CN104503214A - Making method and display device for computer-generated semi-panoramic color rainbow hologram - Google Patents

Abstract

A making method for a computer-generated semi-panoramic color rainbow hologram is characterized by comprising the following steps: step 1, determining the position, size and distance relationship between a semi-circular observation window and a hologram; step 2, analyzing the frequency domain position and the frequency bandwidth under the corresponding observation window; and step 3, calculating the frequency spectrums of the three primary colors in the frequency domain, synthesizing the frequency spectrums, carrying out inverse Fourier transform on the frequency spectrum obtained from synthesis to obtain the optical field distribution on a holographic plane, and introducing reference light and object light and carrying out interference to obtain a computer-generated semi-panoramic color rainbow hologram. The following beneficial effects are achieved: the noise effect in the process of optical shooting is avoided; no optical recording platform or complex optical path design is needed, and a hologram can be made on an ordinary computer; semi-panoramic color rainbow holograms of virtual objects and large natural scenes, and real objects or scenes can be made; and compared with the traditional strip-shaped observation window, a semi-panoramic color rainbow hologram has obvious advantages and is more convenient to use.

Description

The method for making of computing mechanism half panorama colour rainbow hologram and display device

Technical field

The present invention relates to a kind of making field of rainbow hologram, particularly relate to method for making and the display device of the plate half panorama colour rainbow hologram of a kind of computing mechanism.

Background technology

Existing plate panorama rainbow holography utilizes the method for optical holography to carry out single stage method or two-step rainbow holographic process, and optical system is very complicated, and has very high requirement to shooting environmental, the monochromatic rainbow holography display of whole realization.Foreign scholar proposes some holographic recording systems, and by the mode record disc-type rainbow holography of spatial reuse, register system is complicated, and due to the instability of optical system, the noise of reproduction image is also more serious.Along with the development of computer technology and holographic straight-writing system, the method of calculation holographic is likely utilized to realize plate panorama rainbow holography, Qian Huiguo etc. proposed the plate panorama of computing mechanism in 2005 holographic, the more careful transport property describing light field, give the reconstruction results of a simple three-dimensional model, east unit etc. do not take reference light method to set up more cleverly, are combined by calculation holographic and carry out the making of panorama holography, give preliminary result with optical holography.But the hologram that two kinds of methods realize is all monochromatic holographic, actual optics reproduction effects is unsatisfactory.

Summary of the invention

The noise of, reproduction image complicated for monochromatic rainbow holography display in existing panorama rainbow holography technology, the register system shortcomings such as also more serious, actual optics reproduction effects is unsatisfactory, the invention provides the method for making of the plate half panorama colour rainbow holography of a kind of computing mechanism, without the need to optical recording platform, dummy object can be realized, the holographic production of large scene object.Only need personal computer and holographic output system both can make.

The technical scheme of this method for making is:

A method for making for computing mechanism half panorama colour rainbow hologram, is characterized in that the method includes the steps of:

Step one, determines half ring-like observation window and hologram size and position relationship,

Step 2, analyzes the frequency domain position under corresponding observation window and frequency span,

Step 3, calculate the frequency spectrum of three primary colors object light respectively, then in frequency domain, Spectrum synthesizing is carried out, this frequency spectrum is the frequency spectrum of object light, by carrying out the optical field distribution that inverse Fourier transform obtains on holographic facet to synthesis frequency spectrum, introduce reference light and object light afterwards and carry out interference and obtain the plate half panorama colour rainbow hologram of computing mechanism.Export and chemical treatment through holographic output system, obtaining can the hologram of white light reconstruction.

