CN104007648B - The numerical reconstruction method of digital holographic imaging systems and hologram - Google Patents
The numerical reconstruction method of digital holographic imaging systems and hologram Download PDFInfo
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Abstract
The present invention provides a kind of numerical reconstruction method of digital holographic imaging systems and hologram, and in order to photographic subjects thing, and with the storage of hologram data, described system comprises：Signal light, it is irradiated by light source and is formed after this object；Image detector, 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 detector, wherein this light pipe has a reflecting surface, the signal light of part via this light pipe reflective surface laggard to this image detector.The present invention can make acquisition signal be equivalent to the picture element sum of several times image detector, therefore can break through the limitation of space frequency range, shortens the measurement time of hologram.
Description
Technical field
The present invention relates to a kind of holographic technique, the numerical value weight of espespecially a kind of digital holographic imaging systems and hologram
Construction method.
Background technology
Holography（holography）It is a kind of reproducing technology of 3 D stereoscopic image, it is only different from general photography
Store brightness data, holography stores brightness（intensity）And phase（phase）Data, when with suitable light source shine
Penetrate hologram sheet（hologram）Carry out image reconstruction（reconstruct）When, can true as 3 D stereoscopic image reappear in
Former record position.
In general, holography is the light beam launching laser, by spectroscope（beam splitter）It is divided into twice
Light beam, a branch of as reference beam, another bundle irradiates object, and object forms scattering after the irradiation of this light beam, object light with
Reference beam interferes formation light and shade interference fringe, and is got off by negative writing.
Digital holographic art（digital holography）It is a kind of by charge coupled cell（charge-
Coupled device, CCD）Obtain and process the technology of holographic interference data, through numerical value is carried out to data obtained by measurement
Rebuild（numerical reconstruction）, typical digital holographic can set up the three-dimensional surface of object or its
Depth information.
However, in existing digital holographic technology, whether adopted which kind of framework, final numerical computations all can be subject to
Restriction to space frequency range（spatial bandwidth limit）, to be explained with following equation：
A×B<f(N) (1)
Wherein A is viewing area（Field ofview, FOV）, B is the inverse B=1/u of resolution, and u is resolution, and N is
Image detector（image detector）Picture element sum.That is, image detector, such as CCD, recordable image money
Material is limited.In order to break through the restriction of space frequency range, a kind of existing aperture synthesis（aperture synthesis）Technology,
It passes through to translate image detector so as to carry out two-dimensional scan, with equivalent Cheng Genggao picture element sum, the clever solution of this mode
The picture element of image detector limits, but image detector is carried out with translation and can increase system complexity and significantly elongate measurement
Time, its difficulty is had on practice.
Content of the invention
The purpose of the present invention is to provide a kind of numerical reconstruction method of digital holographic imaging systems and hologram, to contract
The measurement time of short hologram, simplified system complexity, lift the quality of reconstructed image simultaneously.
For reaching above-mentioned purpose, the present invention provides a kind of digital holographic imaging systems, in order to photographic subjects thing, and with holography
Image data stores, and described system comprises：Signal light, it is irradiated by light source and is formed after this object；Image detector, in order to
Record this signal interference of light striped；And light pipe, it is arranged in the light path of this signal light and this object and this image
Between detector, wherein this light pipe has a reflecting surface, and the signal light of part laggard arrives via the reflective surface of this light pipe
This image detector.
Another aspect of the present invention provide a kind of hologram numerical reconstruction method it is adaptable to shoot object and image
It is provided with the optics framework of light pipe, methods described comprises step between detector：Capture object using image detector
Interfere image；This interference video conversion is data matrix；Multiple sides along this data matrix carry out multiple mirror, to expand into
One new data matrix；And numerical reconstruction is carried out to this new data matrix, divided with the field obtaining this object place plane
Cloth.
Digital holographic imaging systems proposed by the invention are in the light path of signal light, between object and image detector
It is provided with light pipe, this light pipe has reflecting surface or fully reflecting surface, can be used for collecting the signal light of wide-angle.Coordinate this
The numerical reconstruction method of bright proposed hologram, can make captured signal be equivalent to the picture element of several times image detector
Sum, therefore the limitation of space frequency range can be broken through.Compared to the technology of existing aperture synthesis, the present invention can shorten hologram
The measurement time, simplified system complexity, the quality of reconstructed image can be lifted simultaneously.
