CN104090477B - A kind of three-dimensional panoramic show method of low-coherent light - Google Patents

Abstract

The present invention relates to optical technical field, a kind of three-dimensional panoramic show method of low-coherent light.Because matrix multiple can be realized by some system of optical elements, the present invention proposes a kind of algorithm that need not and iterate, calculate, and is multiplied based on pseudo inverse matrix and frequency domain filtering carrys out reconstructed object, and the present invention has can be with the potentiality of Optical Implementation.On the one hand, it is a kind of new algorithm being different from ordinary reduction program, simple easily realization, substantially possesses the function of optimized algorithm, it is possible to partial holograms data convert object.On the other hand, the theoretical model of this algorithm shows, two-phonon process also can realize compressed sensing function, points the direction for follow-up technology development.Numerical simulation result shows, the method has good feasibility, and reduction effect is good, theoretical abundant, reaches to apply requirement.

Description

A kind of three-dimensional panoramic show method of low-coherent light

Technical field

The present invention relates to optical technical field, a kind of three-dimensional panoramic show method of low-coherent light.

Background technology

Compressed sensing was applied to image procossing and imaging system in recent years, in terms of holography, was mainly used in numeral complete Breath field.The feature of compressed sensing is, when signal some conversion base under can with rarefaction representation time, by sensing matrix and signal Being multiplied, obtain measured value, in simple terms, it obtains model is exactly matrix multiple, as shown in formula (1).If the number in measured value Meet the condition shown in formula (2) according to amount, and sensing matrix meets constraint isometry condition, as shown in formula (3), then just can Logical too small amount of measured value data and sensing matrix, utilize multi-signal restructing algorithm to accurately reproduce out by signal.Signal Reconstruction can be solved as shown in formula (4) by solving a minimum norm problem, and progressively develop and multiple solve think of Road, such as matching pursuit algorithm, the minimum full calculus of variations etc., is all to utilize programming in a computer, repeatedly iteration and solving in addition Realize.

Y=Φ x (1)

M=O [Klog (N/K)] (2)

$(1-{\mathrm{\δ}}_K)\left|\right|x|{|}_2^2\≤|\left|\mathrm{\Φ}x\right|{|}_2^2\≤(1+{\mathrm{\δ}}_K)\left|\right|x|{|}_2^2---\left(3\right)$

$\begin{array}{ccc}\hat{x}=\arg \min \left|\right|x|{|}_1& s.t.& y=\mathrm{\Φ}x\end{array}---\left(4\right)$

The process of this display is consistent with the process of digital hologram.Digital hologram utilizes optical means in Charged Couple unit Record the hologram of object on part, utilize algorithm reduction object in a computer, as inversely propagated, call other algorithms etc..Pressure Contracting is perceived as object and reduces in a computer and provide a new thinking, it is possible to a small amount of hologram data accurate reproduction Go out three-dimensional body, thus realize the compression of data volume.At present, the compressed sensing utilization in digital hologram field is just towards to object Detection, reduction direction develop.Compressed sensing technology is applied to digital hologram field by mine-laying enlightening etc. at first, it is proposed that compression sense Know the basic framework combined with digital hologram, from the hologram of two dimension, restore the object data of three-dimensional.Auspicious Vincents etc. exist It is also proposed the concept of compression Fresnel hologram on the basis of this, and be blocked object with its accurate reproduction, the most theoretically Propose use compression chromatography hologram reconstructing object guarantees condition.The rugged good first-class of hole achieves various dimensions (depth information, pole Change information, colouring information) reduction of object.Clements etc. utilize compressed sensing principle to combine single pixel detector and realize thing The detection of body.These all development to digital hologram have facilitation.

Although the feature that compressed sensing uses optimized algorithm to realize reduction in a computer can reduce data volume, but nothing Method is applied and is being calculated holographic field, and reason is, calculates holography and utilizes computer to obtain hologram, utilizes optical instrument to go to reproduce three Dimension object, and the Optimization Solution algorithm iterated can not realize by light path.

