CN108519729A - A kind of large scale high-resolution color Fresnel holographic production method and display system - Google Patents
A kind of large scale high-resolution color Fresnel holographic production method and display system Download PDFInfo
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
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Abstract
The invention discloses a kind of large scale high-resolution color Fresnel holographic production methods and display system, method to include the following steps：The influence that analysis space sampling reproduces Fresnel hologram picture point gives the Parameter Conditions that colored Fresnel holographic is realized；Three primary colors Fresnel hologram is calculated separately to 3 D color object, the size of each color cell hologram is designed according to Parameter Conditions, it is designed with gap between two adjacent color cell hologram sizes, three primary colors Fresnel hologram is decomposed and recombinated according to the size of each color cell hologram and the gap parameter of adjacent color unit hologram, colored Fresnel hologram is obtained；Pass through designed optical system imaging chromatic grating picture, chromatic grating picture and each color unit holography graph parameter and position consistency in colored Fresnel hologram, colored Fresnel hologram is positioned over chromatic grating image planes and is adjusted, realizes large scale high-resolution color Fresnel holographic Three-dimensional Display.
Description
Technical field
The invention belongs to the technical fields that hologram three-dimensional is shown, and in particular to a kind of large scale high-resolution color Fresnel is complete
Cease production method and display system.
Background technology
Hologram three-dimensional is shown, utilizes the true stereoscopic display of principle of holography realization, it can be seen that all spies of stereoscopic display
Parallax effect is levied and had, the phase and amplitude information of three-dimensional scenic can be completely reproduced using this technology, is at present by state
Border is generally recognised as ideal dimension display technologies.Large scale holography therein, it is main include calculate rainbow holography,
It calculates image plane holographic and calculates Fresnel holographic, but above-mentioned holographic display all has disadvantage, specifically, calculates rainbow holography only
Include the parallax in a direction；Although and calculate image plane holographic can with white light reconstruction, its show the three-dimensional scenic depth of field it is unsuitable
It is excessive, color blurring and line fuzzy problem are will produce once excessive；It calculates Fresnel holographic and arbitrary depth of field scene may be implemented
Three-dimensional Display generally requires and uses relevant laser light source as illumination light, realizes monochromatic display.
One (Hiroshima, Tsuchiyama, Kyoji Matsushima.Full-color of existing disclosed document
large-scaled computer generated holograms using RGB color filters[J].Optics
Express,2017,25(3):2016-2030.), document two (Y.Tsuchiyama, K.Matsushima, S.Nakahara,
and Y.Sakamoto,Full-color high-definition CGH using color filter and filter
Design based on simulation [C], in Imaging and Applied Optics.2017) in use one kind
Colored Fresnel holographic display methods, the method use three-color filters, and colour filter is plated in and is made of three primary colors hologram
Color hologram on, realize colored Fresnel holographic as light source using three monochromatic LEDs of red, green, blue and show, but the party
There are following drawbacks for method：
1, when carrying out illumination reproduction using different three monochromatic LEDs of red, green, blue, required colour filter needs root
It redesigns and replaces according to the spatial distribution of LED；
2, when the hologram size and unit hologram size that are calculated change, there is still a need for set colour filter again
It counts and replaces；
3, the technique of counterpoint difficulty between colour filter and unit hologram is big, and flexibility is poor；
4, not to due to space samples, theory analysis carried out to the picture point situation of hologram reconstruction picture, and space samples pair
There is influence in hologram reconstruction picture；
5, three monochromatic LED light-emitting areas of used red, green, blue are larger, the image caused by light-emitting area it is fuzzy also compared with
It is serious.
Large scale colour Fresnel holographic Three-dimensional Display can be used for many aspects such as product, advertisement, cultural relic exhibition, in order to
The more flexible realization large scale colour Fresnel holographic Three-dimensional Display of energy, and the difficulty and cost of display are reduced, the present invention carries
Go out a kind of production method of large scale high-resolution color Fresnel hologram and for showing that large scale high-resolution color is luxuriant and rich with fragrance
The display system of Nie Er holograms.
Invention content
The purpose of the present invention is to solve the above problem, a kind of large scale high-resolution color Fresnel holographic is provided
Production method and the system shown for large scale high-resolution color Fresnel hologram.
