CN115373247B - Conical surface hologram rapid generation method based on bidirectional phase compensation - Google Patents
Conical surface hologram rapid generation method based on bidirectional phase compensation Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/0443—Digital holography, i.e. recording holograms with digital recording means
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/0493—Special holograms not otherwise provided for, e.g. conoscopic, referenceless holography
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
- G03H1/0808—Methods of numerical synthesis, e.g. coherent ray tracing [CRT], diffraction specific
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
- G03H1/0866—Digital holographic imaging, i.e. synthesizing holobjects from holograms
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/0443—Digital holography, i.e. recording holograms with digital recording means
- G03H2001/045—Fourier or lensless Fourier arrangement
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Abstract
The invention provides a conical surface hologram rapid generation method based on bidirectional phase compensation. The method comprises two parts of conical surface hologram rapid generation and hologram reconstruction. The method comprises the steps of obtaining a conical surface diffraction field distribution consisting of the line diffraction fields by obtaining the line diffraction fields on the conical surface under a radius corresponding to a certain height, performing sparse line recording, performing bidirectional phase compensation by using an optical path difference, obtaining a hologram by encoding, and reconstructing by using a chromatography. Compared with the traditional method, the method has the advantages that the generation speed of the conical hologram is improved by 3 times, and a reconstruction result similar to the traditional method is obtained; the method solves the problem of the generation speed of the conical hologram for the first time.
Description
Technical Field
The invention relates to a holographic display technology, in particular to a conical surface hologram generating method.
Background
Holographic displays have received great attention as an ideal true three-dimensional display technology. With the development of computers and spatial light modulators, the implementation of computational holography to realize dynamic holographic display has become the mainstream of research. However, computing holograms is limited by the physical device size limitations of the spatial light modulator resulting in limited display viewing angles. Compared with the traditional cylindrical surface hologram, the conical surface hologram not only has a 360-degree horizontal field angle, but also has a larger vertical field angle, and is hopeful to thoroughly solve the problem of limited calculated holographic field angle, so that the conical surface hologram becomes a recent research hot spot. However, there is still a technical problem to be solved in cone surface calculation holography, namely: because of the structural characteristics of the conical surfaces, the radii at different heights are different, so that one-dimensional integration exists in the calculation formula, and the hologram generation speed is low. So how to increase the cone hologram generation speed needs to be solved.
Disclosure of Invention
Aiming at the problem that the one-dimensional integration is slow in hologram generation speed, the invention provides a conical surface hologram rapid generation method based on bidirectional phase compensation. The proposed method can increase the speed of hologram generation by a multiple and ensure high reconstruction quality. The method comprises two parts of conical surface hologram rapid generation and hologram reconstruction.
The conical surface hologram rapid generation method comprises the following five steps: (1) obtaining a line diffraction field on a conical surface under a radius corresponding to a certain height, (2) obtaining conical surface diffraction field distribution consisting of the line diffraction fields, (3) performing sparse line recording, (4) performing bidirectional phase compensation by utilizing an optical path difference, and (5) encoding to obtain a hologram, wherein the hologram reconstruction comprises the following steps: reconstructing the generated hologram.
The line diffraction field on the conical surface under the radius corresponding to a certain height is obtained according to the formula U of the traditional conical surface diffraction calculation model d =∫IFFT[FFT(U s )×FFT(h)]dz, obtaining radius R of conical surface at a certain height d [i]Corresponding line diffraction field H i ={IFFT[FFT(U s )×FFT(h)]}| Rd[i] Wherein U is d Indicating the conical diffraction field, U s For object plane, h is the point spread function, +.dz is the one-dimensional integral in the vertical direction, FFT {.cndot } and IFFT {.cndot }, represent the fast Fourier transform and the inverse fast Fourier transform, R d The radius of the conical surface is represented, and i is a positive integer.
