CN103235477A - Pure phase holographic projection method for inclined plane - Google Patents

Abstract

The invention discloses a pure phase holographic projection method for an inclined plane. The method comprises the following steps: 1) arranging projection equipment: sequentially arranging a phase spatial light modulator, a beam splitter prism, a lens and a screen, arranging a single-color laser and a polarizing sheet on the same side of the beam splitter prism, and connecting the phase spatial light modulator with a computer; 2) determining parameters in a system such as an inclined angle of the inclined plane, the sampling interval and resolution of the spatial light modulator, and the focal distance of the lens; 3) performing iterative calculation by using coordinate rotation, an interpolation algorithm and a fractional order Fourier transformation and inverse transformation formula to obtain the phase of a two-dimensional image; and 4) transmitting a phase hologram to the phase spatial light modulator through the computer, and projecting the phase hologram to an inclined screen at an appointed position by using the phase spatial light modulator. According to the holographic projection method, the two-dimensional image which is reconstructed by the hologram can be projected to the inclined plane at a random position behind the lens, and the distance of the inclined plane can be conveniently controlled.

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

The propagation of optical field distribution in the space for traditional calculating clinoplane, the general method that adopts is: the optical field distribution of at first calculating reference planes by the rotation of coordinate in angular spectrum territory, and then come the optical field distribution on the calculation holographic face by light plane-parallel communication theory (as the angular spectrum method) in the space, in this case, the optical field distribution that obtains at holographic facet is the form of complex amplitude, namely comprise amplitude information and phase information simultaneously, therefore to realize the modulation of pure phase position, must carry out phase encoding to complex amplitude, thereby increase complicacy and error.And on the other hand, for traditional pure phase position line holographic projections, the phase hologram map generalization is to adopt 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 and calculating such as need not encode by iteration.But in this technology, imaging surface is parallel with holographic facet, and phase hologram can only carry out projection in the plane parallel with holographic facet in the space, and projection imaging becomes all the time on the back focal plane of lens, image-forming range is the focal length of lens just, for practical application certain restriction is arranged.

Summary of the invention

Goal of the invention: a kind of pure phase position holographic projection methods of clinoplane is provided, the two dimensional image of hologram reconstructing is projected on the clinoplane of any distance in the space, and the focal length that does not need to change lens is controlled to the distance of picture; And modulation system reduces complexity of traditional methods and degree of error for the modulation of pure phase position.

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 may further comprise the steps:

Step 1) is laid projector equipment: phase spatial light modulator 1, Amici prism 2, lens 3 and inclination screen 4 are laid successively, made phase spatial light modulator 1, Amici prism 2, lens 3 and screen 4 be on same the straight line; Simultaneously, mono-colour laser 5 and polaroid 6 are laid in the same side at 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 can be injected in the phase spatial light modulator 1 after by Amici prism 2; Phase spatial light modulator 1 and the computing machine 7 that generates phase hologram are connected by data line; Phase spatial light modulator 1 residing position forms holographic facet x ₀, screen 4 residing positions form clinoplane x;

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

Step 3) according to the rotation of coordinate relation, is set up reference planes x _rAnd the relation of the optical field distribution between the 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 the formula (1), and f (x ', y ') be the light field complex amplitude function of clinoplane x, x ', y ' is the independent variable of f (x ', y '), the coordinate of each point on the expression clinoplane, F (u ', v ') be the angular spectrum function of clinoplane x, u ', v ' are the coordinate in corresponding angular spectrum space, (u v) is reference planes x to G _rThe angular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u v)) represents from clinoplane x to reference planes x _rCoordinate transform, (x y) is reference planes x to g _rLight field complex amplitude function, x, y are the coordinate of each point on the reference planes.FT is Fourier transform, FT ^-1Be inverse Fourier transform;

Step 4), focal distance f and the reference surface x of measuring and calculating lens 3 _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 the function propagated of light:

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

In the 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 ₀Be F (x ₀) independent variable, i is imaginary unit, λ is the wavelength of the plane wave that sends of mono-colour laser 5, a is the exponent number of Fourier Transform of Fractional Order, f _eBe 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 the focal distance f of lens (3) as the formula (3):

Z=fRQ formula (3);

Step 5), determine the exponent number a of system's mid-score rank Fourier transform according to formula (3) after, the holographic facet x that utilizes formula (1) and formula (2) to determine ₀And tilt and carry out iterative computation as the propagation of the light field between the x of plane relation, obtain clinoplane x and go up two dimensional image at holographic facet x ₀On phase hologram;

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

Wherein, described step 5) may further comprise the steps:

Step 5.1), the light field complex amplitude multiply by phase factor according to amplitude factor to be represented, makes holographic facet x ₀Amplitude factor be 1, phase factor is random phase;

Step 5.2), according to the reference planes x shown in the formula (2) _rLight field complex amplitude function, obtain reference planes x _rOn the light field COMPLEX AMPLITUDE;

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

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

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

Step 5.6), recycling Fourier Transform of Fractional Order formula inverse transformation formula as the formula (4) calculates holographic facet x ₀On the 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), with holographic facet x ₀On the light field complex amplitude in amplitude factor replace holographic facet x with unit strength value 1 ₀On the light field complex amplitude in phase factor remain unchanged;

Step 5.8), repeating step 5.1) to 5.7), iterate, up to holographic facet x ₀On adjacent twice light field complex amplitude in the root-mean-square error of phase factor after 0.05, stop iteration, obtain holographic facet x ₀On the phase factor of light field complex amplitude, will stop the holographic facet x that obtains after the iteration 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 the formula (5), φ ₀The holographic facet x that obtains after the expression iteration ₀On the phase factor value of light field complex amplitude, φ represents the holographic facet x through obtaining after the phase encoding ₀On the phase factor value of light field complex amplitude.

Beneficial effect: the 1. pure phase position of clinoplane modulation.The present invention combines the communication theory of traditional clinoplane in the space with Gerschberg-Saxton (GS) algorithm, obtained the phase place recovery algorithms of clinoplane image, this algorithm is propagated to the contrary of clinoplane to propagation and the holographic facet of holographic facet based on clinoplane, apply amplitude at clinoplane and holographic facet respectively and retrain to carry out loop iteration, finally the PHASE DISTRIBUTION that is optimized at holographic facet.Utilize pure phase bit space photomodulator, can the clinoplane in the space obtain the reconstructed image of two dimensional image.With traditional clinoplane imaging modulation phase ratio, the hologram that this method obtains is phase-only hologram, has very high light diffraction efficiency, and after the iterative computation by certain number of times, the error of reconstructed 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 be projected in phase hologram on the clinoplane of any distance behind the lens, does not need to change the focal length of lens according to the distance of imaging.Phase-only hologram is to adopt the iterative algorithm based on Fourier Transform of Fractional Order to generate, when using phase type spatial light modulator to carry out projection, according to the characteristics of Fourier Transform of Fractional Order, the hologram that utilizes this method to generate can be image projection on the clinoplane of any distance behind the lens.Therefore, the present invention has not only realized the pure phase position projection on clinoplane, and can control easily and be inclined to the image planes distance.

Description of drawings

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

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

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

Embodiment

Below in conjunction with accompanying drawing the present invention is done further explanation.

As shown in Figure 1, a kind of pure phase position holographic projection methods of clinoplane may further comprise the steps:

Step 1) is laid projector equipment: phase spatial light modulator 1, Amici prism 2, lens 3 and inclination screen 4 are laid successively, made phase spatial light modulator 1, Amici prism 2, lens 3 and screen 4 be on same the straight line.Simultaneously, mono-colour laser 5 and polaroid 6 are laid in the same side at 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 can be injected in the phase spatial light modulator 1 after by Amici prism 2.Phase spatial light modulator 1 and the computing machine 7 that generates phase hologram are connected by data line.Phase spatial light modulator 1 residing position forms holographic facet x ₀, screen 4 residing positions form clinoplane x.

