mm, used to simulate different longitudinal displacements of the object relative to the Fourier plane. .

[0024] Furthermore, adjustable circular apertures are respectively set in the optical path after the first spatial light modulator 13 and the second spatial light modulator 22. By adapting and adjusting the aperture of the apertures, high-order diffraction light and stray speckle can be efficiently filtered out, thereby optimizing the imaging quality and improving the imaging signal-to-noise ratio.

[0025] The detection module 3 includes a CCD camera and a data processing unit. The CCD camera is positioned on the back focal plane, i.e., the imaging plane, of the second lens 23. The CCD camera has a pixel size of 3.45μm × 3.45μm, a pixel count of 2050 × 2448, and a dynamic range of no less than 60dB, enabling it to accurately record image plane light intensity information under different conditions. The CCD camera is connected to the data processing unit via a data transmission line to achieve real-time acquisition and storage of imaging data.

[0026] Based on the aforementioned 4f system Fourier plane imaging device based on cross-phase modulation, this embodiment also provides a 4f system Fourier plane imaging method based on cross-phase modulation, such as... Figure 2 As shown, the specific steps include: Step S1: Set the cross-phase intensity factor according to the expected depth of field range and imaging quality requirements. A set of candidate values; using computer-generated holographic technology, each of the candidate values ​​in the set... The cross phases corresponding to the values ​​are respectively encoded into phase diagrams. The phase diagrams are used to phase-modulate the incident Gaussian beam to generate a Gaussian beam carrying cross-phase modulation. Step S2: Encode the two-dimensional image of the object to be tested into a hologram using computer generation to form an object representation equivalent to having a transmission function; adjust the position of the object representation along the optical axis so that it is initially positioned at the Fourier plane position of the 4f optical system, and traverse a preset longitudinal displacement around this position. scope; Step S3: Traverse each cross phase intensity factor according to the candidate value set. In each At this value, a first-order diffracted beam is selected from the corresponding cross-phase modulated Gaussian beam as the illumination beam to illuminate the object representation and traverse the longitudinal displacement. Range; each corresponding group Value and The value, after undergoing two Fourier transforms by the 4f optical system, yields the corresponding image plane light field distribution on the imaging plane. ; Step S4: Use the image plane light field distribution at the Fourier plane as the reference image. Calculate the current With the reference image The degree of similarity is used to select the optimal cross-phase intensity factor. and effective longitudinal displacement This range enables depth-of-field expansion and distortion suppression.

[0027] Further, in step S1, the method for generating a Gaussian beam carrying cross-phase modulation includes: Based on the expected depth of field range (the target effective depth of field in this embodiment is not less than 80mm) and imaging quality requirements, a discrete set of candidate values ​​is set according to a preset gradient. All candidate values ​​are positive, ensuring the stability and consistency of the imaging results; The mathematical expression for the cross phase is: ,in For cross phase intensity factor, , These are the spatial coordinate parameters of the light field. Using computer-generated holography, each parameter in the candidate value set is... The cross-phase encoding corresponding to the value is a phase map, and the resolution of the phase map matches the pixel resolution of the first spatial light modulator 13 to ensure accurate loading of phase modulation.

[0028] The generated The phase diagrams corresponding to the values ​​are sequentially loaded onto the first spatial light modulator 13. After the Gaussian beam is reflected by the first spatial light modulator 13, a Gaussian beam carrying the corresponding cross-phase modulation is obtained. The positive first-order diffracted light of this modulated beam is selected as the illumination light through an aperture to ensure the energy utilization rate and phase purity of the illumination light, and the intensity ratio of the first-order diffracted light is not less than 30%.

[0029] Further, in step S2, two sample patterns with different structural features are selected as the objects to be tested, and their two-dimensional images are encoded into holograms using computer-generated holographic technology. These holograms are equivalent to objects with corresponding transmission functions. ( , Object representation in spatial frequency coordinates, transmission function The amplitude range is 0-1, and the phase range is 0-2π.

[0030] The encoded object representation hologram is loaded onto the second spatial light modulator 22, and the position of the second spatial light modulator 22 is adjusted so that it is initially positioned on the Fourier plane of the 4f optical system (i.e. the back focal plane of the first lens 21). The initial positioning error is ensured to be no more than ±0.5mm by calibration with a laser collimator.

[0031] Longitudinal displacement To represent the position of an object relative to the ideal Fourier plane, a preset longitudinal displacement is set. The range is [-100mm, 100mm], where A negative z value indicates that the object is located to the left of the Fourier plane, while a positive z value indicates that the object is located to the right of the Fourier plane, and can cover... to The axial range is determined to ensure a comprehensive assessment of depth-of-field performance. The second spatial light modulator 22 is controlled to move within this range in steps of 0.5 mm along the optical axis, pausing for 1 second after each step to ensure optical path stability before imaging.

