CN103235477B - A kind of pure phase position holographic projection methods of clinoplane - Google Patents

Abstract

The invention discloses a kind of pure phase position holographic projection methods of clinoplane, comprise the following steps: 1) lay projector equipment: phase spatial light modulator, Amici prism, lens and screen are laid successively, lay mono-colour laser and polaroid in the same side of Amici prism, phase spatial light modulator is connected with computing machine; 2) parameter in certainty annuity, as the pitch angle of clinoplane, the sampling interval of spatial light modulator and resolution, the focal length of lens; 3) utilize rotation of coordinate, interpolation algorithm and Fourier Transform of Fractional Order and inverse transformation formula carry out iterative computation, obtain the phase place of two dimensional image; 4) be transferred in phase spatial light modulator by computing machine by this phase hologram, phase hologram projects on the inclination screen of assigned address by recycling phase spatial light modulator.This holographic projection methods can make the two dimensional image of hologram reconstructing be projected on the clinoplane of any distance after lens, and the distance of clinoplane can control easily.

Description

A kind of pure phase position holographic projection methods of clinoplane

Technical field

The present invention relates to a kind of holographic projection methods, particularly relate to a kind of pure phase position holographic projection methods of clinoplane.

Background technology

For the optical field distribution propagation in space of traditional calculating clinoplane, the method of general employing is: the optical field distribution first being carried out computing reference plane by the rotation of coordinate in angular spectrum territory, and then by light in space plane-parallel communication theory (as angular spectrum method) carry out the optical field distribution on calculation holographic face, in this case, the optical field distribution that holographic facet obtains is the form of complex amplitude, namely comprise amplitude information and phase information simultaneously, therefore phase-only modulation will be realized, phase encoding must be carried out to complex amplitude, thus add complicacy and error.And on the other hand, for traditional pure phase position line holographic projections, phase hologram map generalization adopts classical Gerschberg-Saxton (GS) iterative algorithm, this is a kind of iterative algorithm based on Fourier transform, and it can directly obtain the phase information of two dimensional image by iteration and not need the calculating such as coding.But in this technology, imaging surface and holographic facet are parallel, and phase hologram can only plane parallel with holographic facet in space project, and projection imaging becomes all the time on the back focal plane of lens, the focal length of image-forming range i.e. lens, has certain restriction for practical application.

Summary of the invention

Goal of the invention: the pure phase position holographic projection methods providing a kind of clinoplane, can make on the clinoplane of two dimensional image projection any distance in space of hologram reconstructing, and not need the focal length changing lens to be controlled to the distance of picture; And modulation system is phase-only modulation, reduce complicacy and the degree of error of classic method.

Technical scheme: for solving the problems of the technologies described above, the pure phase position holographic projection methods of a kind of clinoplane of the present invention, comprises the following steps:

Step 1), lay projector equipment: phase spatial light modulator 1, Amici prism 2, lens 3 and inclination screen 4 are laid successively, make phase spatial light modulator 1, Amici prism 2, lens 3 and screen 4 be on same straight line; Simultaneously, mono-colour laser 5 and polaroid 6 is laid in the same side of Amici prism 2, polaroid 6 is between Amici prism 2 and mono-colour laser 5, the plane wave that mono-colour laser 5 sends becomes polarized light by polaroid 6, and polarized light is by being injected in phase spatial light modulator 1 after Amici prism 2; Phase spatial light modulator 1 is connected by data line with the computing machine 7 generating phase hologram; Position residing for phase spatial light modulator 1 forms holographic facet x ₀, the position residing for screen 4 forms clinoplane x;

Step 2), set up virtual reference planes x _r, reference planes x _rbe same center with clinoplane x and with holographic facet x ₀parallel;

Step 3), according to rotation of coordinate relation, set up reference planes x _rand the optical field distribution relation between clinoplane x:

F(u′，v′)＝FT[f(x′，y′)]

G (u, v)=F (α ^-1(u, v), β ^-1(u, v)) and=F (u ', v ') formula (1)

g(x，y)＝FT ^-1[G(u，v)]

In formula (1), the light field complex amplitude function that f (x ', y ') is clinoplane x, x ', y ' is the independent variable of f (x ', y '), represents coordinate of each point on clinoplane, F (u ', v ') be the angular spectrum function of clinoplane x, u ', v ' be the coordinate in corresponding angular spectrum space, G (u, v) is reference planes x _rangular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u, v)) represent from clinoplane x to reference planes x _rcoordinate transform, g (x, y) is reference planes x _rlight field complex amplitude function, x, y be in reference planes each point coordinate.FT is Fourier transform, FT ^-1for inverse Fourier transform;

