CN104360708A - Rapid computer-generated holography algorithm based on trigonometric function look-up table - Google Patents

Abstract

The invention belongs to the field of computer-generated holography and particularly relates to a rapid computer-generated holography algorithm based on a trigonometric function look-up table. The rapid computer-generated holography algorithm is characterized in that based on computer-generated holography through a point source method, the trigonometric function look-up table deduces an original formula and simplifies the phase position part related to redundancy computation through mathematical approach transformation and trigonometric function identical transformation so as to generate two phase position look-up tables containing depth information. The generative process adopts parallel computing, is high in speed and accuracy, and contains all phase position information of objects (including three-dimensional and two-dimensional objects); in addition, the internal memory usage is less, the repeated utilization factor is high, and the application range is wide. Moreover, the parallel optimization is performed on the algorithm, parallel computing is adopted during the table look-up addressing and computing processes, and the computer-generated holography speed is effectively accelerated.

Description

A kind of quick calculation holographic algorithm based on trigonometric function look-up table

Technical field

The invention belongs to calculation holographic field, be specifically related to a kind of quick calculation holographic algorithm based on trigonometric function look-up table.

Background technology

Although calculation holographic can integrated application computer technology and holographic technique, good 3-D display effect can be obtained, but the space-bandwidth product of hologram is very large, this brings huge pressure to the computing velocity, storage volume etc. of computing machine, governs real-time calculating transmission and the display of computed hologram.Point source method is classical calculation holographic algorithm, and during application point source method calculating three-dimensional body hologram, computing velocity this problem slow is just abnormal outstanding.The physical process of the complete simulated optical holography of point source method calculation holographic algorithm (Ray-tracing), three-dimensional body is regarded as pointolite set spatially, give the initial phase that pointolite is random, each pointolite is concerned with at holographic facet with reference light respectively, more all stacks up and can generate the hologram of three-dimensional body.Point source method calculation holographic can provide the three-dimensional information that object is complete, but object point computed hologram brings huge operand one by one, makes its computing velocity extremely low.For this problem, the people such as Mark Lucent propose famous look-up table (Look-up Table, LUT) (M.Lucente, Interactive computation of holograms using a look-up table, J.Electronic Imaging2 (1), 28-35 (1993)), the hologram calculated in advance of each for three-dimensional article space object point is stored, when the hologram of a calculating three-dimensional body, only need obtain the corresponding PFP of each object point of three-dimensional body from the data stored, then linear superposition can obtain the hologram of three-dimensional body.But this initial look-up table drawback is obvious, the first corresponding hologram of each brightness of three-dimensional body object point different from position, internal memory shared by look-up table will reach TB rank.Therefore, this look-up table cannot meet actual requirement of experiment.In order to meet practical application in an experiment, a series of look-up table optimized algorithm based on point source method is suggested in succession.2009, the people such as Korean science man Kim achieve a kind of new look-up table (Novel-Look-up Table, N-LUT) method, to reduce internal memory use amount, but the look-up table after reducing remains GB rank, improve N-LUT method again in the recent period, called after RLE-basedN-LUT method after improving, the internal memory of look-up table can be reduced an order of magnitude by the method again.The internal memory of three dimensional lookup table reduces much by Split Look-up Tables (S-LUT) loop up table that the people such as the Yuechao Pan of Singapore propose.

The new inquiring arithmetic called after trigonometric function look-up table (Trigonometric look-up table, T-LUT) that the present invention proposes.By the formula of original point source method is carried out the identical change of a series of mathematics, wherein majority is trigonometric function identical transformation, and the internal memory of look-up table is reduced to the degree suitable with S-LUT look-up table.But in the speed that look-up table generates, can be more quick, also can be more accurate in the data generated.In conjunction with the programming of CUDA framework, parallel idea is added T-LUT algorithm, namely parallel optimization has been carried out to point source method.Shown by series of experiments, in T-LUT look-up table, internal memory shared by look-up table is minimum in numerous loop up table, adopts the computing velocity of the calculation holographic of T-LUT look-up table to have very large lifting.

