CN105158894A - Lens-free phase micro-tomography device based on color LED array illumination and image reconstruction method - Google Patents

Abstract

The invention discloses a lens-free phase micro-tomography device based on color LED array illumination and an image reconstruction method thereof. The lens-free phase micro-tomography device comprises an LED array, a sample stage and a camera which are sequentially arranged to form an imaging system, wherein the LED array is placed at the bottom of the whole imaging system, a photosensitive surface of a central LED pixel of the LED array is placed on an optical axis of the whole imaging system, and image reconstruction is achieved by using the lens-free phase micro-tomography device. Without the aid of any imaging optical elements, the lens-free phase micro-tomography device simplifies system structure, reduces microscope size, and greatly reduces cost; the lens-free phase micro-tomography device can obtain refractive index tomography images of samples, thereby achieving marker-free ''true three-dimensional imaging'' of biological cell samples, and significantly improving flexibility and versatility of the microscope.

Description

Based on color LED matrix lamp without lens phase micro tomography device and image reconstructing method

Technical field

The invention belongs to optical microphotograph imaging technique, particularly a kind of based on color LED matrix lamp without lens phase micro tomography device and image reconstructing method.

Background technology

Optical microscope, since sixties the 17th century is used to biomedical observation, has been the core instrument of biomedical examination and analysb always.The appearance of phasecontrast microscope, differential interference phase-contrast microscope, fluorescent microscope, laser confocal microscope greatly facilitates the raising of life science level, they with higher resolution and image quality for medical diagnosis on disease, the early diagnosis of especially great malignant disease provides strong imaging evidence, becomes important tool indispensable in current clinical medicine.But these microscopic systems still based on the imaging mode of " being gained as seen ", do not make full use of the power of the modern signal processing equipment such as computing machine.What constantly reform along with function and performance in addition is that microscopic system itself is also increasingly expensive, heavy, complicated and be difficult to safeguard.Can under the prerequisite ensureing its image quality if just think, realize the volume miniaturization of microscopy apparatus, with low costization, easy and simple to handleization, greatly must reduce the threshold that medical treatment detects, for the area that resources supplIes is limited provides quick, cheap care diagnostic (point-of-caretest, POCT) instrument, early diagnosis that is anxious for poverty-stricken area, critically ill patient provides advantage with timely treatment.

Realize the volume miniaturization of microscopy apparatus, with low costization, easy and simple to handleization critical path be " without lens " (lens-free) and " unmarked " (label-free)." without lens " are as the term suggests be exactly do not adopt traditional optical lens to imaging of samples.As everyone knows, the most expensive in microscope parts are exactly take microcobjective as the optical element of representative.If illumination and imaging optical path can be simplified, abandon expensive heavy optical lens and realize without lens micro-imaging, must greatly reduce microscopical cost, simultaneously for the miniaturization of total system, lightweight provide more possibilities." unmarked " refers to and does not adopt any dyeing pre-service to sample, and relies on itself absorbed inside or refractive index difference (phase shift caused) to carry out imaging, and this can simplify the preparation process of sample greatly.Unmarked imaging is otherwise known as noninvasive imaging or non-intrusion type (invasive) imaging, because which obviating adverse effect that conventional fluorescent probe produces cytoactive (as the specificity of fluorescence probe, the photobleaching that strong exciting light causes and phototoxicity, and gene Pignus pignoris infects).For the undyed biological cell sample of major part, because of its weak absorbing at visible light wave range (water white transparency), so must by means of Phase imaging.Ze Nike phase contrast microtechnic and differential interference phase-contrast microtechnic are unmarked (qualitative) phase imaging method the most classical, but they cannot provide quantitative phase information, thus be not suitable for standardized analysis and diagnosis (not bright pine. phasecontrast microscope and interference microscope [M] Science Press, 1966.).By contrast, quantitative phase imaging technique can provide the quantitative phase determined by sample physical thickness and specific refractivity information due to it, has become unmarked micro imaging method ideal at present.Information optics, holography and to calculate the fast development of image optics be provide a feasible solution without lens and unmarked imaging in recent years: once the quantitative phase information of light field can be obtained, just can carry out the anti-diffraction of numerical value to light wave fields in a computer, realize " digital refocusing ", and without the need to any imaging len.In order to obtain quantitative phase information, method the most classical is exactly interference effect (as interfered micro-and the Digital holographic microscopy) (Ma Lihong by means of light wave, Wang Hui, Jin Hongzhen, Deng. the experimental study [J] of Digital holographic microscopy quantitative phase imaging. Chinese laser, 2012,39 (3): 209-215.).Though this mode eliminates imaging len, additionally introduce costliness, heavy LASER Light Source, thus do not have volume and the cost of effective reduction system.In addition interferometric method itself is to the rigors of measurement environment, and the speckle noise that high coherence light source is introduced also shows that it is not realize the ideal style without lens micro-imaging.