Further, the concrete methods of realizing of described step one is:

Watch window is semicircular distribution, has axially symmetric structure, carries out principle analysis with a cross section.Object width is w _o, viewing plane is h to object distance, and narrow annular channel centre distance is r to the distance of axle, and the width of semi-circular form is w _s, at watch window place, object primaries will accurately overlap, and therefore for the subtended angle θ of z-axis, primaries is identical, but three primary colors optical wavelength is different, therefore has different spatial frequencys.Three primary colors optical wavelength is respectively λ _r, λ _g, λ _b, frequency radius is expressed as:

$\begin{array}{c}{f}_r=\frac{\sin \left(\mathrm{\θ}\right)}{{\mathrm{\λ}}_r}=\frac{r}{{\mathrm{\λ}}_r\sqrt{r^2+h^2}}\\ f_g=\frac{\sin \left(\mathrm{\θ}\right)}{{\mathrm{\λ}}_g}=\frac{r}{{\mathrm{\λ}}_g\sqrt{r^2+h^2}}\\ f_b=\frac{\sin \left(\mathrm{\θ}\right)}{{\mathrm{\λ}}_b}=\frac{r}{{\mathrm{\λ}}_b\sqrt{r^2+h^2}}\end{array}---\left(1\right)$

Wherein, f _rfor the frequency radius of object red component, f _gfor object green component frequency radius, f _bfor the frequency radius of object blue component.

Further, the concrete methods of realizing of described step 2 is:

On object, the angle of summit A and slit lower limb D line and z-axis is , the line of object lower limb B and slit coboundary C and z-axis angle determine the bandwidth that slit limits, for three primary colors light wave, frequency span is respectively:

$\begin{array}{c}\mathrm{\Δ}{f}_r=\frac{\sin \left({\∂}_1\right)}{{\mathrm{\λ}}_r}-\frac{\sin \left({\∂}_2\right)}{{\mathrm{\λ}}_r}=\frac{1}{{\mathrm{\λ}}_r}[\frac{r+\frac{w_s}{2}+\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}-\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\λ}}_r}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+4h^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+4h^2}}]\\ \mathrm{\Δ}{f}_g=\frac{\sin \left({\∂}_1\right)}{{\mathrm{\λ}}_g}-\frac{\sin \left({\∂}_2\right)}{{\mathrm{\λ}}_g}=\frac{1}{{\mathrm{\λ}}_g}[\frac{r+\frac{w_s}{2}+\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}-\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\λ}}_g}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+4h^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+4h^2}}]\\ \mathrm{\Δ}{f}_b=\frac{\sin \left({\∂}_1\right)}{{\mathrm{\λ}}_b}-\frac{\sin \left({\∂}_2\right)}{{\mathrm{\λ}}_b}=\frac{1}{{\mathrm{\λ}}_b}[\frac{r+\frac{w_s}{2}+\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}-\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\λ}}_b}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+4h^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+4h^2}}]\end{array}---\left(2\right)$

Wherein, Δ f _rfor the frequency span of object red component, Δ f _gfor object green component frequency span, Δ f _bfor the frequency span of object blue component.According to spatial domain and frequency domain relation, when object width is w _otime, the sampling interval Δ f in its frequency domain is:

$\mathrm{\Δf}=\frac{1}{w_o}---\left(3\right)$

The final hologram calculated is image plane holographic, hologram size w _hwith dimension of object w _oidentical, the sampling interval of hologram is Δ h, then holographic facet sampling number M is:

$m=\frac{w_h}{\mathrm{\Δh}}=\frac{w_o}{\mathrm{\Δh}}---\left(4\right)$

The scope of the coordinate f then in frequency domain is:

$-\frac{M}{2}\mathrm{\&Delta;f}<f<\frac{M}{2}\mathrm{\&Delta;f}---\left(5\right)$

Further, the concrete methods of realizing of described step 3 is:

(1) sample according to dimension of object and hologram and observe the relation of slit, the resolution (M of frequency spectrum _fx, N _fy) and the coordinate range of frequency spectrum, respectively piecemeal process is carried out to three primary colors frequency spectrum;

The resolution of each block of red component is (M _fxr, N _fyr), then the resolution of the frequency spectrum of green and each block of blue component is expressed as:

$\begin{array}{c}{M}_{\mathrm{fxg}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_g}{M}_{\mathrm{fxr}};N_{\mathrm{fyg}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_g}{N}_{\mathrm{fyr}}\\ M_{\mathrm{fxb}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_b}{M}_{\mathrm{fxr}};N_{\mathrm{fyb}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_b}{N}_{\mathrm{fyr}}\end{array}---\left(6\right)$

