CN104090477A - Low-coherent-light three-dimensional holographic displaying method - Google Patents

Abstract

The invention relates to the technical field of optics and specifically relates to a low-coherent-light three-dimensional holographic displaying method. Because matrix multiplication can be realized by specific optical element systems, the invention proposes an algorithm which does not need repeated iteration or calculation and reproduces objects based on pseudo-inverse matrix multiplication and frequency domain filtering. The algorithm has an optical realization potential. On one hand, the algorithm is a novel algorithm which is different from a common restoring program, simple and easy to realize, provided with algorithm optimization function and capable of using part of hologram data to restore objects; and on the other hand, a theory model of the algorithm shows that an optical process is also capable of realizing a compression perception function so that a direction is indicated for follow-up technology development. A numerical simulating result shows that the method has excellent feasibility and is excellent in restoring effect, sufficient in theory and capable of meeting application demands.

Description

A kind of 3D hologram display packing of low-coherent light

Technical field

The present invention relates to optical technical field, be specially a kind of 3D hologram display packing of low-coherent light.

Background technology

Compressed sensing was applied in recent years image and processed and imaging system, aspect holographic, was mainly used in digital hologram field.The feature of compressed sensing is, in the time that signal can rarefaction representation under some transform-based, by sensing matrix and signal multiplication, obtains measured value, and in simple terms, it obtains model is exactly matrix multiple, shown in (1).If the data volume in measured value meets the condition shown in formula (2), and sensing matrix meets constraint isometry condition, shown in (3), so just can, by a small amount of measured value data and sensing matrix, utilize multi-signal restructing algorithm that signal is reproduced out exactly.Signal reconstruction problem can be by solving minimum l ₁norm problem is solved shown in (4), and progressively develops the multiple thinking that solves, and as matching pursuit algorithm, the minimum full variational method etc., is all in computing machine, to utilize programming, and iteration is realized with solving repeatedly.

y＝Φx (1)

M＝O[K log(N/K)] (2)

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

$\hat{x}=\arg \min {\left|\right|x\left|\right|}_{1}s.t.y=\mathrm{\Φx}---\left(4\right)$

The process of this demonstration is consistent with the process of digital hologram.The optical means of utilizing digital hologram records the hologram of object on charge coupled cell, utilizes algorithm reduction object in computing machine, as reverse propagation, call other algorithms etc.Compressed sensing provides a new thinking for object reduces in computing machine, and can accurately restore three-dimensional body with a small amount of hologram data, thereby realizes the compression of data volume.At present, compressed sensing in the utilization in digital hologram field just towards the detection to object, reduction future development.Mine-laying enlightening etc. is applied to compressed sensing technology digital hologram field at first, has proposed the basic framework that compressed sensing combines with digital hologram, restores three-dimensional object data from two-dimentional hologram.Auspicious Vincents etc. have also proposed the concept of compression Fresnel hologram on this basis, and with its accurate object that is blocked that reduces, have proposed theoretically subsequently to use the condition of guaranteeing of compressing chromatography hologram reconstructing object.The rugged good first-class of hole has realized the reduction of various dimensions (depth information, polarization information, colouring information) objects.Clements etc. utilize compressed sensing principle to realize the detection to object in conjunction with single pixel detector.These all have facilitation to the development of digital hologram.

Although the feature that compressed sensing is used optimized algorithm to realize reduction in computing machine can reduce data volume, but cannot be applied in calculation holographic field, reason is, calculation holographic utilizes computing machine to obtain hologram, utilize optical instrument to remove to reproduce three-dimensional body, and the Optimization Solution algorithm iterating can not be realized by light path.

If can realize by optical means the function of computer program, not only can reduce so data volume, can reduce the size of spatial light modulator simultaneously, reduce the restriction of hardware device, save cost, and the speed that light path realizes computing is fast more a lot of than computing machine, substantially can complete moment, and the development of holographic technique is had to huge facilitation.

Summary of the invention

(1) technical matters that will solve

Because matrix multiple can be realized by some system of optical elements, the present invention proposes a kind of algorithm of iterating, calculating of not needing, and multiplies each other and frequency domain filtering reproduces object based on pseudo inverse matrix, and the present invention has potentiality that can Optical Implementation.