Brief description
Figure 1A shows the configuration diagram of the digital holographic imaging systems of the present invention.
Figure 1B shows another configuration diagram of the digital holographic imaging systems of the present invention.
Fig. 2A 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 display is the schematic diagram tilting according to the side wall of light pipe in the embodiment of present invention realization.
Fig. 6 shows the schematic flow sheet of the numerical reconstruction method of hologram of the present invention.
Fig. 7 shows the schematic diagram of the digital holographic imaging systems of realization according to embodiments of the present invention.
Fig. 8 A to Fig. 8 F shows the signal in the hologram numerical reconstruction method of the present invention, data matrix expanded
Figure.
Specific embodiment
The present invention proposes a kind of digital holographic imaging systems, adds light pipe in signal light path（light pipe）, profit
In the light path of signal light, object（The object to be shot）To CIS（As CCD, CMOS）Between plus leaded light
Pipe, to collect the signal light of wide-angle by the reflecting surface of light pipe, and when subsequently carrying out numerical reconstruction, by image matrix
Duplication to overcome the picture element of CIS to limit, breach space frequency range（spatial bandwidth）Limitation, significantly
Promote the quality of reconstructed image.
Refer to Figure 1A and Figure 1B, the configuration diagram of the digital holographic imaging systems of its display present invention.The present invention's
Digital holographic imaging systems comprise signal light 11, and it is irradiated by light source and is formed after object；Image detector 16, in order to record
The interference fringe of this signal light 11；And light pipe 14, it is arranged in the light path of signal light 11, object and image detector 16
Between, wherein light pipe 14 has a reflecting surface, the signal light of part via this light pipe 14 reflective surface laggard to image
Detector 16.The reflecting surface of this light pipe 14 is used for collecting the signal light of wide-angle, and this is equivalent to the reflecting surface in light pipe 14
Mirror position on be also provided with image detector 16, the so equivalent picture element sum improving image detector 16.
In figure ia, formed signal light 11 light source with irradiate object light source be same light source, signal light 11 be with
The light that this light source sends interferes and produces interference fringe.Additionally, as shown in Figure 1B, image detector 16 is record signal
The interference fringe that light 11 and reference light 12 interfere and produce, it is possible to use same light source is through spectroscope（beam
splitter,BS）It is divided into twice light beam, as reference light 12, another road light beam is formed after irradiating object wherein one light beam
Signal light 11.In specific embodiment, this light source can be light-emittingdiode（light emitted diode,LED）Light source or
Laser（laser）Light source.Also wavelength tuning control element can be added when light source is for laser light source（As acousto-optic modulator）So as in
One light beam or twice light beam produce wavelength shift, to play extrapolation interferometer（heterointerferometer）Function.
Light pipe 14 can be realized in two ways, and the side of first light pipe 14 is coated with reflectance coating；It two is guide-lighting
Pipe 14 is solid, and light is reflected by the total reflection using interface, without plating reflectance coating.The horizontal tangent plane of light pipe 14 is most preferably
Rectangle or triangle, tetragon, pentagon, hexagon or other polygon.
Digital holographic imaging systems proposed by the invention are in the light path of signal light 11, object and image detector 1
It is provided with light pipe 14 between 6, this light pipe 14 has reflecting surface or fully reflecting surface, can be used for collecting the signal of wide-angle
Light, when subsequently carrying out numerical reconstruction, the signal that captured can equivalent what several times image detector 16 picture element sum, therefore can dash forward
The limitation of broken space frequency range.Compared to existing aperture synthesis（aperture synthesis）Technology, the present invention can shorten
The measurement time of hologram, simplified system complexity, the quality of reconstructed image can be lifted simultaneously.
Fig. 2A shows the schematic diagram of the digital holographic imaging systems of first embodiment of the invention.In first embodiment of the invention
In, irradiate object 15 using the light source of approximate spherical wave 112, sphere wave source and object 15, on same optical axis, come
Interfere with each other from the diffraction light of object 15 with spherical wave 112, signal, object 15 and image interfered in image detector 16 record
It is provided with light pipe 14, the side wall of light pipe 14 has reflecting surface or fully reflecting surface, can be used to collect big angle between detector 16
The interference signal of degree.