Wherein, the volume coordinate that (x, y, z) is three-dimensional data, (M _fxg, N _fyg) represent the resolution of the frequency spectrum of green component each block, (M _fxb, N _fyb) represent the resolution of the frequency spectrum of blue component each block;

Block count in frequency domain is respectively:

$\begin{array}{c}{m}_r=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxr}}};n_r=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyr}}}\\ m_g=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxg}}};n_g=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyg}}}\\ m_b=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxb}}};n_r=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyb}}}\end{array}---\left(7\right)$

Wherein the block count of red component is m _rrow n _rrow, the block count of green component is m _grow n _grow, the block count of blue component is m _brow n _brow.

(2) according to frequency partitions number and frequency coordinate, carry out section technique respectively to three-primary-color image frequency spectrum, result of calculation remains three groups of temporary files;

The calculation procedure of red spectrum is as follows: be m by whole Dividing in frequency domain _rrow n _rrow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when

and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _rf _xm); θ _y=acsin (λ _rf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three dimensional point cloud, take out its green component data, and be resolution M by its interpolation _fxr* N _fyr, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxr* N _fyrfull null matrix, the order of its data according to block number is preserved;

The calculation procedure of green frequency spectrum is as follows: be m by whole Dividing in frequency domain _grow n _grow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when

and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _gf _xm); θ _y=acsin (λ _gf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three dimensional point cloud, take out its green component, and be resolution M by its interpolation _fxg* N _fyg, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxg* N _fygfull null matrix, the order of its data according to block number is preserved;

The calculation procedure of blue spectrum is as follows: be m by whole Dividing in frequency domain _brow n _brow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when

and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _bf _xm); θ _y=acsin (λ _bf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three dimensional point cloud, take out its blue component, and be resolution M by its interpolation _fxb* N _fyb, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxb* N _fybfull null matrix, the order of its data according to block number is preserved;

(3) according to frequency spectrum coordinate position relation, RGB frequency spectrum data is fused into an overall data, piecemeal saves as temporary file;

(4) object light complex amplitude in calculation holographic plane, in hologram plane, object light complex amplitude is the inverse Fourier transform of (3) step synthesis frequency spectrum, adopts the mode of horizontal one dimension inverse Fourier transform and the combination of Vertical one dimensional inverse Fourier transform to realize two inverse Fourier transforms of whole frequency spectrum data;

Basic skills is, for certain data line, ephemeral data identical for all columns is read in internal memory, splices and combines into a two-dimensional matrix, carries out line direction inverse Fourier transform to this matrix, saves as ephemeral data after transformation results being split.Namely one dimension line direction Fourier transform is realized to all row relax of advancing, because the data in frequency domain are only present in half frequent territory, only needs process to have the calculating in valid data region;

For the row determined, read the ephemeral data side that all line numbers of previous step generation are identical, be combined into a two-dimensional matrix, then carry out the one dimension inverse Fourier transform on column direction, save as temporary file after transformation results being split, and preserve each small block data amplitude maximum A _mij;

According to all small block data amplitude maximum A that previous step calculates _mijin maximal value A _max;

(5) hologram calculates, and for the data that (4) step is preserved, the physical coordinates of each blocks of data is known, and the computation process of hologram is expressed as:

Read (i, j) individual data, ask its phase place with amplitude A (x _ij, y _ij), wherein (x _ij, y _ij) be the coordinate in this region, reference light is the directional light of vertical incidence, and its phase place is expressed as:

Wherein C is a constant.

Adopt Burch coding to carry out holography to calculate, (i, j) block holographic distribution is expressed as:

Utilize holographic straight-writing system, hologram is exported, carry out the process such as developing fixing, the plate half panorama colour rainbow hologram for white light reconstruction can be obtained.