(2) technical scheme

In order to solve the problems of the technologies described above, the invention provides a kind of 3D hologram display packing of low-coherent light, described method is divided into following steps:

The first step: fresnel diffraction formula is carried out to discretize and matrixing processing; The complex amplitude of the each pixel on hologram equal object intensity a little and corresponding location factor product and, and said process is expressed as to the form of matrix multiple;

Second step: for measured value, namely hologram data, chooses according to certain ratio and mode, is arranged in a new measured value u _new, by the row reservation accordingly of former sensing matrix, form a new sensing matrix Φ _new;

The 3rd step: calculate Φ _newsvd and pseudo inverse matrix

The 4th step: will with u _newmultiply each other;

The 5th step: product is arranged as to original size and carries out Fourier transform, by suitable frequency domain filtering, noise filtering is also only retained to the spectrum information of the original;

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

Preferably, described method multiplies each other to realize reduction by pseudo inverse matrix, carries out frequency domain filtering removal noise to going back preimage, obtains original objects information.

Preferably, matrix multiple, Fourier transform and frequency domain filtering can be realized by the mode of optics.

(3) beneficial effect

On the one hand, it is a kind of new algorithm that is different from common reducing program, and principle is simple easily to be realized, and substantially possesses the function of optimized algorithm, can, with part hologram data reduction object, realize compression.

On the other hand, the theoretical model of this algorithm shows, two-phonon process also can be realized compressed sensing function, for follow-up technical development points the direction.

Numerical simulation result shows, the method has good feasibility, and reduction effect is good, fully theoretical, reaches application requirements.

Brief description of the drawings

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is that fresnel diffraction communication process and the discretize thereof of an embodiment of 3D hologram display packing of a kind of low-coherent light according to the present invention processed schematic diagram;

Fig. 2 is the matrixing computation process schematic diagram of the fresnel diffraction of an embodiment of 3D hologram display packing of a kind of low-coherent light according to the present invention;

Fig. 3 is the bulk treatment process flow diagram flow chart of an embodiment of 3D hologram display packing of a kind of low-coherent light according to the present invention.

Embodiment

Below in conjunction with Figure of description and embodiment, the specific embodiment of the present invention is described in further detail.Following examples are only for the present invention is described, but can not be used for limiting the scope of the invention.

The first step: fresnel diffraction formula is carried out to discretize and matrixing processing.

Formula (5) is fresnel diffraction formula, the fresnel diffraction formula that formula (6) is discretize, the complex amplitude of the each pixel on hologram equal object intensity a little and corresponding location factor product and, said process is expressed as to the form of matrix multiple, shown in (7).

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

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

u＝CPo＝Φo (7)

Second step: for measured value, namely hologram data, chooses according to certain ratio and mode, is arranged in a new measured value u _new, by the row reservation accordingly of former sensing matrix, form a new sensing matrix Φ _new.

The 3rd step: calculate Φ _newsvd, shown in (8).

Calculate pseudo inverse matrix shown in (9).

Φ _new＝USV ^H＝U(Δ 0)V ^H (8)

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

The 4th step: will with u _newmultiply each other, shown in (10).

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

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

The 5th step: product is arranged as to original size and carries out Fourier transform, and in its Fourier spectrum, original signal and noise are separated, therefore also only retains noise filtering the spectrum information of original signal by suitable frequency domain filtering.

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

Above embodiment is only for the present invention is described, but not limitation of the present invention.Although the present invention is had been described in detail with reference to embodiment, those of ordinary skill in the art is to be understood that, technical scheme of the present invention is carried out to various combinations, revises or is equal to replacement, do not depart from the spirit and scope of technical solution of the present invention, all should be encompassed in the middle of claim scope of the present invention.

Claims (3)

1. a 3D hologram display packing for low-coherent light, described method is divided into following steps:

The first step: fresnel diffraction formula is carried out to discretize and matrixing processing; The complex amplitude of the each pixel on hologram equal object intensity a little and corresponding location factor product and, and said process is expressed as to the form of matrix multiple;

Second step: for measured value, namely hologram data, chooses according to certain ratio and mode, is arranged in a new measured value u _new, by the row reservation accordingly of former sensing matrix, form a new sensing matrix Φ _new;

The 3rd step: calculate Φ _newsvd and pseudo inverse matrix

The 4th step: will with u _newmultiply each other;

The 5th step: product is arranged as to original size and carries out Fourier transform, by suitable frequency domain filtering, noise filtering is also only retained to the spectrum information of the original;

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

2. the 3D hologram display packing of a kind of low-coherent light according to claim 1, is characterized in that, described method multiplies each other to realize reduction by pseudo inverse matrix, carries out frequency domain filtering removal noise to going back preimage, obtains original objects information.

3. the 3D hologram display packing of a kind of low-coherent light according to claim 2, is characterized in that, matrix multiple, Fourier transform and frequency domain filtering can be realized by the mode of optics.