Summary of the invention

The object of the present invention is to provide a kind of based on color LED matrix lamp without lens phase micro tomography device and image reconstructing method thereof, not by means of any optical element, and carried out the three-dimensional chromatography micro-image of reconstruction of objects by the mode of post-processed.

The technical solution realizing the object of the invention is: a kind of based on color LED matrix lamp without lens phase micro tomography device, comprise the LED array, sample stage, the camera formation imaging system that set gradually, this LED array is placed in the bottom of whole imaging system, and the photosurface of the most central LED pixel of LED array is positioned on the optical axis of whole imaging system.

Based on the image reconstructing method realized without lens phase micro tomography device of color LED matrix lamp, step is as follows:

Step one: image acquisition, LED array, as the light source without lens microscope, lights wherein each LED pixel in turn, and the illuminating color of each LED pixel is respectively red/green/indigo plant lights successively, irradiates the image that collected by camera after sample is corresponding;

Step 2: for each LED pixel or each light angle, employing solves light intensity transmission equation and realizes phase recovery;

Step 3: by the plane of delineation COMPLEX AMPLITUDE U obtained under each LED pixel obtained in step 2 or each light angle _zm(x, y), m=1,2 ..., M is mapped in the three-dimensional frequency spectrum of thing function;

Step 4: adopt the method for positive constraint iteration to recover the frequency spectrum of disappearance, after iteration completes, the three-dimensional article function f finally obtained _n(x, y, z) is the refractive index tomographic map into object under test.

The present invention compared with prior art, its remarkable advantage: (1) is not such as, by means of any imaging optic element, microcobjective, tube lens etc.; Thus simplied system structure, reduce microscope volume, greatly reduce costs.(2) digital focus of sample can be realized flexibly, namely " first take pictures and focus on afterwards ", without the need to the mechanical condition function of complexity.(3) the refractive index tomographic map of sample can be obtained, thus realize unmarked " the true three-dimensional imaging " of biological cell sample, thus significantly improve microscopical dirigibility with multi-functional.Due to this three large advantage, this micro imaging method is expected to be used widely in various fields such as botany, zoology, cell biology, semiconductor, material science, nanometer technology, life science, medical diagnosiss.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Accompanying drawing explanation

Fig. 1 be the present invention is based on color LED matrix lamp without lens phase micro tomography schematic diagram of device.

Fig. 2 be the present invention is based on color LED matrix lamp without lens phase micro tomography image reconstructing method process flow diagram.

Fig. 3 is the refractive index tomographic map (x, y plane) obtained Parascaris equorum embryonated egg section reconstruct without lens phase micro tomography device that the present invention is based on color LED matrix lamp.

Fig. 4 is the refractive index tomographic map (x, z-plane) obtained Parascaris equorum embryonated egg section reconstruct without lens phase micro tomography device that the present invention is based on color LED matrix lamp

Fig. 5 is the refractive index chromatography three-dimensional visualization result obtained Parascaris equorum embryonated egg section reconstruct without lens phase micro tomography device that the present invention is based on color LED matrix lamp.

Embodiment

Composition graphs 1, the present invention is based on comprising without lens phase micro tomography device the LED array 1, sample stage 2, the camera 3 that set gradually and forming imaging system of color LED matrix lamp, this LED array 1 is placed in the bottom of whole imaging system, and the photosurface of the most central LED pixel of LED array 1 is positioned on the optical axis of whole imaging system.The axial distance L of sample stage 2 and LED array 1 is generally between 20mm-100mm.The distance z of camera 3 and sample stage 2 generally should much smaller than L, between 5 μm of-2mm.