The method for obtaining the conical surface diffraction field distribution consisting of the row diffraction fields is based on the first step, and converts the conical surface diffraction distribution into a combination of the row diffraction fields corresponding to the radiuses at different heights, namely U d =[H 1 ;H 2 ;···H N ]Wherein H is 1 Represents the diffraction field of line 1 on the conical surface, H N The diffraction field of the nth row on the cone is shown, where N represents the number of samples in the vertical direction.
The sparse line recording is performed by obtaining a sparse line recording surface U sparse Spark (·) where spark (·) represents that only one of the rows is taken for direct calculation every few rows, where the parameter D of the function spark (·) is odd, representing direct calculation every D rows.
The bidirectional phase compensation by utilizing the optical path difference is to obtain the phase of the adjacent row by adopting a bidirectional phase compensation method, and when D is 3, H i Respectively compensating adjacent two lines of the pattern as H ’ i+1 =H i X exp (jk. DELTA.d) and H ’ i-1 =H i X exp (-jk. DELTA.d), thereby obtaining U d ’ | D=3 =[···H ’ i-1 ;H i ; H ’ i+1 ···](i=3n—1), where j is an imaginary unit, k is a wave number, Δd is a compensation distance between adjacent rows, U d ’ Representing compensated conical surface derivativesThe field of view, n is a positive integer, and when D is any other value, the diffraction profile is expressed as U d ’ | D =[···H ’ i-(D-1)/2 ···H ’ i-2 ; H ’ i-1 ; H i ; H ’ i+1 ; H ’ i+2 ···H ’ i+(D-1)/2 ···] (i=D n-(D-1)/2)。
The hologram obtained by encoding is obtained by using a formula U holo =Encode（U d ’ | D ) Encoding to obtain hologram U holo Encode (∙) represents the encoding function.
The reconstruction of the generated hologram is carried out by utilizing a chromatography method according to the hologram obtained in the step five to obtain a reconstructed image.
The method has the beneficial effects that: compared with the traditional conical surface holographic calculation method, the provided conical surface hologram rapid generation method based on the bidirectional phase compensation has the advantages that the hologram generation speed is improved by 3 times, and the peak signal-to-noise ratio is reduced by 0.34dB; the method solves the problem of the holographic calculation speed of the conical surface for the first time, and has a very large application scene.
Drawings
FIG. 1 is a schematic diagram of a hologram generating computational model of the present invention.
Fig. 2 is a schematic diagram of bi-directional phase compensation according to the present invention. 2 (b) is a schematic diagram with a sparse line recording parameter D of 3, i.e., one line is taken out of every three lines to directly calculate and two adjacent lines are phase-compensated, and 2 (c) is a schematic diagram with a sparse line recording parameter D of 5, i.e., one line is taken out of every five lines to directly calculate and four adjacent lines are phase-compensated.
FIG. 3 is a graph of hologram generation time results at different D and different tilt angles according to the present invention.
FIG. 4 is a graph of the quality results of hologram reconstruction at different D and tilt angles according to the present invention, with PSNR as a measure.
Detailed Description
An exemplary embodiment of a method for rapidly generating a conical hologram based on bi-directional phase compensation according to the present invention will be described in detail below, and the method will be described in further detail. It is noted herein that the following examples are given by way of further illustration only and are not to be construed as limiting the scope of the present invention, as those skilled in the art will make numerous insubstantial modifications and adaptations of the process in light of the above teachings, and yet remain within the scope of the invention.
The method for rapidly generating the conical hologram based on the bidirectional phase compensation comprises two parts, namely rapid generation of the conical hologram and reconstruction of the hologram.
The conical surface hologram rapid generation method comprises the following five steps: (1) obtaining a line diffraction field on a conical surface under a radius corresponding to a certain height, (2) obtaining conical surface diffraction field distribution consisting of the line diffraction fields, (3) performing sparse line recording, (4) performing bidirectional phase compensation by utilizing an optical path difference, and (5) encoding to obtain a hologram, wherein the hologram reconstruction comprises the following steps: reconstructing the generated hologram.
