CN101452581A - Rapid generation method for calculating holographic cartoon - Google Patents

Abstract

The invention discloses a quick generation method for computer-generated holographic animations, which comprises the following steps: (1) by carrying out uniform sapling to an object light field, obtaining a transformed holograph surface light field through discrete Fourier transform, and generating a computer-generated holograph; and (2) judging whether or not the next frame animation generates translation, and if the next frame animation generates translation, directly computing the phase change in the holograph surface light field and reflecting the change in the holograph surface light field of the next frame; and judging whether or not the next frame animation generates rotation, and if the next frame animation generates rotation, rotating the holograph surface light field of a current frame with the same angle, sampling again according to the position of original sampling point, reflecting the change in phrase and mould to the holograph surface light field of the next frame and generating the computer-generated holograph of the next frame. The method realizes real time display of computer-generated holograph animation, reduces redundant computing, saves large computing time, has low requirements on hardware equipment and is low in investment and easy to implement.

Description

A kind of quick generation method of calculating holographic cartoon

Technical field

The present invention relates to utilize holographic technique to obtain the method for optical imagery, specifically is a kind of quick generation method of calculating holographic cartoon.

Background technology

Hologram can write down the intensity and the phase information of thing light wave simultaneously, can reproduce the three-dimensional image of object realistically, and its range of application has covered fields such as commodity virtual display, advertisement, amusement, education and art, has shown huge market potential.Computed hologram is generally to be to go out hologram by COMPUTER CALCULATION, is generated on the transparent film by plotting apparatus or printer then.Therefore, the generation of computed hologram does not need complexity and accurate coherent light equipment, and can produce in the real world and the hologram of non-existent object, and can carry out the adjustment of parameter easily.

Animation has more superiority with respect to static images.Though there are some technology can produce static computed hologram at present, the method that produces calculating holographic cartoon is reported seldom.In existing technology, the main method that produces calculating holographic cartoon is, regards every frame animation as a width of cloth static images, utilizes the method for static calculation hologram to make then.The holographic map generalization of static calculation itself needs a large amount of calculating, and the quantity of per second animation frame generally will reach 15 frames, and therefore, prior art generates calculating holographic cartoon needs great calculated amount.

Cooperating of some new technology utilization computed holograms and spatial light modulator can be at space display holography picture, and need not use holofilm.Like this, as long as, just can form holographic cartoon by the real time altering computed hologram.But its technical bottleneck is that the generation of computed hologram needs very big calculated amount, therefore, uses static computed hologram technology to generate the method for animation frame and infeasible continuously apace.

Summary of the invention

The invention reside in and overcome the deficiencies in the prior art, the quick generation method of the calculating holographic cartoon that a kind of convenience is simple and easy, efficient is high, equipment requirements is low is provided.

The objective of the invention is by following scheme implementation: a kind of quick generation method of calculating holographic cartoon may further comprise the steps:

(1) the input animation sequence is equidistantly sampled to the thing light field of first frame, carries out discrete Fourier transform (DFT), obtains hologram page light field after the conversion according to formula:

$U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})=\underset{m=0}{\overset{N_x-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N_y-1}{\mathrm{\&Sigma;}}}{U}_o(\mathrm{m\&Delta;x},\mathrm{n\&Delta;y})\exp \left[\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{pm}}{N_x}+\frac{\mathrm{qn}}{N_y})\right]$

Wherein, (x y) is the coordinate on plane, thing light field place, U _o(x y) is the thing light field, and (u v) is the coordinate on plane, hologram page light field place, U _h(p Δ u, q Δ v) can note by abridging and make U _h(p q), is hologram page light field, j ²=-1, sampling number is N _xN _y, N _xAnd N _yAll get 2 power, m, n are the numberings of thing light field sampled point, and p, q are the numberings of hologram page light field sampled point, and the span of p, q is identical with the scope of m, n;

(2) the hologram page light field of establishing after step (1) conversion is made up of a plurality of expressions unit, on each expression unit the aperture of a rectangle as diffraction is set, and calculates rectangular correlation parameter, i.e. each rectangular height w on each expression unit by formula _yWith the offset delta of rectangle apart from the expression unit center at its place:

(a) try to achieve each rectangular height w by following formula _y:

$w_y=\frac{h\left|U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right|}{\mathrm{Max}\left(\left|U_h\right|\right)}$