In order to reach foregoing invention purpose, the present invention uses following technical scheme：
A kind of large scale high-resolution color Fresnel holographic production method, includes the following steps：
Step 1 analyzes the influence that space samples reproduce Fresnel hologram picture point, it is complete to give colored Fresnel
Cease the Parameter Conditions realized；
Step 2 calculates separately three primary colors Fresnel hologram to 3 D color object；
Step 3, by chromatic grating formed by the unit hologram dimensional parameters of colored Fresnel hologram and display system
The dimensional parameters of picture are set as consistent, according to Parameter Conditions, design the size of each color cell hologram, adjacent two face
It is designed with gap between color element hologram size；By three primary colors hologram according to the size of each color cell hologram, phase
It there are gap between two adjacent color cell holograms, is split and is recombinated, form large scale high-resolution color Fresnel
Holographic, holographic figure.
Further, the step 1 specifically includes：
1.1 obtain sampled-grating parameter, calculate the COMPLEX AMPLITUDE after space samples；
1.2 hologram transmissivities are space samples Fresnel hologram, calculate believe comprising reference light on holographic facet accordingly
Under the COMPLEX AMPLITUDE of breath, Fresnel approximation and ignore the constant phase factor, finally obtains the light field after spatial sampling and shake again
Width is distributed；
1.3 are reproduced with former reference light, obtain the light field complex amplitude of hologram outgoing, the light field in image plane, light intensity,
The dimension limit of the multistage picture point of reproduction image, the extension width of picture point, spatial sampling hologram.
For easy analysis, analyzed in the form of the spatial sampling of one-dimensional hologram.
Further, the step 1.1 is specifically, sampled-grating g (xh) can be expressed as：
Wherein WhxFor the length of hologram in the x direction, a is light transmission part, and d is the period of sampled-grating, xhFor holography
The coordinate of figure in the x direction；
Assuming that hologram COMPLEX AMPLITUDE is τh(xh), then the COMPLEX AMPLITUDE after space samples can be written as：
Further, the step 1.2 is specially：It can be indicated comprising the COMPLEX AMPLITUDE with reference to optical information on holographic facet
For：
τh(xh)=o (xh)exp{i[φo(xh)-φr(xh)]} (3)
Wherein o (xh) be object light amplitude, φo(xh) be object light phase, φr(xh) reference light phase；
Under Fresnel approximation, only considers that object is a luminous point, send out divergent spherical wave, and reference light is another shines
Point, sends out spherical wave, ignores the constant phase factor, has：
Wherein (xo,zo) be object point coordinate, (xr,zr) be reference light luminous point coordinate,For wave number, λ is light
Wave wavelength.
Formula (3) can be brought into formula (4) and obtained by the light field COMPLEX AMPLITUDE after spatial sampling：：
It can be expressed as after bringing formula (4) into formula (5) expansion：
Further, the step 1.3 is specially：
When the reconstruction of hologram, the identical light of reference light used when being recorded with hologram is reproduced, that is, it is one to reproduce light
The coordinate of the divergent spherical wave that point is sent out, the luminous point is (xr,zr), it is identical with former reference light,
I.e.The light field complex amplitude being then emitted from hologram can be expressed as：
It can be written as in the light field of image plane：
WhereinIndicate object point and the distance with reference to light coordinate；
Light intensity can be expressed as：
Wherein n is the diffraction time of diffraction light.xiFor the coordinate of the picture point of reproduction.
Reproduction image is multistage picture point, and the coordinate of multistage picture point is：
Wherein xoOriginal point coordinates, that is, ideal image point coordinate, the intensity of multistage picture point by's
Modulation.When a=± 1 (n/d), picture point amplitude is 0, at this time nc=± (d/a), ncIndicate the level of the positive and negative level-one picture point of political affairs.It is other
The amplitude very little of high level can be ignored；When the sampling period, d was larger, the extension for the multistage picture point that formula (10) indicates is not
It can be spatially separating, but energy is concentrated mainly in the range of ± 1 grade of picture point, i.e.,Within in range.It therefore can be with
The range is regarded as to the equivalent picture point of a diffusion, if the size of the picture point in the viewing demand that disclosure satisfy that human eye,
The extension of picture point is negligible to the fuzzy of reproduction image.
The extension width of picture point is：
△xi=2 λ zo/a (11)
IfMeet：
Wherein δEFor the angle of minimum resolution of human eye, 1.5 ' (4.35 × 10 are traditionally arranged to be in engineering-4rad).Formula (11)
Equal sign is taken, the dimension limit of spatial sampling hologram can be found out：
Formula (13) is exactly the minimum dimension of unit hologram.