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

Step 3) according to the rotation of coordinate relation, is set up reference planes x _rAnd the relation of the optical field distribution between the 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 the formula (1), and f (x ', y ') be the light field complex amplitude function of clinoplane x, x ', y ' is the independent variable of f (x ', y '), the coordinate of each point on the expression clinoplane, F (u ', v ') be the angular spectrum function of clinoplane x, u ', v ' are the coordinate in corresponding angular spectrum space, (u v) is reference planes x to G _rThe angular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u v)) represents from clinoplane x to reference planes x _rCoordinate transform, (x y) is reference planes x to g _rLight field complex amplitude function, x, y are the coordinate of each point on the reference planes.FT is Fourier transform, FT ^-1Be inverse Fourier transform.

Step 4), focal distance f and the reference surface x of measuring and calculating lens 3 _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 the function propagated of light:

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

In the 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 ₀Be F (x ₀) independent variable, i is imaginary unit, λ is the wavelength of the plane wave that sends of mono-colour laser 5, a is the exponent number of Fourier Transform of Fractional Order, f _eBe 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 the focal distance f of lens 3 as the formula (3):

Z=fRQ formula (3);

Step 5), determine the exponent number a of system's mid-score rank Fourier transform according to formula (3) after, the holographic facet x that utilizes formula (1) and formula (2) to determine ₀And tilt and carry out iterative computation as the propagation of the light field between the x of plane relation, obtain clinoplane x and go up two dimensional image at holographic facet x ₀On phase hologram.

Wherein, step 5) may further comprise the steps:

Step 5.1), the light field complex amplitude multiply by phase factor according to amplitude factor to be represented, makes holographic facet x ₀Amplitude factor be 1, phase factor is random phase.

Step 5.2), according to the reference planes x shown in the formula (2) _rLight field complex amplitude function, obtain reference planes x _rOn the light field COMPLEX AMPLITUDE.

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

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

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

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

Step 5.6), recycling Fourier Transform of Fractional Order formula inverse transformation formula as the formula (4) calculates holographic facet x ₀On the 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), with holographic facet x ₀On the light field complex amplitude in amplitude factor replace holographic facet x with unit strength value 1 ₀On the light field complex amplitude in phase factor remain unchanged.

Step 5.8), repeating step 5.1) to 5.7), iterate, up to holographic facet x ₀On adjacent twice light field complex amplitude in the root-mean-square error of phase factor after 0.05, stop iteration, obtain holographic facet x ₀On the phase factor of light field complex amplitude, will stop the holographic facet x that obtains after the iteration 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 the formula (5), φ ₀The holographic facet x that obtains after the expression iteration ₀On the phase factor value of light field complex amplitude, φ represents the holographic facet x through obtaining after the phase encoding ₀On the phase factor value of light field complex amplitude.

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

Among the present invention, phase hologram is loaded in the 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 behind the Amici prism 2, inject spatial light modulator 1, light wave carries out phase place 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 behind lens 3, the distance of clinoplane and lens can be regulated by the exponent number of control Fourier Transform of Fractional Order, the distance that different exponent number is corresponding different, image can be projected on the clinoplane of any distance and not be subjected to the restriction of the focal length of lens.

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 the process of two dimensional image in line holographic projections, adopt the light channel structure of Fourier Transform of Fractional Order correspondence to realize this process.In the measuring and calculating process of hologram, the communication theory of light field between the clinoplane with combine with traditional GS iterative algorithm, and calculate the diffraction propagation of light in the space with Fourier Transform of Fractional Order, and finally obtain the phase-only hologram of clinoplane by iteration.In process of reconstruction, phase hologram is loaded in the phase spatial light modulator 1, by the irradiation of rebuilding light wave the light generation phase place of each pixel is modulated, and imaging on the clinoplane behind the lens 3.

