A Large Field-of-View Hologram Calculation Method Based on Carrier Frequency Multiplexing

Abstract

A large field of view hologram calculation method based on carrier frequency multiplexing relates to the technical field of information optics. Firstly, the size of the 3D input image is preprocessed. Therefore, the original large field of view input image is layered and cut into a sub-input image sequence with a size not greater than that of the hologram. Secondly, the sub-hologram of the sub-input image sequence is solved by using the hologram diffraction propagation calculation method. Thirdly, the x-y offset distance of the cut sub-hologram reconstruction is calculated according to each layer of the large field of view input image, and the diffraction propagation deflection carrier frequency factor corresponding to each sub-hologram is calculated. Fourthly, each sub-hologram is multiplied by the corresponding carrier frequency factor, and the spatial multiplexing of each sub-hologram multiplied by the corresponding carrier frequency factor is superimposed to form the final hologram. The present application realizes that the size of the input image can be greater than that of the hologram.

Description

Technical Field

[0001] This invention relates to the field of information optics technology, and in particular to a method for calculating large field-of-view holograms based on carrier frequency multiplexing. Background Technology

[0002] Holography is a technique that records the amplitude and phase information of light waves through interference fringes. It can record or reproduce three-dimensional light field information using two-dimensional planar information, and has important applications and prospects in holographic microscopy, holographic measurement, true 3D display, optical tweezers, and optical micro / nano fabrication. With the development of computer technology, computer-generated holograms can be calculated by simulating the diffraction of a three-dimensional light field onto a two-dimensional plane, thus overcoming various limitations of optical holograms. Based on the diffraction distance, computational holograms are divided into Fourier holograms, image-plane holograms, and Fresnel holograms. The reconstructed field of view of a Fourier hologram is proportional to the wavelength and the focal length of the Fourier lens, and inversely proportional to the spatial resolution of the holographic fringes; therefore, the maximum field of view is reconstructed after the fringes reach the sampling frequency. Image-plane holograms are suitable for white light reconstruction, but the reconstructable stereo depth is limited, resulting in a short propagation distance and a field of view that will not exceed the hologram size. While Fresnel holograms can theoretically achieve large field-of-view recording and reproduction of any three-dimensional scene, they are affected by various factors such as band-limited destructive interference during the calculation process, and currently cannot achieve large field-of-view recording.

[0003] Fresnel hologram calculation methods are mainly divided into iterative and non-iterative methods. Iterative methods primarily utilize phase optimization algorithms to obtain pure phase holograms with high diffraction efficiency. The core of the calculation is the plane-to-plane diffraction propagation calculation, using methods such as Fast Fourier Transform and angular spectral methods. Non-iterative methods also directly calculate the complex amplitude distribution at the target distance using diffraction propagation, and then combine this with complex complex amplitude encoding methods to generate the hologram, including ray tracing, layered Fresnel propagation, and their upgraded versions. Except for ray tracing, the size of the hologram generated by both iterative and non-iterative methods is equal to the size of the input light field. This is because the amplitude / phase constraint in iterative methods requires both to be the same, and the plane-to-plane diffraction propagation calculation in non-iterative methods also requires the two sizes to be the same; even if they differ, it's due to different sampling, and the pixel resolution remains the same. However, ray tracing can directly obtain the hologram through point-to-point calculation between the input image and the hologram plane, without considering size differences. Because the hologram of each object point in the actual calculation process is a series of concentric ring Fresnel zone plates, its effective size is limited by the sampling bandwidth and the destructive interference of adjacent object points. This results in object points with large angles away from the central axis recording very little fringe information, leading to a significant decrease in the reconstructed energy of these object points. Consequently, the energy distribution of the entire reconstructed light field is severely uneven, making it impossible to achieve large field-of-view reconstruction with uniform light field energy distribution. To date, no reported method has been able to record hologram calculations for scenes larger than the hologram size. Summary of the Invention

[0004] Current reported hologram calculation methods all require the input image to be the same size as the hologram matrix, making it impossible to record holograms larger than the hologram size. To achieve large field-of-view hologram recording and reconstruction, this invention proposes a large field-of-view hologram calculation method based on carrier frequency reuse, thereby enabling the input image size to be larger than the hologram size.