Wherein, h is the height of expression unit, | X| represents to ask the mould of X, and function Max represents maximizing;

(b) try to achieve by following formula and represent respectively on the hologram page light field in the unit that rectangle is apart from the offset delta of the expression unit center at its place:

$\mathrm{\&delta;}=\frac{\mathrm{\&lambda;}\arg \left[U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right]}{2\mathrm{\&pi;}\sin 2\mathrm{\&theta;}}$

Wherein, λ is a wavelength, and function arg represents to get the argument main value, the angle when 2 θ are reconstruct between incident light and holographic facet normal;

According to rectangular w in each unit _yWith the δ parameter, generate computed hologram, promptly holoframe passes through the reconstruct of thing light field and produces new animation frame;

(3) judged whether the residue animation frame, if not then animation end; The kinematic parameter that then continues to calculate the next frame animation is arranged, and promptly this animation transverse translation is apart from x _dWith the longitudinal translation distance y _dAnd the anglec of rotation d of this animation;

(4) the translation distance x in the kinematic parameter of the next frame animation of trying to achieve according to step (3) _dWith the longitudinal translation distance y _dAnd the anglec of rotation α of this animation, judge that next frame is compared with present frame whether to change, if no change then changes step (3); If change, the translation distance x in the kinematic parameter of the next frame animation of trying to achieve according to step (3) then _dWith the longitudinal translation distance y _dJudge whether translation of animation, if step (5) is then directly carried out in no translation, if there is translation then to pass through the phase change Φ of each sampled point of formula calculation holographic drawing light field _PqWith represent that respectively rectangle is apart from the offset delta of the expression unit center at its place in the unit on the hologram page light field of calculating after the translation ":

Phase change Φ according to each sampled point of formula calculation holographic drawing light field _Pq:

${\mathrm{\&Phi;}}_{\mathrm{pq}}=2\mathrm{\&pi;}(\frac{{\mathrm{px}}_d}{m}+\frac{{\mathrm{qy}}_d}{n})$

This phase change is reflected to present frame hologram page light field, is about to U _h(p, q) superior phase factor exp (j Φ on former basis _Pq).

According to representing that respectively rectangle is apart from the offset delta of the expression unit center at its place in the unit on the hologram page light field after the formula calculating translation ":

${\mathrm{\&delta;}}_d=-\frac{{\mathrm{\&lambda;\&Phi;}}_{\mathrm{<figure-callout\; id="2"\; label="pq"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">pq</figure-callout>}}}{2\mathrm{\&pi;}\sin 2\mathrm{\&theta;}}$

δ′＝δ+δ _d

$\mathrm{\&delta;}\&prime;\&prime;=\left\{\begin{array}{c}\mathrm{\&delta;}\&prime;-\mathrm{\&lambda;}/\sin 2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;>\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;,-\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\&le;\mathrm{\&delta;}\&prime;\&le;\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;+\mathrm{\&lambda;}/\sin 2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;<-\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\end{array}\right.$

δ _dRectangular displacement in the expression unit that the expression animation causes because of translation, δ be former frame represent rectangle in the unit apart from the expression unit center at its place side-play amount, δ ' for present frame represent rectangle in the unit apart from the expression unit center at its place side-play amount, δ " be the correction to δ ', the phase place that makes its expression is between-π～π;

(5) anglec of rotation α in the kinematic parameter of the next frame animation of trying to achieve according to step (3) judges next frame compares with present frame whether rotation is arranged, if then directly generate computed hologram without spin, reconstruct produces animation frame through the thing light field then; If rotation is arranged then to the hologram page light field rotation alpha of present frame:

Hologram page light field U with present frame _h(p, frequency spectrum center q) obtains U move on to the center of matrix from the initial point of matrix after _c(r, s), the present frame coordinate is that (r, s), its scope is-N _x/ 2≤r≤N _x/ 2-1 ,-N _y/ 2≤s≤N _y/ 2-1, after rotation, the coordinate of corresponding sampled point is (r ', s '):

$\left\{\begin{array}{c}r\&prime;=r\&times;\cos \left(\mathrm{\&alpha;}\right)+s\&times;\sin \left(\mathrm{\&alpha;}\right)\\ s\&prime;=-r\&times;\sin \left(\mathrm{\&alpha;}\right)+s\&times;\cos \left(\mathrm{\&alpha;}\right)\end{array}\right.$

Postrotational hologram page light field is U _c(r ', s ') adopts arest neighbors sample mode or bilinear interpolation sample mode to carry out resampling to postrotational hologram page light field, and the hologram page light field of establishing after the sampling is

, then

The frequency spectrum center be moved back into the initial point of matrix from the center of matrix, promptly convert the hologram page light field U that represents with the positive frequency coefficient to _h(p q), changes step (2) then.