Summary of the invention

The object of this invention is to provide a kind of lookup table algorithm---trigonometric function loop up table calculating three-dimensional body holography fast, the method can under the prerequisite of not sacrificing hologram reconstruction picture quality, by carrying out a series of mathematical approach, the identical change of mathematics to point source method prime formula, the three-dimensional variable of look-up table addressing splits and becomes two-dimentional variable the most at last, generate the internal memory of look-up table to greatly reduce, the complexity of computing formula has and simplifies significantly simultaneously.

The present invention compared with the existing methods, has following features:

1 has possessed the problem effectively solving other look-up table committed memory super larges while other lookup table algorithm reduce the advantage calculating repeating data.Look-up table of the present invention obviously reduces.

2, three dimensional lookup table formation speed is fast, and precision is high.

3, the realization of algorithm is on GPU, adopt CUDA parallel computation, generating hologram speed.

Accompanying drawing explanation

The accompanying drawing of the present invention's " new inquiring arithmetic of a kind of quick calculating three-dimensional body holography " has 5.

Fig. 1 is T-LUT algorithmic derivation process flow diagram provided by the invention.

Fig. 2 is T-LUT algorithm calculation holographic optimum experimental process schematic provided by the invention.

Fig. 3 is the final parallel optimization process flow diagram of T-LUT algorithm provided by the invention.

Fig. 4 is that T-LUT algorithm GPU parallel generation hologram reconstruction picture provided by the invention is with point source method CPU generating hologram reproduction image comparison diagram.

Fig. 5 is that the holographic speed of GPU parallel computation of T-LUT algorithm provided by the invention is with point source method CPU calculation holographic velocity contrast.

Embodiment

Below in conjunction with accompanying drawing and subordinate list, the present invention's " new inquiring arithmetic of a kind of quick calculating three-dimensional body holography " is described further.

Fig. 1 is T-LUT algorithmic derivation process flow diagram provided by the invention.

The preliminary mathematic(al) representation of point source method is:

$I(x_h,y_h)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{A}_j\cos \left[\frac{2\mathrm{\π}}{\mathrm{\λ}}\sqrt{{\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2+z_j^2}\right]---\left(1\right)$

There is sampling interval physically in object space sampling, is set as 5-20 holographic facet sampling interval doubly, then the Δ x in formula (1) ²=(px _j-qx _h) ², Δ y ²=(py _j-qy _h) ², q here loads the sampling interval of hologram, and namely q=8 μm, p to be object space sampling interval the be 5-20 of q doubly.In reproduced image system, exist and rebuild distance z _j> > Δ x, z _j> > Δ y, can obtain by binomial is approximate: $\sqrt{{\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2+z_j^2}=z_j+\frac{1}{{2z}_j}({\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2),$ Then formula (1) can abbreviation be:

$I(x_h,y_h)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{A}_j\cos \left\{\frac{2\mathrm{\π}}{\mathrm{\λ}}\right[z_j+\frac{1}{{2z}_j}({\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2)\left]\right\}---\left(2\right)$

Holographic phase extracting section is calculated, namely by formula (2) this part calculates for each pixel on holographic facet, is constantly carry out double counting.The present invention is to provide a kind of pure phase look-up table, the phase bit position of this double counting is precalculated stored in form.

$\mathrm{Table}=\cos \left\{\frac{2\mathrm{\π}}{\mathrm{\λ}}\right[z_j+\frac{1}{{2z}_j}({\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2)\left]\right\}---\left(3\right)$

In optical reproduction picture system, reference light wavelength X is fixing, rebuilds distance z _jcan people for choosing.In order to simplify calculating, here by z _jbe taken as the integral multiple of λ, so it is the integral multiple of 2 π.Then according to trigonometric function character, formula (3) can be reduced to:

Table＝cos[c ₁(Δx ²+Δy ²)] (4)

Wherein (for two-dimentional calculation holographic look-up table, z _jfor constant), here by Δ x ²+ Δ y ²be normalized, the Δ x occurred in later formula, Δ y be respectively, ax _j-x _hand ay _j-y _h, wherein a is the maximal value of the p/q chosen herein, i.e. a=20.(namely object space sampling interval mostly is 20 times of holographic facet most).Continue formula (4) abbreviation

Table＝cos(c ₁Δx ²)cos(c ₁Δy ²)-sin(c ₁Δx ²)sin(c ₁Δy ²) (5)

Obviously from formula (5), we obtain calculative two-dimensional look-up table and are:

$\left\{\begin{array}{c}{\mathrm{Table}}_1=\cos \left(c_1{\mathrm{\Δt}}^2\right)\\ {\mathrm{Table}}_2=\sin \left(c_1{\mathrm{\Δt}}^2\right)\end{array}\right.---0\≤t\≤N---\left(6\right)$

When object space sampled point is three-dimensional point set, then in depth information z _jcan not be regarded it as constant again, this season then formula (6) can turn to:

$\left\{\begin{array}{c}{\mathrm{Table}}_1=\cos \left(\frac{c}{z_j}{\mathrm{\Δt}}^2\right)\\ {\mathrm{Table}}_2=\sin \left(\frac{c}{z_j}{\mathrm{\Δt}}^2\right)\end{array}\right.0\≤t\≤N---\left(7\right)$

The three-dimensional T-LUT trigonometric function look-up table that Here it is finally decides.

Fig. 2 is T-LUT algorithm calculation holographic optimum experimental process schematic provided by the invention.

In experiment, mainly the CUDA programming of GPU end carried out to T-LUT algorithm and optimized, according to optical reproduction as experimental result and generate holographic speed, having carried out repeatedly optimizing to T-LUT algorithm.

Fig. 3 is the final parallel optimization process flow diagram of T-LUT algorithm provided by the invention.

In Fig. 3, the mode carrying out weighing between the degree of concurrence that final parallel optimization takes data buffer storage committed memory amount and data to calculate is carried out.The computer memory of this suboptimization application can allow GPU keep peak value computing velocity, and thread proportioning is different according to object point hits different ratio, and the basis of in the past testing achieves certain speed-optimization again.This suboptimization, while achieving the lifting in speed, can not produce restriction to object point sampling.

Fig. 4 is that T-LUT algorithm GPU parallel generation hologram reconstruction picture provided by the invention is with point source method CPU generating hologram reproduction image comparison diagram.

Can find out in Fig. 4 that T-LUT algorithm GPU parallel generation hologram reconstruction picture element amount does not reduce.

Fig. 5 is that the holographic speed of GPU parallel computation of T-LUT algorithm provided by the invention is with point source method CPU calculation holographic velocity contrast.

Can find out in Fig. 5 that the speed of the final parallel optimization generating hologram of T-LUT algorithm is obviously promoted, different according to sampled point quantity, speed does not promote 30-100 doubly not etc. relative to point source method CPU computing.

Claims (7)

1. the quick calculation holographic algorithm based on trigonometric function look-up table, it is characterized in that: this lookup table algorithm is on the basis of point source method calculation holographic, the phase bit position of prime formula is extracted, and the repeatedly mathematic(al) manipulation such as trigonometric function identical change approximate through binomial again, the relative position relation variable of the object space related in formula with holographic facet is split, substantially reduce the internal memory of look-up table, again through CUDA multiple programming, generate one group of (two) pure phase look-up table.Finally, this look-up table is utilized to be simplified by point source method prime formula, by CUDA multiple programming, implementation algorithm.

2. a kind of quick calculation holographic algorithm based on trigonometric function look-up table according to claim 1, is characterized in that: this look-up table is pure phase look-up table.

3. the lookup table algorithm of a kind of quick calculating three-dimensional body according to claim 1 holography, is characterized in that: this look-up table adopts CUDA programming to generate, and generative process adopts double precision parallel computation.

4. a kind of quick calculation holographic algorithm based on trigonometric function look-up table according to claim 1, is characterized in that: this look-up table comprises the whole phase informations needed for computed hologram, and the internal memory shared by form is very little.

5. a kind of quick calculation holographic algorithm based on trigonometric function look-up table according to claim 1, is characterized in that: this look-up table had both been applicable to two-dimensional bodies calculation holographic and has also been applicable to three-dimensional body calculation holographic.

6. a kind of quick calculation holographic algorithm based on trigonometric function look-up table according to claim 1, it is characterized in that: this look-up table does not need double counting, the hologram of size in look-up table allowed band, and the calculation holographic of the object point hits being no more than look-up table computer capacity all can directly use.

7. a kind of quick calculation holographic algorithm based on trigonometric function look-up table according to claim 1, it is characterized in that: the hologram that this lookup table algorithm generates on video card, its optical reproduction picture is compared to the original point source method of application, hold the reproduction image of generating hologram at CPU, quality does not reduce.