Summary of the invention
Technical matters: can only modulate the two-dimensional space complex light field for overcoming at present full phase spatial light modulator, the invention provides a kind of modulator approach of three dimensions complex light field, this method can be modulated the complex light field amplitude on a plurality of imaging planes simultaneously.
Technical scheme: the technical solution adopted for the present invention to solve the technical problems is:
Adopt the full phase spatial light modulator 2 of coherent source 1 irradiation, the coherent light of full phase spatial light modulator 2 exit planes is propagated through optical imaging system 3 and is arrived first imaging plane 4, coherent light continues to propagate at free space, and arrive second imaging plane 5 successively, a plurality of imaging planes such as the 3rd imaging plane 6 are at the setting regions of each imaging plane (A for example
1, A
2, A
3) in, distribution of amplitudes satisfies setting value (F for example
1(x, y), F
2(x, y), F
3(x, y)).The communication process of coherent light meets scalar diffraction principle (list of references 4:JosephW.Goodman, ' Introduction to Fourier Optics, Third Edition ', Electronic Industry Press, 2006), and the propagator of free space is:
Wherein, λ is the coherent light wavelength, and z is a propagation distance.
Full phase spatial light modulator 2 is only modulated the phase place of incident coherent light, and amplitude remains unchanged.
Optical imaging system 3 can be the free space that does not comprise any optical module, it also can be the system that comprises one or more coaxial lens, adopt lens can dwindle the space distribution scope of complex light field, enlarge angle of diffraction, or be the picture of amplification on the contrary at optical imaging system 3 exit planes.
For realizing the modulation of three dimensions complex light field, on the direction of propagation of three dimensions complex light field, preestablish a plurality of imaging planes, thereby be the distribution of the plane complicated light field of a plurality of two-dimensional imagings with the distribution of three dimensions complex light field is discrete, the setting regions of each imaging plane (A for example
1, A
2, A
3), and (the F for example of the distribution of amplitudes setting value in setting regions
1(x, y), F
2(x, y), F
3(x, y)) by departure process decision, thereby can realize the modulation of any three dimensions complex light field.Method provided by the present invention can realize adopting single full phase spatial light modulator 2 projection picture rich in detail on any three-dimension curved surface, realizes that 3 D stereo shows.
At definite imaging plane, and each imaging plane setting regions (A for example
1, A
2, A
3) and (F for example of the distribution of amplitudes setting value in setting regions
1(x, y), F
2(x, y), F
3Under (x, y)) condition, the PHASE DISTRIBUTION function of full phase spatial light modulator 2 is determined by following method:
This method adopts coherent source to shine full phase spatial light modulator 2, propagates through optical imaging system 3, modulates the distribution of amplitudes of complex light field simultaneously on a plurality of imaging planes, and the method includes the steps of:
1) setting regions of a plurality of imaging plane complex light fields is determined in initialization and set the initial plane of iteration, and the distribution of amplitudes setting value, determines the initial phase distribution function of full phase spatial light modulator 2,
2) complex light field forward-propagating distance z 1, promptly the complex light field of full phase spatial light modulator 2 exit planes has been propagated distance z 1 through optical imaging system 3, has arrived first imaging plane 4,
3) apply first imaging plane, 4 amplitude conditions, promptly preestablishing regional A
1In, revised distribution of amplitudes function Amp
1' (x is y) with setting value F
1(x y) equates, and at regional A
1Outward, remain unchanged, the PHASE DISTRIBUTION function remains unchanged,
4) complex light field forward-propagating distance z 2, i.e. the complex light field propagation distance z2 of first imaging plane, 4 outgoing arrives second imaging plane 5,
5) apply second imaging plane, 5 amplitude conditions, promptly preestablishing regional A
2In, revised distribution of amplitudes function Amp
2' (x is y) with setting value F
2(x y) equates, and at regional A
2Outward, remain unchanged, the PHASE DISTRIBUTION function remains unchanged,
6) complex light field forward-propagating distance z 3, i.e. the complex light field propagation distance z3 of second imaging plane, 5 outgoing arrives the 3rd imaging plane 6,
7) apply the 3rd imaging plane 6 amplitude conditions, promptly preestablishing regional A
3In, revised distribution of amplitudes function Amp
3' (x is y) with setting value F
3(x y) equates, and at regional A
3Outward, remain unchanged, the PHASE DISTRIBUTION function remains unchanged,
8) calculate and judge that whether first, second and third imaging plane rebuild distribution of amplitudes function error all less than setting value, if error less than setting threshold σ, then iteration finishes, otherwise continues step 9),
9) complex light field backpropagation distance z 1+z2+z3, i.e. the complex light field backpropagation z1+z2+z3 of the 3rd imaging plane 6 outgoing arrives full phase spatial light modulator 2 exit planes,
10) apply full phase spatial light modulator 2 exit plane amplitude conditions, be about to distribution of amplitudes function Amp
4(x y) be modified to even distribution, and the PHASE DISTRIBUTION function remains unchanged,
11) iterative loop step 2)~and step 10), error stops iteration less than setting threshold σ in step 8).