To better implement the present invention, step (5) is described by the hologram page light field resampling of arest neighbors sample mode to present frame, specifically is meant:

Wherein, function round represents round.

Step (5) is described by using the hologram page light field resampling of bilinear interpolation sample mode to present frame, specifically is meant:

After the former figure rotation, on its figure some the numerical value of (r ', s ') pass through symbol by apart from its four nearest somes decisions

To r ', s ' rounds up and down respectively, just can obtain these four points with rounded coordinate, obtains new hologram page light field through the following formula interpolation:

After considering former figure rotation, its light field field of definition with wait to ask the field of definition of light field inconsistent, if

In any one does not exist, then get $U_h^{\&prime;\&prime;}(r,s)=0.$

Action principle of the present invention is: the generation of a frame holographic cartoon is a two-dimension fourier transform problem in essence, first frame of animation calculates circuitous phase type hologram by classic method, next, judge at first whether the next frame animation translation has taken place, if translation has taken place, then directly calculate the situation of change of phase place on the hologram page light field, and this variation is reflected in the circuitous phase type hologram face light field of next frame; And then judge whether to have taken place rotation, if rotate, then present frame hologram page light field is rotated same angle, and according to the position resampling of former sampled point, the variation with phase place and mould is reflected in the circuitous phase type hologram face light field of next frame then.By above-mentioned steps, just can avoid each frame animation all to carry out Fourier transform, and directly produce calculating holographic cartoon, calculated amount significantly reduces.

The present invention compared with prior art has following advantage and beneficial effect:

(1) saved a large amount of computing times, traditional method is to produce calculating holographic cartoon by calculating each frame animation respectively, this need carry out a large amount of Fourier transforms, very consuming time, the while also is difficult to reach the purpose of real-time demonstration, and the present invention is according to the inner link of computed hologram in translation in the time domain and rotation animation and the frequency domain, directly according to translation and rotation parameter, utilize the computed hologram of initial frame, directly obtain the computed hologram of other each frame, eliminated and calculated redundancy.

If the number of thing light field sampled point is m * n, the static calculation hologram need calculate two dimension discrete fourier transform, and its calculated amount is:

The complex multiplication number of times:

Complex addition number of times: mn (log ₂Mn).

In addition, need the parameter of expression unit on the calculation holographic drawing light field, promptly the height of rectangle diffraction aperture and position need with constant level real multiplications and addition, and therefore amount is at long last: O (mn).The computation complexity of static calculation hologram is O (mnlog like this ₂The computation complexity of mn), Here it is each frame of classic method calculating holographic cartoon.

New method only need be calculated the Fourier transform of first frame, and its calculated amount is a constant, and the calculated amount of first frame is shared each frame of back, if the animation frame number is more, this calculated amount can be ignored.Expression cell parameters on other each frame utilizes new method directly to calculate according to the parameter of its former frame, each expression unit constant level real multiplications and addition, and therefore the calculated amount of every frame animation is: O (mn).

As seen from the above analysis, the computation complexity of each frame of classic method calculating holographic cartoon is O (mnlog ₂Mn), the calculated amount of the every frame animation of new method is: O (mn).The time complexity of new method has been saved one to the order of magnitude than classic method.Contrast by experiment, the computing time that new method needs is than low two orders of magnitude of classic method, as shown in Figure 1.

(2) realized the possibility that calculating holographic cartoon shows in real time, because calculated amount limits greatly, still do not utilize at present the computed hologram technology to generate the real world applications that animation frame shows in real time continuously, the enforcement of this patent can produce the 3-D view of dynamic change apace in the space, realize real 3-D display, effect is true to nature.

(3) requirements on hardware equipment is low, less investment, easier realization.As use classic method, because its calculated amount is very big, so need more expensive specialized hardware, present imaging system needs relevant devices such as projection screen mostly, need install and fix equipment in occasions such as large evening party, squares, with generally removing later, both lost time waste of manpower again, financial resources, material resources; And use quick calculation method of the present invention, and having reduced the equipment input, computed hologram adapted space photomodulator just can be at space display holography picture.