Further, according to projection view angles (θ _x, θ _y) concrete grammar of obtaining the projected image of three dimensional point cloud is: three-dimensional point cloud model data layout is (x, y, z, r, g, b), wherein (x, y, z) be the volume coordinate of three-dimensional data, the color value that (r, g, b) is space object;

(1) coordinate (x under utilizing rotation matrix to calculate New Century Planned Textbook _n, y _n, z _n)

$\left[\begin{array}{c}{x}_n\\ y_n\\ z_n\end{array}\right]=T\left[\begin{array}{c}x\\ y\\ z\end{array}\right]---\left(10\right)$

Wherein T is rotation matrix, is expressed as:

$T=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\&theta;}}_x\right)& \sin \left({\mathrm{\&theta;}}_x\right)\\ 0& -\sin \left({\mathrm{\&theta;}}_x\right)& \cos \left({\mathrm{\&theta;}}_x\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\&theta;}}_y\right)& 0& -\sin \left({\mathrm{\&theta;}}_y\right)\\ 0& 1& 0\\ \sin \left({\mathrm{\&theta;}}_y\right)& 0& \cos \left({\mathrm{\&theta;}}_y\right)\end{array}\right]---\left(11\right)$

(2) to z _ncarry out size sequence, and according to clooating sequence to x _n, y _n, r, g, b sort;

(3) arranging image sampling interval is Δ x, and Δ y is according to x _n, y _nmaximin, select suitable projection window matrix mask, mask initial value is all 0, mask matrix resolution is (si, ti, 3), meet condition be:

$\frac{\max \left(x_n\right)-\min \left(x_n\right)}{\mathrm{dx}}<\mathrm{si};\frac{\max \left(y_n\right)-\min \left(y_n\right)}{\mathrm{dy}}<\mathrm{ti}---\left(12\right)$

(4) by cycle criterion projection relation, the coordinate of subpoint in projection window is:

$\mathrm{idx}=\mathrm{round}(\frac{x_n}{\mathrm{dx}}+\mathrm{si}/2);\mathrm{idy}=\mathrm{round}(\frac{y_n}{\mathrm{dy}}+\mathrm{ti}/2);---\left(13\right)$

Whether the numerical value judging (idx, idy) place in mask matrix is 0, if zero, then by this corresponding color value assignment to mask correspondence position, i.e. mask (idx, idy, 1)=r; Mask (idx, idy, 2)=g; Mask (idx, idy, 3)=b; Otherwise be filled before this position is described, current point for being blocked a little, by judging the projected image under most this visual angle of Zhongdao to all three dimensional point clouds.

The present invention have also been devised a kind of display device of the hologram adopting said method to be made, this device is divided into three-decker, a white light Halogen lamp LED is installed at bottom center, the second layer places convex lens, bottom equals the focal length of convex lens to the distance of the second layer, can ensure that light wave that Halogen lamp LED sends is by after convex lens being a quasi-parallel white light.A rectangular opening is opened at top layer center, is used for placing hologram, and the quasi-parallel white light vertical illumination hologram sent from bottom, people can overlook around this device the stereo colour picture watching plate half panorama colour rainbow hologram.White light Halogen lamp LED, lens and top layer rectangular opening are coaxially arranged.

The invention has the beneficial effects as follows:

1. avoid the noise effect in optical pickup process, realize colour optics reproduction effects, better than existing technology;

2., without the need to optical recording platform and complex optical path design, the making of hologram can be realized on a common computer;

3. can realize half panorama colour rainbow hologram of dummy object and large natural scene, actual object or scene, reproduction effects color is gorgeous, three-dimensional true to nature, can view and admire for multiple people simultaneously.

4., compared to traditional bar shaped watch window, half panorama colour rainbow hologram has obvious advantage, uses more convenient.