[0005] Figure 1 A flowchart of a hologram calculation method based on carrier frequency reuse is given. The method includes three processes: sub-hologram calculation, carrier frequency reuse, and coherent superposition to generate the final hologram.

[0006] First, the 3D large field-of-view image is preprocessed to increase its size. The 3D large field-of-view image U is then divided into 2D large field-of-view images U at different depths along the diffraction propagation direction z. z Its mathematical expression is:

[0007] U z (x,y)=U(x,y,z). (1)

[0008] Where x, y, and z represent the 3D large field-of-view image U and the 2D large field-of-view image U, respectively. z The coordinates in the 2D large field-of-view image U z The subscript z corresponds to the coordinate z of the 3D large field-of-view image. Then, the 2D large field-of-view images U at different depth layers are... z Cropped into a sequence of sub-input images smaller than or equal to the hologram size. Figure 2 The diagram illustrates the principle of cropping a 2D large field-of-view image into 3×3 sub-input images. Preferably, the number of cropped sub-image sequences should be determined based on the size of the 3D large field-of-view image and the size of the hologram. Furthermore, the 3D large field-of-view image should first be segmented into a series of 2D large field-of-view images with different axial depths, and then cropped into sub-image sequences of corresponding sizes according to the aforementioned method. Let U be the 2D large field-of-view image at a certain depth z. z If (x, y), then the mathematical expression for this preprocessing operation is:

[0009]

[0010] Among them, U subz_m_n For 2D large field-of-view images U z The m-th row and n-th column sub-input image is given, where x' and y' represent the coordinates of the sub-input image. The maximum number of sub-images in the horizontal and vertical directions is M and N, respectively, and X and Y represent the coordinates of the 2D large field-of-view image U. z The resolution is such that X / M and Y / N are the sub-input image U. subz_m_n The resolution. Wherein, the sub-input image U subz_m_n The resolution should be less than or equal to the resolution of the final hologram H(u,v).

[0011] Second, sub-holograms are calculated for each sub-input image sequence using holographic diffraction propagation methods. Diffraction propagation algorithms such as angular spectral diffraction, Fresnel diffraction propagation, and neural network algorithms can be used. The resulting sub-hologram sequence corresponds to the sub-input image sequence. The reconstructed image size of each sub-hologram is smaller than or equal to the spatial dimension of that sub-hologram. The mathematical expression for this process is as follows:

[0012] H subz_m_n (u,v)=Frenl.{U subz_m_n (x′,y′)}. (3)

[0013] The operator Frenl.{} is the surface-to-surface diffraction propagation operator. When different surface-to-surface diffraction propagation algorithms are used for calculation, the operator is adapted accordingly to the algorithm.

[0014] Third, based on the size of each layer of 2D large field-of-view image, the xy offset distance of each cropped sub-hologram is calculated, and the diffraction propagation deflection carrier frequency factor corresponding to each sub-hologram is calculated. The carrier frequency factor is used to deflect the diffraction propagation direction of the reconstructed image from the sub-hologram, ensuring that the sub-input image is reconstructed at the corresponding xy position. For example... Figure 3 As shown, the uv plane is the sub-hologram corresponding to the (m, n)th sub-input image. Its reconstructed image should be offset into the dashed box in the xy plane, so that a 2D large field-of-view image U at the current reconstruction distance z can be stitched together. z (x,y). The distance between the two planes is the diffraction propagation distance z, d of the second step Frenl.{}. x and d y The sub-input images U corresponding to the current sub-hologram are respectively subz_m_n Center point offset from 2D large field of view image U z The distance between the center points (x, y) and the carrier frequency factor is θ, which represents the diffraction deflection angles in the transverse and longitudinal directions, respectively. x θ y Its relationship with the reproduction distance z and spatial displacement d x d y The relationship between them is:

[0015]

[0016] The carrier frequency factor P can be obtained from the grating diffraction formula. subz_m_n The formula for calculating is: , where j is the imaginary unit:

[0017]

[0018] Fourth, each sub-hologram is multiplied by its respective carrier frequency factor, and the sub-holograms multiplied by their respective carrier frequency factors are spatially multiplexed and superimposed to form the final hologram. The calculation formula is as follows:

[0019]