LED array 1 is as microscopical lighting source, and it is redgreenblue LED array, and its typical wavelengths is ruddiness λ _r=635nm, green glow λ _g=525nm and blue light λ _b=475nm.And the center of LED array 1 is on the optical axis of whole imaging system.In general, the LED number comprised in LED array 1 should more than 8 × 8, and between each LED pixel, center distance representative value is 3-10mm, the photosurface typical sizes 50-200 μm of each LED pixel.These parameters, the center distance comprised between the size of LED pixel and brightness, the wavelength of illumination and LED pixel can be known from producer's handbook or be obtained by measurement.In LED array 1, each LED pixel is all by realizing lighting separately, and its color must controlled (it be red/green/blue for namely can switching illuminating color at any time, and three illumination intensity will be controlled to strict conformance).This need adopt the hardware driving circuit matched, the specific implementation of hardware driving circuit has had many mature technologies, master controller can adopt (but being not limited to) single-chip microcomputer, ARM or programmable logic device (PLD) etc., concrete methods of realizing can reference: (Guo Baozeng, Deng Chun seedling. the LED display control system based on FPGA designs [J]. liquid crystal and display, 2010,25 (3): 424-428.)

The effect of sample stage 2 is carrying samples, and the axial distance L of itself and LED array 1 is generally between 20mm-100mm.Its best lateral orientation is adjustable, to make microscope can observe the zones of different of sample.The effect of camera 3 is taken through the image formed after sample light diffraction, and it can be colored or gray scale camera.The distance z of itself and sample stage 2 generally should much smaller than L, between 5 μm of-2mm (after parameter z, extended meeting is used here: the photosurface of z and camera 3 and the distance of sample stage 2).

Composition graphs 2, the present invention is based on color LED matrix lamp without lens phase micro tomography image reconstructing method, its step is as follows:

Step one: image acquisition.LED array 1, as the light source without lens microscope, lights wherein each LED pixel in turn, and the illuminating color of each LED pixel is respectively red/green/indigo plant lights successively, and after irradiating sample, camera 3 gathers corresponding image.If comprise M LED in whole LED array altogether, take M × 3 width image so altogether, be denoted as I _zRm(x, y), I _zGm(x, y), I _zBm(x, y), m=1,2 ..., M, the wherein two-dimensional coordinate of (x, y) representative image plane, the image of subscript R, corresponding red/green/blue illumination wavelengths of G, B difference, subscript m represents the sequence number m=1 of LED pixel, and 2 ..., M.Wherein descend target z to represent this physical quantity and be positioned at the plane of delineation.It claims I below _zRm(x, y), I _zGm(x, y), I _zBmthe plane of delineation R, G, B component light distribution that (x, y) is corresponding m LED pixel.Because the locus of each LED pixel is different, the light angle corresponding to it is also different.

Step 2: for each LED pixel (or each light angle), employing solves light intensity transmission equation and realizes phase recovery.In this step, for each LED pixel in LED array 1, by the plane of delineation R, G, B component light distribution I of LED pixel _zRm(x, y), I _zGm(x, y), I _zBm(x, y) reconstructs corresponding PHASE DISTRIBUTION.Owing to comprising M LED in whole LED array altogether, this step will be carried out for M LED in fact respectively, namely (for each LED pixel, employing solves light intensity transmission equation, and to realize Phase Retrieve Algorithm completely the same, only has input picture to adopt corresponding I to amount to M time _zRm(x, y), I _zGm(x, y), I _zBm(x, y), m=1,2 ..., M).

The detailed process of this step is:

The first step: by I _zRm(x, y), I _zGm(x, y), I _zBm(x, y) three width image carry out registration, namely ensure their perfect alignment and measure-alike.Concrete registration Algorithm is not the key content of this patent, can adopt as cross-correlation, the existing techniques in realizing such as Fourier phase correlation method, here subscript m represents that this operation is carried out respectively for M LED, m=1,2 ... namely M amounts to M time, the image of subscript R, corresponding red/green/blue illumination wavelengths of G, B difference.

Second step: converse I _zRm(x, y), I _zGm(x, y), I _zBmthe plane of delineation corresponding to (x, y) and the equivalent distances between object plane:

z _G＝z

$z_R=\frac{{\mathrm{\λ}}_R}{{\mathrm{\λ}}_G}{z}_G$

$z_B=\frac{{\mathrm{\λ}}_B}{{\mathrm{\λ}}_G}{z}_G$

Wherein z is the axial distance on sample range sensor surface.