[0032] Further, in step S3, according to the candidate value set In sequence, the cross-phase maps loaded on the first spatial light modulator 13 are switched sequentially, and the intensity factors of each cross-phase map are traversed. .

[0033] In each At this value, the cross-phase modulated Gaussian beam (positive first-order diffracted light) output by the first spatial light modulator 13 undergoes a Fourier transform via the first lens 21 and then illuminates the object representation loaded by the second spatial light modulator 22. After the object representation modulates the spectrum, the transmitted light undergoes an inverse Fourier transform via the second lens 23, forming a corresponding image plane light field distribution on the imaging plane (the plane where the CCD camera is located). The collected light intensity distribution satisfies the formula... ,in Let X be the electric field intensity of the imaging surface, and let X and Y be the coordinates of the imaging surface.

[0034] In each Under this value, the second spatial light modulator 22 is controlled to traverse the longitudinal displacement z range. Each corresponds to a group Value and Value, the light field distribution of the image plane acquired by the CCD camera in one pass. And the acquired image data is sorted into " The naming convention of "u-z-image" is used to store the data in the data processing unit to ensure data traceability. In this embodiment, a total of 2400 images were collected, consisting of 3 u-values ​​× 400 z-values ​​× 2 samples.

[0035] Further, in step S4, each sample is selected in the Fourier plane ( ) place, The image plane light field distribution at that time is used as the reference image. The baseline image, after visual evaluation and sharpness analysis, has the best initial imaging quality.

[0036] The similarity index (SDI) is used to measure the current light field distribution on the image plane. and benchmark images The similarity between two objects is calculated using the following formula: , SDI is the image spatial coordinate parameter, with a value ranging from [0,1]. A larger value indicates better image quality. This integration operation is implemented through computer programming to calculate each... The SDI corresponding to the combination of z-value and z-value.

[0037] The SDI threshold is set to 0.8 for each cross-phase intensity factor. traverse the The effective longitudinal displacement is determined by the continuous range of z values ​​with an SDI of not less than 0.8, which includes all longitudinal displacements z corresponding to the value. Interval; if there exist discrete z values ​​with SDI not less than 0.8, only the longest continuous segment is taken as the effective longitudinal displacement. Interval. Calculated: when When, the effective longitudinal displacement z interval is The interval length is ; when When, the effective longitudinal displacement z interval is The interval length is ; when When, the effective longitudinal displacement z interval is The interval length is .

[0038] According to the preset priority, first compare each The effective longitudinal displacement corresponding to the value The longer the interval, the higher the priority; if the interval lengths are the same, the average value of all SDIs within the valid intervals is compared. In this embodiment, The corresponding effective interval length is the longest (117.9 mm), and its average SDI value within the effective interval is 0.89, which is higher than... (Average 0.83) and (Average 0.86), therefore, filtering As the optimal cross phase intensity factor.

[0039] Using the selected optimal cross phase intensity factor In its corresponding effective longitudinal displacement z interval The two samples were imaged, and the resulting images were clear with minimal distortion, achieving the technical effects of depth extension and distortion suppression.

[0040] To comprehensively verify the feasibility, stability, and core performance advantages of the Fourier plane direct imaging technology based on cross-phase modulation of this invention, a systematic verification was conducted through a combination of numerical simulation and physical experiments. The specific verification process and results are as follows: Based on the classical 4f optical system theory, a theoretical simulation model that perfectly matches the parameters of the actual experiment is constructed, such as... Figure 3As shown in (a), in this simulation model, the 4f system mainly consists of two lenses, a first lens 21 and a second lens 23, each with a focal length of 150mm. The distance between the two lenses is set to 2f (i.e., 300mm), forming a standard Fourier imaging link. The incident light field is set to the beam waist radius. A Gaussian beam introduces an intersecting phase distribution at the light source surface. ,in The cross-phase intensity factor is used to regulate the coupling degree of the light field between two orthogonal spatial coordinates. The complex amplitude of the object to be imaged is directly applied to the back focal plane (i.e., the Fourier plane) of the first lens 21. The light intensity distribution of the imaging surface is obtained by numerically simulating the Fourier transform of the first lens 21, the modulation effect of the object on the spectrum, and the inverse Fourier transform process of the second lens 23. This completes the simulation imaging process.

[0041] Two typical object samples with different structural features were selected (sample 1 is a cross-shaped pattern, and sample 2 is a ring-shaped pattern). Their complex amplitudes were applied to the Fourier plane, and the cross-phase intensity factor was set. Simulation imaging was performed. The simulation results are as follows: Figure 3 As shown in (b), (a1) and (b1) are the original sample patterns at the Fourier plane, and (a2) and (b2) are the corresponding image plane simulation output results. The results show that even if the object is located on the Fourier plane, an unconventional object plane, the imaging surface can still form a clear and recognizable object outline with the assistance of cross-phase modulation, accurately restoring the overall structural information of the object, and directly verifying the core feasibility of the imaging method of this invention.