Above-mentioned steps is a loop iteration process, the starting point of the iteration in the step 1) can be the exit plane of full phase spatial light modulator 2, also can be any one plane in the three dimensions, for example first imaging plane 4, or second imaging plane 5 or the 3rd imaging plane 6.
The researchist can change iteration order as required in this area, or increase nested loop iterative process, for example can increase the nested loop iterative process in the step 9), elder generation's backpropagation is to first imaging plane 4, and between first imaging plane 4, second imaging plane 5 and the 3rd imaging plane 6, carry out repeatedly iteration, and then turn back to the exit plane of full phase spatial light modulator 2.
The PHASE DISTRIBUTION function of full phase spatial light modulator 2 can adopt analytical method solving, (list of references 3), or use analytical method to find the solution as the initial value in the step 1), and beginning interative computation from step 1) again, the error in step 8) is less than setting threshold σ.
The coherent light of above-mentioned steps discussion is the monochromatic light of single wavelength, also can carry out interative computation respectively at the coherent light of a plurality of wavelength, the coherent light of a plurality of wavelength can adopt the mode of time-sharing multiplex to modulate by spatial light modulator 2, thereby realizes full-color image.
Above-mentioned steps 2) ignore the influence of optical imaging system 3 emergent pupils in, also can be by increasing distribution that lens make complex light field less than emergent pupil, thus avoid the influence of emergent pupil to imaging.
Optical imaging system 3 can be not limited free space in the above-mentioned steps, also can be the system that one or more coaxial lens are formed.
The number of imaging plane in the above-mentioned steps, and the setting regions of imaging plane and distribution of amplitudes setting value be by the distribution decision of three dimensions complex light field, being about to the discrete sampling of three dimensions complex light field is a plurality of parallel two dimensional surfaces.The researchist can increase or reduce imaging plane as required in this area.
Beneficial effect: the present invention modulates the complex light field amplitude on a plurality of imaging planes simultaneously, thereby realize the modulation of full phase spatial light modulator to three dimensions complex light field distribution of amplitudes, projection, realization 3 D stereo that this method can be implemented on any three-dimension curved surface show.
Embodiment
Figure 1 shows that the synoptic diagram of full phase spatial light modulator reconstruction of three-dimensional spatial complex light field, mainly comprise: coherent source 1, full phase spatial light modulator 2, optical imaging system 3, the first imaging planes 4, the second imaging planes 5, the three imaging planes 6.Wherein coherent source 1 can be relevant planar light, and promptly the emergent light of solid, gas or semiconductor laser also can be to disperse or restrain sphere light through the planar light that collimation lens forms, and is promptly formed by concavees lens or convex lens by relevant planar light.The full phase spatial light modulator 2 of coherent source 1 direct irradiation, the liquid display that full phase spatial light modulator 2 can be a transmission-type, reflective LCoS display or reflective MEMS mirror array etc. have the pure phase position modulator (phase only spatial light modulator) of 0~2 π modulation range, when adopting reflective spatial light modulator, can increase spectroscope, incident coherent source 1 is through full phase spatial light modulator 2, the amplitude of its space each point is constant, but phase place changes.Phase place is passed through optical imaging system 3 through the coherent light of ovennodulation, and the communication process of its coherent light meets the scalar diffraction principle, and optical imaging system 3 can be not limited free space.Optical imaging system 3 also can be made up of one or more coaxial lens, realizes the functions such as convergent-divergent of optical imagery process, and propagator can adopt the operator method to calculate on the light ray propagation direction successively and try to achieve (list of references 4) at this moment.For example, optical imaging system 3 is made up of coaxial lens, and its communication process is expressed as with the operator method:
Wherein, U
0(x y) is the optical field distribution function of optical imaging system 3 input planes, U
1(ξ η) is the optical field distribution function of output plane, and f is the focal length of lens, d
1, d
2Be propagation distance, and satisfy d
1+ d
2=z
1The researchist can derive the propagator of a plurality of lens combinations as required in this area.