Above-mentioned theory is it is found that carry out spatial sampling to high-resolution Fresnel hologram reduces under certain condition
The data volume of hologram, but still disclosure satisfy that the requirement of human eye viewing 3-D view.Region between two sampling units, can
To calculate the hologram of the other Color Channel of 3 D color object, by spatial reuse, realize that colored Fresnel holographic is shown.
The present invention also provides a kind of a kind of high-resolution colored Fresnel holograms of large scale corresponding with the above method
Display system, including,
Light source, for generating illumination light；
Lens system, the light for sending out light source are converted into approximate planar light；
Imaging system, for the chromatic grating of Computer Design to be imaged；
Diaphragm is used for the size of limiting light source luminous point, reduces since the size that shines is big caused as fuzzy；
Computer for designing chromatic grating, and chromatic grating is transferred in optical projection system and is imaged；
Adjustment frame is carried out for the position of the whole colored Fresnel hologram of tune with chromatic grating formed by imaging system
Colored Fresnel holographic Three-dimensional Display may be implemented when location matches are consistent in location matches.
Further, the lens system includes that the diverging light that LED is sent out is converged to the lens of a bit, is placed in the convergent point
Spatial filter, the size for limiting convergent point only allows a tuftlet light to enter follow-up system；And placed at rear
Lens, spatial filter are located on the front focal plane of postposition lens, and the light beam sent out after being limited by spatial filter carries out accurate
Directly, planar light is formed, subsequent LCD is illuminated.
Further, the laser or single-chip LED that the light source corresponds to red, green, blue light wave using three.
Further, when the light source uses tri-color laser, the light that red, green, blue tri-color laser is sent out passes through respectively
Three beam-expanding collimation systems form plane wave, illuminate three amplitude types LCD, three amplitude type LCD and computer phase respectively
Even, three Color Channels of the colored raster images of design are loaded into three amplitude type LCD by the computer respectively, and three are shaken
The light that width type LCD is sent out closes Shu Houzai by Amici prism BS and passes through imaging len lensiChromatic grating is imaged, H is imaged in
Plane, H planes are to place the position of modulation frame, and colored Fresnel hologram, the size with chromatic grating are placed on adjustment frame
Match, realizes colored Fresnel hologram Three-dimensional Display；
Alternatively, when the light source is using three single-chip LED for corresponding to red, green, blue light wave, three color mono-chip single-colours
LEDr、LEDg、LEDbIt is connected with controller, controller is used to control the switch and brightness adjustment of each monochromatic single-chip LED, institute
State three color mono-chip single-colour LEDLEDr、LEDg、LEDbIt is located at three lens lens1、lens3、lens5The first two times of focal plane
Place, in three lens lens1、lens3、lens5Two times of focal plane difference placement space filter Filter afterwards1、Fliter2、
Filter3, size of the spatial filter for limiting the light beam sent out by lens rear focal point, only permission one, center cell
The light beam that domain is sent out enters follow-up system, the quality for entering follow-up lighting system light is improved, in spatial filter Filter1、
Fliter2、Filter3Lens lens is placed respectively in rear2、lens4、lens6, spatial filter Filter1、Fliter2、
Filter3It is located at lens lens2、lens4、lens6Previous times of focal length at, through three spatial filter Filter1,
Fliter2,Filter3The light sent out passes through lens respectively2、lens4、lens6Three amplitude type LEDlcd of back lightingr、lcdg、
lcdb, three amplitude type LCD are connected with computer, and three Color Channels of the colored raster images of design are loaded into three respectively
In amplitude type LCD, beam is closed by Amici prism BS by the light of three amplitude type LCD, passes through imaging len lens lateriIt will be color
Color grating image images in H planes, and modulation frame is placed in H planes, colored Fresnel hologram is placed on adjustment frame, with colour
The size of grating matches, and realizes colored Fresnel hologram Three-dimensional Display.
Further, the orthogonal polarization in the front and back placement polarization direction of each amplitude type LCD of three amplitude type LCD
Piece is used for amplitude modulation.
Further, the imaging len lensiIt is composed using two Fourier transform lenses closely.
The chromatic grating of the illuminated holograms obtained using this method and system can be reproduced as size and position are all adjustable
The various sizes of high-resolution color Fresnel hologram of different colours unit.