3rd step: by the I after second step registration _zRm(x, y), I _zGm(x, y), I _zBm(x, y) three width image carry out diff, obtain the axial differential of light intensity

${\[\frac{\∂I}{\∂z}\]}_m=\frac{{\left({\mathrm{\Δz}}_B\right)}^2(I_{zRm}-I_{zGm})-{\left({\mathrm{\Δz}}_R\right)}^2(I_{zBm}-I_{zGm})}{{\mathrm{\Δz}}_R{\mathrm{\Δz}}_B({\mathrm{\Δz}}_B-{\mathrm{\Δz}}_R)},$

Wherein Δ z _r=z _r-z _g, Δ z _b=z _b-z _g

4th step: by the axial differential of light intensity with plot of light intensity as I (x, y)=I _zGm(x, y), by solving light intensity transmission equation, obtains plane of delineation phase _zm(x, y),

${\mathrm{\φ}}_{zm}(x,y)=-k{\▿}^{-2}\▿\·\[I^{-1}(x,y)\▿{\▿}^{-2}{\[\frac{\∂I(x,y)}{\∂z}\]}_m\]$

In formula inverse Laplace's operation symbol, for gradient operator, be vector dot, k is wave number, with operational symbol is all realized by Fourier transform, namely

${\▿}^{-2}\{\·\}=F^{-1}\left\{F\right\{\·\left\}\frac{1}{-4{\mathrm{\π}}^2(u^2+v^2)}\right\}$

$\▿\{\·\}=F^{-1}\left\{j2\mathrm{\π}uF\right\{\·\},j2\mathrm{\π}vF\{\·\left\}\right\}$

Wherein F represents Fourier transform, and (u, v) is the frequency domain coordinates corresponding with volume coordinate (x, y), and j is imaginary unit.Known image plane phase distribution phi _m(x, y), plane of delineation COMPLEX AMPLITUDE U _zm(x, y) just can obtain by down

$U_{zm}(x,y)=\sqrt{I_{zGm}(x,y)}\exp \[{\mathrm{j\φ}}_{zm}(x,y)\]$

5th step: plane of delineation COMPLEX AMPLITUDE U _zmthe distance of (x, y) " anti-spread "-z, thus just got back on the object plane at the place of object own, obtain the COMPLEX AMPLITUDE U on object plane _m(x, y)

U _zm(x,y)＝F ^-1{F{U _zm(x,y)}H _-z(u,v)},

In formula, Fourier transform and inverse transformation are referred to as F and F respectively ^-1, (u, v) representative is relative to the frequency domain coordinates of (x, y); H _-z(u, v) is angular spectrum transition function, and its form is

$H_{-z}(u,v)=\exp \[-j\frac{2\mathrm{\π}z}{{\mathrm{\λ}}_B}\sqrt{1-{\left(\mathrm{\λ}u\right)}^2-{\left(\mathrm{\λ}v\right)}^2}\]$

λ in formula _bfor the blue optical wavelength that throws light on, j is imaginary unit, here H _-z-z in subscript represents the object plane at the distance arrival place of object of anti-spread-z own.

Step 3: by the plane of delineation COMPLEX AMPLITUDE U obtained under each LED pixel (or each light angle) obtained in step 2 _zm(x, y), m=1,2 ..., M is mapped in the three-dimensional frequency spectrum of thing function.This step also can be subdivided into:

The first step: under Rytov is approximate, by the plane of delineation COMPLEX AMPLITUDE U obtained under each LED pixel (or each light angle) obtained in step 2 _zm(x, y), m=1,2 ..., M is expressed as the approximate lower scattered field of Rytov

$U^s{zm}_{}(x,y)=U_{zm}(x,y)ln\left(\frac{U_{zm}(x,y)}{mean2\left\{\right|U_{zm}(x,y)\left|\right\}}\right)$

Wherein the mean value of image is got in mean2{} representative, the approximate lower scattered field U of Rytov _zmits two-dimensional Fourier transform of (x, y) is denoted as { U ^s _zm(x, y) }

Second step: the approximate lower scattered field two-dimensional Fourier transform of the Rytov obtained under each LED pixel (or each light angle) obtained in the first step be mapped in the three-dimensional frequency spectrum of thing function according to the following rules:

$\tilde{F}(K_x,K_y,K_z)=\frac{{\mathrm{ik}}_z}{\mathrm{\π}j}{\tilde{U}}_{zm}^s(u,v,z=0)$

In formula the three-dimensional Fourier transform (three-dimensional frequency spectrum) of thing function F, (K _x, K _y, K _z) be the spatial frequency of object; The spatial frequency (u, v) of itself and scattered field and k _zbetween pass be

K _x＝u-u _x0,

K _y＝v-u _y0,

K _z＝k _z

Wherein u _x0with u _y0for the spatial frequency of illumination light.After this step, the three-dimensional frequency spectrum of thing function be filled, but due to LED number of pixels (light angle number) limited, still have subregion to lack.