Step 4), the focal distance f of measuring and calculating lens 3 and reference surface x _rdistance z between relation:

According to the Fourier Transform of Fractional Order formula of formula (2), set up holographic facet x ₀with reference surface x _rbetween light propagate function:

$g\left(x\right)=\∫F\left(x_0\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (\mathrm{a\π}/2)})\right]d{x}_0$ Formula (2)

In formula (2), g (x) is reference surface x _rlight field complex amplitude function, x is the independent variable of g (x), F (x ₀) be holographic facet x ₀light field complex amplitude function, x ₀for F (x ₀) independent variable, i is imaginary unit, and λ is the wavelength of the plane wave that mono-colour laser 5 sends, and a is the exponent number of Fourier Transform of Fractional Order, f _efor standard focal length, f _e=fsin (a pi/2)=z/tan (a π/4), makes Q=sin (a pi/2), R=tan (a π/4), then f _e=fQ=z/R;

Secondly, by f _e=fQ=z/R can obtain reference planes x _rdistance z and the relation of focal distance f of lens (3) such as formula shown in (3):

Z=fRQ formula (3);

Step 5), after the exponent number a according to formula (3) certainty annuity mid-score rank Fourier transform, utilize the holographic facet x that formula (1) and formula (2) are determined ₀and tilt to carry out iterative computation as the light propagation relation between plane x, to obtain on clinoplane x two dimensional image at holographic facet x ₀on phase hologram;

Step 6), according to step 5) phase hologram that obtains, be transferred in phase spatial light modulator 1 by computing machine 7 by this phase hologram, phase hologram scioptics 3 project on the inclination screen 4 of assigned address by recycling phase spatial light modulator 1.

Wherein, described step 5) comprise the following steps:

Step 5.1), light field complex amplitude is multiplied by phase factor according to amplitude factor and represents, makes holographic facet x ₀amplitude factor be 1, phase factor is random phase;

Step 5.2), the reference planes x according to formula (2) _rlight field complex amplitude function, obtain reference planes x _ron light field COMPLEX AMPLITUDE;

Step 5.3), the clinoplane x light field complex amplitude represented according to formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains the light field complex amplitude on clinoplane x;

Step 5.4), the gray-scale value of the amplitude factor in the light field complex amplitude on clinoplane x with the two dimensional image that will rebuild is replaced, and the phase factor in the light field complex amplitude on clinoplane x remains unchanged;

Step 5.5), the clinoplane x light field complex amplitude shown in recycling formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains reference planes x _ron light field complex amplitude;

Step 5.6), recycle and calculate holographic facet x such as formula the Fourier Transform of Fractional Order formula inverse transformation formula shown in (4) ₀on light field complex amplitude;

$F\left(x_0\right)=\∫g\left(x\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (-\mathrm{a\π}/2)})\right]dx$ Formula (4);

Step 5.7), by holographic facet x ₀on light field complex amplitude in amplitude factor unit strength value 1 replace, holographic facet x ₀on light field complex amplitude in phase factor remain unchanged;

Step 5.8), repeat step 5.1) to 5.7), iterate, until holographic facet x ₀on adjacent twice light field complex amplitude in the root-mean-square error of phase factor be less than 0.05 after stop iteration, obtain holographic facet x ₀on the phase factor of light field complex amplitude, the holographic facet x obtained after will iteration being stopped according to formula (5) ₀on the phase factor of light field complex amplitude carry out phase encoding, obtain phase hologram;

$\mathrm{\φ}=255-\left[\frac{({\mathrm{\φ}}_0+\mathrm{\π})\×255}{2\mathrm{\π}}\right]$ Formula (5)

In formula (5), φ ₀the holographic facet x obtained after representing iteration ₀on the phase factor value of light field complex amplitude, φ represents the holographic facet x obtained after phase encoding ₀on the phase factor value of light field complex amplitude.