Description of drawings

Fig. 1 is the relativity presentation graphs of the inventive method and classic method execution time;

Fig. 2 is the synoptic diagram that incident light produces circuitous phase place;

Fig. 3 is the structural representation of expression unit in the hologram page light field;

Fig. 4 (a) is the synoptic diagram of thing light field;

Fig. 4 (b) is the synoptic diagram of computed hologram;

Fig. 5 (a) is the original object plane light field synoptic diagram before the translation;

Fig. 5 (b) is the synoptic diagram of the original calculation hologram before the translation;

Fig. 5 (c) is the synoptic diagram of the computed hologram after the translation;

Fig. 5 (d) is the synoptic diagram of the thing light field reconstruct after the translation;

Fig. 6 is that the hologram page light field rearranges;

Fig. 7 is that the hologram page light field is rotated;

Fig. 8 (a) is the synoptic diagram of original thing light field;

Fig. 8 (b) is the synoptic diagram of original hologram face light field rotation 0 degree back thing light field reconstruct;

Fig. 8 (c) is the synoptic diagram of original hologram face light field rotation π/12 back thing light field reconstruct;

Fig. 8 (d) is the synoptic diagram of original hologram face light field rotation π/6 back thing light field reconstruct;

Fig. 8 (e) is the synoptic diagram of original hologram face light field rotation π/4 back thing light field reconstruct;

Fig. 8 (f) is the synoptic diagram of original hologram face light field rotation π/3 back thing light field reconstruct;

Fig. 8 (g) is the synoptic diagram that original hologram face light field is rotated 5 π/12 back thing light field reconstruct;

Fig. 8 (h) is the synoptic diagram of thing light field reconstruct behind the original hologram face light field rotation pi/2;

Fig. 9 is the process flow diagram that calculating holographic cartoon produces.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited thereto.

The quick generation method of this calculating holographic cartoon may further comprise the steps, as shown in Figure 9:

(1) the input animation sequence is equidistantly sampled to the thing light field of first frame, carries out discrete Fourier transform (DFT), if having a focal length is the infinitely great lens of f, thing light field and hologram page light field lay respectively on the forward and backward focal plane of these lens, and establishing wavelength is λ, then hologram page light field U _h(u is v) with thing light field U _o(x, y) pass between is:

$U_h(u,v)=\frac{1}{\mathrm{\&lambda;f}}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}{\&Integral;U}_o(x,y)\exp [-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;f}}(\mathrm{ux}+\mathrm{vy})]\mathrm{dxdy}$

J wherein ²=-1, constant factor 1/ λ f can give up, and it only has influence on the brightness of holographic images.The sampling interval that makes the hologram plane for (Δ u, Δ are (Δ x, Δ y) with the sampling interval of object plane v), and the thing light field is applied random phase, carry out discrete Fourier transform (DFT) by following formula and obtain the hologram page light field:

$U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})=\underset{m=0}{\overset{N_x-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N_y-1}{\mathrm{\&Sigma;}}}{U}_o(\mathrm{m\&Delta;x},\mathrm{n\&Delta;y})\exp \left[\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{pm}}{N_x}+\frac{\mathrm{qn}}{N_y})\right]---\left(1\right)$

Wherein, sampling number is N _xN _y, N _xAnd N _yAll get 2 power, m, n are the numberings of thing light field sampled point, and p, q are the numberings of hologram page light field sampled point, and the span of p, q is identical with the scope of m, n.

(2) as shown in Figure 2, adopt circuitous phase method to represent computed hologram.If with a plane wave illumination hologram sheet from axle, the direction of incident beam and the angle between hologram sheet are 2 θ, the optical field distribution that then shines on the hologram page is:

U _p(x，y)＝exp[-j2πxsin2θ/λ]

As shown in Figure 3, calculation holographic drawing light field is divided into N _xN _yIndividual expression unit, each represents that the unit equals λ/sin2 θ at the width of x direction, and like this, incident light is period profile in each expression between unit, and each inside, unit has comprised-all phase places of π～π.Each represents that the unit is unqualified at y direction height value h, and height value h increases, and then the brightness of imaging increases.A fourier coefficient is all represented in each expression unit, on the expression unit, a rectangle is set, as the aperture of diffraction.