The line diffraction field on the conical surface under the radius corresponding to a certain height is obtained according to the formula U of the traditional conical surface diffraction calculation model d =∫IFFT[FFT(U s )×FFT(h)]dz, obtaining radius R of conical surface at a certain height by using two-dimensional Fourier transform d [i]Corresponding line diffraction field H i ={IFFT[FFT(U s )×FFT(h)]}| Rd[i] Wherein U is d Indicating the conical diffraction field, U s For object plane, h is the point spread function, +.dz is the one-dimensional integral in the vertical direction, FFT {.cndot } and IFFT {.cndot }, represent the fast Fourier transform and the inverse fast Fourier transform, R d The radius of the conical surface is represented, and i is a positive integer.
The method for obtaining the conical surface diffraction field distribution consisting of the row diffraction fields is based on the first step, and converts the conical surface diffraction distribution into a combination of the row diffraction fields corresponding to the radiuses at different heights, namely U d =[H 1 ;H 2 ;···H N ]Wherein H is 1 Represents the diffraction field of line 1 on the conical surface, H N The diffraction field of the nth row on the cone is shown, where N represents the number of samples in the vertical direction.
The process is carried outSparse line recording is compared with the calculation of diffraction distribution of each line, the method obtains a sparse line recording surface U sparse The value of spark (D) is increased, where spark (·) represents that only one of the rows is taken for direct calculation every few rows, where the parameter D of the function spark (·) is odd, representing direct calculation every D rows. When D is 3, only the middle row is taken for calculation in every three rows of conical diffraction fields.
The bidirectional phase compensation by utilizing the optical path difference is to obtain the phases of adjacent rows by adopting a bidirectional phase compensation method to improve the compensation efficiency, and when D is 3, H i Respectively compensating adjacent two lines of the pattern as H ’ i+1 =H i X exp (jk. DELTA.d) and H ’ i-1 =H i X exp (-jk·Δd), offset distance Δd=h between adjacent rows c Tan. Alpha./N, thereby obtaining U d ’ | D=3 =[···H ’ i-1 ;H i ; H ’ i+1 ···](i=3n—1), where j is an imaginary unit, k is a wave number, U d ’ Represents the compensated conical diffraction field, n is a positive integer, H c Is the height of the conical surface, alpha is the inclination angle, and tan alpha is the tangent value of alpha; when D is any other value, the diffraction profile is denoted as U d ’ | D =[···H ’ i-(D-1)/2 ···H ’ i-2 ; H ’ i-1 ; H i ; H ’ i+1 ; H ’ i+2 ···H ’ i+(D-1)/2 ···] (i=D n-(D-1)/2)。
The encoding method adopted for obtaining the hologram by encoding is a bi-phase and amplitude truncation method, so that the hologram is obtained.
And (3) reconstructing the generated hologram according to the hologram obtained in the step (V), and reconstructing by using a chromatography to obtain a reconstructed image.
In the example of the present invention, a 1024 x 512 gray scale image is used. The wavelength, the radius of the cylindrical surface and the radius of the upper surface of the conical surface are respectively 250 mu m, 70mm and 7mm. Fig. 3 shows the time required to generate a 1024 x 512 cone hologram for cases 1,3,5,7, 9. The result shows that the method can doubly improve the calculation speed. Fig. 4 shows the peak signal to noise ratio corresponding to the reconstructed image for cases D1, 3,5,7, 9. The result shows that when the D is 3, the method can obtain a reconstruction result similar to the conventional method, and the peak signal-to-noise ratio is reduced along with the increase of the D.