Beneficial effect: the 1. phase-only modulation of clinoplane.Traditional clinoplane communication theory in space combines with Gerschberg-Saxton (GS) algorithm by the present invention, obtain the Phase Retrieve Algorithm of clinoplane image, this algorithm is based on clinoplane to the propagation and holographic facet to the inverse propagation of clinoplane of holographic facet, apply amplitude constraint at clinoplane and holographic facet respectively and carry out loop iteration, the PHASE DISTRIBUTION be finally optimized on holographic facet.Utilize pure phase spatial light modulator, the reconstruction picture of two dimensional image can be obtained by clinoplane in space.Compared with modulating with traditional clinoplane imaging, the hologram that this method obtains is phase-only hologram, has very high light diffraction efficiency, and after iterative computation by certain number of times, the error of rebuilding image can be very little, and image quality is more increased than classic method.

2. image-forming range can arbitrarily change.The holographic projection methods that the present invention adopts can, on the clinoplane of phase hologram projection any distance after the lens, not need to change the focal length of lens according to the distance of imaging.Phase-only hologram adopts the iterative algorithm based on Fourier Transform of Fractional Order to generate, when using phase type spatial light modulator to project, according to the feature of Fourier Transform of Fractional Order, the hologram that profit generates in this way can on the clinoplane of image projection any distance after the lens.Therefore, the present invention not only achieves the pure phase projection on clinoplane, and can control easily to be inclined to image planes distance.

Accompanying drawing explanation

Fig. 1 is step 1 of the present invention) the projector equipment location drawing;

Fig. 2 is step 1 of the present invention) in graph of a relation between each plane;

Fig. 3 is the iterative algorithm diagram of phase hologram of the present invention.

Embodiment

Below in conjunction with accompanying drawing the present invention done and further explain.

As shown in Figure 1, a kind of pure phase position holographic projection methods of clinoplane, comprises the following steps:

Step 1), lay projector equipment: phase spatial light modulator 1, Amici prism 2, lens 3 and inclination screen 4 are laid successively, phase spatial light modulator 1, Amici prism 2, lens 3 and screen 4 are on same straight line.Simultaneously, mono-colour laser 5 and polaroid 6 is laid in the same side of Amici prism 2, polaroid 6 is between Amici prism 2 and mono-colour laser 5, the plane wave that mono-colour laser 5 sends becomes polarized light by polaroid 6, and polarized light is by being injected in phase spatial light modulator 1 after Amici prism 2.Phase spatial light modulator 1 is connected by data line with the computing machine 7 generating phase hologram.Position residing for phase spatial light modulator 1 forms holographic facet x ₀, the position residing for screen 4 forms clinoplane x.

Step 2), set up virtual reference planes x _r, reference planes x _rbe same center with clinoplane x and with holographic facet x ₀parallel.

Step 3), according to rotation of coordinate relation, set up reference planes x _rand the optical field distribution relation between clinoplane x:

F(u′，v′)＝FT[f(x′，y′)]

G (u, v)=F (α ^-1(u, v), β ^-1(u, v)) and=F (u ', v ') formula (1)

g(x，y)＝FT ^-1[G(u，v)]

In formula (1), the light field complex amplitude function that f (x ', y ') is clinoplane x, x ', y ' is the independent variable of f (x ', y '), represents coordinate of each point on clinoplane, F (u ', v ') be the angular spectrum function of clinoplane x, u ', v ' be the coordinate in corresponding angular spectrum space, G (u, v) is reference planes x _rangular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u, v)) represent from clinoplane x to reference planes x _rcoordinate transform, g (x, y) is reference planes x _rlight field complex amplitude function, x, y be in reference planes each point coordinate.FT is Fourier transform, FT ^-1for inverse Fourier transform.

Step 4), the focal distance f of measuring and calculating lens 3 and reference surface x _rdistance z between relation:

According to the Fourier Transform of Fractional Order formula of formula (2), set up holographic facet x ₀with reference surface x _rbetween light propagate function:

$g\left(x\right)=\∫F\left(x_0\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (\mathrm{a\π}/2)})\right]d{x}_0$ Formula (2)

In formula (2), g (x) is reference surface x _rlight field complex amplitude function, x is the independent variable of g (x), F (x ₀) be holographic facet x ₀light field complex amplitude function, x ₀for F (x ₀) independent variable, i is imaginary unit, and λ is the wavelength of the plane wave that mono-colour laser 5 sends, and a is the exponent number of Fourier Transform of Fractional Order, f _efor standard focal length, f _e=fsin (a pi/2)=z/tan (a π/4), makes Q=sin (a pi/2), R=tan (a π/4), then f _e=fQ=z/R.

