Large-view-field hologram calculation method based on carrier frequency multiplexing

Abstract

The invention discloses a large-view-field hologram calculation method based on carrier frequency multiplexing, and relates to the technical field of information optics. First, size preprocessing is performed on a 3D input image. Therefore, an original large-field-of-view input image is layered and then cut into sub-input image sequences not larger than the size of the hologram layer by layer. Secondly, sub-hologram solving is carried out on the sub-input image sequences through a hologram diffraction propagation calculation method; thirdly, analyzing and calculating the x-y offset distance reconstructed by cutting the sub-holograms according to each layer of large-view-field input image, and calculating the diffraction propagation offset frequency factor corresponding to each sub-hologram; and fourthly, performing dot multiplication on each sub-hologram by the respective carrier frequency factor, and performing spatial multiplexing and superposition on each sub-hologram subjected to dot multiplication by the corresponding carrier frequency factor to form a final hologram. The size of the input image can be larger than that of the hologram.

Description

Technical Field

[0001] The present invention relates to the field of information optics technology, and in particular to a large-field-of-view hologram calculation method based on carrier frequency multiplexing. Background Art

[0002] Holography is a technology that can record the amplitude and phase information of light waves through interference fringes. It can use two-dimensional plane information to record or reproduce three-dimensional light field information. It has important applications and prospects in the fields of holographic microscopic imaging, holographic measurement, true three-dimensional display, optical tweezers, optical micro-nano processing, etc. With the development of computer technology, computer-generated holograms can get rid of various limitations of optical hologram acquisition by simulating the diffraction of three-dimensional light fields to propagate to two-dimensional planes to calculate holograms. According to the division of diffraction distance, computational holograms are divided into Fourier holograms, image holograms, and Fresnel holograms. The reconstructed field of view of Fourier holograms is proportional to the wavelength and the focal length of the Fourier lens, and inversely proportional to the spatial resolution of the hologram fringes. Therefore, the maximum field of view is reconstructed after the fringes reach the sampling frequency. Image holograms are suitable for white light reproduction, but the reconstructed stereo depth is limited, resulting in a short propagation distance and a field of view that will not be larger than the hologram size. In theory, Fresnel holograms can achieve large-field-of-view recording and reproduction of any three-dimensional scene. However, the calculation process is affected by various factors such as band-limited destructive interference, and large-field-of-view recording is currently not possible.

[0003] The calculation methods of Fresnel holograms are mainly divided into iterative methods and non-iterative methods. The iterative method mainly uses the phase optimization algorithm to obtain a pure phase hologram with high diffraction efficiency. Among them, the core of the calculation is the diffraction propagation calculation between planes, such as methods based on fast Fourier transform and angular spectrum method. The non-iterative method also uses diffraction propagation to directly calculate the complex amplitude distribution at the target distance, and then combines a complex complex amplitude encoding method to generate a hologram, including ray tracing, layered Fresnel propagation, and their upgrade methods. In the above methods, except for the ray tracing method, 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 constraints in the iterative method require the two to be the same, and the surface-to-surface diffraction propagation calculation in the non-iterative method also requires the two to be the same size. Even if they are different, it is due to different sampling, and the pixel resolution is still the same. However, the ray tracing method can directly obtain the hologram through point-to-point calculation between the input image and the hologram plane without considering the size difference. Since the hologram of each object point in the actual calculation process is a series of concentric rings in the form of Fresnel zone plates, its effective size will be limited by the sampling bandwidth and the destructive interference of adjacent object points. This results in very little fringe information being recorded for object points that are far away from the central axis, which causes the reconstruction energy of these object points to drop significantly, resulting in serious uneven energy distribution of the entire reconstructed light field, making it impossible to achieve large-field reconstruction with uniform light field energy distribution. So far, no reported method has been able to record hologram calculation methods with scene sizes larger than the hologram size. Summary of the invention

[0004] The currently reported hologram calculation methods all require that the input image and the hologram matrix be the same size, and cannot record a computational hologram larger than the hologram size. In order to achieve the recording and reconstruction of holograms with a large field of view, the present invention proposes a large field of view hologram calculation method based on carrier frequency multiplexing, thereby achieving that the input image size can be larger than the hologram size.

[0005] Figure 1 A flow chart of a hologram calculation method based on carrier frequency multiplexing is given, which includes three processes: sub-hologram calculation, carrier frequency multiplexing, and coherent superposition to generate a final hologram.