Claims (2)
1. The method for rapidly generating the conical hologram based on the bidirectional phase compensation is characterized by comprising two parts, namely rapid generation of the conical hologram and reconstruction of the hologram; the specific description of the conical surface hologram rapid generation process is as follows: step one, firstly, according to a formula U of a traditional conical surface diffraction calculation model d =∫IFFT[FFT(U s )×FFT(h)]dz, obtaining radius R of conical surface at a certain height d [i]Corresponding line diffraction field H i ={IFFT[FFT(U s )×FFT(h)]}| Rd[i] Wherein U is d Indicating the conical diffraction field, U s For object plane, h is the point spread function, +.dz is the one-dimensional integral in the vertical direction, FFT {.cndot } and IFFT {.cndot }, represent the fast Fourier transform and the inverse fast Fourier transform, R d The radius of the conical surface is represented, i is a positive integer; step two, based on the step one, converting the diffraction distribution of the conical surface into a combination of diffraction fields of corresponding rows of radiuses at different heights, namely U d =[H 1 ;H 2 ;···H N ]Wherein H is 1 Represents the diffraction field of line 1 on the conical surface, H N Representing the diffraction field of the nth row on the conical surface, where N represents the number of samples in the vertical direction; step three, obtaining a sparse line recording surface U sparse Spark (·) where spark (·) represents that only one of the rows is taken for direct calculation every few rows, where the parameter D of the function spark (·) is odd, representing direct calculation every D rows; obtaining the phase of adjacent lines by adopting a bidirectional phase compensation method, and when D is 3, H i Respectively compensating adjacent two lines of the pattern as H ’ i+1 =H i X exp (jk. DELTA.d) and H ’ i-1 =H i X exp (-jk. DELTA.d), thereby obtaining U d ’ | D=3 =[···H ’ i-1 ;H i ; H ’ i+1 ···](i=3n—1), where j is an imaginary unit, k is a wave number, Δd is a compensation distance between adjacent rows, U d ’ Represents the compensated conical diffraction field, n is a positive integer, and when D is any other value, the diffraction distribution is represented as U d ’ | D =[···H ’ i-(D-1)/2 ···H ’ i-2 ; H ’ i-1 ; H i ; H ’ i+1 ; H ’ i+2 ···H ’ i+(D-1)/2 ···](i= D n- (D-1)/2); step five, utilizing a formula U holo =Encode（U d ’ | D ) Encoding to obtain hologram U holo Encode (∙) represents the encoding function; the conical surface hologram reconstruction process is specifically described as follows: and (3) reconstructing the hologram obtained in the step (V) by using a chromatography to obtain a reconstructed image.
2. The method for rapidly generating the conical hologram based on the bidirectional phase compensation according to claim 1, wherein the sparse line parameters D are 3,5,7 and 9.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1558410A (en) * | 2003-02-28 | 2004-12-29 | ���µ�����ҵ��ʽ���� | Optical pickup |
| US6948127B1 (en) * | 2001-12-10 | 2005-09-20 | Cisco Technology, Inc. | Interface for compressed video data analysis |
| CN1750144A (en) * | 2004-08-30 | 2006-03-22 | 夏普株式会社 | Hologram laser unit and optical pickup apparatus |
| CN113589671A (en) * | 2021-07-01 | 2021-11-02 | 四川大学 | Conical surface holographic display method for enlarging vertical field angle |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6948127B1 (en) * | 2001-12-10 | 2005-09-20 | Cisco Technology, Inc. | Interface for compressed video data analysis |
| CN1558410A (en) * | 2003-02-28 | 2004-12-29 | ���µ�����ҵ��ʽ���� | Optical pickup |
| CN1750144A (en) * | 2004-08-30 | 2006-03-22 | 夏普株式会社 | Hologram laser unit and optical pickup apparatus |
| CN113589671A (en) * | 2021-07-01 | 2021-11-02 | 四川大学 | Conical surface holographic display method for enlarging vertical field angle |
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| "Bi-directional phase compensation to accelerate conical hologram generation";peiding wang;《Displays》;第1-8页 * |
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