Secondly, by f _e=fQ=z/R can obtain reference planes x _rdistance z and the relation of focal distance f of lens 3 such as formula shown in (3):

Z=fRQ formula (3);

Step 5), after the exponent number a according to formula (3) certainty annuity mid-score rank Fourier transform, utilize the holographic facet x that formula (1) and formula (2) are determined ₀and tilt to carry out iterative computation as the light propagation relation between plane x, to obtain on clinoplane x two dimensional image at holographic facet x ₀on phase hologram.

Wherein, step 5) comprise the following steps:

Step 5.1), light field complex amplitude is multiplied by phase factor according to amplitude factor and represents, makes holographic facet x ₀amplitude factor be 1, phase factor is random phase.

Step 5.2), the reference planes x according to formula (2) _rlight field complex amplitude function, obtain reference planes x _ron light field COMPLEX AMPLITUDE.

Step 5.3), the clinoplane x light field complex amplitude represented according to formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains the light field complex amplitude on clinoplane x.

Step 5.4), the gray-scale value of the amplitude factor in the light field complex amplitude on clinoplane x with the two dimensional image that will rebuild is replaced, and the phase factor in the light field complex amplitude on clinoplane x remains unchanged.

The gray-scale value of two dimensional image with imread statement process picture, can obtain the gray-scale value of image in computing machine matlab software.Use statement A=imread (' B.jpg ') in a program, B is figure title, and form is jpg, this statement declaration of will be exactly the gray scale exporting picture B, the A obtained is exactly the gray scale of image, in picture, be called gray scale.In the present invention, in matlab software, above-mentioned statement is used to obtain the gray-scale value of two dimensional image.The two dimensional image that will rebuild refers to the two dimensional image that will be projected on screen.

Step 5.5), the clinoplane x light field complex amplitude shown in recycling formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains reference planes x _ron light field complex amplitude.

Step 5.6), recycle and calculate holographic facet x such as formula the Fourier Transform of Fractional Order formula inverse transformation formula shown in (4) ₀on light field complex amplitude;

$F\left(x_0\right)=\∫g\left(x\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (-\mathrm{a\π}/2)})\right]dx$ Formula (4);

Wherein, each alphabetical implication of (4) formula is consistent with alphabetical implication in (2) formula.

Step 5.7), by holographic facet x ₀on light field complex amplitude in amplitude factor unit strength value 1 replace, holographic facet x ₀on light field complex amplitude in phase factor remain unchanged.

Step 5.8), repeat step 5.1) to 5.7), iterate, until holographic facet x ₀on adjacent twice light field complex amplitude in the root-mean-square error of phase factor be less than 0.05 after stop iteration, obtain holographic facet x ₀on the phase factor of light field complex amplitude, the holographic facet x obtained after will iteration being stopped according to formula (5) ₀on the phase factor of light field complex amplitude carry out phase encoding, obtain phase hologram;

$\mathrm{\φ}=255-\left[\frac{({\mathrm{\φ}}_0+\mathrm{\π})\×255}{2\mathrm{\π}}\right]$ Formula (5)

In formula (5), φ ₀the holographic facet x obtained after representing iteration ₀on the phase factor value of light field complex amplitude, φ represents the holographic facet x obtained after phase encoding ₀on the phase factor value of light field complex amplitude.

Step 6), according to step 5) phase hologram that obtains, be transferred in phase spatial light modulator 1 by computing machine 7 by this phase hologram, phase hologram scioptics 3 project on the inclination screen 4 of assigned address by recycling phase spatial light modulator 1.

In the present invention, phase hologram is loaded in phase spatial light modulator 1 by computing machine 7, the monochromatic green glow that mono-colour laser 5 sends becomes polarized light by polaroid 6, then by after Amici prism 2, inject spatial light modulator 1, light wave carries out phase-modulation back reflection and goes out in phase spatial light modulator 1, after Amici prism 2 and lens 3, imaging is carried out in space after lens 3, the distance of clinoplane and lens can be regulated by the exponent number controlling Fourier Transform of Fractional Order, the distance that different exponent numbers is corresponding different, not by the restriction of the focal length of lens on the clinoplane that image can be projected to any distance.