[0042] To characterize the depth-of-field extension capability and distortion suppression characteristics of this invention, a cross-phase intensity factor is set. The candidate value is , , Focus only The positive value, when When the sign changes, the imaging results are symmetrically distributed relative to the origin), and the object is displaced longitudinally along the optical axis relative to the ideal Fourier plane by a displacement z (a negative z indicates that the object is located to the left of the Fourier plane). (Positive values ​​indicate positions on the right), the system examines different... and The intensity distribution pattern of the image plane under the combined effect. Simulation results are as follows: Figure 4 As shown, as the distance of the object from the Fourier plane increases (|z| increases), the directional stretching distortion and rotation of the reconstructed image gradually increase, and the sign of z causes the image deformation and rotation directions to be opposite; while with the cross phase intensity factor As the cross-phase intensity factor increases, the overall image size tends to shrink, and the degree of directional stretching distortion and rotation amplitude are significantly reduced. This result quantitatively verifies that the present invention can control the cross-phase intensity factor. This effectively suppresses imaging distortion, providing key technical support for depth-of-field extension.

[0043] Based on the core parameters of the simulation model, a physical experimental system is built, such as... Figure 1 As shown, the system consists of a light source module 1, a 4f Fourier imaging module 2, and a detector module 3 arranged sequentially along the optical path. Two sample patterns consistent with those in the simulation experiment are selected, and their transmission function holograms are loaded onto the second spatial modulator 22, with cross-phase intensity factors set. The second spatial modulator 22 was initially positioned in the Fourier plane (z=0) for imaging experiments. The experimental results are as follows: Figure 5 As shown, (a1) and (b1) are the sample patterns loaded by the second spatial modulator 22, and (a2) and (b2) are the imaging results acquired by the CCD camera. The experimental imaging results are compared with... Figure 3 The simulation results in (b) show a high degree of agreement in terms of contour morphology, detailed structure and distortion trend, further verifying the accuracy of the theoretical model and numerical prediction of the present invention; at the same time, it shows that the experimental system has a simple structure, is easy to calibrate, and the imaging results are stable and reliable.

[0044] To quantify the depth-of-field performance of this invention, a similarity index (SDI) is introduced as an evaluation metric to characterize the object's displacement at different longitudinal directions. The similarity between the image intensity at a certain point and the image intensity at the Fourier plane (z=0mm). During the experiment, cross-phase intensity factors were set sequentially. for , , The second spatial modulator 22 was adjusted to traverse different longitudinal displacements z along the optical axis, and imaging results under various working conditions were simultaneously acquired and the corresponding SDI values ​​were calculated. Experimental results are as follows: Figure 6 As shown in (a), with the cross phase intensity factor As the longitudinal displacement increases, the SDI value increases. The effective distribution range has been significantly broadened; Figure 6 As shown in (b), , and The corresponding effective imaging intervals (continuous z-values ​​for SDI ≥ 0.8) lengths are 51.9 mm, 82.2 mm, and 117.9 mm, respectively. These results confirm that increasing the cross-phase intensity factor... It can significantly improve the system's depth of field, enhance the tolerance to longitudinal misalignment of objects, and effectively overcome the technical bottlenecks of traditional 4F systems that are sensitive to axial displacement of objects and have limited depth of field. It is especially suitable for practical application scenarios where it is difficult to accurately locate objects in the Fourier plane.

[0045] Through systematic verification via numerical simulation and physical experiments, the feasibility and stability of the Fourier plane direct imaging technology based on cross-phase modulation of this invention have been fully demonstrated. Simulation experiments verified that this method can achieve direct imaging of objects in the Fourier plane, and that imaging distortion can be suppressed by adjusting the cross-phase intensity factor u. The physical experiments showed a high degree of agreement with the simulation results, and confirmed that this technology can significantly extend the system's depth of field and improve its tolerance to longitudinal object displacement. Furthermore, the experimental system has a simple structure, is easy to build and integrate, and has low requirements for mechanical stability and environmental disturbances, laying a solid foundation for its subsequent application in optical metrology, biomedical imaging, and spectral domain sensing.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] 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.