Accompanying drawing explanation

Fig. 1 reconstruction of hologram schematic diagram

The holographic analysis chart of the plate half panorama colour rainbow of Fig. 2 computing mechanism

Fig. 3 red component frequency spectrum calculates schematic diagram

Fig. 4 synthesizes spectrum diagram

The display device figure of Fig. 5 hologram

Fig. 6, Fig. 7, Fig. 8, Fig. 9 are the holographic reconstructed image figure under different visual angles

Embodiment

With reference to figure 1, L represents illumination light, H is hologram, O is holographic reconstructed image, S is a radius is the watch window of r, the distance of watch window distance holographic facet is h, when with collimated white light illuminated holograms, the viewing area of a ring-type will be formed in the plane of distance hologram h, as shown in the figure, viewing area is split into two parts, semi-ring region 4 and semi-ring region 5, when human eye is at viewing area 4, the accurate color three-dimensional image that hologram reproduces can be seen, when human eye moves, the color three dimensional image of different visual angles will be seen, when human eye is watched in viewing area 5, it is seen that the conjugate image of hologram reconstruction, due in ring-type viewing area only half region can see three-dimensional colour effect accurately, this hologram we be referred to as half panorama colour rainbow hologram.

Fig. 4 is the distribution situation of overall spectrum, and 6 represent red spectrum data, and 7 represent green frequency spectrum data, and 8 represent blue spectrum data, and each little lattice represents a temporary file preserved on computers.

According to frequency spectrum coordinate position relation, RGB frequency spectrum data is fused into an overall data, piecemeal saves as temporary file, and wherein in grid, each little lattice represents a temporary file preserved on computers.

According to above-mentioned principle and method, calculate the plate half panorama colour rainbow hologram of a width computing mechanism.

The resolution of hologram is 84000*84000, holographic facet sampling interval is 0.57um, hologram size is about 4.7cm*4.7cm, and observation window distance holographic facet distance is 1m, and the width observing slit is 3mm, the radius of circular ring type slit is 30cm, adopt matlab to carry out programming, utilize parfor to carry out parallel computation, adopt individual notebook (acer-v3-571G, i5-2450M dual core processor) calculate, about four hours consuming time of the calculating of whole hologram.

Fig. 5 is the display device of hologram, and wherein 1 represents white light halogen light source, and 2 represent lens, and 3 represent holographic dry plate.The quasi-parallel white light vertical illumination hologram sent from bottom, people can overlook around this device the stereo colour picture watching plate half panorama colour rainbow hologram.

Fig. 6, Fig. 7, Fig. 8, Fig. 9 provide several results of the reconstruction of hologram, and in figure, lighter and holographic dry plate relative position are fixed, and use Canon EOS 550D camera direct pictures taken from different perspectives.From reconstruction results, the method can provide the holographic 3 D colour display of half panorama, and stereoeffect is true to nature, and color reduction accurately, can meet a kind of novel three-dimensional display technique that multiple people watches simultaneously, have important using value.

Illustrating above to the preferred embodiments of the present invention and principle, for those of ordinary skill in the art, according to thought provided by the invention, embodiment will change, and these changes also should be considered as protection scope of the present invention.

Claims (6)

1. a method for making for computing mechanism half panorama colour rainbow hologram, is characterized in that the method includes the steps of:

Step one, determines semi-circular observation window and hologram location, size and distance relation,

Step 2, analyzes the frequency domain position under corresponding observation window and frequency span,

Step 3, the calculating of three primary colors frequency spectrum is carried out respectively in frequency domain, then carry out Spectrum synthesizing, by carrying out the optical field distribution that inverse Fourier transform obtains on holographic facet to synthesis frequency spectrum, introduce reference light and object light and carry out interference and obtain the plate half panorama colour rainbow hologram of computing mechanism.

2. the method for making of computing mechanism half panorama colour rainbow hologram according to claim 1, is characterized in that: the concrete methods of realizing of described step one is:

Watch window is semicircular distribution, and have axially symmetric structure, adopt a cross section to carry out principle analysis, object width is w _o, watch window plan range object distance is h, and semi-circular window center is r to the distance of central shaft, and the width of semi-circular window is w _s, when watching at watch window place, object primaries will accurately overlap, and therefore z-axis subtended angle θ is identical for primaries, but three primary colors optical wavelength is different, therefore has different spatial frequencys; Three primary colors optical wavelength is respectively λ _r, λ _g, λ _b, frequency radius is expressed as:

$f_r=\frac{\sin \left(\mathrm{\&theta;}\right)}{{\mathrm{\&lambda;}}_r}=\frac{r}{{\mathrm{\&lambda;}}_r\sqrt{r^2+h^2}}$

