CN104007648A - Digital holographic imaging system and numerical reconstruction method of holographic image - Google Patents

Abstract

The invention provides a digital holographic imaging system and a numerical reconstruction method of a holographic image so as to shoot a target object and store the shot target as holographic image data. The system includes signal light formed by illumination of the target object by a light source; an image detector used for recording interference fringes of the signal light; a light guide pipe which is arranged on a light path of the signal light and between the target object and the image detector, wherein the light guide pipe is provided with a reflecting face and part of the signal light enters the image detector after being reflected by the reflecting face of the light guide pipe. The digital holographic imaging system and the numerical reconstruction method of the holographic image can enable captured signals to be equivalent to several times of the sum of pixels of the image detector and thus limitation of a spatial frequency width can be broken through and the measurement time of the holographic image can be shortened.

Description

The numerical reconstruction method of digital holographic imaging systems and hologram

Technical field

The present invention relates to a kind of holographic technique, the numerical reconstruction method of espespecially a kind of digital holographic imaging systems and hologram.

Background technology

Holography (holography) is a kind of reproducing technology of 3 D stereoscopic image, it is different from general photography and has only stored brightness data, holographic photography has stored the data of brightness (intensity) and phase (phase), in the time irradiating hologram sheet (hologram) with suitable light source and carry out image reconstruction (reconstruct), the 3 D stereoscopic image as true can be reappeared in former record position.

In general, holographic photography is by the light beam of laser transmitting, be divided into twice light beam by spectroscope (beam splitter), a branch of conduct is with reference to light beam, another bundle irradiates object, object forms scattering after this light beam irradiates, and object light and reference beam are interfered formation light and shade interference fringe mutually, and are got off by negative writing.

Digital hologram photography (digital holography) is a kind of by charge coupled cell (charge-coupled device, CCD) obtain and process the technology of holographic interference data, the data of passing through measurement and obtain is carried out numerical reconstruction (numerical reconstruction), and typical digital hologram photography can be set up three-dimensional surface or its depth information of object.

But in existing digital hologram camera work, no matter be to adopt which kind of framework, final numerical evaluation all can be subject to the restriction (spatial bandwidth limit) of space frequency range, explains with following formula:

A×B<f(N) (1)

Wherein A is viewing area (field ofview, FOV), the B=1/u reciprocal that B is resolution, and u is resolution, N is the picture element sum of image detecting device (image detector).That is to say, image detecting device, as CCD, recordable image data is limited.In order to break through the restriction of space frequency range, the technology of existing a kind of aperture synthesis (aperture synthesis), it is by translation image detecting device, make it carry out two-dimensional scan, with equivalent Cheng Genggao picture element sum, the solution that this mode is clever the picture element restriction of image detecting device, increase system complexity and significantly elongate the measurement time but image detecting device is carried out to translation meeting, in practice, have its difficulty.

Summary of the invention

The present invention's object is to provide a kind of numerical reconstruction method of digital holographic imaging systems and hologram, to shorten the measurement time of hologram, simplifies system complexity, promotes the quality of reconstructed image simultaneously.

For reaching above-mentioned purpose, the invention provides a kind of digital holographic imaging systems, in order to photographic subjects thing, and with hologram data storage, described system comprises: signal light, it forms after irradiating this object by light source; Image detecting device, in order to record this signal interference of light striped; And light pipe, be arranged in the light path of this signal light and between this object and this image detecting device, wherein this light pipe has reflecting surface, and the signal light of part is laggard to this image detecting device via the reflecting surface reflection of this light pipe.

The present invention provides a kind of numerical reconstruction method of hologram on the other hand, is provided with the optics framework of light pipe between object and the image detecting device that is applicable to take, and described method comprises step: utilize image detecting device to capture the interference image of object; Be data matrix by this interference video conversion; Repeatedly mirror is carried out on multiple limits along this data matrix, to expand into a new data matrix; And this new data matrix is carried out to numerical reconstruction, to obtain the field distribution of this object place plane.

Digital holographic imaging systems proposed by the invention is provided with light pipe in the light path of signal light, between object and image detecting device, and this light pipe has reflecting surface or fully reflecting surface, can be used for collecting the signal light of wide-angle.Coordinate the numerical reconstruction method of hologram proposed by the invention, can make captured signal be equivalent to the picture element sum of several times image detecting device, therefore can break through the limitation of space frequency range.Compared to the technology of existing aperture synthesis, the present invention can shorten the measurement time of hologram, simplifies system complexity, can promote the quality of reconstructed image simultaneously.

Brief description of the drawings

Figure 1A shows the configuration diagram of the present invention's digital holographic imaging systems.

Figure 1B shows another configuration diagram of the present invention's digital holographic imaging systems.

Fig. 2 A shows the schematic diagram of the digital holographic imaging systems of first embodiment of the invention.

Fig. 2 B shows the schematic diagram of the digital holographic imaging systems of second embodiment of the invention.

Fig. 2 C shows the schematic diagram of the digital holographic imaging systems of third embodiment of the invention.

Fig. 2 D shows the schematic diagram of the digital holographic imaging systems of fourth embodiment of the invention.

Fig. 2 E shows the schematic diagram of the digital holographic imaging systems of fifth embodiment of the invention.

Fig. 2 F shows the schematic diagram of the digital holographic imaging systems of sixth embodiment of the invention.

Fig. 3 A shows the schematic diagram of the digital holographic imaging systems of seventh embodiment of the invention.

Fig. 3 B shows the schematic diagram of the digital holographic imaging systems of eighth embodiment of the invention.