For the needs of circuitous phase method itself, rectangular width w _xLittle more a lot of than the expression cell width, but consider diffraction efficiency, again can not be too narrow.Here select w _xFor:

$\frac{\mathrm{\&lambda;}}{16\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}}\&le;w_x\&le;\frac{\mathrm{\&lambda;}}{8\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}}$

Rectangular height w _yBe directly proportional with the mould of fourier coefficient, with the maximal value of all fourier coefficient moulds be expressed as Max (| U _h|), w then _yObtain by following formula:

$w_y=\frac{h\left|U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right|}{\mathrm{Max}\left(\left|U_h\right|\right)}$

Wherein, h is the height of expression unit, | X| represents to ask the mould of any plural X, and function Max represents maximizing;

Rectangular elements is directly proportional with the phase place of fourier coefficient apart from the offset delta of the expression unit center at its place, can be obtained by following formula:

$\mathrm{\&delta;}=\frac{\mathrm{\&lambda;}\arg \left[U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right]}{2\mathrm{\&pi;}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}}$

Wherein, λ is a wavelength, and function arg represents to get the argument main value;

Suppose that the thing light field represented to pass through the calculating of above-mentioned steps so as Fig. 4 (a) by piece image, just can obtain calculation holographic Fig. 4 (b) that a width of cloth is represented by circuitous phase method.

(3) judged whether the residue animation frame, if not then animation end; The kinematic parameter that then continues to calculate the next frame animation is arranged, and promptly this animation transverse translation is apart from x _dWith the longitudinal translation distance y _dAnd the anglec of rotation α of this animation.

(4) the translation distance x in the kinematic parameter of the next frame animation of trying to achieve according to step (3) _dWith the longitudinal translation distance y _dAnd the anglec of rotation α of this animation, judge that next frame is compared with present frame whether to change, if no change then changes step (3); If change, then the transverse translation in the kinematic parameter of the next frame animation of trying to achieve according to step (3) is apart from x _dWith the longitudinal translation distance y _dJudge whether translation of animation, if step (5) is then directly carried out in no translation, if there is translation then to pass through the phase change Φ of each sampled point of formula calculation holographic drawing light field _PqWith represent respectively on the calculation holographic drawing light field that rectangle is apart from the offset delta of the expression unit center at its place in the unit ":

Original hologram face light field U _hObtain through formula (1), then the hologram page light field U after the conversion _h' be:

U _h′(pΔu，qΔv)＝U _h(pΔu，qΔv)exp(-jΦ _pq)

Wherein ${\mathrm{\&Phi;}}_{\mathrm{pq}}=2\mathrm{\&pi;}(\frac{{\mathrm{px}}_d}{m}+\frac{{\mathrm{qy}}_d}{n})$

The following formula explanation can be asked phase change according to translation distance.The variation of phase place is reflected in the expression unit, is the variation of rectangle diffraction aperture far from the side-play amount at center.Therefore, need variation, be directly changed into the offset delta of rectangle diffraction aperture " this phase place.Like this, just do not needed Fourier transform once more.Rectangular displacement δ in the expression unit that causes because of the animation translation _dFor:

${\mathrm{\&delta;}}_d=-\frac{{\mathrm{\&lambda;\&Phi;}}_{\mathrm{<figure-callout\; id="2"\; label="pq"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">pq</figure-callout>}}}{2\mathrm{\&pi;}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}}---\left(2\right)$

Its former frame that is added to is represented in the unit rectangle on the offset delta of the expression unit center at its place, obtain present frame represent the offset delta of rectangular expression unit center apart from its place in the unit ':

δ′＝δ+δ _d (3)

With representing that respectively rectangle is apart from the offset delta of the expression unit center at its place in the unit on the hologram page light field after formula (4) the calculating translation ":

$\mathrm{\&delta;}\&prime;\&prime;=\left\{\begin{array}{c}\mathrm{\&delta;}\&prime;-\mathrm{\&lambda;}/\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;>\mathrm{\&lambda;}/2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;,-\mathrm{\&lambda;}/2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\&le;\mathrm{\&delta;}\&prime;\&le;\mathrm{\&lambda;}/2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;+\mathrm{\&lambda;}/\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;<-\mathrm{\&lambda;}/2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A200810220610E00171.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\end{array}\right.---\left(4\right)$

" be the correction to δ ', the phase place that makes its expression is between-π～π for δ.