Step 4: adopt positive constraint iteration method recover disappearance frequency spectrum: according to priori, when known sample refractive index be greater than around medium refractive index, thing function should f (x, y, z) should perseverance just be.Therefore adopt the method for following positive constraint iteration to recover the frequency spectrum of disappearance:

The first step: the three-dimensional frequency spectrum of thing function in initialization step three middle absent region is 0, is denoted by here the n comprised in subscript represents iterations, here initialization procedure n=0, is referred to as the three-dimensional frequency spectrum of revised thing function.

Second step: by the three-dimensional frequency spectrum of revised thing function ask three-dimensional inverse Fourier transform, obtain three-dimensional article function f _n(x, y, z)

$f_n(x,y,z)=F^{-1}\left\{{\tilde{F}}_n^{\′}(K_x,K_y,K_z)\right\}$

3rd step: by three-dimensional article function f _nthe element assignment being less than 0 in (x, y, z) is 0, obtain revised three-dimensional article function f ' _n(x, y, z).

4th step: by revised three-dimensional article function f ' _n(x, y, z) remaps to frequency domain after carrying out three-dimensional Fourier transform, obtains the three-dimensional frequency spectrum of thing function

${\tilde{F}}_n(K_x,K_y,K_z)=F\left\{f_n(x,y,z)\right\}$

5th step: by the three-dimensional frequency spectrum of original function the three-dimensional frequency spectrum of the thing function that middle absent region obtains by the 4th step corresponding region replaces.This completes the iterative process of one bout, and make n ← n+1, and get back to second step continue execution go down.Generally speaking, iteration is performed 20 times to 50 times by the second to the five step.

After iteration completes, the three-dimensional article function f finally obtained _n(x, y, z) is the refractive index tomographic map of object under test.

In order to verify the imaging capability without lens microscope that the present invention is based on LED light source, we carry out without lens imaging to the section of Parascaris equorum embryonated egg.Fig. 3 reconstructs the refractive index tomographic map (x, y plane) obtained.The details of sample is high-visible, and its index distribution is between 1.34 to 1.42.Fig. 4 is the x of refractive index tomographic map, z-plane, can find out because sample is one deck slice, so cell is almost distributed between skim.Phase place chromatography lateral resolution is about about 3um, and axial resolution is at about 5um.Fig. 5 is refractive index chromatography three-dimensional visualization result.This result indicates the present invention can not realize high-quality refractive index tomographic map by any optical imaging lens, thus realizes unmarked " true three-dimensional imaging " micro-imaging of biological cell sample.

Claims (8)

1. one kind based on color LED matrix lamp without lens phase micro tomography device, it is characterized in that comprising the LED array (1), sample stage (2), camera (3) the formation imaging system that set gradually, this LED array (1) is placed in the bottom of whole imaging system, and the photosurface of the most central LED pixel of LED array (1) is positioned on the optical axis of whole imaging system.

2. according to claim 1 based on color LED matrix lamp without lens phase micro tomography device, it is characterized in that sample stage (2) is 20mm-100mm with the axial distance L of LED array (1), camera (3) is 5 μm of-2mm with the distance z of sample stage (2).

3. according to claim 1 based on color LED matrix lamp without lens phase micro tomography device, it is characterized in that LED array (1) is as microscopical lighting source, it is redgreenblue LED array, and wavelength is ruddiness λ _r=635nm, green glow λ _g=525nm and blue light λ _b=475nm.