Fig. 2 B shows the schematic diagram of the digital holographic imaging systems of second embodiment of the invention.Second embodiment of the invention with
The difference of first embodiment is：In a second embodiment, sphere wave source deviate from optical axis that is to say, that sphere wave source with
Object 15, not on same optical axis, so can solve sphere wave source and easily produce on same optical axis with object 15
The problem of larger noise.
Fig. 2 C shows the schematic diagram of the digital holographic imaging systems of third embodiment of the invention.Third embodiment of the invention with
The difference of first embodiment and second embodiment is：In the third embodiment, sphere wave source and object 15 are all disposed within
In plane parallel to the surface of image detector 16, and in addition introduce another road light beam irradiation object 15, spherical wave 112 is then
As reference light, in order to produce interference fringe, generally and reference light is produced from same thunder to the light beam of this irradiation object
Penetrate light source, third embodiment of the invention can reduce the generation of noise.
Fig. 2 D, Fig. 2 E and Fig. 2 F show the numeral of fourth embodiment of the invention, the 5th embodiment and sixth embodiment respectively
The schematic diagram of holographic imaging systems.Embodiment shown in Fig. 2 D, Fig. 2 E and Fig. 2 F is by the ball in Fig. 2A, Fig. 2 B and Fig. 2 C respectively
Face ripple 112 replaces with plane wave 114.That is, in addition to irradiating object 15 using sphere wave source, the present invention also may be used
Using plane wave or tiltedly beat plane wave illumination object 15, and the light source of other wavefront is also suitable for it.Additionally, shown in Fig. 2 F
In sixth embodiment, it is using plane wave 114 as reference light, and in addition introduces another road light beam to irradiate object 15, this photograph
Generally and reference light is produced from same laser light source to penetrate the light beam of object.
Fig. 3 A, Fig. 3 B and Fig. 3 C show the numeral of seventh embodiment of the invention, the 8th embodiment and the 9th embodiment respectively
The schematic diagram of holographic imaging systems.All there is in digital holographic imaging systems shown in Fig. 3 A, Fig. 3 B and Fig. 3 C an optics unit
Part, i.e. spectroscope 17, signal light and reference light can be directed to image detector 16 by spectroscope 17 simultaneously is interfered, light
The light that source is formed after irradiating object 15 is referred to as signal light, is claimed through another road light that spectroscope 17 guides by same light source
Make reference light,, in order to be interfered with signal light, this reference light can be plane wave for it（The 7th enforcement as shown in Figure 3A
Example）, tiltedly beat plane wave（The 8th embodiment as shown in Figure 3 B）, spherical wave（The 9th embodiment as shown in Figure 3 C）Or other classes
The waveform of type, generally and reference light is produced from same laser light source to the light beam of this irradiation object.
Fig. 4 A to Fig. 4 F shows tenth embodiment of the invention to the digital holographic imaging systems of the 15th embodiment respectively
Schematic diagram.Embodiment shown in Fig. 4 A to Fig. 4 F is in the embodiment shown in Fig. 2A to Fig. 2 F respectively, in the light path of signal light
Upper setting lens 18 or lens group, to adjust the distribution of signal light field.
Fig. 4 G and Fig. 4 H shows sixteenth embodiment of the invention and the digital holographic imaging systems of the 17th embodiment respectively
Schematic diagram.The 16th embodiment shown in Fig. 4 G of the present invention and the difference of Fig. 3 A are：In this embodiment, in signal light
In light path, between object 15 and spectroscope 17, it is provided with lens 18 or lens group, to adjust the distribution of signal light field.The present invention
The 17th embodiment shown in Fig. 4 H and the difference of Fig. 3 A are：In this embodiment, in the light path of signal light, spectroscope 1
It is provided with lens 18 or lens group, to adjust the distribution of interference fringe between 7 and image detector 16.
Fig. 4 I to Fig. 4 K shows eighteenth embodiment of the invention to the digital holographic imaging systems of the 20th embodiment respectively
Schematic diagram.Embodiment shown in Fig. 4 I is to replace with the plane wave 1 14 in Fig. 4 G tiltedly to beat plane wave, the reality shown in Fig. 4 J
Applying example is to replace with the plane wave 114 in Fig. 4 H tiltedly to beat plane wave, and the embodiment shown in Fig. 4 K is by the plane in Fig. 4 H
Ripple 114 replaces with spherical wave.