The holographic projection methods of clinoplane of the present invention utilizes the rotation of coordinate in angular spectrum space and Fourier Transform of Fractional Order formula to calculate phase hologram, and reproduce in line holographic projections in the process of two dimensional image, adopt light channel structure corresponding to Fourier Transform of Fractional Order to realize this process.In the measuring and calculating process of hologram, the communication theory of light field between clinoplane is combined with traditional GS iterative algorithm, and calculate light diffraction propagation in space by Fourier Transform of Fractional Order, and obtain the phase-only hologram of clinoplane eventually through iteration.In process of reconstruction, phase hologram is loaded in phase spatial light modulator 1, produces phase-modulation by the irradiation of reconstructed wave to the light of each pixel, and imaging on clinoplane after lens 3.

Embodiment: the wavelength adopting mono-colour laser 5 to send is that the monochromatic green glow of 532 nanometers projects; The phase spatial light modulator that phase spatial light modulator 1 adopts BNS company of the U.S. to produce, its specification is 512 × 512 pixels, and pel spacing is 15 microns; The focal distance f of lens 3 is 0.5 meter.

Arrange clinoplane 4 after lens 3, the angle of inclination of clinoplane is α=30 °, and direction is rotate around y-axis.The plane vertical with optical axis sets up virtual reference planes, and reference planes and clinoplane have identical center, and parallel with holographic facet.Holographic facet, lens 3 and reference planes form the optical system of a Fourier Transform of Fractional Order, reference planes are z=0.7m to the distance of lens, therefore according to formula z=ftan (a π/4) sin (a pi/2) of exponent number and distance, the exponent number being easy to the Fourier Transform of Fractional Order of the system that calculates is a=1.25, then with the y-axis at the place, center of reference planes for turning axle, rotate the position that 30 ° can obtain clinoplane.Wherein, according to the theoretical model of Fourier Transform of Fractional Order, phase spatial light modulator 1 arrives reference planes x to the distance of lens 3 with lens 3 _rdistance z be the same.

According to the above-mentioned parameter determined, the iterative algorithm shown in Fig. 3 is adopted to carry out iterative diffusion between clinoplane and holographic facet, holographic facet applies unit amplitude constraint condition, the gray scale of two dimensional image is applied as constraint condition at clinoplane, after iteration, holographic facet obtains PHASE DISTRIBUTION, after coding, obtains phase hologram.

The phase hologram obtained is loaded in spatial light modulator 1 through computing machine 7, just can obtain the corresponding two dimensional image rebuild at clinoplane 4.Therefore, if projection imaging on the clinoplane wanting any distance after the lens, as long as determine the distance of the angle of clinoplane and the center of plane and lens, then phase hologram is obtained with the propagation computing method of clinoplane and iterative algorithm, can on the clinoplane wanting imaging reconstruction from projections imaging, and this projection pattern is pure phase projection, there is very high light diffraction efficiency and image quality.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. a pure phase position holographic projection methods for clinoplane, is characterized in that: comprise the following steps:

Step 1), lay projector equipment: phase spatial light modulator (1), Amici prism (2), lens (3) and inclination screen (4) are laid successively, make phase spatial light modulator (1), Amici prism (2), lens (3) and screen (4) be on same straight line; Simultaneously, mono-colour laser (5) and polaroid (6) is laid in the same side of Amici prism (2), polaroid (6) is positioned between Amici prism (2) and mono-colour laser (5), the plane wave that mono-colour laser (5) sends becomes polarized light by polaroid (6), and polarized light can be injected in phase spatial light modulator (1) by after Amici prism (2); Phase spatial light modulator (1) is connected by data line with the computing machine (7) generating phase hologram; Position residing for phase spatial light modulator (1) forms holographic facet x ₀, the position residing for screen (4) forms clinoplane x;

Step 2), set up virtual reference planes x _r, reference planes x _rbe same center with clinoplane x and with holographic facet x ₀parallel;

Step 3), according to rotation of coordinate relation, set up reference planes x _rand the optical field distribution relation between clinoplane x:

F(u',v')＝FT[f(x',y')]

G (u, v)=F (α ^-1(u, v), β ^-1(u, v))=F (u', v') formula (1)

g(x,y)＝FT ^-1[G(u,v)]

In formula (1), the light field complex amplitude function that f (x', y') is clinoplane x, x', y' is the independent variable of f (x', y'), represents the coordinate of each point on clinoplane, F (u', v') be the angular spectrum function of clinoplane x, u', v' are the coordinate in corresponding angular spectrum space, G (u, v) is reference planes x _rangular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u, v)) represent from clinoplane x to reference planes x _rcoordinate transform, g (x, y) is reference planes x _rlight field complex amplitude function, x, y be in reference planes each point coordinate; FT is Fourier transform, FT ^-1for inverse Fourier transform;