Compared with prior art, the present invention advantageous effect is：
1. the chromatic grating of illuminated holograms is all adjustable as size and position, different colours unit difference size can be reproduced
Colored Fresnel hologram；
2. by adjusting frame, it may be convenient to realize the location matches of colored Fresnel hologram and chromatic grating picture；
3. by spatial filter, the size for the light beam that limitation system is sent out by lens rear focal point only allows center one
The light beam that a zonule is sent out enters follow-up system, improves the quality for entering follow-up lighting system light, reduces due to illumination light ruler
It is very little it is too big caused by image it is fuzzy.
4. can adjusting the color of reproduction image by the brightness of control chromatic grating, capable of realizing the three-dimensional of color change
Display effect；
It is influence according to grating sampling to hologram and according to line is fuzzy and color 5. Fresnel hologram design parameter
What fuzzy theory was designed, there is scientific and reliability.
Description of the drawings
Fig. 1 is large scale high-resolution color Fresnel holographic design diagram；
Fig. 2 is hologram space samples schematic diagram；
Fig. 3 is the large scale high-resolution color Fresnel holographic Three-dimensional Display as lighting source based on tri-color laser
System；
Fig. 4 is beam-expanding collimation system schematic diagram；
Fig. 5 is three-dimensional as the large scale high-resolution color Fresnel holographic of lighting source based on three color single-chip LED
Display system；
Fig. 6 is the equivalent model 1 that hologram calculates；
Fig. 7 is the equivalent model 2 that hologram calculates；
Fig. 8 is the view and reconstruction of hologram result figure for the former three-dimension object for testing one；
Fig. 9 is the reconstruction results figure for testing two.
Specific implementation mode
In order to more specifically describe the present invention, below by the mode of specific embodiment combination attached drawing to skill of the invention
Art scheme is described in detail explanation.
Embodiment 1
The present embodiment as shown in Figure 1, be a kind of schematic diagram that large scale high-resolution color Fresnel holographic designs and produces,
Hor、Hog、HobThe Fresnel hologram of the red, green, blue component that are calculated by color body three primary color components, each
It is divided into multiple horizontal stripes, HorgbIt is that the colored Fresnel holographic formed after recombination is split by the hologram of three primary color components
Figure；In order to avoid the color cross-talk between the unit hologram of two different colours, there are one between two unit holograms
Fixed gap, width wp。
It is the influence of the information redundancy and spatial sampling of concrete analysis hologram to holographic reconstructed image below：
Assuming that hologram length is wh=65mm, diffraction distance is distance of distinct vision z=25cm, most sensitive using human eye
Wavelength X=555nm is calculated, and the image spot size for obtaining hologram reconstruction is λ z/wh=0.0021mm.In engineer application, one
As take resolution angles of 1.5 ' (4.35e-3rad) as human eye, the distance between distinguishable two points at distance of distinct vision 25cm
For 0.1075mm.It can be seen that the limit of resolution of the image resolution ratio that can be provided of hologram considerably beyond human eye, from resolution
From the perspective of rate, there is prodigious information redundancies for hologram；Therefore, if reducing the data volume of hologram, and cause
Picture point variation be that human eye is non, then the information content of reduction on final reproduction effects, there will be no influences, reduce
A kind of mode of information content is exactly to carry out space samples to hologram.
One complete hologram is sampled, as hologram space samples, it is complete to space samples Fresnel below
Breath display carries out theory analysis to the influence for reproducing picture point：
It is the actual conditions that human eye watches three-dimensional image by hologram in Fig. 2, as shown in Fig. 2, human eye is by receiving by office
The tiny light beam of portion's hologram diffraction to human eye watches three-dimensional scenic, if human eye is moved to the picture point that B points are watched from A points
The distinguishable variation of human eye is had no, then the hologram between A points and B points can remove, people can met using this method
The data volume and calculation amount of computed hologram are reduced in the case of eye viewing demand, this also exactly carries out Fresnel hologram empty
Between the basic point of departure that samples.Region between E and E' is the range that human eye can see object point A, is recorded by hologram
The angle that object point A sends out light wave determines that hologram is bigger, then the range that can watch A points is bigger.zoFor object point A to holography
The distance in face.
Influence of the following analysis space samples Fresnel hologram to reproduction picture point.