If the function of computer program can optically be realized, then data volume can not only be reduced, the most permissible The size of reduction spatial light modulator, reduces the restriction of hardware device, cost-effective, and light path realizes the speed of computing than meter Calculation machine is a lot of soon, substantially can complete moment, and the development to holographic technique has huge facilitation.

Summary of the invention

(1) to solve the technical problem that

Because matrix multiple can be realized by some system of optical elements, the present invention proposes one and need not repeatedly change Generation, the algorithm calculated, be multiplied based on pseudo inverse matrix and frequency domain filtering carry out reconstructed object, and the present invention has can diving with Optical Implementation Power.

(2) technical scheme

In order to solve above-mentioned technical problem, the invention provides a kind of three-dimensional panoramic show method of low-coherent light, described Method is divided into following steps:

The first step: fresnel diffraction formula is carried out discretization and matrixing processes；Each pixel on hologram Complex amplitude equal to object intensity a little and corresponding location factor product and, and said process is expressed as matrix phase The form taken advantage of；

Second step: for measured value, namely hologram data, choose according to certain ratio and mode, be arranged in one Individual new measured value u_new, corresponding for former sensing matrix row is retained, constitutes a new sensing matrix Φ_new；

3rd step: calculate Φ_newSingular value decomposition and pseudo inverse matrix

4th step: willWith u_newIt is multiplied；

5th step: product is arranged as original size and carries out Fourier transformation, by suitable frequency domain filtering making an uproar Sound filters and only retains the spectrum information of the original；

6th step: after frequency domain filtering, then carry out an inverse Fourier transform, obtain the image of the original.

Preferably, described method be multiplied by pseudo inverse matrix realize reduction, to go back preimage carry out frequency domain filtering remove make an uproar Sound, obtains original objects information.

Preferably, matrix multiple, Fourier transformation and frequency domain filtering can realize by the way of optics.

(3) beneficial effect

On the one hand, it is a kind of new algorithm being different from ordinary reduction program, and principle the most easily realizes, and substantially possesses The function of optimized algorithm, it is possible to partial holograms data convert object, it is achieved compression.

On the other hand, the theoretical model of this algorithm shows, two-phonon process also can realize compressed sensing function, for rear Continuous technology development points the direction.

Numerical simulation result shows, the method has good feasibility, and reduction effect is good, theoretical abundant, and reaching should With requiring.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to Other accompanying drawing is obtained according to these accompanying drawings.

Fig. 1 is that the fresnel diffraction of one embodiment of three-dimensional panoramic show method according to a kind of low-coherent light of the present invention passes Broadcast process and sliding-model control schematic diagram thereof；

Fig. 2 is the fresnel diffraction of one embodiment of three-dimensional panoramic show method according to a kind of low-coherent light of the present invention Matrixing calculates process schematic；

Fig. 3 is the disposed of in its entirety process of one embodiment of three-dimensional panoramic show method according to a kind of low-coherent light of the present invention Flow chart.

Detailed description of the invention

Below in conjunction with Figure of description and embodiment, the detailed description of the invention of the present invention is described in further detail.With Lower embodiment is merely to illustrate the present invention, but can not be used for limiting the scope of the present invention.

The first step: fresnel diffraction formula is carried out discretization and matrixing processes.

Formula (5) is fresnel diffraction formula, and formula (6) is the fresnel diffraction formula of discretization, each picture on hologram The complex amplitude of vegetarian refreshments equal to object intensity a little and corresponding location factor product and, said process is expressed as square The form that battle array is multiplied, as shown in formula (7).