4., based on the image reconstructing method realized without lens phase micro tomography device of color LED matrix lamp, it is characterized in that step is as follows:

Step one: image acquisition, LED array (1) is as the light source without lens microscope, light wherein each LED pixel in turn, and the illuminating color of each LED pixel is respectively red/green/indigo plant lights successively, after irradiating sample, camera (3) gathers corresponding image;

Step 2: for each LED pixel or each light angle, employing solves light intensity transmission equation and realizes phase recovery;

Step 3: by the plane of delineation COMPLEX AMPLITUDE U obtained under each LED pixel obtained in step 2 or each light angle _zm(x, y), m=1,2 ..., M is mapped in the three-dimensional frequency spectrum of thing function;

Step 4: adopt the method for positive constraint iteration to recover the frequency spectrum of disappearance, after iteration completes, the three-dimensional article function f finally obtained _n(x, y, z) is the refractive index tomographic map into object under test.

5. the image reconstructing method realized without lens phase micro tomography device based on color LED matrix lamp according to claim 4, is characterized in that in step one, if comprise M LED in whole LED array altogether, takes M × 3 width image so altogether, be denoted as I _zRm(x, y), I _zGm(x, y), I _zBm(x, y), m=1,2 ..., M, the wherein two-dimensional coordinate of (x, y) representative image plane, the image of subscript R, corresponding red/green/blue illumination wavelengths of G, B difference, m represents the sequence number m=1 of LED pixel, and 2 ... M, z represents this physical quantity and is positioned at the plane of delineation, i.e. the photosurface of camera 3 and the distance of sample stage 2, I _zRm(x, y), I _zGm(x, y), I _zBmthe plane of delineation R, G, B component light distribution that (x, y) is corresponding m LED pixel.

6. the image reconstructing method realized without lens phase micro tomography device based on color LED matrix lamp according to claim 4, it is characterized in that in step 2, for each LED pixel in LED array (1), by the plane of delineation R, G, B component light distribution I of LED pixel _zRm(x, y), I _zGm(x, y), I _zBm(x, y) reconstructs corresponding PHASE DISTRIBUTION, and detailed process is:

The first step: by I _zRm(x, y), I _zGm(x, y), I _zBm(x, y) three width image carry out registration, namely ensure their perfect alignment and measure-alike, m represents that this operation is carried out respectively for M LED, m=1,2 ..., namely M amounts to M time, the image of subscript R, corresponding red/green/blue illumination wavelengths of G, B difference;

Second step: converse I _zRm(x, y), I _zGm(x, y), I _zBmthe plane of delineation corresponding to (x, y) and the equivalent distances between object plane:

z _G＝z

$z_R=\frac{{\mathrm{\λ}}_R}{{\mathrm{\λ}}_G}{z}_G$

$z_B=\frac{{\mathrm{\λ}}_B}{{\mathrm{\λ}}_G}{z}_G$

Wherein z is the axial distance on sample range sensor surface;

3rd step: by the I after second step registration _zRm(x, y), I _zGm(x, y), I _zBm(x, y) three width image carry out diff, obtain the axial differential of light intensity

${\[\frac{\∂I}{\∂z}\]}_m=\frac{{\left({\mathrm{\Δz}}_B\right)}^2(I_{zRm}-I_{zGm})-{\left({\mathrm{\Δz}}_R\right)}^2(I_{zBm}-I_{zGm})}{{\mathrm{\Δz}}_R{\mathrm{\Δz}}_B({\mathrm{\Δz}}_B-{\mathrm{\Δz}}_R)}$

Wherein Δ z _r=z _r-z _g, Δ z _b=z _b-z _g;

4th step: by the axial differential of light intensity with plot of light intensity as I (x, y)=I _zGm(x, y), by solving light intensity transmission equation, obtains plane of delineation phase _zm(x, y),

${\mathrm{\φ}}_{zm}(x,y)=-k{\▿}^{-2}\▿\·\[I^{-1}(x,y)\▿{\▿}^{-2}{\[\frac{\∂I(x,y)}{\∂z}\]}_m\]$

▽ in formula ^-2be inverse Laplace's operation symbol, ▽ is gradient operator, and be vector dot, k is wave number, ▽ and ▽ ^-2operational symbol is all realized by Fourier transform, namely

${\▿}^{-2}\{\·\}=F^{-1}\left\{F\right\{\·\left\}\frac{1}{-4{\mathrm{\π}}^2(u^2+v^2)}\right\}$

▽{·}＝F ^-1{j2πuF{·},j2πvF{·}}

Wherein F represents Fourier transform, and (u, v) is the frequency domain coordinates corresponding with volume coordinate (x, y), and j is imaginary unit; Known image plane phase distribution phi _m(x, y), plane of delineation COMPLEX AMPLITUDE U _zm(x, y) just can obtain by down