[0020] This invention solves the problems of band-limited reconstruction and destructive interference between adjacent points that limit the reconstruction range during hologram reconstruction by cropping the 3D large field-of-view image into smaller sub-input images. Since the carrier frequency factor only changes the propagation direction and does not alter the content of the reconstructed image, the method of this invention only changes the spatial position of the reconstructed image of the sub-hologram, without affecting the reconstructed image of the sub-hologram. Therefore, this method can reconstruct a 3D large field-of-view image larger than the hologram size using a hologram of a certain size through carrier frequency multiplexing. Attached Figure Description

[0021] Figure 1: Flowchart of a large field-of-view hologram calculation method based on carrier frequency reuse.

[0022] Figure 2 This is a schematic diagram illustrating the principle of a large field-of-view hologram calculation method based on carrier frequency reuse.

[0023] Figure 3 This is a schematic diagram of the deflection angle of the carrier frequency factor pair hologram diffraction direction.

[0024] Figure 4 This is an example of a large field-of-view hologram calculation and reproduction effect based on carrier frequency reuse.

[0025] Figure 5 This is a comparison of the reconstruction size between the traditional algorithm and the carrier frequency reuse hologram-based algorithm. Detailed Implementation

[0026] The following is for reference. Figure 4 The specific embodiments and features of the present invention are described in detail.

[0027] Traditional hologram calculation methods are based on surface-to-surface diffraction propagation calculations, which requires the input image size to be the same as the hologram size. While point-source-based ray tracing methods can overcome this constraint, when the object point deviates from the hologram region, the fringes recorded in the hologram region are band-limited, and the destructive interference of adjacent point fringes significantly reduces the fringe contrast. Therefore, this method cannot record or reproduce large field-of-view images. The carrier frequency multiplexing method proposed in this invention, as described above, crops a large field-of-view image into small-sized sub-input images, calculates sub-holograms of the sub-input images, multiplies them by different carrier frequency factors according to the cropping position, and finally superimposes and multiplexes them to generate a hologram of the large field-of-view image.

[0028] Taking a hologram with a sampling interval of 8μm, a resolution of 1920×1080 pixels, and a diffraction reconstruction distance of 500mm as an example, the maximum field of view that can be reconstructed is calculated to be 33.2mm×33.2mm according to the diffraction formula. Furthermore, for the sake of clarity in this embodiment, a 2D large field-of-view image with a single depth z of 500mm and a size of 25.9mm×25.9mm is used as an example. First, according to the first step described above, keeping the object light field sampling constant at 8μm, the 2D large field-of-view image U with a resolution (X, Y) of (3240, 3240) is... in Nine sub-input images U are cropped into (M, N) sub-images of (3, 3). subz_m_n Its pixel resolution is 1080×1080, such as Figure 4 As shown. Secondly, according to the second step described above, nine sub-input images U are calculated using a traditional hologram generation algorithm. subz_m_n Corresponding sub-hologram H subz_m_nPreferably, the diffraction propagation process employs angular spectrum diffraction, and the calculated results are as follows: Figure 4 The nine sub-holograms described above. Third, based on the third step described above, calculate the offset re-frequency factor corresponding to each sub-hologram. For example... Figure 4 As shown, the offset distance (d) between the (1,1)th sub-input image and the optical axis center is... x d y The distance is (-8.64mm, 8.64mm), and the diffraction reconstruction distance is 500mm. The carrier frequency factor P corresponding to the sub-input image is calculated according to the formula (4) and the formula (5). subz_1_1 Furthermore, the carrier frequency factor P of other sub-input images is calculated based on their corresponding offset distance and reconstruction distance. subz_m_n Finally, according to the fourth step described above, the nine sub-holograms H are... subz_m_n Multiply each by its corresponding carrier frequency factor P subz_m_n The complex amplitudes after dot product are then summed and superimposed to obtain the final hologram. Because the carrier frequency factors of each sub-hologram can deflect and diffract the reconstructed light field, at a reconstruction distance of 500mm, the corresponding sub-input image can be reconstructed to the corresponding spatial position, thus obtaining the final 2D large field-of-view image. This achieves the recording and reconstruction of a large field-of-view image using a small-size hologram. Furthermore, the 3D large field-of-view image is divided into 2D large field-of-view images of different depths according to the diffraction propagation direction z. The 2D large field-of-view images of different z-depths are then reconstructed by layer diffraction, ultimately reconstructing the 3D large field-of-view image.