[0006] First, the 3D large field of view image is pre-processed. The 3D large field of view image U is divided into 2D large field of view images U at different depths according to the diffraction propagation direction z. z . Its mathematical expression is:

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

[0008] Among them, 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 of the 2D large field of view image U z The subscript z of the 3D large field of view image corresponds to the coordinate z of the 3D large field of view image. z Crop the input image sequence into sub-images smaller than or equal to the hologram size. Figure 2 The principle of cutting a 2D large field of view image into 3×3 sub-input images is illustrated in FIG. Preferably, the number of cut sub-image sequences should be determined according to 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 divided into a series of 2D large field of view images with different axial depths, and then cut into sub-image sequences of corresponding sizes according to the above method. Suppose the 2D large field of view image at a certain depth z is U z (x,y), then the mathematical expression of the preprocessing operation is:

[0009]

[0010] Among them, U subz_m_n For the 2D large field image U z The mth row and nth column of the sub-input image, 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, and X and Y are the coordinates of the 2D large field of view image U z The resolution of the sub-input image U is thus X / M and Y / N. subz_m_n The resolution of 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, the hologram diffraction propagation calculation method is used to solve the sub-holograms of the sub-input image sequence. The diffraction propagation algorithm can be selected from the angular spectrum diffraction algorithm, the Fresnel diffraction propagation algorithm, the neural network algorithm, etc. The sub-hologram sequence corresponding to the sub-input image sequence is calculated, and the reconstructed image size of each sub-hologram is less than or equal to the spatial size of the sub-hologram. The mathematical expression of the processing process is:

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

[0013] Among them, the operator Frenl.{} is the surface-to-surface diffraction propagation operator. When different surface-to-surface diffraction propagation algorithms are selected for calculation, the operator is adapted according to the algorithm.

[0014] Third, the xy offset distance of each sub-hologram after cutting is calculated according to the size of each layer of 2D large field of view image, and the diffraction propagation deviation carrier factor corresponding to each sub-hologram is calculated. The carrier factor is used to deflect the diffraction propagation direction of the sub-hologram reconstructed image to ensure that the sub-input image is reconstructed at the corresponding xy position. Figure 3 As shown in the figure, the uv plane is the sub-hologram corresponding to the (m, n)th sub-input image, and its reconstructed image should be offset to the dotted box in the xy plane, so that the 2D large field of view image U at the current reconstruction distance z can be spliced. z (x, y). The distance between the two planes is the diffraction propagation distance z of the second step Frenl.{}, d x and d y are the sub-input images U corresponding to the current sub-hologram subz_m_n The center point deviates from the 2D large field of view image U z The distance between the center point (x, y). Therefore, the diffraction deflection angles of the carrier frequency factor in the horizontal and vertical directions are θ x ,θ y , which is related to the reproduction distance z and the spatial displacement d x d y The relationship between them is:

[0015]

[0016] According to the grating diffraction formula, the carrier frequency factor P can be obtained subz_m_n The calculation formula is, where j is the imaginary unit:

[0017]

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

[0019]

[0020] The present invention solves the problem of limited reconstruction range caused by band limitation and destructive interference of adjacent points during hologram reconstruction by cutting the 3D large field of view image into the small-sized sub-input images. Since the carrier frequency factor only changes the propagation direction and does not change the content of the reconstructed image, the method of the present invention only changes the spatial position of the sub-hologram reproduction image, but does not affect the reconstructed image of the sub-hologram. Therefore, the method can realize the reconstruction of a 3D large field of view image larger than the size of the hologram using a hologram of a certain size through carrier frequency multiplexing. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1:Computational flow chart of the large-field-of-view hologram calculation method based on carrier frequency multiplexing.

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

[0023] Figure 3 It is a schematic diagram of the deflection angle of the diffraction direction of the sub-hologram due to the carrier frequency factor.

[0024] Figure 4 The invention is an implementation scheme and reproduction effect of large-field-of-view hologram calculation based on carrier frequency multiplexing.

[0025] Figure 5 It is a comparison of the reconstruction size between the traditional algorithm and the carrier frequency multiplexing hologram algorithm. DETAILED DESCRIPTION

[0026] Reference below Figure 4 Typical embodiments of the present invention and their features are described in detail.

[0027] The core of the traditional hologram calculation method is based on face-to-face diffraction propagation calculation, which requires that the input image size be the same as the hologram size. Although the point source-based ray tracing method can break this constraint, when the object point deviates from the hologram area, the stripes recorded in the hologram area are affected by the band limitation and the destructive interference of adjacent point stripes, and the stripe contrast is significantly reduced. Therefore, this method cannot record and reproduce large field of view images. The method based on carrier frequency multiplexing proposed in the present invention is as described above, by cutting the large field of view image into small-sized sub-input images, calculating the sub-holograms of the sub-input images respectively, and multiplying different carrier frequency factors according to the cutting position, and finally superimposing and multiplexing to generate a hologram of the large field of view image.