(5) anglec of rotation α in the kinematic parameter of the next frame animation of trying to achieve according to step (3) judges next frame compares with present frame whether rotation is arranged, if then directly generate computed hologram without spin, reconstruct produces animation frame through the thing light field then; If rotation is arranged then to the hologram page light field rotation alpha of present frame, adopt arest neighbors sample mode or bilinear interpolation sample mode to carry out resampling, the hologram page light field after the sampling is

, then

The frequency spectrum center be moved back into the initial point of matrix from the center of matrix, change step (2) then;

If the hologram page light field of animation present frame is U _h(p, q), if the U that does not have the translation animation then to obtain for former frame _h(p Δ u, q Δ v), otherwise be to obtain in the step (3)

Because they obtain by discrete Fourier transform (DFT), so U _h(p, q) each value representation is the positive frequency coefficient, they all first to limit.In order to implement " rotation ", promptly rotate around true origin, therefore to rearrange.As Fig. 6, with the hologram page light field U of present frame _h(p, frequency spectrum center q) obtains U move on to the center of matrix from the initial point of matrix after _c(r, s), here-N _x/ 2≤r＜N _x/ 2 ,-N _y/ 2≤s＜N _y/ 2:

With the present frame coordinate (r, s) after the rotation, the coordinate of corresponding sampled point is (r ', s '):

$\left\{\begin{array}{c}r\&prime;=r\&times;\cos \left(\mathrm{\&alpha;}\right)+s\&times;\sin \left(\mathrm{\&alpha;}\right)\\ s\&prime;=-r\&times;\sin \left(\mathrm{\&alpha;}\right)+s\&times;\cos \left(\mathrm{\&alpha;}\right)\end{array}\right.$

If postrotational hologram page light field is U _c(r ', s '), as dotted portion among Fig. 7.Because the expression of former frame hologram page light field is in a horizontal flat vertical rectangular extent, therefore in this zone, resample, make the present frame hologram page light field form that obtains be the solid line part among Fig. 7.In the part of both region overlappings, can resample by arest neighbors sampling or bilinear interpolation sample mode, non-overlapped part is approximately 0.

Postrotational hologram page light field is resampled, and the hologram page light field of establishing after the sampling is

Then

The frequency spectrum center be moved back into the initial point of matrix from the center of matrix, promptly convert the hologram page light field U that represents with the positive frequency coefficient to _h(p, q).

To better implement the present invention, step (5) is described by the hologram page light field resampling of arest neighbors sample mode to present frame, specifically is meant:

Wherein, function round represents round.

Step (5) is described by using the hologram page light field resampling of bilinear interpolation sample mode to present frame, specifically is meant:

After the former figure rotation, on it some the numerical value of (r ', s ') pass through symbol by apart from its four nearest somes decisions

To r ', s ' rounds up and down respectively, just can obtain these four points with rounded coordinate.Obtain new hologram page light field through the following formula interpolation:

After considering former figure rotation, its light field field of definition with wait to ask the field of definition of light field inconsistent, if

In any one does not exist, then get $U_h^{\&prime;\&prime;}(r,s)=0.$

Because thing light field signal is at time domain internal rotation angle degree α, then the hologram page light field in the frequency domain is rotated same angle, therefore, according to this characteristic, after calculating the hologram page light field of animation present frame, only need this hologram page light field anglec of rotation α just can be obtained the computed hologram of next frame animation, thereby avoid reusing Fourier transform, accelerate arithmetic speed greatly.

Fig. 5 (a) has shown the reconstruct situation of animation object plane light field after obtaining new hologram page light field after a series of translations to Fig. 5 (d).Be the original object plane light field of 256 * 256 sampled points in Fig. 5 (a), represent the present frame in the animation, can obtain the computed hologram shown in Fig. 5 (b) according to the method in step 1, the step 2.Literal in the thing light field move right 100 sampling interval, move down 80 sampling interval after, form the computed hologram of next frame animation, see Fig. 5 (c), it is to be obtained by the method that step 4 is introduced.Utilize the computed hologram reconstruct thing light field of Fig. 5 (c), can get next frame animation shown in Fig. 5 (d).Comparison diagram 5 (a) and Fig. 5 (d) as can be known, new method can effectively be worked.