Fig. 3 C shows the schematic diagram of the digital holographic imaging systems of ninth embodiment of the invention.

Fig. 4 A shows the schematic diagram of the digital holographic imaging systems of tenth embodiment of the invention.

Fig. 4 B shows the schematic diagram of the digital holographic imaging systems of eleventh embodiment of the invention.

Fig. 4 C shows the schematic diagram of the digital holographic imaging systems of twelveth embodiment of the invention.

Fig. 4 D shows the schematic diagram of the digital holographic imaging systems of thriteenth embodiment of the invention.

Fig. 4 E shows the schematic diagram of the digital holographic imaging systems of fourteenth embodiment of the invention.

Fig. 4 F shows the schematic diagram of the digital holographic imaging systems of fifteenth embodiment of the invention.

Fig. 4 G shows the schematic diagram of the digital holographic imaging systems of sixteenth embodiment of the invention.

Fig. 4 H shows the schematic diagram of the digital holographic imaging systems of seventeenth embodiment of the invention.

Fig. 4 I shows the schematic diagram of the digital holographic imaging systems of eighteenth embodiment of the invention.

Fig. 4 J shows the schematic diagram of the digital holographic imaging systems of nineteenth embodiment of the invention.

Fig. 4 K shows the schematic diagram of the digital holographic imaging systems of twentieth embodiment of the invention.

Fig. 5 A to Fig. 5 D shows that the sidewall of light pipe in the embodiment realizing according to the present invention is the schematic diagram tilting.

Fig. 6 shows the schematic flow sheet of the numerical reconstruction method of the present invention's hologram.

Fig. 7 shows the schematic diagram of the digital holographic imaging systems realizing according to the embodiment of the present invention.

Fig. 8 A to Fig. 8 F shows the schematic diagram of in the present invention's hologram numerical reconstruction method, data matrix being expanded.

Embodiment

The present invention proposes a kind of digital holographic imaging systems, in signal light path, add light pipe (light pipe), utilize in the light path of signal light, object (object that wish is taken) adds light pipe between image sensor (as CCD, CMOS), collect the signal light of wide-angle by the reflecting surface of light pipe, and follow-up while carrying out numerical reconstruction, by the picture element restriction that copies to overcome image sensor of image matrix, break through the limitation of space frequency range (spatial bandwidth), the quality of significantly promoting reconstructed image.

Refer to Figure 1A and Figure 1B, it shows the configuration diagram of the present invention's digital holographic imaging systems.Digital holographic imaging systems of the present invention comprises signal light 11, and it forms after irradiating object by light source; Image detecting device 16, in order to record the interference fringe of this signal light 11; And light pipe 14, being arranged in the light path of signal light 11, between object and image detecting device 16, wherein light pipe 14 has reflecting surface, and the signal light of part is laggard to image detecting device 16 via the reflecting surface reflection of this light pipe 14.The reflecting surface of this light pipe 14 is used for collecting the signal light of wide-angle, and this is equivalent to also be provided with image detecting device 16 in the mirror position of the reflecting surface of light pipe 14, and so equivalence has promoted the picture element sum of image detecting device 16.

In Figure 1A, the light source that forms signal light 11 is same light source with the light source that irradiates object, and signal light 11 is that the light that sends with this light source is mutually interfered and produced interference fringe.In addition, as shown in Figure 1B, image detecting device 16 is to record signal light 11 mutually to interfere and the interference fringe of generation with reference light 12, can use same light source through spectroscope (beam splitter, BS) be divided into twice light beam, wherein one light beam, as with reference to light 12, forms signal light 11 after another road light beam irradiates object.In embodiment, this light source can be light-emittingdiode (light emitted diode, LED) light source or laser (laser) light source.In the time that light source is laser light source, also can add wavelength controlling element (as, acousto-optic modulator), make wherein one light beam or twice light beam produce wavelength shift, to bring into play the function of extrapolation interferometer (heterointerferometer).

Light pipe 14 can be realized in two ways, and the side of first light pipe 14 is coated with reflectance coating; Its two be light pipe 14 for solid, utilize the total reflection of interface that light is reflected, and do not need to plate reflectance coating.Horizontal tangent plane the best of light pipe 14 is rectangle, can be also triangle, quadrilateral, pentagon, hexagon or other polygon.

Digital holographic imaging systems proposed by the invention is provided with light pipe 14 in the light path of signal light 11, between object and image detecting device 16, this light pipe 14 has reflecting surface or fully reflecting surface, can be used for collecting the signal light of wide-angle, follow-up while carrying out numerical reconstruction, the signal capturing can equivalent what several times image detecting device 16 picture element sum, therefore can break through the limitation of space frequency range.Compared to the technology of existing aperture synthesis (aperture synthesis), the present invention can shorten the measurement time of hologram, simplifies system complexity, can promote the quality of reconstructed image simultaneously.

Fig. 2 A shows the schematic diagram of the digital holographic imaging systems of first embodiment of the invention.In first embodiment of the invention, use the light source of approximate spherical wave 112 to irradiate object 15, spherical wave light source and object 15 are on same optical axis, diffraction light and spherical wave 112 from object 15 interfere with each other, signal interfered in image detecting device 16 records, between object 15 and image detecting device 16, be provided with light pipe 14, the sidewall of light pipe 14 has reflecting surface or fully reflecting surface, can be used to collect the interference signal of wide-angle.