Fig. 5 A to Fig. 5 D display is the schematic diagram tilting according to the side wall of light pipe in the embodiment of present invention realization.With this
The vertical example with image detector 16 plane of light pipe 14 side wall shown in bright Figure 1A with Figure 1B is compared, and in the present invention, leads
The side wall of light pipe 14 can also be arranged to tilt, as shown in Fig. 5 A to Fig. 5 D.It is preferred that the side wall of light pipe 14 and perpendicular bisector
Angle can be between -70 ° to+70 °.Additionally, the cross-sectional area of light pipe 14 can be more than or less than the face of image detector 16
Long-pending that is to say, that the cross-sectional area of light pipe 14 be not required to identical with the area of image detector 16.
Refer to Fig. 6, the schematic flow sheet of the numerical reconstruction method of hologram of its display present invention.The present invention is carried
For hologram numerical reconstruction method it is adaptable to be provided with the light of light pipe between the object that shoots and image detector
Learn framework, methods described comprises the steps of.
Step S10：Capture the interference image of object using image detector.
Step S12：This interference video conversion is data matrix.
Step S14：Multiple sides along this data matrix carry out multiple mirror, to expand into a new data matrix.
Step S16：Numerical reconstruction is carried out to this new data matrix, to obtain the field distribution of this object place plane.
Refer to Fig. 7, with the digital holographic imaging systems shown in Fig. 7, holographic shadow proposed by the invention will be described below
The numerical reconstruction method of picture.Digital holographic imaging systems shown in Fig. 7 irradiate mesh using the divergent spherical wave that point source is produced
Mark thing 15, reference light 12 also be divergent spherical wave, produce reference light 12 point source be located at same with object 15 parallel to
The plane of image detector 16, light pipe 14 is located between object 15 and image detector 16, and image detector 16 receives
Signal light 11 and reference light 12 and the signal light 11 through light pipe 14 side wall reflection and reference light 12 to script.
Before carrying out the numerical reconstruction of hologram, HDR technique for taking can be adopted, preferable to obtain quality
Hologram.This is because signal crossover after light pipe multiple reflections is together, now finer in order to obtain image
Change, can increase the dynamic range of pick-up image（dynamic range）, store image detail with more bit groups.Clapping
When taking the photograph object, first same picture is carried out with the exposure of multiple different time, then by captured multiple pictures with high dynamic range
Enclose image technology to be recombinated, you can obtain the interference image of HDR, the interference image by this HDR can
Reconstruct the hologram of high-quality.
It is assumed that acquired image after above-mentioned steps is as shown in Figure 8 A, if the angle of inclination of guide-lighting tube side wall is 0 degree, warp
By hardware by acquired video conversion be two-dimensional data matrix（U00）Afterwards, then in the way of mirror, this two-dimensional data matrix is expanded
Greatly, the degree that it expands is limited to the specular reflectivity of light pipe and the dynamic range of image detector.And the mode expanding is
Constantly this data matrix is carried out mirror to one of side.For example, by the data matrix shown in Fig. 8 A to the right mirror
Become Fig. 8 B, Fig. 8 B become Fig. 8 C to top mirror, Fig. 8 C is become Fig. 8 D to left side mirror, Fig. 8 D is become Fig. 8 E to following mirror,
Follow such mode data matrix constantly can be expanded, the data matrix after being expanded with this is carried out numerical reconstruction and can dash forward
The restriction of broken space frequency range.The data matrix number table procured function U that each is increased newly by hereI, j(x, y), as shown in Figure 8 F,
In the data matrix of formation, each newly-increased matrix is expressed as afterwards：
Uij(x, y)=U00((-1)ix,(-1)jy), (2)
If considering light pipe specular reflectivity（Re）Caused impact, each newly-increased matrix can be modified to：
Uij(x, y)=U00((-1)ix,(-1)jy)/Re|i|+|j|, (3)
The matrix that formula (2) or formula (3) are extended to is named as Umn, it is signal light（Smn）With reference light（Rmn）
The result of interference, is expressed as follows：
Then, numerical reconstruction is carried out to this new data matrix, to obtain the field distribution of this object place plane, wherein
In addition to will being used for the signal item rebuild, other items are noise item.To useRebuild, then need to be multiplied by UmnAnd it is transferred to objective plane towards the positive direction（I.e. object place plane）；To useRebuild, then need UmnTake advantage of
Upper Rmn, and back transfer is to objective plane, so-called back transfer is that transmission distance is multiplied by minus 1.It is noted that RmnFor ginseng
Examine light and be transferred to U through free spacemnReference light distribution in the range of extension matrix, rather than U00In the range of reference light distribution warp
Matrix-expand forms.