[0028] Taking the hologram sampling interval of 8μm, the hologram resolution of 1920×1080 pixels, and the diffraction reconstruction distance of 500mm as an example, the maximum field of view that can be reconstructed is calculated as 33.2mm×33.2mm according to the diffraction formula. Furthermore, for the convenience of the description of 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 taken as an example. First, according to the first step, keep the object light field sampling 8μm unchanged, and convert the 2D large field of view image U with a resolution (X, Y) of (3240, 3240) in Cropped into nine sub-input images U with (M, N) = (3, 3) subz_m_n Its pixel resolution is 1080×1080. Figure 4 Secondly, according to the second step, the nine sub-input images U are calculated using the traditional hologram generation algorithm. subz_m_n The corresponding sub-hologram H subz_m_nPreferably, the diffraction propagation process uses angular spectrum diffraction, and the calculation is as follows: Figure 4 The nine sub-holograms described in the above. Third, according to the third step, the offset re-frequency factor corresponding to each sub-hologram is calculated. Figure 4 As shown in the figure, the offset distance (d x , d y ) is (-8.64mm, 8.64mm), and its 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 corresponding carrier frequency factor P of other sub-input images is calculated according to the corresponding offset distance and reconstruction distance. subz_m_n Finally, according to the fourth step, the nine sub-holograms H subz_m_n Multiply the corresponding carrier frequency factor P respectively subz_m_n , and then sum and superimpose the complex amplitudes after the point product to obtain the final hologram. Because the carrier frequency factor of each sub-hologram can deflect and diffract its reconstructed light field, at a reconstruction distance of 500mm, the corresponding sub-input image can be reconstructed to the corresponding spatial position, thereby obtaining the final 2D large field of view image, realizing the small-size hologram recording and reproduction of large field of view images. 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, and the 2D large field of view images of different z depths are reproduced by layer diffraction, and finally the 3D large field of view image is reproduced.

[0029] picture Figure 5 Shown is a comparison of the reconstructed images of the method of the present invention and the traditional hologram algorithm. The first row uses the traditional hologram calculation method, the second row uses the method of the present invention, and the first column is all 2D large field of view images, where the red dotted border is the hologram size. The 2D large field of view image is calculated by the method of the present invention to obtain a small-sized hologram, and loaded onto the SLM for optical reconstruction. The third column is the optical reconstruction result of the corresponding algorithm. The traditional algorithm can only reconstruct the regional image corresponding to the hologram size in the 2D large field of view image, while the method of the present invention can completely reconstruct a 2D large field of view image with a size of 25.9mm*25.9mm at the reconstruction position.

Claims

1. A method for calculating a large-field-of-view hologram based on carrier frequency multiplexing, characterized in that: First, the 3D large field of view image U is pre-processed in size. The first step of the pre-processing is to divide the 2D large field of view image U into different depth layers according to the diffraction propagation direction z. z , the mathematical expression of the hierarchical operation is: U z (x,y)=U(x,y,z). (1) Among them, the 2D large field of view image U z The subscript represents the 2D large field of view image at the corresponding z depth. The second step of the preprocessing is to respectively process the 2D large field of view image U at each z depth. z Perform a cutting process, the mathematical expression of the cutting process is: Among them, U subz_m_n is the sub-input image, the subscript represents the sub-input image at the mth row and nth column at the z depth, its horizontal and vertical maximum values ​​are M and N, and X and Y are the 2D large field of view image U z Resolution Second, the hologram diffraction propagation calculation method is used to solve the sub-holograms of the sub-input image sequence. The diffraction propagation algorithm uses the angular spectrum diffraction algorithm, the Fresnel diffraction propagation algorithm or the neural network algorithm; the sub-hologram sequence corresponding to the sub-input image sequence is calculated, and the reconstructed image size of each sub-hologram is less than or equal to the spatial size of the sub-hologram. The mathematical expression of the processing process is: H subz_m_n (u,v)=Frenl.{U subz_m_n (x′,y′)}. (3) Among them, the operator Frenl.{} is the Fresnel diffraction propagation operator. When different algorithms are selected for calculation, the operator is adapted according to the algorithm. Third, the xy offset distance of the reconstructed cut sub-hologram is calculated according to the analysis of each layer of the large field of view input image, and the diffraction propagation deviation carrier factor corresponding to each sub-hologram is calculated; the carrier factor is used to deflect the diffraction propagation direction of the sub-hologram reconstructed image to ensure 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 to the dotted box of the xy plane, so as to splice 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.{}, 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 point (x, y); therefore, the diffraction deflection angles of the carrier frequency factor in the horizontal and vertical directions are θ x ,θ y , which is related to the reproduction distance z and the spatial displacement d x d y The relationship between them is: According to the grating diffraction formula, the carrier frequency factor is calculated as follows, where j represents the imaginary part; Fourth, each sub-hologram is point-multiplied by its own carrier frequency factor, and the sub-holograms with different carrier frequency factors are spatially multiplexed and superimposed to form the final hologram; the calculation formula is:

2. The hologram calculation method according to claim 1, characterized in that: In the above-mentioned 2D large field of view image cropping process, it is necessary to ensure that the sub-input image U subz_m_n The resolution is less than or equal to the resolution of the hologram H(u,v).

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

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