Fig. 2 B shows the schematic diagram of the digital holographic imaging systems of second embodiment of the invention.The difference of second embodiment of the invention and the first embodiment is: in a second embodiment, spherical wave light source has departed from optical axis, that is to say that spherical wave light source and object 15 be not on same optical axis, so can solve spherical wave light source and the object 15 easy problem that produces larger noise on same optical axis.

Fig. 2 C shows the schematic diagram of the digital holographic imaging systems of third embodiment of the invention.The difference of third embodiment of the invention and the first embodiment and the second embodiment is: in the 3rd embodiment, spherical wave light source and object 15 are all arranged in the plane on the surface that is parallel to image detecting device 16, and introduce in addition another road light beam irradiates object 15,112 conducts of spherical wave are with reference to light, in order to produce interference fringe, this light beam that irradiates object conventionally and reference light produce from same laser light source, third embodiment of the invention can reduce the generation of noise.

Fig. 2 D, Fig. 2 E and Fig. 2 F show respectively the schematic diagram of the digital holographic imaging systems of fourth embodiment of the invention, the 5th embodiment and the 6th embodiment.The spherical wave 112 in Fig. 2 A, Fig. 2 B and Fig. 2 C is replaced with plane wave 114 by embodiment shown in Fig. 2 D, Fig. 2 E and Fig. 2 F.That is to say, except using spherical wave light source to irradiate object 15, the present invention also can use plane wave or tiltedly beat plane wave illumination object 15, and the light source of other wavefront is also suitable for it.In addition, in the 6th embodiment shown in Fig. 2 F, be using plane wave 114 as with reference to light, and introduce in addition another road light beam irradiates object 15, this light beam that irradiates object conventionally and reference light produce from same laser light source.

Fig. 3 A, Fig. 3 B and Fig. 3 C show respectively the schematic diagram of the digital holographic imaging systems of seventh embodiment of the invention, the 8th embodiment and the 9th embodiment.At Fig. 3 A, in digital holographic imaging systems shown in Fig. 3 B and Fig. 3 C, all there is an optical element, it is spectroscope 17, spectroscope 17 can be directed to image detecting device 16 by signal light and reference light simultaneously interferes, the light that light source irradiates object 15 rear formation is called signal light, by same light source through spectroscope 17 guide and come another road light be called reference light, it is in order to interfere with signal light, this reference light can be plane wave (the 7th embodiment as shown in Figure 3A), tiltedly tie ground roll (the 8th embodiment as shown in Figure 3 B), the waveform of spherical wave (the 9th embodiment as shown in Figure 3 C) or other types, this light beam that irradiates object conventionally and reference light produce from same laser light source.

Fig. 4 A to Fig. 4 F shows respectively the schematic diagram of the digital holographic imaging systems of tenth embodiment of the invention to the 15 embodiment.Embodiment shown in Fig. 4 A to Fig. 4 F is respectively in the embodiment shown in Fig. 2 A to Fig. 2 F, and lens 18 or lens combination are set in the light path of signal light, to adjust the distribution of signal light field.

Fig. 4 G and Fig. 4 H show respectively the schematic diagram of the digital holographic imaging systems of sixteenth embodiment of the invention and the 17 embodiment.The 16 embodiment shown in Fig. 4 G of the present invention and the difference of Fig. 3 A are: in this embodiment, in the light path of signal light, between object 15 and spectroscope 17, be provided with lens 18 or lens combination, to adjust the distribution of signal light field.The 17 embodiment shown in Fig. 4 H of the present invention and the difference of Fig. 3 A are: in this embodiment, in the light path of signal light, between spectroscope 17 and image detecting device 16, be provided with lens 18 or lens combination, to adjust the distribution of interference fringe.

Fig. 4 I to Fig. 4 K shows respectively the schematic diagram of the digital holographic imaging systems of eighteenth embodiment of the invention to the 20 embodiment.Embodiment shown in Fig. 4 I replaces with the plane wave in Fig. 4 G 1 14 tiltedly to tie ground roll, embodiment shown in Fig. 4 J replaces with the plane wave in Fig. 4 H 114 tiltedly to tie ground roll, and the plane wave in Fig. 4 H 114 is replaced with spherical wave by the embodiment shown in Fig. 4 K.

Fig. 5 A to Fig. 5 D shows that the sidewall of light pipe in the embodiment realizing according to the present invention is the schematic diagram tilting.Compare with examples image detecting device 16 planes with Figure 1A of the present invention is vertical with light pipe 14 sidewalls shown in Figure 1B, in the present invention, the sidewall of light pipe 14 also can be arranged to, as shown in Fig. 5 A to Fig. 5 D.Preferably, the sidewall of light pipe 14 and the angle of perpendicular bisector can be between-70 ° to+70 °.In addition, the cross-sectional area of light pipe 14 can be greater than or less than the area of image detecting device 16, that is to say, the cross-sectional area of light pipe 14 does not need identical with the area of image detecting device 16.

Refer to Fig. 6, it shows the schematic flow sheet of the numerical reconstruction method of the present invention's hologram.The numerical reconstruction method of hologram provided by the present invention, is applicable to be provided with the optics framework of light pipe between the object taken and image detecting device, and described method comprises following steps.

Step S10: the interference image that utilizes image detecting device acquisition object.

Step S12: be data matrix by this interference video conversion.

Step S14: repeatedly mirror is carried out on the multiple limits along this data matrix, to expand into a new data matrix.

Step S16: this new data matrix is carried out to numerical reconstruction, to obtain the field distribution of this object place plane.