$U_{zm}(x,y)=\sqrt{I_{zGm}(x,y)}\exp \[{\mathrm{j\φ}}_{zm}(x,y)\]$

5th step: plane of delineation COMPLEX AMPLITUDE U _zmthe distance of (x, y) " anti-spread "-z, thus just got back on the object plane at the place of object own, obtain the COMPLEX AMPLITUDE U on object plane _m(x, y)

U _zm(x,y)＝F ^-1{F{U _zm(x,y)}H _-z(u,v)},

In formula, Fourier transform and inverse transformation are referred to as F and F respectively ^-1, (u, v) representative is relative to the frequency domain coordinates of (x, y); H _-z(u, v) is angular spectrum transition function, and its form is

$H_{-z}(u,v)=\exp \[-j\frac{2\mathrm{\π}z}{{\mathrm{\λ}}_B}\sqrt{1-{\left(\mathrm{\λ}u\right)}^2-{\left(\mathrm{\λ}v\right)}^2}\]$

λ in formula _bfor the blue optical wavelength that throws light on, j is imaginary unit, H _-zthe subscript-z distance that represents anti-spread-z arrive the object plane at the place of object own.

7. the image reconstructing method realized without lens phase micro tomography device based on color LED matrix lamp according to claim 4, is characterized in that being realized by two steps in step 3, namely

The first step: under Rytov is approximate, by the plane of delineation COMPLEX AMPLITUDE U obtained under each LED pixel obtained in step 2 or each light angle _zm(x, y), is expressed as the approximate lower scattered field of Rytov, m=1,2 ..., M:

${U^s}_{zm}(x,y)=U_{zm}(x,y)ln\left(\frac{U_{zm}(x,y)}{mean2\left\{\right|U_{zm}(x,y)\left|\right\}}\right)$

Wherein the mean value of image is got in mean2{} representative, the approximate lower scattered field U of Rytov _zmits two-dimensional Fourier transform of (x, y) is denoted as ${\tilde{U}}_{zm}^s(u,v)=F\left\{{U^s}_{zm}(x,y)\right\};$

Second step: the approximate lower scattered field two-dimensional Fourier transform of the Rytov obtained under each LED pixel obtained in the first step or each light angle be mapped in the three-dimensional frequency spectrum of thing function as follows:

$\tilde{F}(K_x,K_y,K_z)=\frac{{\mathrm{ik}}_z}{\mathrm{\π}j}{\tilde{U}}_{zm}^s(u,v,z=0)$

In formula the three-dimensional Fourier transform of thing function F, (K _x, K _y, K _z) be the spatial frequency of object; The spatial frequency (u, v) of itself and scattered field and k _zbetween pass be

K _x＝u-u _x0,

K _y＝v-u _y0,

K _z＝k _z

Wherein u _x0with u _y0for the spatial frequency of illumination light, after this step, the three-dimensional frequency spectrum of thing function be partially filled.

8. the image reconstructing method realized without lens phase micro tomography device based on color LED matrix lamp according to claim 4, is characterized in that being realized by five steps in step 4, namely

The first step: the three-dimensional frequency spectrum of thing function in initialization step three middle absent region is 0, is denoted by be referred to as the three-dimensional frequency spectrum of revised thing function, n represents iterations, initialization procedure n=0;

Second step: by the three-dimensional frequency spectrum of revised thing function ask three-dimensional inverse Fourier transform, obtain three-dimensional article function f _n(x, y, z)

$f_n(x,y,z)=F^{-1}\left\{{\tilde{F}}_n^{\′}(K_x,K_y,K_z)\right\}$

3rd step: by three-dimensional article function f _nthe element assignment being less than 0 in (x, y, z) is 0, obtains revised three-dimensional article function

4th step: by revised three-dimensional article function remap after carrying out three-dimensional Fourier transform to frequency domain, obtain the three-dimensional frequency spectrum of thing function

${\tilde{F}}_n(K_x,K_y,K_z)=F\left\{f_n(x,y,z)\right\}$

5th step: by the three-dimensional frequency spectrum of original function the three-dimensional frequency spectrum of the thing function that middle absent region obtains by the 4th step corresponding region replace, this completes the iterative process of one bout, and make n ← n+1, and get back to second step continue execution go down, after iteration completes, the three-dimensional article function f finally obtained _n(x, y, z) is the refractive index tomographic map into object under test.