Fig. 8 (a) has shown animation object plane light field after a series of rotations to Fig. 8 (h), the reconstruct situation behind each the frame computed hologram that obtains by the arest neighbors interpolation sampling.Can see, between each anglec of rotation of 0～pi/2, except that having the sharp image at interval two ends, each middle image all has ghost image, its rule is: increase since 0 with rotation angle, image expands a plurality of gradually from independent one, and the distance between them also increases gradually; After rotation angle surpassed π/4, a plurality of images were gathered gradually, and after rotation angle reaches pi/2, are merged into an independent picture.

Above-mentioned animation effect can produce a kind of effect of change in the space, and the virtual display that is used for the space article can bring good visual experience.The reason that produces this animation is, when the postrotational resampling of hologram page light field, can cause phase place than mistake, have ghost image after the reconstruct.But when the anglec of rotation was the integral multiple of pi/2, the resample points grid overlapped fully with the crude sampling dot grid, so sampling error is very little, can obtain quite accurate reconstruct, so be an independent image.

The foregoing description is a preferred implementation of the present invention; but embodiments of the present invention are not limited by the examples; other any do not deviate from the change done under spirit of the present invention and the principle, it is main to revise, substitute, combination, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (3)

1, a kind of quick generation method of calculating holographic cartoon may further comprise the steps:

(1) the input animation sequence is equidistantly sampled to the thing light field of first frame, carries out discrete Fourier transform (DFT), obtains hologram page light field after the conversion according to formula:

$U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})=\underset{m=0}{\overset{N_x-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N_y-1}{\mathrm{\&Sigma;}}}{U}_o(\mathrm{m\&Delta;x},\mathrm{n\&Delta;y})\exp \left[j2\mathrm{\&pi;}(\frac{\mathrm{pm}}{N_x}+\frac{\mathrm{qn}}{N_y})\right]$

Wherein, (x y) is the coordinate on plane, thing light field place, U _o(x y) is the thing light field, and (u v) is the coordinate on plane, hologram page light field place, U _h(p Δ u, q Δ v) can note by abridging and make U _h(p q), is hologram page light field, j ²=-1, sampling number is N _xN _y, N _xAnd N _yAll get 2 power, m, n are the numberings of thing light field sampled point, and p, q are the numberings of hologram page light field sampled point, and span is identical with the scope of m, n;

(2) the hologram page light field of establishing after step (1) conversion is made up of a plurality of expressions unit, on each expression unit the aperture of a rectangle as diffraction is set, and calculates rectangular correlation parameter, i.e. each rectangular height w on each expression unit by formula _yWith the offset delta of rectangle apart from the expression unit center at its place:

(a) try to achieve each rectangular height by following formula:

$w_y=\frac{h\left|U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right|}{\mathrm{Max}\left(\left|U_h\right|\right)}$

Wherein, h is the height of expression unit, | X| represents to ask the mould of X, and function Max represents maximizing;

(b) try to achieve by following formula and represent respectively on the hologram page light field in the unit that rectangle is apart from the offset delta of the expression unit center at its place:

$\mathrm{\&delta;}=-\frac{\mathrm{\&lambda;}\arg \left[U_h(\mathrm{p\&Delta;u},\mathrm{q\&Delta;v})\right]}{2\mathrm{\&pi;}\sin 2\mathrm{\&theta;}}$

Wherein, λ is a wavelength, and function arg represents to get the argument main value, the angle when 2 θ are reconstruct between incident light and holographic facet normal;

According to rectangular w in each unit _yWith the δ parameter, generate computed hologram, promptly holoframe passes through the reconstruct of thing light field and produces new animation frame;

(3) judged whether the residue animation frame, if not then animation end; The kinematic parameter that then continues to calculate the next frame animation is arranged, and promptly this animation transverse translation is apart from x _dWith the longitudinal translation distance y _dAnd the anglec of rotation α of this animation;

(4) the translation distance x in the kinematic parameter of the next frame animation of trying to achieve according to step (3) _dWith the longitudinal translation distance y _dAnd the anglec of rotation α of this animation, judge that the next frame animation is compared with the present frame animation whether to change, if no change then changes step (3); If change, the translation distance x in the kinematic parameter of the next frame animation of trying to achieve according to step (3) then _dWith the longitudinal translation distance y _dJudge whether translation of animation, if step (5) is then directly carried out in no translation, if there is translation then to pass through the phase change Φ of each sampled point on the formula calculation holographic drawing light field _PqWith represent that respectively rectangle is apart from the offset delta of the expression unit center at its place in the unit on the hologram page light field of calculating after the translation ":