Refer to Fig. 7, below will the numerical reconstruction method of hologram proposed by the invention be described with the digital holographic imaging systems shown in Fig. 7.Digital holographic imaging systems shown in Fig. 7 is used the divergent spherical wave that pointolite produced to irradiate object 15, reference light 12 is also divergent spherical wave, the pointolite that produces reference light 12 is positioned at and the same plane that is parallel to image detecting device 16 of object 15, light pipe 14 between object 15 and image detecting device 16, the signal light 11 that receives script on image detecting device 16 and reference light 12 and signal light 11 and reference light 12 through light pipe 14 sidewall reflects.

Before carrying out the numerical reconstruction of hologram, can adopt high dynamic range technique for taking, to obtain preferably hologram of quality.This is because signal overlaps in together after light pipe multiple reflections, now in order to obtain the finer variation of image, can increase the dynamic range (dynamic range) of pick-up image, stores image detail with multidigit tuple more.In the time of photographic subjects thing, first same picture is carried out repeatedly the exposure of different time, again captured multiple pictures is recombinated with high dynamic-range image technology, the interference image of high dynamic range can be obtained, the hologram of high-quality can be reconstructed by the interference image of this high dynamic range.

Supposing image obtained after above-mentioned steps as shown in Figure 8 A, if the angle of inclination of light pipe sidewall is 0 degree, is two-dimensional data matrix (U via hardware by obtained video conversion ₀₀) after, then in the mode of mirror, this two-dimensional data matrix is expanded, the degree of its expansion is limited to the specular reflectance of light pipe and the dynamic range of image detecting device.And the mode expanding is for constantly carrying out mirror by this data matrix to one of them limit.For instance, data matrix shown in Fig. 8 A is become to Fig. 8 B to the right mirror, Fig. 8 B is become to Fig. 8 C to top mirror, Fig. 8 C is become to Fig. 8 D to left side mirror, Fig. 8 D is become to Fig. 8 E to following mirror, following such mode can constantly expand data matrix, and the data matrix after expanding with this carries out numerical reconstruction can break through the restriction of space frequency range.At this, each newly-increased data matrix number table is reached to function U _{i, j}(x, y), as shown in Figure 8 F, in the data matrix of finally formation, each newly-increased matrix representation is:

U _ij(x,y)＝U ₀₀((-1) ⁱx,(-1) ^jy), (2)

If consider the impact that light pipe specular reflectance (Re) causes, each newly-increased matrix can be modified to:

U _ij(x,y)＝U ₀₀((-1) ⁱx,(-1) ^jy)/Re ^|i|+ ^|j|, (3)

The matrix called after U that formula (2) or formula (3) are extended to _mn, it is signal light (S _mn) and reference light (R _mn) result of interference, be expressed as follows:

$U_{\mathrm{mn}}={\left|R_{\mathrm{mn}}\right|}^2+{\left|S_{\mathrm{mm}}\right|}^2+R_{\mathrm{mn}}{S}_{\mathrm{mn}}^{*}+R_{\mathrm{mn}}^{*}{S}_{\mathrm{mn}},,---\left(4\right)$

Then, this new data matrix is carried out to numerical reconstruction, to obtain the field distribution of this object place plane, wherein, except the signal item that will be used for rebuilding, other is noise item.If use rebuild, need Umn to be multiplied by and be passed to towards the positive direction objective plane (being object place plane); If use rebuild, need U _mnbe multiplied by R _mn, and back transfer is to objective plane, so-called back transfer is that transmission distance is multiplied by negative 1.Should be noted R _mnfor reference light is passed to U through free space _mnreference light within the scope of extension matrix distributes, but not U ₀₀reference light in scope distributes and forms through matrix-expand.

But, now on objective plane, except having desired signal, also there are other noises, the mode that removes these noises comprises phase shift interference art (phase shift interferometer), recursive algorithm (iterative algorithm), spatial filtering method (spacial filter) etc., does not repeat them here.

If reference light is a divergent spherical wave, and the pointolite of objective plane and reference light is in the same plane, because the distribution of spherical wave on image detecting device is equivalent to the PHASE DISTRIBUTION of a spherical lens, in the time that objective plane and image detecting device distance is enough long, the field distribution on objective plane is equivalent to U _mncarry out the result that the conversion of Fu's formula is obtained, can use fast fourier transform to calculate at this, to obtain the field distribution on objective plane:

Target=FFT(U _mn)， (5)

Though if the pointolite of objective plane and reference light is in the same plane, the pointolite hypertelorism of object and reference light, can add a phase term to carry out translation,

$T\arg \mathrm{et}=\mathrm{FFT}\left\{U_{\mathrm{mn}}\exp \right[i2\mathrm{\&pi;}(x_{\mathrm{mn}}\frac{\mathrm{\&Delta;x}}{{\mathrm{\&lambda;z}}_0}+y_{\mathrm{mn}}\frac{\mathrm{\&Delta;y}}{{\mathrm{\&lambda;z}}_0})\left]\right\},---\left(6\right)$

Wherein Δ x and Δ y are respectively at x and the translation distance in y direction, (x _mn, y _mn) be the coordinate system of matrix after expansion, be expressed as follows:

$x_{\mathrm{mn}}=t_1{B}_x-\frac{{\mathrm{mL}}_x}{2},---\left(7\right)$

$y_{\mathrm{mn}}=t_2{B}_y-\frac{{\mathrm{nL}}_y}{2},---\left(8\right)$

Wherein L _xwith L _ythe length of the capture scope that is respectively image detecting device in x and y direction, t ₁represent the t in coordinate matrix ₁row (column), t ₂represent the t in coordinate matrix ₂row (row), B _xand B _ybe respectively the picture element spacing (pixel pitch) of image detecting device in x and y direction.