However, now also there are other noises in addition to having desired signal on objective plane, remove these noises
Mode comprises Phaseshifting interferometry（phase shift interferometer）, recursive algorithm（iterative
Algorithm), spatial filtering method（spacial filter）Deng will not be described here.
If reference light is a divergent spherical wave, and objective plane is in the same plane with the point source of reference light, then
Because distribution on image detector for the spherical wave is equivalent to the PHASE DISTRIBUTION of spherical lenss, when objective plane is detectd with image
When survey device distance is enough long, the field distribution on objective plane is equivalent to UmnCarry out the result that the conversion of Fu's formula is obtained, here can
Calculated using fast fourier transform, to obtain the field distribution on objective plane：
Target=FFT(Umn), (5)
If though objective plane is in the same plane with the point source of reference light, the point source of object and reference light away from
From a phase term too far, then can be added to be translated, that is,
Wherein Δ x and Δ y is respectively in x and translation distance in y-direction, (xmn, ymn) for expansion after matrix coordinate
System, is expressed as follows：
Wherein LxWith LyIt is respectively the capture scope of the image detector length on x and y direction, t1Represent coordinate matrix
In t1Row（column）, t2Represent the t in coordinate matrix2OK（row）, BxAnd ByIt is respectively image detector in x and y side
Picture element spacing upwards（pixel pitch）.
If objective plane is not in the same plane with the point source of reference light, calculation is complex.First, make
Use RmnOrIt is multiplied by Umn, to obtain SmnMatrix, that is, represent the matrix of signal light.If using following formula：
It is the actual distance in space that the transmission distance that the field distribution of objective plane used then will be rebuild back；If using such as
Lower formula：
Smn=RmnUmn, (10)
The transmission distance that the field distribution of objective plane used then to be rebuild back and be multiplied by minus 1 for the actual distance in space.
Calculation described in formula (5)-(10) is simplification calculation in particular cases, if system is unsatisfactory for simplifying
Condition, it will usually propagate to calculate by arbitrarily using angular spectrum when after to expansion, new data matrix carries out numerical reconstruction
Beginning plane is transferred to the optical field distribution of arbitrary target plane, after the expression such as of its calculation：
FU1=FET (U0)exp(i2πz/λ(1-α2-β2)0.5), (11)
α=t1λ/Lx0, (12)
β=t2λ/Ly0, (13)
Wherein λ is optical source wavelength, and FFT is fast fourier transform, U0For initial planar, U1For objective plane, FU1For mesh
The spectrum distribution of mark plane, Lx0With Ly0It is respectively U0Length on x and y direction for the capture scope, t1Represent in matrix
t1Row, t2Represent the t in matrix2OK, z represents transmission distance.Finally, with fast Flourier inverse transform（IFFT）Obtain target
The field distribution of plane is：
U1=IFFT(FU1). (14)
The shortcoming of formula (11) to (14) calculating is directly used to be limited to the solution of initial planar for the resolution of objective plane
Analysis degree, to use UmnObtain the objective plane image of high-res, the estimation in the transmission of space need to be carried out.In the transmission of space
Calculation can be：(1) initial planar is carried out interpolation expansion；(2) initial planar being carried out interpolation expansion, to be cut into decile bigger
Little propagated；(3) two-period form Fresnel is used to change（Fresnel transform）；And (4) use Rayleigh-Suo Mofei
That formula（Rayleigh-Sommfeld formula）Direct integral, division as after：
（1）Initial planar is carried out interpolation expansion
By SmnThe equidistant interpolation of matrix expands the matrix for M × N times, the frequency spectrum of objective plane（TargetF）Can be by following public affairs
Formula calculates：
TargetF=FFT (Smn)exp(i2πzz0/λ(1-α2-β2)0.5), (15)
α=t1λ/mLx, (16)
β=t2λ/nLy, (17)
Wherein LxWith LyIt is respectively the capture scope of the image detector length on x and y direction, t1Masterpiece mark matrix
In t1Row, t2T in masterpiece mark matrix2OK, zoRepresent the distance between objective plane and image detector.Finally,
With fast Flourier inverse transform（IFFT）Obtain objective plane field distribution be：
Target=IFFT(TargetF) (18)
（2）Initial planar is carried out interpolation expansion be cut into aliquot-sized again and propagated
First, by SmnThe equidistant interpolation of matrix is expanded to M × N times, then it is divided into D on x and y directionxAnd DyEqual portions, are expressed as
Sdij, Sdij（I.e. x direction diEqual portions, y direction djEqual portions）, it is centrally located at
Respectively each equal portions are propagated to objective plane center.