Coherent light arrives first imaging planes 4 by optical imaging system 3 back, preestablishes regional A on first imaging plane 4
1, the distribution of amplitudes of light field meets setting value F
1(x, y).Coherent light propagates into second imaging plane 5 through first imaging plane 4, preestablishes regional A on second imaging plane 5
2, the distribution of amplitudes of light field meets setting value F
2(x, y).Coherent light propagates into the 3rd imaging plane 6 through second imaging plane 5, preestablishes regional A on the 3rd imaging plane 6
3, the distribution of amplitudes of light field meets setting value F
3(x, y).
Provided three imaging planes among Fig. 1, the researchist can increase or reduce imaging plane as required in this area.
Figure 2 shows that the phase bit recovery process flow diagram of three dimensions complex light field, promptly in the light field distribution of amplitudes function F of given first imaging plane 4
1(x, y), the light field distribution of amplitudes function F of second imaging plane 5
2(x, y) and the light field distribution of amplitudes function F of the 3rd imaging plane 6
3(x under prerequisite y), obtains the method for the PHASE DISTRIBUTION function of full phase-modulator 2, and this solution procedure is called phase bit recovery (phase retrieval) problem again, and alternative manner and analytic method two classes are arranged at present, the preferred alternative manner of the present invention, and its step is as follows:
1) initial plane of iteration and the initial value of definite complex light field are promptly set in initialization.The present invention preferably adopts the exit plane of full phase spatial light modulator 2, and the distribution of amplitudes of complex light field is evenly to distribute, and its numerical value satisfies:
And in the light communication process, gross energy is answered conservation, and the initial phase of complex light field distributes can be set at stochastic distribution, or with the PHASE DISTRIBUTION of similar pictures as initial value.
2) complex light field forward-propagating distance z 1, promptly the complex light field of full phase spatial light modulator 2 exit planes has been propagated distance z 1 through optical imaging system 3, has arrived first imaging plane 4.At this moment, the amplitude A mp of complex light field
1(x is y) with phase place Pha
1(x, y) distribution function can be calculated by formula (1) or (2) and obtain.In preceding iteration several times, amplitude A mp
1(x, y) distribution function and setting value F
1(x y) differs greatly.
3) apply first imaging plane, 4 amplitude conditions, promptly in order to be implemented in the Modulation and Amplitude Modulation on a plurality of imaging planes, to step 2) in amplitude A mp
1(x, y) distribution function is revised, and the PHASE DISTRIBUTION function remains unchanged.Revised distribution of amplitudes function satisfies:
Promptly preestablishing regional A
1In, revised distribution of amplitudes function Amp
1' (x is y) with setting value F
1(x y) equates, and at regional A
1Outward, remain unchanged, for accelerating speed of convergence, formula (4) can adopt method for rapidly converging (list of references 1).
4) complex light field forward-propagating distance z 2, i.e. the complex light field of first imaging plane, 4 outgoing has been propagated distance z 2, has arrived second imaging plane 5.At this moment, the amplitude A mp of complex light field
2(x is y) with phase place Pha
2(x, y) distribution function can be calculated by formula (1) and obtain.In preceding iteration several times, amplitude A mp
2(x, y) distribution function and setting value F
2(x y) differs greatly.
5) apply second imaging plane, 5 amplitude conditions, promptly in order to be implemented in the Modulation and Amplitude Modulation on a plurality of imaging planes, to the amplitude A mp in the step 4)
2(x, y) distribution function is revised, and the PHASE DISTRIBUTION function remains unchanged.Revised distribution of amplitudes function satisfies:
Promptly preestablishing regional A
2In, revised distribution of amplitudes function Amp
2' (x is y) with setting value F
2(x y) equates, and at regional A
2Outward, remain unchanged, for accelerating speed of convergence, formula (5) can adopt method for rapidly converging (list of references 1).