If the pointolite of objective plane and reference light is not in the same plane, account form is comparatively complicated.First, use R _mnor be multiplied by U _mn, to obtain S _mnmatrix, represents the matrix of signal light.If use following formula:

$S_{\mathrm{mn}}=R_{\mathrm{mn}}^{*}{U}_{\mathrm{mn}},---\left(9\right)$

Will rebuild back the transmission distance that the field distribution of objective plane uses is the actual distance in space; If use following formula:

S _mn＝R _mnU _mn, (10)

To rebuild back transmission distance that the field distribution of objective plane uses and be multiplied by negative 1 for the actual distance in space.

The described account form in formula (5)-(10) is simplification account form in particular cases; if system does not meet simplified condition; in the time that the data matrix to new after expanding carries out numerical reconstruction; conventionally can propagate to calculate the optical field distribution that is passed to arbitrary target plane by any initial plane with angular spectrum, its account form is expressed as is rear:

FU ₁＝FET(U ₀)exp(i2πz/λ(1-α ²-β ²) ^0.5), (11)

α＝t ₁λ/L _x0, (12)

β＝t ₂λ/L _y0, (13)

Wherein λ is optical source wavelength, and FFT is fast fourier transform, U ₀for initial plane, U ₁for objective plane, FU ₁for the spectrum distribution of objective plane, L _x0with L _y0be respectively U ₀the length of capture scope in x and y direction, t ₁represent the t in matrix ₁row, t ₂represent the t in matrix ₂oK, distance is transmitted in z representative.Finally, taking fast Flourier inverse transform (IFFT) obtain objective plane field distribution as:

U ₁=IFFT(FU ₁)。(14)

The resolution that the shortcoming that directly uses formula (11) to (14) calculating is objective plane is limited to the resolution of initial plane, if will use U _mnthe objective plane image that obtains high-res, need carry out the estimation in the transmission of space.The account form that transmit in space can be: initial plane is carried out interpolation expansion by (1); (2) initial plane being carried out to interpolation expansion is cut into aliquot-sized again and propagates; (3) use two-period form Fresnel conversion (Fresnel transform); And (4) use Rayleigh-Suo Mofeier formula (Rayleigh-Sommfeld formula) direct integral, division is as rear:

(1) initial plane is carried out to interpolation expansion

By S _mnthe equidistant interpolation expansion of matrix is M × N matrix doubly, and the frequency spectrum (TargetF) of objective plane can be calculated by following formula:

TargetF＝FFT(S _mn)exp(i2πzz ₀/λ(1-α ²-β ²) ^0.5), (15)

α＝t ₁λ/mL _x, (16)

β＝t ₂λ/nL _y, (17)

Wherein L _xwith L _ythe length of the capture scope that is respectively image detecting device in x and y direction, t ₁t in masterpiece mark matrix ₁row, t ₂t in masterpiece mark matrix ₂oK, z _orepresent the distance between objective plane and image detecting device.Finally, taking fast Flourier inverse transform (IFFT) obtain objective plane field distribution as:

Target=IFFT(TargetF) (18)

(2) initial plane being carried out to interpolation expansion is cut into aliquot-sized again and propagates

First, by S _mnthe equidistant interpolation of matrix is expanded to M × N doubly, then it is divided into D in x and y direction _xand D _yequal portions, are expressed as Sd _ij, Sd _ij(be x direction d _iequal portions, y direction d _jequal portions), be centered close to respectively each equal portions are transmitted to objective plane center.

Then, use angular spectrum circulation way calculates the angular spectrum distribution that is passed to objective plane, as follows:

FSd _ij＝FFT(Sd _ij)exp(i2πz ₀/λ(1-α ²-β ²) ^0.5), (19)

Consider Sd _ijposition, can calculate Targetd _ijangular spectrum in objective plane center is distributed as:

${T\arg \mathrm{etFd}}_{\mathrm{ij}}=$

${\mathrm{FSd}}_{\mathrm{ij}}(v_x,v_y)\exp (-i2\mathrm{\&pi;}(v_x{\mathrm{mL}}_x(\frac{d_i-0.5}{D_x}-\frac{1}{2})+v_y{\mathrm{nL}}_y(\frac{d_j-0.5}{D_y}-\frac{1}{2}))),---\left(20\right)$

Wherein (v _x, v _y) be the coordinate system of angular spectrum, be expressed as follows:

v _x＝t ₁/mL _x, (21)

v _y＝t ₂/nL _y, (22)

After using and calculating angular spectrum that each mirror amplification matrix reaches objective plane and distribute with upper type, the angular spectrum that obtain objective plane after being added that then can each angular spectrum distributes distributes, as follows:

$T\arg \mathrm{etF}=\underset{i=1}{\overset{D_x}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{D_y}{\mathrm{\&Sigma;}}}T\arg \mathrm{et}{\mathrm{Fd}}_{\mathrm{ij}},---\left(23\right)$

Finally, obtain the field distribution of objective plane with fast Flourier inverse transform, the account form of same formula (18), is expressed as follows:

Target=IFFT(TargetF)。(24)

(3) two-period form Fresnel Transform

The field distribution that can use Fresnel Transform to calculate objective plane in the time that objective plane and image detecting device distance is enough long, S _mnin the air coordinates of each element correspondence be:

$x_{\mathrm{mn}}=t_1{B}_x-\frac{{\mathrm{mL}}_x}{2},---\left(25\right)$

$y_{\mathrm{mn}}=t_2{B}_y-\frac{{\mathrm{nL}}_y}{2},---\left(26\right)$

Wherein t ₁represent the t in coordinate matrix ₁row, t ₂represent the t in coordinate matrix ₂oK, B wherein _xand B _ybe respectively the picture element spacing of image detecting device in x and y direction.