$f_g=\frac{\sin \left(\mathrm{\&theta;}\right)}{{\mathrm{\&lambda;}}_g}=\frac{r}{{\mathrm{\&lambda;}}_g\sqrt{r^2+h^2}}---\left(1\right)$

$f_b=\frac{\sin \left(\mathrm{\&theta;}\right)}{{\mathrm{\&lambda;}}_b}=\frac{r}{{\mathrm{\&lambda;}}_b\sqrt{r^2+h^2}}$

, wherein, f _rfor the frequency radius of object red component, f _gfor object green component frequency radius, f _bfor the frequency radius of object blue component.

3. the method for making of computing mechanism half panorama colour rainbow hologram according to claim 1, is characterized in that: the concrete methods of realizing of described step 2 is

On object, the angle of summit A and form lower limb D line and z-axis is the line of object lower limb B and form coboundary C and z-axis angle determine the bandwidth that form limits, for three primary colors light wave, frequency span is respectively:

$\begin{array}{c}{\mathrm{\&Delta;f}}_r=\frac{\sin \left({\&PartialD;}_1\right)}{{\mathrm{\&lambda;}}_r}-\frac{\sin \left({\&PartialD;}_2\right)}{{\mathrm{\&lambda;}}_r}=\frac{1}{{\mathrm{\&lambda;}}_r}[\frac{r+\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\&lambda;}}_r}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+{4h}^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+{4h}^2}}]\end{array}$

$\begin{array}{c}{\mathrm{\&Delta;f}}_g=\frac{\sin \left({\&PartialD;}_1\right)}{{\mathrm{\&lambda;}}_g}-\frac{\sin \left({\&PartialD;}_2\right)}{{\mathrm{\&lambda;}}_g}=\frac{1}{{\mathrm{\&lambda;}}_g}[\frac{r+\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\&lambda;}}_g}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+{4h}^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+{4h}^2}}]\end{array}$

$\begin{array}{c}{\mathrm{\&Delta;f}}_b=\frac{\sin \left({\&PartialD;}_1\right)}{{\mathrm{\&lambda;}}_b}-\frac{\sin \left({\&PartialD;}_2\right)}{{\mathrm{\&lambda;}}_b}=\frac{1}{{\mathrm{\&lambda;}}_b}[\frac{r+\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r+\frac{w_s}{2}+\frac{w_o}{2})}^2+h^2}}-\frac{r-\frac{w_s}{2}\frac{w_o}{2}}{\sqrt{{(r-\frac{w_s}{2}-\frac{w_o}{2})}^2+h^2}}]\\ =\frac{1}{{\mathrm{\&lambda;}}_b}[\frac{2r+w_s+w_o}{\sqrt{{(2r+w_s+w_o)}^2+{4h}^2}}-\frac{2r-w_s-w_o}{\sqrt{{(2r-w_s-w_o)}^2+{4h}^2}}]\end{array}---\left(2\right)$

, wherein, Δ f _rfor the frequency span of object red component, Δ f _gfor object green component frequency span, Δ f _bfor the frequency span of object blue component;

According to spatial domain and frequency domain relation, when object width is w _otime, the sampling interval Δ f in its frequency domain is:

$\mathrm{\&Delta;f}=\frac{1}{w_o}---\left(3\right)$

, final calculated hologram is image plane holographic, hologram size w _hwith dimension of object w _oidentical, the sampling interval of hologram is Δ h, then holographic facet sampling number M is:

$M=\frac{w_h}{\mathrm{\&Delta;h}}=\frac{w_o}{\mathrm{\&Delta;h}}---\left(4\right)$

, then the scope of the coordinate f in frequency domain is:

$-\frac{M}{2}\mathrm{\&Delta;f}<f<\frac{M}{2}\mathrm{\&Delta;f}---\left(5\right).$

4. the method for making of computing mechanism half panorama colour rainbow hologram according to claim 1, is characterized in that: the concrete methods of realizing of described step 3 is