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

Clinoplane 4 is set behind the lens 3, and the angle of inclination of clinoplane is α=30 °, and direction is to rotate around the y axle.Set up virtual reference planes on the plane vertical with optical axis, reference planes have identical center with clinoplane, and parallel with holographic facet.Holographic facet, lens 3 and reference planes are formed 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 that is easy to the Fourier Transform of Fractional Order of the system that calculates is a=1.25, y axle with the place, center of reference planes is turning axle then, rotates 30 ° of positions that can obtain clinoplane.Wherein, according to the theoretical model of Fourier Transform of Fractional Order, phase spatial light modulator 1 is to the distance and lens 3 to reference planes x of lens 3 _rDistance z be the same.

According to above-mentioned definite parameter, adopting iterative algorithm shown in Figure 3 to carry out iteration between clinoplane and holographic facet propagates, apply unit amplitude constraint condition at holographic facet, apply the gray scale of two dimensional image as constraint condition at clinoplane, through after the iteration, obtain PHASE DISTRIBUTION at holographic facet, through obtaining phase hologram behind the coding.

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

The above only is preferred implementation of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the principle 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. the pure phase position holographic projection methods of a clinoplane is characterized in that: may further comprise the steps:

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

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

Step 3) according to the rotation of coordinate relation, is set up reference planes x _rAnd the relation of the optical field distribution between the 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 the formula (1), and f (x ', y ') be the light field complex amplitude function of clinoplane x, x ', y ' is the independent variable of f (x ', y '), the coordinate of each point on the expression clinoplane, F (u ', v ') be the angular spectrum function of clinoplane x, u ', v ' are the coordinate in corresponding angular spectrum space, (u v) is reference planes x to G _rThe angular spectrum function, u, v are the coordinate in corresponding angular spectrum space, (α ^-1(u, v), β ^-1(u v)) represents from clinoplane x to reference planes x _rCoordinate transform, (x y) is reference planes x to g _rLight field complex amplitude function, x, y are the coordinate of each point on the reference planes.FT is Fourier transform, FT ^-1Be inverse Fourier transform;

Step 4), focal distance f and the reference surface x of measuring and calculating lens (3) _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 the function propagated of light:

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

In the 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 ₀Be F (x ₀) independent variable, i is imaginary unit, λ is the wavelength of the plane wave that sends of mono-colour laser (5), a is the exponent number of Fourier Transform of Fractional Order, f _eBe 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 the focal distance f of lens (3) as the formula (3):

Z=fRQ formula (3);

Step 5), determine the exponent number a of system's mid-score rank Fourier transform according to formula (3) after, the holographic facet x that utilizes formula (1) and formula (2) to determine ₀And tilt and carry out iterative computation as the propagation of the light field between the x of plane relation, obtain clinoplane x and go up two dimensional image at holographic facet x ₀On phase hologram;

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

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

Step 5.1), the light field complex amplitude multiply by phase factor according to amplitude factor to be represented, makes holographic facet x ₀Amplitude factor be 1, phase factor is random phase;

Step 5.2), according to the reference planes x shown in the formula (2) _rLight field complex amplitude function, obtain reference planes x _rOn the light field COMPLEX AMPLITUDE;

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

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

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

Step 5.6), recycling Fourier Transform of Fractional Order formula inverse transformation formula as the formula (4) calculates holographic facet x ₀On the 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), with holographic facet x ₀On the light field complex amplitude in amplitude factor replace holographic facet x with unit strength value 1 ₀On the light field complex amplitude in phase factor remain unchanged;

Step 5.8), repeating step 5.1) to 5.7), iterate, up to holographic facet x ₀On adjacent twice light field complex amplitude in the root-mean-square error of phase factor after 0.05, stop iteration, obtain holographic facet x ₀On the phase factor of light field complex amplitude, will stop the holographic facet x that obtains after the iteration 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 the formula (5), φ ₀The holographic facet x that obtains after the expression iteration ₀On the phase factor value of light field complex amplitude, φ represents the holographic facet x through obtaining after the phase encoding ₀On the phase factor value of light field complex amplitude.

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