[0029] picture Figure 5 The image shown is a comparison between the reconstructed images produced by the method of this invention and traditional hologram algorithms. The first row uses the traditional hologram calculation method, the second row uses the method of this invention, and the first column shows 2D large field-of-view images, with the red dashed border indicating the hologram size. The method of this invention calculates a small-sized hologram from the 2D large field-of-view image and loads it onto an SLM for optical reconstruction. The third column shows the optical reconstruction results of the corresponding algorithm. Traditional algorithms can only reconstruct the region image corresponding to the hologram size in the 2D large field-of-view image, while the method of this invention can completely reconstruct a 2D large field-of-view image with a size of 25.9mm*25.9mm at the reconstruction location.

Claims

1. A large field of view hologram calculation method based on carrier frequency multiplexing, characterized in that: First, the 3D large field of view image U is preprocessed in size, the first step of the preprocessing being to divide the 2D large field of view image U into different depth layers in the diffraction propagation direction z z The mathematical expression of the layering operation is: U z (x,y) = U(x,y,z). (1) Wherein, the 2D large field of view image U z The subscript represents the corresponding 2D large field of view image under z depth, and the second step of the preprocessing is to respectively cut the 2D large field of view image U z The mathematical expression of the cutting processing is: wherein U subz_m_n is a sub-input image, the subscript m,n denotes the mth row and nth column of the sub-input image at the z-depth, M and N are the maximum horizontal and vertical values of the sub-input image, and X and Y are the resolutions of the 2D large field of view image U z . Second, the sub-hologram solving is performed on the sub-input image sequence respectively by using a hologram diffraction propagation calculation method, and a sub-hologram sequence corresponding to the sub-input image sequence is calculated, wherein the diffraction propagation algorithm is selected from an angular spectrum diffraction algorithm, a Fresnel diffraction propagation algorithm or a neural network algorithm; the reconstructed image size of each sub-hologram in the sub-hologram sequence is less than or equal to the spatial size of the sub-hologram, and the mathematical expression of the processing process is as follows: H subz_m_n (u, v) = Frenl.{U subz_m_n (x', y'). (3) wherein the operator Frenl.{} is a Fresnel diffraction propagation operator, and the operator is adapted according to the algorithm when different algorithms are selected for calculation; Third, based on the analytical calculation of the xy offset distance of the cropped sub-hologram reconstruction according to the large field-of-view input image of each layer, the diffraction propagation deflection carrier frequency factor corresponding to each sub-hologram is calculated; the carrier frequency factor is used to deflect the diffraction propagation direction of the reconstructed image of the sub-hologram, ensuring that the sub-input image is reconstructed at the corresponding xy position; the uv plane is the sub-hologram corresponding to the m_nth sub-input image, and its reconstructed image should be offset into the dashed box of the xy plane, thereby stitching together the original large field-of-view input image U at the current reconstruction distance z. z (x,y); the distance between the two planes is the diffraction propagation distance z of the second step Frenl.{}, and dx and dy are the sub-input images U corresponding to the current sub-hologram. subz_m_n The center point deviates from the original large field-of-view input image U z The distance between the center points (x, y) is given by the carrier frequency factor; therefore, the diffraction deflection angles in the transverse and longitudinal directions are θ, respectively. x θ y Its relationship with the reproduction distance z and spatial displacement d x d y The relationship between them is: According to the grating diffraction formula, the carrier frequency factor calculation formula is as follows, and j represents an imaginary part; Fourth, each sub-hologram is multiplied by the carrier frequency factor thereof, and each sub-hologram multiplied by different carrier frequency factors is spatially multiplexed and superimposed to form a final hologram; and the calculation formula is as follows:

2. The hologram computation method according to claim 1, characterized in that, In the 2D large field of view image cutting process, the resolution of the sub-input image U subz_m_n is less than or equal to the resolution of the hologram H(u, v).

3. The hologram computation method according to claim 1, characterized by, The diffraction propagation calculation method of the sub-hologram in the second step is a Fresnel diffraction propagation algorithm or a neural network algorithm.

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