In two-period form Fresnel Transform, first paragraph transmission is passed to intermediary's plane with Fresnel Transform, this intermediary's plane and S _mnat a distance of z _a, with thing z apart _b, the resolution magnification in final goal plane is z _bwith z _aratio, therefore by total distance z _oand target magnification (Mag), can calculate:

$z_a=\frac{z_0}{1+\mathrm{Mag}},---\left(27\right)$

$z_b=\frac{\mathrm{Mag}\&CenterDot;z_0}{1+\mathrm{Mag}},---\left(28\right)$

Now, be passed to the field distribution S in intermediary's plane _midcan be calculated by following mode:

$S_{\mathrm{mid}}=\mathrm{FFT}\left[S_{\mathrm{mn}}\exp \left(\frac{\mathrm{\&pi;i}}{\mathrm{\&lambda;}}\frac{x_{\mathrm{mn}}^2+y_{\mathrm{mn}}^2}{z_a}\right)\right]\exp \left(\frac{\mathrm{\&pi;i}}{\mathrm{\&lambda;}}\frac{x_{\mathrm{mid}}^2+y_{\mathrm{mid}}^2}{z_a}\right),---\left(29\right)$

Wherein (x _mid, y _mid) be the coordinate system of intermediary's plane, be expressed as follows:

$x_{\mathrm{mid}}=\frac{t_1{\mathrm{\&lambda;z}}_a}{{\mathrm{mL}}_x}-\frac{{\mathrm{\&lambda;z}}_a}{{2B}_x},---\left(30\right)$

$y_{\mathrm{mid}}=\frac{t_2{\mathrm{\&lambda;z}}_a}{{\mathrm{nL}}_y}-\frac{{\mathrm{\&lambda;z}}_a}{{2B}_y},---\left(31\right)$

In two-period form Fresnel Transform, second segment transmission is to be passed to objective plane by intermediary's plane, and the field distribution of objective plane is expressed as follows:

$T\arg \mathrm{et}=\mathrm{FFT}\left(S_{\mathrm{mid}}\exp \left(\frac{\mathrm{\&pi;i}}{\mathrm{\&lambda;}}\frac{x_{\mathrm{mid}}^2+y_{\mathrm{mid}}^2}{z_b}\right)\right)\exp \left(\frac{\mathrm{\&pi;i}}{\mathrm{\&lambda;}}\frac{{\mathrm{\&xi;}}^2+{\mathrm{\&eta;}}^2}{z_b}\right),---\left(32\right)$

The coordinate system that wherein (ξ, η) is objective plane, by adjusting z _awith z _bratio can adjust the resolution of image, be expressed as follows:

$\mathrm{\&xi;}=\frac{z_b}{z_a}{x}_{\mathrm{mn}},---\left(33\right)$

(4) use Rayleigh-Sommfeld direct integral

Use Rayleigh-Sommfeld Diffracion Theory, wherein in Smn, the air coordinates of each element correspondence is as follows:

$x_{\mathrm{mn}}=t_1{B}_x-\frac{{\mathrm{mL}}_x}{2},---\left(35\right)$

z _mn＝0, (37)

The coordinate that makes objective plane is (ξ, η, z _o), can obtain objective plane and S _mnin the distance r of each picture element be

$r=\sqrt{{(x_{\mathrm{mn}}-\mathrm{\&xi;})}^2+{(y_{\mathrm{mn}}-\mathrm{\&eta;})}^2+{(z_{\mathrm{mn}}-z_0)}^2},---\left(38\right)$

Above formula substitution Rayleigh-Sommfeld Diffracion Theory is carried out to integration, and the field distribution that obtains objective plane is:

$T\arg \mathrm{et}={\&Integral;\&Integral;S}_{\mathrm{mn}}\frac{\exp \left(\mathrm{jkr}\right)}{r}\frac{z_0}{r}{\mathrm{dx}}_{\mathrm{mn}}{\mathrm{dy}}_{\mathrm{mn}}---\left(39\right)$

When the tilt angle theta of the light pipe sidewall angle of perpendicular bisector (with) equals 0 while spending (as shown in FIG. 1A and 1B), the matrix U of amplification _ijwith original data matrix U ₀₀be arranged on the same plane of space.If the tilt angle theta of light pipe sidewall is not equal to 0 degree (as shown in Fig. 5 A to Fig. 5 D), though the mode of available mirror is by this data matrix expansion, the matrix U of its amplification _ijnot can with original data matrix U ₀₀position in space on same plane, the matrix U of now mirror amplification _ijmust in space, rotate 2 θ angles.

Due to the matrix U of mirror amplification _ijwith original matrix U ₀₀not in same plane, cannot extrapolate in aforementioned mode the Electric Field Distribution of objective plane, two kinds of settling modes below the account form of therefore transmitting in space need be used: (1) Rayleigh-Sommfeld direct integral; And (2) fast fourier transform solution of light propagation between rotation and displacement plane each other in free space.