Then, the angular frequency Spectral structure being transferred to objective plane is calculated using angular spectrum circulation way, as follows：
FSdij=FFT (Sdij)exp(i2πz0/λ(1-α2-β2)0.5), (19)
Consider SdijPosition, Targetd can be calculatedijAngular spectrum in objective plane center is distributed as：
Wherein (vx, vy) for angular spectrum coordinate system, be expressed as follows：
vx=t1/mLx, (21)
vy=t2/nLy, (22)
Reach after the angular frequency Spectral structure of objective plane using each mirror amplification matrix is calculated with upper type, then can be by each angle
Spectrum distribution obtains the angular frequency Spectral structure of objective plane after being added, as follows：
Finally, obtain the field distribution of objective plane, the calculation of same formula (18) with fast Flourier inverse transform, represent
As follows：
Target=IFFT(TargetF). (24)
（3）Two-period form Fresnel Transform
When objective plane and image detector distance is enough long can using Fresnel Transform calculate objective plane it
Field distribution, SmnThe air coordinates of middle each element correspondence is：
Wherein t1Represent the t in coordinate matrix1Row, t2Represent the t in coordinate matrix2OK, wherein BxAnd ByIt is respectively
Picture element spacing on x with y direction for the image detector.
In two-period form Fresnel Transform, first paragraph transmission is transferred to intermediary's plane with Fresnel Transform,
This intermediary's plane and SmnAt a distance of za, with thing at a distance of zb, the resolution amplification in final goal plane is zbWith zaRatio, therefore
By always apart from zoAnd target magnification（Mag）, can calculate：
Now, it is transferred to the field distribution S in intermediary's planemidCan be calculated by the following manner：
Wherein (xmid, ymid) for intermediary's plane coordinate system, be expressed as follows：
In two-period form Fresnel Transform, second segment transmission is to be transferred to objective plane by intermediary's plane, and target is put down
The field distribution in face is expressed as follows：
Wherein (ξ, η) is the coordinate system of objective plane, is adjusted by zaWith zbRatio can adjust the resolution of image,
It is expressed as follows：
（4）Using Rayleigh-Sommfeld direct integral
Using Rayleigh-Sommfeld Diffracion Theory, the air coordinates of each element correspondence in wherein Smn
As follows：
zmn=0, (37)
The coordinate making objective plane is (ξ, η, zo), then can obtain objective plane and SmnIn each picture element apart from r be
By above formula substitution Rayleigh-Sommfeld Diffracion Theory be integrated, obtain objective plane it
Field distribution is：
Tilt angle theta when guide-lighting tube side wall（The i.e. angle with perpendicular bisector）During equal to 0 degree（As shown in FIG. 1A and 1B）,
The matrix U of amplificationijWith original data matrix U00It is positioned in the space on same plane.If the tilt angle theta of guide-lighting tube side wall is not
Equal to 0 degree（As shown in Fig. 5 A to Fig. 5 D）Though, can use the mode of mirror to expand this data matrix, the matrix U of its amplificationijNo
Can be with original data matrix U00Position is in space on same plane, the matrix U of now mirror amplificationijMust revolve in space
Turn 2 θ angles.
Matrix U due to mirror amplificationijWith original matrix U00It is impossible to be calculated in aforementioned mode not in approximately the same plane
Go out the Electric Field Distribution of objective plane, the therefore calculation in the transmission of space need to use following two settling modes：(1)
Rayleigh-Sommfeld direct integral；And (2) in free space light and between displacement plane mutually rotating propagate fast
Fast fourier transform solution.