6) complex light field forward-propagating distance z 3, i.e. the complex light field of second imaging plane, 5 outgoing has been propagated distance z 3, has arrived the 3rd imaging plane 6.At this moment, the amplitude A mp of complex light field
3(x is y) with phase place Pha
3(x, y) distribution function can be calculated by formula (1) and obtain.In preceding iteration several times, amplitude A mp
3(x, y) distribution function and setting value F
3(x y) differs greatly.
7) apply the 3rd imaging plane 6 amplitude conditions, promptly in order to be implemented in the Modulation and Amplitude Modulation on a plurality of imaging planes, to the amplitude A mp in the step 6)
3(x, y) distribution function is revised, and the PHASE DISTRIBUTION function remains unchanged.Revised distribution of amplitudes function satisfies:
Promptly preestablishing regional A
3In, revised distribution of amplitudes function Amp
3' (x is y) with setting value F
3(x y) equates, and at regional A
3Outward, remain unchanged, for accelerating speed of convergence, formula (6) can adopt method for rapidly converging (list of references 1).
8) calculate and judge that whether first, second and third imaging plane rebuild distribution of amplitudes function error all less than setting value.At setting regions A
1, A
2, A
3In, calculate F respectively
1(x, y) and Amp
1(x, y), F
2(x, y) and Amp
2(x, y), F
3(x, y) and Amp
3(the error criterion function can adopt root mean square (RMS) or square error (MSE) for x, the y) error between.If error is less than setting threshold σ, then iteration finishes, otherwise continues step 9).
9) complex light field backpropagation distance z 1+z2+z3, i.e. the complex light field backpropagation z1+z2+z3 of the 3rd imaging plane 6 outgoing arrives full phase spatial light modulator 2 exit planes.The propagator of backpropagation can adopt the operator method to be derived by the forward-propagating function.For example, free space backpropagation function is:
U
1(ξ,η)=R[-z
1-z
2-z
3]{U
0(x,y)}(7)。
Thus, can calculate the distribution of amplitudes function Amp that obtains full phase spatial light modulator 2 exit plane complex light fields
4(x is y) with PHASE DISTRIBUTION function Pha
4(x, y).In preceding iteration several times, amplitude A mp
4(x, y) evenly distributional difference is bigger shown in distribution function and the formula (3).
10) apply full phase spatial light modulator 2 exit plane amplitude conditions, promptly to the distribution of amplitudes function Amp in the step 9)
4(x y) revises, and the PHASE DISTRIBUTION function remains unchanged.Revised distribution of amplitudes function satisfies:
Amp
3′(x,y)=I(8)。
11) iterative loop step 2)~and step 10), error stops iteration less than setting threshold σ in step 8), at this moment PHASE DISTRIBUTION function Pha
4(x y) is the PHASE DISTRIBUTION function of full phase spatial light modulator 2.
Iterative algorithm shown in Fig. 2 is a starting point with the exit plane of full phase spatial light modulator 2, because iterative process is a cyclic process, the researchist can be the iteration starting point with any one plane in the iterative process as required in this area, for example with first imaging plane 4 as the iteration starting point.For improving the iterative process speed of convergence, the researchist can change the order of iterative process as required in this area, or increase the nested loop iterative process, for example carry out repeatedly between first imaging plane 4, second imaging plane 5 and the 3rd imaging plane 6 loop iteration and then and the exit plane of full phase spatial light modulator 2 between carry out loop iteration.For improving the iterative process speed of convergence, the researchist can also adopt analytical method solving in this area between some imaging plane, or uses the analytical method solving initial value, carries out interative computation again.
Iterative algorithm shown in Fig. 2 can be used for the coherent light of single wavelength, also can be used for the coherent light of a plurality of wavelength, and each wavelength adopts the mode of time-sharing multiplex.For example red, green, blue three chromatic coherent light are modulated respectively, thereby realized full-color image by timesharing.
In the iterative algorithm shown in Figure 2, a plurality of imaging planes preestablish regional A
1, A
2, A
3By curved projection surfaces or the decision of the space distribution of three-dimensional body, the researchist can increase or reduce imaging plane as required in this area.
The emergent pupil of optical imaging system 3 is influential to final imaging among Fig. 1, can ignore the influence of emergent pupil in iterative algorithm shown in Figure 2, or scioptics make the distribution of complex light field less than emergent pupil.
Optical imaging system 3 can be the system that one or more coaxial lens are formed among Fig. 1, and the researchist can increase or reduce optical module as required in this area, and derives corresponding propagator and carry out interative computation.