(1) according to dimension of object and hologram sampling and the relation of observation window, the resolution M of frequency spectrum _fx* N _fyand the coordinate range of frequency spectrum, respectively section technique is carried out to three primary colors frequency spectrum;

The resolution of each block of red component is M _fxr* N _fyr, then the resolution of the frequency spectrum of green and each block of blue component is expressed as:

$M_{\mathrm{fxg}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_g}{M}_{\mathrm{fxr}};N_{\mathrm{fyg}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_g}{N}_{\mathrm{fyr}}$

$M_{\mathrm{fxb}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_b}{M}_{\mathrm{fxr}};N_{\mathrm{fyb}}=\frac{{\mathrm{\&lambda;}}_r}{{\mathrm{\&lambda;}}_b}{N}_{\mathrm{fyr}}---\left(6\right)$

, wherein M _fxg* N _fygrepresent the resolution of each block frequency spectrum of green component, M _fxb* N _fygrepresent the resolution of each block frequency spectrum of blue component;

Block count in frequency domain is respectively:

$m_r=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxr}}};n_r=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyr}}}$

$m_g=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxg}}};n_g=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyg}}}---\left(7\right)$

$m_b=\frac{M_{\mathrm{fx}}}{M_{\mathrm{fxb}}};n_r=\frac{N_{\mathrm{fy}}}{N_{\mathrm{fyb}}}$

, wherein the block count of red component is m _rrow n _rrow, the block count of green component is m _grow n _grow, the block count of blue component is m _brow n _brow;

(2) according to frequency partitions number and frequency coordinate, carry out section technique respectively to three-primary-color image frequency spectrum, result of calculation saves as three groups of temporary files;

The calculation procedure of red spectrum is as follows: be m by whole Dividing in frequency domain _rrow n _rrow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _rf _xm); θ _y=acsin (λ _rf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three-dimensional body, take out its red component data, and be resolution M by its interpolation _fxr* N _fyr, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxr* N _fyrfull null matrix, the order of its data according to block number is preserved;

The calculation procedure of green frequency spectrum is as follows: be m by whole Dividing in frequency domain _grow n _grow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _gf _xm); θ _y=acsin (λ _gf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three-dimensional body, take out its green component, and be resolution M by its interpolation _fxg* N _fyg, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxg* N _fygfull null matrix, the order of its data according to block number is preserved;

The calculation procedure of blue spectrum is as follows: be m by whole Dividing in frequency domain _brow n _brow, for piece frequency domain (i, j) of wherein, calculate the frequency values (f of this block central point _xm, f _ym), judge the frequency domain whether this position is positioned at half ring-like watch window and determines, when and f _ymwhen > 0 meets, according to (f _xm, f _ym) obtain projection view angles angle (θ _x, θ _y), wherein θ _x=acsin (λ _bf _xm); θ _y=acsin (λ _bf _ym), according to projection view angles (θ _x, θ _y), obtain the projected image of three-dimensional body, take out its blue component, and be resolution M by its interpolation _fxb* N _fyb, carry out Fourier transform, preserved by the sequencing of its data according to block number, when this block frequency spectrum is not in the spectral range that watch window determines, generating a resolution is M _fxb* N _fybfull null matrix, the order of its data according to block number is preserved;

(3) according to frequency spectrum coordinate position relation, RGB frequency spectrum data is fused into overall spectrum data, piecemeal saves as temporary file;

(4) object light complex amplitude in calculation holographic plane, in hologram plane, object light complex amplitude is the inverse Fourier transform of (3) step synthesis frequency spectrum, adopts the mode of horizontal one dimension inverse Fourier transform and the combination of Vertical one dimensional inverse Fourier transform to realize two inverse Fourier transforms of whole frequency spectrum data;

Basic skills is, for certain data line, ephemeral data identical for all columns is read in internal memory, splices and combines into a two-dimensional matrix, carries out line direction inverse Fourier transform to this matrix, saves as ephemeral data after transformation results being split; Namely one dimension line direction Fourier transform is realized to all row relax of advancing, because the data in frequency domain are only present in half frequent territory, only needs process to have the calculating in valid data region;