Step 4), the focal distance f of measuring and calculating lens (3) and reference planes x _rdistance z between relation:

According to the Fourier Transform of Fractional Order formula of formula (2), set up holographic facet x ₀with reference planes x _rbetween light propagate function:

$g\left(x\right)=\∫F\left(x_0\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (\mathrm{a\π}/2)})\right]d{x}_0$ Formula (2)

In formula (2), g (x) is reference planes x _rlight field complex amplitude function, x is the independent variable of g (x), F (x ₀) be holographic facet x ₀light field complex amplitude function, x ₀for F (x ₀) independent variable, i is imaginary unit, and λ is the wavelength of the plane wave that mono-colour laser (5) sends, and a is the exponent number of Fourier Transform of Fractional Order, f _efor standard focal length, f _e=fsin (a pi/2)=z/tan (a π/4), makes Q=sin (a pi/2), R=tan (a π/4), then f _e=fQ=z/R;

Secondly, by f _e=fQ=z/R can obtain reference planes x _rdistance z and the relation of focal distance f of lens (3) such as formula shown in (3):

Z=fRQ formula (3);

Step 5), after the exponent number a according to formula (3) certainty annuity mid-score rank Fourier transform, utilize the holographic facet x that formula (1) and formula (2) are determined ₀with the light propagation relation between clinoplane x carries out iterative computation, to obtain on clinoplane x two dimensional image at holographic facet x ₀on phase hologram;

Step 6), according to step 5) phase hologram that obtains, be transferred in phase spatial light modulator (1) by computing machine (7) by this phase hologram, phase hologram scioptics (3) project on the inclination screen (4) of assigned address by recycling phase spatial light modulator (1).

2. the pure phase position holographic projection methods of a kind of clinoplane according to claim 1, is characterized in that: described step 5) comprise the following steps:

Step 5.1), light field complex amplitude is multiplied by phase factor according to amplitude factor and represents, makes holographic facet x ₀amplitude factor be 1, phase factor is random phase;

Step 5.2), the reference planes x according to formula (2) _rlight field complex amplitude function, obtain reference planes x _ron light field COMPLEX AMPLITUDE;

Step 5.3), the clinoplane x light field complex amplitude represented according to formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains the light field complex amplitude on clinoplane x;

Step 5.4), the gray-scale value of the amplitude factor in the light field complex amplitude on clinoplane x with the two dimensional image that will rebuild is replaced, and the phase factor in the light field complex amplitude on clinoplane x remains unchanged;

Step 5.5), the clinoplane x light field complex amplitude shown in recycling formula (1) and reference planes x _rthe relation of light field complex amplitude, obtains reference planes x _ron light field complex amplitude;

Step 5.6), recycle and calculate holographic facet x such as formula the Fourier Transform of Fractional Order formula inverse transformation formula shown in (4) ₀on light field complex amplitude;

$F\left(x_0\right)=\∫g\left(x\right)\·\exp \left[\mathrm{i\π}(\frac{{x_0}^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}+\frac{x^2}{\mathrm{\λ}{f}_e\tan (-\mathrm{a\π}/2)}-\frac{2x_{0}x}{\mathrm{\λ}{f}_e\sin (-\mathrm{a\π}/2)})\right]dx$ Formula (4);

Step 5.7), by holographic facet x ₀on light field complex amplitude in amplitude factor unit strength value 1 replace, holographic facet x ₀on light field complex amplitude in phase factor remain unchanged;

Step 5.8), repeat step 5.1) to 5.7), iterate, until holographic facet x ₀on adjacent twice light field complex amplitude in the root-mean-square error of phase factor be less than 0.05 after stop iteration, obtain holographic facet x ₀on the phase factor of light field complex amplitude, the holographic facet x obtained after will iteration being stopped according to formula (5) ₀on the phase factor of light field complex amplitude carry out phase encoding, obtain phase hologram;

$\mathrm{\φ}=255-\left[\frac{({\mathrm{\φ}}_0+\mathrm{\π})\×255}{2\mathrm{\π}}\right]$ Formula (5)

In formula (5), φ ₀the holographic facet x obtained after representing iteration ₀on the phase factor value of light field complex amplitude, φ represents the holographic facet x obtained after phase encoding ₀on the phase factor value of light field complex amplitude.