(1) Rayleigh-Sommfeld direct integral

Use Rayleigh-Sommfeld Diffracion Theory to calculate each Target _ij, then it is added each other, with Target ₁₀for example, U ₁₀on the air coordinates of each element correspondence as follows:

$x_{10}=t_1{B}_x\cos \left(2\mathrm{\&theta;}\right)+\frac{L_x}{2},---\left(40\right)$

$y_{10}=t_2{B}_y-\frac{L_y}{2},---\left(41\right)$

z ₁₀＝t ₁B _xsin(2θ), (42)

Wherein t ₁represent the t in coordinate matrix ₁row, t ₂represent the t in coordinate matrix ₂oK, B wherein _xand B _ybe respectively the picture element spacing of image detecting device in x and y direction.With this air coordinates, can calculate and transmit the so far reference light R of position ₁₀, then use the conjugate beam of reference light be multiplied by U ₁₀, obtain S ₁₀matrix, is expressed as follows:

$S_{10}=R_{10}^{*}{U}_{10}---\left(43\right)$

Perpendicular to S ₁₀the vector of unit length of matrix plane is:

$\stackrel{\&RightArrow;}{n}=(-\sin \left(2\mathrm{\&theta;}\right),0,\cos \left(2\mathrm{\&theta;}\right)),---\left(44\right)$

The coordinate of hypothetical target plane is (ξ, η, z _o), S ₁₀in the vector of each element directed objective plane specified point be:

$\stackrel{\&RightArrow;}{r_{10}}=(\mathrm{\&xi;}-x_{10},\mathrm{\&eta;}-y_{10},z_0-z_{10}),---\left(45\right)$

Objective plane and S ₁₀in the distance r of each element ₀₁₀for | r ₀₁₀|, by S ₁₀bring Rayleigh-Sommfeld Diffracion Theory into and can calculate its corresponding Target ₁₀, as follows:

${T\arg \mathrm{et}}_{10}=\&Integral;\&Integral;\&Integral;S_{10}\frac{\exp \left({\mathrm{jkr}}_{10}\right)}{r_{10}}\frac{\stackrel{\&RightArrow;}{r_{10}}\&CenterDot;\stackrel{\&RightArrow;}{n}}{r_{10}\left|n\right|}{\mathrm{dx}}_{10}{\mathrm{dy}}_{10}{\mathrm{dz}}_{10},$

$={\&Integral;\&Integral;S}_{10}\frac{\exp \left({\mathrm{jkr}}_{10}\right)}{r_{10}}\frac{\stackrel{\&RightArrow;}{r_{10}}\&CenterDot;\stackrel{\&RightArrow;}{n}}{r_{10}\left|n\right|}{\mathrm{dX}}_{10}{\mathrm{dY}}_{10}$

Calculate in the same manner each matrix S _ijobjective plane field distribution (the Target of correspondence _ij) after, then the field distribution that various algorithms are obtained is added together, and can obtain the field distribution of objective plane, as follows:

$T\arg \mathrm{et}=\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{T\arg \mathrm{et}}_{\mathrm{ij}},---\left(47\right)$

The speed of above-mentioned account form depends on the number of sampling of objective plane, in the time that number of sampling is too much,

Computer computing velocity will reduce, and one of mode of ameliorating is to use to calculate S _mnany mode extrapolate S ₀₀corresponding Target ₀₀, re-use Rayleigh-Sommfeld Diffracion Theory and calculate Target ₀₀target in addition _ij, then it is added up each other.

(2) the fast fourier transform solution of light propagation between rotation and displacement plane each other in free space

First, use angular spectrum circulation way calculates the angular spectrum distribution that is passed to objective plane, as follows:

FS ₁₀＝FFT(S ₁₀)exp(i2πz ₁₀/λ(1-α ²-β ²) ^0.5), (48)

Wherein transmitting distance is:

$z_{10}=(\frac{z_0}{\cos \left(2\mathrm{\&theta;}\right)}-\frac{L_x\tan \left(2\mathrm{\&theta;}\right)}{2}),---\left(49\right)$

Then, use coordinate rotation matrix that angular spectrum is carried out to coordinate conversion, as follows:

$\left[\begin{array}{c}{v}_{x0}^{\&prime;}\\ v_{y0}^{\&prime;}\\ v_{z0}^{\&prime;}\end{array}\right]={\mathrm{Rot}}_{10}\left[\begin{array}{c}{v}_x\\ v_y\\ v_z\end{array}\right],---\left(50\right)$

Wherein rotation matrix is:

${\mathrm{Rot}}_{10}=\left[\begin{array}{ccc}\cos 2\mathrm{\&theta;}& 0& -\sin 2\mathrm{\&theta;}\\ 0& 1& 0\\ \sin 2\mathrm{\&theta;}& 0& \cos 2\mathrm{\&theta;}\end{array}\right],---\left(51\right)$

By the field distribution FS in former angular spectrum coordinate ₁₀(v _x, v _y, v _z) mapping (mapping) is to the field distribution RFS in new coordinate ₁₀(v _x0', v _y0', v _z0'), if wherein there is v _z0' be less than zero or v _z0' there is imaginary part,

v _z0’<0， (52)

Im[v _z0’]≠0， (53)

Making its corresponding field distribution is zero.Then, the angular spectrum after conversion is distributed and maps in the angular spectrum coordinate being equally spaced and obtain new RFS with interpolation method ₁₀(v _x', v _y', v _z').