For the row determined, read the ephemeral data side that all line numbers of previous step generation are identical, be combined into a two-dimensional matrix, then carry out the one dimension inverse Fourier transform on column direction, save as temporary file after transformation results being split, and preserve each small block data amplitude maximum A _mij;

According to all small block data amplitude maximum A that previous step calculates _mijin maximal value A _max;

(5) hologram calculates, and for the data that (4) step is preserved, the physical coordinates of each blocks of data is known, and the computation process of hologram is expressed as:

Read (i, j) individual data, ask its phase place with amplitude A (x _ij, y _ij), wherein (x _ij, y _ij) be the coordinate in this region, reference light is the directional light of vertical incidence, and its phase place is expressed as:

, wherein C is a constant;

Adopt Burch coding to carry out holography to calculate, (i, j) block holographic distribution is expressed as:

(6) utilize holographic straight-writing system, hologram is exported, carry out the process such as developing fixing, the plate half panorama colour rainbow hologram for white light reconstruction can be obtained.

5. the method for making of computing mechanism half panorama colour rainbow hologram according to claim 4, is characterized in that described according to projection view angles (θ _x, θ _y) concrete grammar of obtaining the projected image of three dimensional point cloud is:

Suppose three-dimensional body data bit three-dimensional point cloud model, data layout is (x, y, z, r, g, b), wherein (x, y, the z) volume coordinate that is three-dimensional data, the color value that (r, g, b) is space object point;

(1) coordinate (x under utilizing rotation matrix to calculate New Century Planned Textbook _n, y _n, z _n)

$\left[\begin{array}{c}{x}_n\\ y_n\\ z_n\end{array}\right]=T\begin{array}{c}\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\end{array}---\left(10\right)$

, wherein T is rotation matrix, is expressed as:

$T=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\&theta;}}_x\right)& \sin \left({\mathrm{\&theta;}}_x\right)\\ 0& -\sin \left({\mathrm{\&theta;}}_x\right)& \cos \left({\mathrm{\&theta;}}_x\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\&theta;}}_y\right)& 0& -\sin \left({\mathrm{\&theta;}}_y\right)\\ 0& 1& 0\\ \sin \left({\mathrm{\&theta;}}_y\right)& 0& \cos \left({\mathrm{\&theta;}}_y\right)\end{array}\right]---\left(11\right);$

(2) to z _ncarry out size sequence, and according to clooating sequence to x _n, y _n, r, g, b sort;

(3) arranging image sampling interval is Δ x, and Δ y, according to x _n, y _nmaximin, select suitable projection window matrix mask, mask initial value is all 0, mask matrix resolution is (si, ti, 3), meet condition be:

$\frac{\max \left(x_n\right)-\min \left(x_n\right)}{\mathrm{dx}}<\mathrm{si};\frac{\max \left(y_n\right)-\min \left(y_n\right)}{\mathrm{dy}}<\mathrm{ti}---\left(12\right);$

(4) by cycle criterion projection relation, the coordinate of subpoint in projection window is:

$\mathrm{idx}=\mathrm{round}(\frac{x_n}{\mathrm{dx}}+\mathrm{si}/2);\mathrm{idy}=\mathrm{round}(\frac{y_n}{\mathrm{dy}}+\mathrm{ti}/2)---\left(13\right);$

Whether the numerical value judging (idx, idy) place in mask matrix is 0, if zero, then by this corresponding color value assignment to mask correspondence position, i.e. mask (idx, idy, 1)=r; Mask (idx, idy, 2)=g; Mask (idx, idy, 3)=b; Otherwise be filled before this position is described, current point for being blocked a little, by judging the colour projection's image finally obtained under this visual angle to all three dimensional point clouds.

6. the display device for the hologram of method making as claimed in claim 5, it is characterized in that this device is divided into three-decker, a white light Halogen lamp LED is installed at bottom center, convex lens are placed at second layer center, bottom equals the focal length of lens to the distance of the second layer, and the rectangular opening that is used for placing hologram is opened at top layer center.White light Halogen lamp LED, lens and top layer rectangular opening are coaxially arranged.