（1）Rayleigh-Sommfeld direct integral
Calculate each Target using Rayleigh-Sommfeld Diffracion Theoryij, then by its phase each other
Plus, with Target10As a example, U10On each element correspondence air coordinates as follows：
z10=t1Bxsin(2θ), (42)
Wherein t1Represent the t in coordinate matrix1Row, t2Represent the t in coordinate matrix2OK, wherein BxAnd ByIt is respectively
Picture element spacing on x with y direction for the image detector.With this air coordinates, the reference light R transmitting so far position can be calculated10,
It is then used by the conjugate beam of reference lightIt is multiplied by U10, obtain S10Matrix, is expressed as follows：
Perpendicular to S10The unit vector of matrix plane is：
The coordinate of hypothesis objective plane is (ξ, η, zo), S10The vector that middle each element points to objective plane specified point is：
Objective plane and S10Middle each element apart from r010For | r010|, then by S10Bring Rayleigh-Sommfeld into
Diffracion Theory can calculate its corresponding Target10, as follows：
Calculate each matrix S in the same mannerijCorresponding objective plane field distribution（Targetij）Afterwards, then by various algorithms
Obtained field distribution is added together, you can obtain the field distribution of objective plane, as follows：
The speed of above-mentioned calculation depends on the number of sampling of objective plane, when number of sampling is excessive,
Computer calculating speed will reduce, and one of mode of ameliorating is to use to calculate SmnAny one mode extrapolate S00Right
The Target answering00, reuse Rayleigh-Sommfeld Diffracion Theory and calculate Target00In addition
Targetij, then it is added up each other.
（2）The fast fourier transform solution of the light propagation and between displacement plane mutually rotating in free space
First, the angular frequency Spectral structure being transferred to objective plane is calculated using angular spectrum circulation way, as follows：
FS10=FFT (S10)exp(i2πz10/λ(1-α2-β2)0.5), (48)
Wherein transmitting distance is：
Then, using coordinate spin matrix, angular spectrum is carried out coordinates translation, as follows：
Wherein spin matrix is：
By the field distribution FS in former angular spectrum coordinate10(vx,vy,vz) mapping（mapping）Field distribution to new coordinate
RFS10(vx0’,vy0’,vz0'), if wherein there is vz0' it is less than zero or vz0' there is imaginary part, that is,
vz0’<0, (52)
Im[vz0'] ≠ 0, (53)
The field distribution then making it corresponding is zero.Then, the angular spectrum distribution after conversion is mapped to equidistantly with interpolation method
New RFS is obtained in the angular spectrum coordinate of distribution10(vx’,vy', vz’).
Then, the center of spectrum distribution is moved to the center of objective plane, displacement is：
Target can be calculated10Spectrum distribution be：
TargetF10=RSF (v 'x, v 'y,v′z)exp(-i2πv′xΔξ10), (55)
Reached after the angular frequency Spectral structure of target object plane using each mirror amplification matrix is calculated with upper type, then by each angular frequency
Spectral structure obtains the angular frequency Spectral structure of thing after being added, as follows：
Finally, the field distribution of objective plane is obtained with fast Flourier inverse transform, as follows：
Target=IFFT(TargetF). (57)
Although the present invention has used, preferred embodiment is disclosed above in sum, and so it is not limited to the present invention, this
Bright those of ordinary skill in the art, without departing from the spirit and scope of the invention, when can make various changes
With retouching, therefore the protection domain of the present invention when depending on after attached the defined person of claim be defined.
Claims (20)
1. a kind of digital holographic imaging systems, in order to photographic subjects thing, and with the storage of hologram data it is characterised in that institute
The system of stating comprises：
Light source, forms the signal light from this object in order to irradiate this object；
Image detector, in order to record this signal interference of light striped；
Light pipe, is arranged in the light path of this signal light and between this object and this image detector, wherein this light pipe
There is reflecting surface, the signal light of part via this light pipe reflective surface laggard to this image detector；And
Hardware, the interference video conversion of interference fringe is data matrix by it, and the multiple sides along this data matrix carry out many secondary mirrors
Penetrate, to expand the new data matrix forming a continuous mirror, and numerical value weight is carried out to the new data matrix of this continuous mirror
Build, to obtain the field distribution of this object place light field.
2. digital holographic imaging systems according to claim 1 it is characterised in that：The horizontal tangent plane of this light pipe is square
Shape.