$u(x,y)=\frac{1}{j\mathrm{\λ}z}\∫\underset{\mathrm{\Σ}}{\∫}o(x_0,y_0)\exp \[jk\frac{{(x-x_0)}^2+{(y-y_0)}^2}{2z}\]{\mathrm{dx}}_0{\mathrm{dy}}_0---\left(5\right)$

$u(x_p,y_p)=\frac{1}{j\mathrm{\λ}z}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\underset{m=1}{\overset{M}{\mathrm{\Σ}}}o(x_{0m},y_{0n})\exp \[jk\frac{{(x_p-x_{0m})}^2+{(y_q-y_{0n})}^2}{2z}\]{\mathrm{\Δx}}_0{\mathrm{\Δy}}_0---\left(6\right)$

U=CPo=Φ o (7)

Second step: for measured value, namely hologram data, choose according to certain ratio and mode, be arranged in one Individual new measured value u_new, corresponding for former sensing matrix row is retained, constitutes a new sensing matrix Φ_new。

3rd step: calculate Φ_newSingular value decomposition, as shown in formula (8).

Calculate pseudo inverse matrixAs shown in formula (9).

Φ_new=USV^H=U (Δ 0) V^H (8)

${\mathrm{\Φ}}_{new}^{-1}=V\left(\begin{array}{c}{\mathrm{\Δ}}^{-1}\\ 0\end{array}\right)U^H---\left(9\right)$

4th step: willWith u_newIt is multiplied, as shown in formula (10).

$\begin{array}{c}{\mathrm{\Φ}}_{new}^{-1}{u}_{new}={\mathrm{\Φ}}_{new}^{-1}{\mathrm{\Φ}}_{new}o=V\left(\begin{array}{cc}{E}_{M\×M}& 0\\ 0& 0\end{array}\right)V^{H}o=V\[E_{N\×N}-\left(\begin{array}{cc}0& 0\\ 0& E_{(N-M)\×(N-M)}\end{array}\right)\]V^{H}o\\ ={\mathrm{VE}}_{N\×N}{V}^{H}o-V\left(\begin{array}{cc}0& 0\\ 0& E_{(N-M)\×(N-M)}\end{array}\right)V^{H}o=o+Ko\end{array}---\left(10\right)$

Visible, product be original signal with noise and, and identical with the dimension of original signal.

5th step: product is arranged as original size and carries out Fourier transformation, in its Fourier spectrum, the original is believed Number it is separated with noise, therefore by suitable frequency domain filtering noise filtering the frequency spectrum that only retains original signal Information.

6th step: after frequency domain filtering, then carry out an inverse Fourier transform, obtain original signal.

Embodiment of above is merely to illustrate the present invention, rather than limitation of the present invention.Although with reference to embodiment to this Bright be described in detail, it will be understood by those within the art that, technical scheme is carried out various combination, Amendment or equivalent, without departure from the spirit and scope of technical solution of the present invention, all should contain the right in the present invention and want Ask in the middle of scope.

Claims (2)

1. a three-dimensional panoramic show method for low-coherent light, described method is divided into following steps:

The first step: fresnel diffraction formula is carried out discretization and matrixing processes；Answering of each pixel on hologram is shaken Width equal to object intensity a little and corresponding location factor product and, and said process is expressed as matrix multiple Form；

Second step: for measured value, namely hologram data, choose according to certain ratio and mode, is arranged in one newly Measured value u_new, corresponding for former sensing matrix row is retained, constitutes a new sensing matrix Φ_new；

3rd step: calculate Φ_newSingular value decomposition and pseudo inverse matrix

4th step: willWith u_newIt is multiplied；

5th step: product is arranged as original size and carries out Fourier transformation, is filtered noise by suitable frequency domain filtering Except the spectrum information the most only retaining the original；

6th step: after frequency domain filtering, then carry out an inverse Fourier transform, obtain the image of the original.

The three-dimensional panoramic show method of a kind of low-coherent light the most according to claim 1, it is characterised in that matrix multiple, Fourier transformation and frequency domain filtering can realize by the way of optics.