Phase change Φ according to each sampled point on the formula calculation holographic drawing light field _Pq:

${\mathrm{\&Phi;}}_{\mathrm{pq}}=2\mathrm{\&pi;}(\frac{{\mathrm{px}}_d}{m}+\frac{{\mathrm{qy}}_d}{n})$

This phase change is reflected to present frame hologram page light field, is about to U _h(p, q) superior phase factor exp (j Φ on former basis _Pq);

Calculate according to formula and to represent respectively on the hologram page light field after the translation in the unit that rectangle is apart from the offset delta ＂ of the expression unit center at its place:

${\mathrm{\&delta;}}_d=-\frac{{\mathrm{\&lambda;\&Phi;}}_{\mathrm{pq}}}{2\mathrm{\&pi;}\sin 2\mathrm{\&theta;}}$

δ′＝δ+δ _d

$\mathrm{\&delta;}\&prime;\&prime;=\left\{\begin{array}{c}\mathrm{\&delta;}\&prime;-\mathrm{\&lambda;}/\sin 2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;>\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;,-\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\&le;\mathrm{\&delta;}\&prime;\&le;\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\\ \mathrm{\&delta;}\&prime;+\mathrm{\&lambda;}/\sin 2\mathrm{\&theta;},\mathrm{\&delta;}\&prime;<-\mathrm{\&lambda;}/2\sin 2\mathrm{\&theta;}\end{array}\right.$

δ _dRectangular displacement in the expression unit that the expression animation causes because of translation, δ be former frame represent rectangle in the unit apart from the expression unit center at its place side-play amount, δ ' for present frame represent rectangle in the unit apart from the expression unit center at its place side-play amount, δ " be the correction to δ ', the phase place that makes its expression is between-π～π;

(5) anglec of rotation α in the kinematic parameter of the next frame animation of trying to achieve according to step (3) judges the next frame animation compares with the present frame animation whether rotation is arranged, if then directly generate computed hologram without spin, reconstruct produces animation frame through the thing light field then; If rotation is arranged then to the hologram page light field rotation alpha of present frame:

Hologram page light field U with present frame _h(p, frequency spectrum center q) obtains U move on to the center of matrix from the initial point of matrix after _c(r, s), the present frame coordinate is that (r, s), its scope is-N _x/ 2≤r≤N _x/ 2-1 ,-N _y/ 2≤s≤N _y/ 2-1, after rotation, the coordinate of corresponding sampled point is (r ', s '):

$\left\{\begin{array}{c}r\&prime;=r\&times;\cos \left(\mathrm{\&alpha;}\right)+s\&times;\sin \left(\mathrm{\&alpha;}\right)\\ s\&prime;=-r\&times;\sin \left(\mathrm{\&alpha;}\right)+s\&times;\cos \left(\mathrm{\&alpha;}\right)\end{array}\right.$

Postrotational hologram page light field is U _c(r ', s ') adopts arest neighbors sample mode or bilinear interpolation sample mode to carry out resampling to postrotational hologram page light field, and the hologram page light field of establishing after the sampling is

Then The frequency spectrum center be moved back into the initial point of matrix from the center of matrix, promptly convert the hologram page light field U that represents with the positive frequency coefficient to _h(p q), changes step (2) then.

2, according to the quick generation method of a kind of calculating holographic cartoon described in the claim 1, it is characterized in that: step (5) is described by the hologram page light field resampling of arest neighbors sample mode to present frame, specifically is meant:

Wherein, function round represents round.

3, according to the quick generation method of a kind of calculating holographic cartoon described in the claim 1, it is characterized in that: step (5) is described by using the hologram page light field resampling of bilinear interpolation sample mode to present frame, specifically is meant:

After the former figure rotation, on it some the numerical value of (r ', s ') pass through symbol by apart from its four nearest somes decisions

To r ', s ' rounds up and down respectively, just can obtain these four points with rounded coordinate, obtains new hologram page light field through the following formula interpolation:

After considering former figure rotation, its light field field of definition with wait to ask the field of definition of light field inconsistent, if

In any one does not exist, then get $U_h^{\&prime;\&prime;}(r,s)=0.$

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