3. digital holographic imaging systems according to claim 1 it is characterised in that：The side wall of this light pipe is arranged to incline
Tiltedly.
4. digital holographic imaging systems according to claim 3 it is characterised in that：The side wall of this light pipe with perpendicular to this
The angle of the perpendicular bisector of the plane of image detector is between -70 ° to+70 °.
5. digital holographic imaging systems according to claim 1 it is characterised in that：This signal is just sent with this light source
Light interferes and produces this interference fringe.
6. digital holographic imaging systems according to claim 1 it is characterised in that：The light source irradiating this object is to dissipate
Spherical wave.
7. digital holographic imaging systems according to claim 1 it is characterised in that：This signal light is interfered with reference light
And produce this interference fringe.
8. digital holographic imaging systems according to claim 7 it is characterised in that：Described digital holographic imaging systems are more wrapped
Containing a spectroscope, this light source is divided into twice light beam through this spectroscope, and wherein one light beam is as this reference light, another road light beam
Form this signal light after irradiating this object.
9. a kind of numerical reconstruction method of hologram is it is adaptable to be provided with leaded light between the object of shooting and image detector
The optics framework of pipe, this light pipe has reflecting surface, and it is used for collecting the signal light from this object of wide-angle, its feature
It is, methods described comprises step：
Using the signal from object by this light pipe and the reflective surface by this light pipe for the image detector detecting
Light, to obtain the interference image of object；
This interference video conversion is data matrix；
Multiple sides along this data matrix carry out multiple mirror, to expand into a new data matrix, this equivalent this image of lifting
The picture element sum of detector；And
Numerical reconstruction is carried out to this new data matrix, to obtain the field distribution of this object place plane.
10. hologram according to claim 9 numerical reconstruction method it is characterised in that：In using this image detecting
Device obtains in the step of interference image of this object, comprises：
Same picture is carried out with the exposure of different time several times；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 characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, if the light of this object and reference light
Source is all located in the approximately the same plane parallel with this image detector surface, and this reference light is divergent spherical wave, then new to this
Data matrix calculated using fast fourier transform, to obtain the field distribution of this object place plane.
The numerical reconstruction method of 12. hologram according to claim 11 it is characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, if this object and this reference light it
Light source is distance, then this new data matrix is multiplied by a phase term and reuses fast fourier transform and counted
Calculate, to obtain the field distribution of this object place plane.
The numerical reconstruction method of 13. hologram according to claim 9 it is characterised in that：Calculating this object institute
During the field distribution of plane, the calculation using angular spectrum propagation carries 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 13 it is characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, is calculating this object place plane
Field distribution during, by initial planar carry out interpolation expand to carry out the estimation in the transmission of space.
The numerical reconstruction method of 15. hologram according to claim 13 it is characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, is calculating this object place plane
Field distribution during, by initial planar carry out interpolation expansion be cut into aliquot-sized again to carry out the estimation in the transmission of space.
The numerical reconstruction method of 16. hologram according to claim 13 it is characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, is calculating this object place plane
Field distribution during, the estimation that carries out in the transmission of space using the conversion of two-period form Fresnel.
The numerical reconstruction method of 17. hologram according to claim 13 it is characterised in that：Side wall in this light pipe
Angle with the perpendicular bisector of the plane of this image detector is θ, in the case that θ is equal to 0 degree, is calculating this object place plane
Field distribution during, carry out the estimation in the transmission of space using Rayleigh-Suo Mofeier formula.
The numerical reconstruction method of 18. hologram according to claim 9 it is characterised in that：If this guide-lighting tube side wall with
The angle of the perpendicular bisector of the plane of this image detector is θ, and it is not equal to 0 degree, then on the one of side to this data matrix
Carry out in the step of mirror, this data matrix is rotated 2 θ angles in space.
The numerical reconstruction method of 19. hologram according to claim 18 it is characterised in that：Calculating this object institute
During the field distribution of plane, carry out the estimation in the transmission of space using Rayleigh-Suo Mofeier formula.
The numerical reconstruction method of 20. hologram according to claim 18 it is characterised in that：Calculating this object institute
During the field distribution of plane, using the quick Fourier of the light propagation and between displacement plane mutually rotating in free space
Leaf conversion solves.
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