Then, the heart among spectrum distribution is moved to the center of objective plane, displacement is:

${\mathrm{\&Delta;\&xi;}}_{10}=\frac{L_x\cos \left(2\mathrm{\&theta;}\right)}{2}+L_x-\tan \left(2\mathrm{\&theta;}\right)[z_0-\frac{L_x\sin \left(2\mathrm{\&theta;}\right)}{2}],---\left(54\right)$

Can calculate Target ₁₀spectrum distribution be:

TargetF ₁₀＝RSF(v′ _x，v′ _y,v′ _z)exp(-i2πv′ _xΔξ ₁₀)， (55)

After using and calculating angular spectrum that each mirror amplification matrix reaches object plane and distribute with upper type, then the angular spectrum that obtains thing after being added that will each angular spectrum distributes distributes, as follows:

$T\arg \mathrm{etF}=\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{T\arg \mathrm{etF}}_{\mathrm{ij}},---\left(56\right)$

Finally, obtain the field distribution of objective plane with fast Flourier inverse transform, as follows:

Target=IFFT(TargetF)。(57)

In sum; although the present invention discloses as above with preferred embodiment; so it is not in order to limit the present invention; persond having ordinary knowledge in the technical field of the present invention; without departing from the spirit and scope of the invention; when doing various changes and retouching, therefore the present invention's protection domain when depending on after the attached claim person of defining be as the criterion.

Claims (20)

1. a digital holographic imaging systems, in order to photographic subjects thing, and with hologram data storage, is characterized in that, described system comprises:

Signal light, it forms after irradiating this object by light source;

Image detecting device, in order to record this signal interference of light striped; And

Light pipe, is arranged in the light path of this signal light and between this object and this image detecting device, and wherein this light pipe has reflecting surface, and the signal light of part is laggard to this image detecting device via the reflecting surface reflection of this light pipe.

2. digital holographic imaging systems according to claim 1, is characterized in that: the horizontal tangent plane of this light pipe is rectangle.

3. digital holographic imaging systems according to claim 1, is characterized in that: the sidewall of this light pipe is arranged to.

4. digital holographic imaging systems according to claim 3, is characterized in that: the sidewall of this light pipe and the angle of perpendicular bisector are between-70 ° to+70 °.

5. digital holographic imaging systems according to claim 1, is characterized in that: this signal is only mutually interfered and produces this interference fringe with the light that this light source sends.

6. digital holographic imaging systems according to claim 1, is characterized in that: the light source that irradiates this object is divergent spherical wave.

7. digital holographic imaging systems according to claim 1, is characterized in that: this signal light and reference light are mutually interfered and produced this interference fringe.

8. digital holographic imaging systems according to claim 7, it is characterized in that: described digital holographic imaging systems more comprises a spectroscope, this light source is divided into twice light beam through this spectroscope, and wherein one light beam, as this reference light, forms this signal light after another this object of road light beam irradiates.

9. a numerical reconstruction method for hologram, is applicable to be provided with the optics framework of light pipe between the object taken and image detecting device, it is characterized in that, described method comprises step:

Utilize the interference image of image detecting device acquisition object;

Be data matrix by this interference video conversion;

Repeatedly mirror is carried out on multiple limits along this data matrix, to expand into a new data matrix; And

This new data matrix is carried out to numerical reconstruction, to obtain the field distribution of this object place plane.

10. the numerical reconstruction method of hologram according to claim 9, is characterized in that: in utilizing this image detecting device to capture in the step of interference image of this object, comprise:

Same picture is carried out to the exposure of several times different time; And

Several captured images are recombinated, to draw the interference image of this object.

The numerical reconstruction method of 11. hologram according to claim 9, it is characterized in that: if this object is all positioned in the same plane parallel with this image detecting device surface with the light source of reference light, and this reference light is divergent spherical wave, use fast fourier transform to calculate to this new data matrix, to obtain the field distribution of this object place plane.

The numerical reconstruction method of 12. hologram according to claim 11, it is characterized in that: if the light source of this object and this reference light is at a distance of a segment distance, this new data matrix is multiplied by a phase term and re-uses fast fourier transform and calculate, to obtain the field distribution of this object place plane.

The numerical reconstruction method of 13. hologram according to claim 9, it is characterized in that: in the process of field distribution of calculating this object place plane, use the account form of angular spectrum propagation to carry out numerical reconstruction to this new data matrix, to obtain the field distribution of this object place plane.

The numerical reconstruction method of 14. hologram according to claim 9, is characterized in that: in the process of field distribution of calculating this object place plane, initial plane is carried out to interpolation expansion to carry out the estimation in the transmission of space.

The numerical reconstruction method of 15. hologram according to claim 14, is characterized in that: in the process of field distribution of calculating this object place plane, initial plane is carried out to interpolation expansion and be cut into aliquot-sized to carry out the estimation in the transmission of space again.

The numerical reconstruction method of 16. hologram according to claim 9, is characterized in that: in the process of field distribution of calculating this object place plane, use two-period form Fresnel to change to carry out the estimation in the transmission of space.

The numerical reconstruction method of 17. hologram according to claim 9, is characterized in that: in the process of field distribution of calculating this object place plane, use Rayleigh-Suo Mofeier formula to carry out the estimation in the transmission of space.

The numerical reconstruction method of 18. hologram according to claim 9, it is characterized in that: if the angle of this light pipe sidewall and perpendicular bisector is θ, it is not equal to 0 degree,, one of them limit of this data matrix is carried out in the step of mirror, this data matrix is rotated to 2 θ angles in space.

The numerical reconstruction method of 19. hologram according to claim 9, is characterized in that: in the process of field distribution of calculating this object place plane, use Rayleigh-Suo Mofeier formula to carry out the estimation in the transmission of space.

The numerical reconstruction method of 20. hologram according to claim 9, it is characterized in that: calculating in the process of field distribution of this object place plane, use in free space the fast fourier transform of the light propagation between rotation each other and displacement plane to solve.