[0050] 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. A Fourier plane imaging method for a 4f system based on cross-phase modulation, characterized in that, Includes the following steps: Step S1: Set the cross-phase intensity factor according to the expected depth of field range and imaging quality requirements. A set of candidate values; using computer-generated holographic technology, each of the candidate values ​​in the set... The cross phases corresponding to the values ​​are respectively encoded into phase diagrams. The phase diagrams are used to phase-modulate the incident Gaussian beam to generate a Gaussian beam carrying cross-phase modulation. Step S2: Encode the two-dimensional image of the object to be tested into a hologram using computer generation to form an object representation equivalent to having a transmission function; adjust the position of the object representation along the optical axis so that it is initially positioned at the Fourier plane position of the 4f optical system, and traverse a preset longitudinal displacement around this position. scope; Step S3: Traverse each cross phase intensity factor according to the candidate value set. In each At this value, a first-order diffracted beam is selected from the corresponding cross-phase modulated Gaussian beam as the illumination beam to illuminate the object representation and traverse the longitudinal displacement. Range; each corresponding group Value and The value, after undergoing two Fourier transforms by the 4f optical system, yields the corresponding image plane light field distribution on the imaging plane. ; Step S4: Use the image plane light field distribution at the Fourier plane as the reference image. Calculate the current With the reference image The degree of similarity is used to select the optimal cross-phase intensity factor. and effective longitudinal displacement This range enables depth-of-field expansion and distortion suppression.

2. The Fourier plane imaging method for a 4f system based on cross-phase modulation according to claim 1, characterized in that: In step S1, the mathematical expression for the cross phase is: ,in , These are the spatial coordinate parameters of the light field.

3. The 4f system Fourier plane imaging method based on cross-phase modulation according to claim 2, characterized in that: In step S1, the incident Gaussian beam satisfies the expression: ， in, This indicates the size of the beam waist.

4. The Fourier plane imaging method for a 4f system based on cross-phase modulation according to claim 1, characterized in that: In step S1, the candidate value set is a discrete value set set according to a preset gradient, and the cross-phase intensity factor... The value is positive.

5. The 4f system Fourier plane imaging method based on cross-phase modulation according to claim 1, characterized in that: The 4f optical system includes a first lens and a second lens, the first lens and the second lens have the same focal length, and the distance between the two lenses is twice the focal length. The first lens performs a Fourier transform on the Gaussian beam carrying cross-phase modulation, and the second lens performs an inverse Fourier transform on the spectrum modulated by the object representation.

6. The 4f system Fourier plane imaging method based on cross-phase modulation according to claim 1, characterized in that: In step S4, calculate the current... With the reference image The method for determining similarity is as follows: ， in, Represents the similarity index. These are the image space coordinate parameters.

7. The Fourier plane imaging method for a 4f system based on cross-phase modulation according to claim 6, characterized in that: The optimal cross-phase intensity factor is selected based on the similarity. and effective longitudinal displacement The interval method is as follows: Set the similarity index The determination threshold is set for each cross-phase intensity factor. The effective longitudinal displacement z-interval is defined according to the following rules: Traverse the All longitudinal displacements corresponding to the value Get each The similarity index SDI corresponding to the value, the similarity index Not lower than the determination threshold The continuous range of values ​​is determined as the effective longitudinal displacement. interval; If there exists a discrete similarity index Not lower than the determination threshold The value is determined by taking only the longest continuous segment as the effective longitudinal displacement. interval; All candidates are processed according to a preset priority. The values ​​are sorted, and the optimal cross-phase intensity factor is selected. : Compare each The effective longitudinal displacement corresponding to the value For interval length, prioritize the longest interval. The value is used as the optimal cross phase intensity factor; If multiple The effective longitudinal displacement of the value With intervals of equal length, compare each The average of all similarity indices (SDI) within the valid range is used, and the index with the highest average SDI is selected. The value is used as the optimal cross-phase intensity factor.

8. A 4f system Fourier plane imaging device based on cross-phase modulation, characterized in that, For implementing the method as described in any one of claims 1 to 7, the apparatus comprises: a light source module, a 4f Fourier imaging module, and a detection module arranged sequentially along the optical axis; The light source module is used to generate and output a Gaussian beam carrying cross-phase modulation; The 4f Fourier imaging module includes a first lens and a second lens arranged sequentially along the optical path. The back focal plane of the first lens is defined as the Fourier plane and is used to set the object to be imaged. The back focal plane of the second lens is defined as the imaging plane. The detection module is disposed on the imaging surface and is used to collect the light field distribution of the imaging surface.

9. The 4f system Fourier plane imaging device based on cross-phase modulation according to claim 8, characterized in that, The light source module includes: Laser source; A beam shaping unit is used to shape the beam emitted by the laser source into a Gaussian beam; And a first spatial light modulator, disposed at the front focal plane of the first lens, for applying cross-phase modulation to the Gaussian beam.

10. The 4f system Fourier plane imaging device based on cross-phase modulation according to claim 8, characterized in that: The 4f Fourier imaging module also includes a second spatial light modulator, which is disposed in the Fourier plane and is used to load a hologram representing the transmission function of the object under test. The position of the second spatial light modulator can be adjusted along the optical axis.

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