In order to study conveniently, theoretical research is carried out with the space samples of one-dimensional hologram.Sampled-grating g (xh) can indicate
For：
Wherein WhxFor the length of hologram in the x direction, a is light transmission part, and d is the period of sampled-grating, xhFor holography
The coordinate of figure in the x direction；
Assuming that hologram COMPLEX AMPLITUDE is τh(xh), then the COMPLEX AMPLITUDE after space samples can be written as：
When hologram calculates, can be expressed as comprising the COMPLEX AMPLITUDE with reference to optical information on holographic facet：
τh(xh)=o (xh)exp{i[φo(xh)-φr(xh)]} (3)
Wherein o (xh) be object light amplitude, φo(xh) be object light phase, φr(xh) reference light phase；
Under Fresnel approximation, only considers that object is a luminous point, send out divergent spherical wave, and reference light is another shines
Point sends out spherical wave, the i.e. influence with the holographic analytical sampling of member to reproduction picture point, ignores the constant phase factor, have：
Wherein (xo,zo) be object point coordinate, (xr,zr) be reference light luminous point coordinate,For wave number, λ is light
Wave wavelength.
Formula (3) can be brought into formula (4) and obtained by the light field COMPLEX AMPLITUDE after spatial sampling：：
It can be expressed as after bringing formula (4) into formula (5) expansion：
When the reconstruction of hologram, the identical light of reference light used when being recorded with hologram is reproduced, that is, it is one to reproduce light
The coordinate of the divergent spherical wave that point is sent out, the luminous point is (xr,zr), it is identical with former reference light,
I.e.The light field complex amplitude being then emitted from hologram can be expressed as：
It can be written as in the light field of image plane：
WhereinIndicate object point and the distance with reference to light coordinate；
Light intensity can be expressed as：
Wherein n is the diffraction time of diffraction light.xiFor the coordinate of the picture point of reproduction.
Reproduction image is multistage picture point, and the coordinate of multistage picture point is：
Wherein xoOriginal point coordinates, that is, ideal image point coordinate, the intensity of multistage picture point by's
Modulation system.When a=± 1 (n/d), picture point amplitude is 0, at this time nc=± (d/a), ncIndicate the level of the positive and negative level-one picture point of political affairs.Its
The amplitude very little of its high level can be ignored；When the sampling period, d was larger, the extension for the multistage picture point that formula (10) indicates
It cannot be spatially separating, but energy is concentrated mainly in the range of ± 1 grade of picture point, i.e.,Within in range.It therefore can
The range to be regarded as to the equivalent picture point of a diffusion, if the size of the picture point in the viewing demand that disclosure satisfy that human eye,
Then the extension of picture point is negligible to the fuzzy of reproduction image.
The extension width of picture point is：
△xi=2 λ zo/a (11)
IfMeet：
Wherein δEFor the angle of minimum resolution of human eye, 1.5 ' (4.35 × 10 are traditionally arranged to be in engineering-4rad).Formula (11)
Equal sign is taken, the dimension limit of spatial sampling hologram can be found out：
Formula (13) is exactly w shown in unit hologram minimum dimension i.e. Fig. 1r,wg,wbThe foundation of design.In reality
When holography display, in several times of unit hologram size reduction, human eye is still diffusion of point image caused by the extension of multistage picture point
The reproduction image that acceptable, that is, human eye is watched is still that clearly, human eye is acceptable, therefore can design smaller list
First hologram size.Part between two unit holograms, if gap is very big, human eye will appear sudden strain of a muscle when watching hologram
It sparkles, referred to as fence effect；In order to avoid fence effect, one such mode is exactly to calculate 3 D color object different colours
The hologram of component is filled in fence region, realizes colored Fresnel hologram, that is, H shown in Fig. 1orgb,
In HorgbIn gap between two color cell holograms be very small, the fence effect caused by the gap can be ignored
Disregard.
Fig. 3 is the designed large scale high-resolution color Fresnel holographic based on three color laser light sources as illumination light
Display system, laser in figurer、laserg、laserbRespectively red, green, blue tri-color laser, the light sent out pass through expansion respectively
Beam colimated light system CE1,CE2,CE3After form plane wave, illuminating three amplitude type LCD respectively, (LCD is front and back to place polarization direction just
The polarizing film of friendship is, it can be achieved that amplitude modulation) lcdr、lcdg、lcdb, three amplitude type LCD are connected with computer, can be by design
Three Color Channels of colored raster images are loaded into respectively in three LCD.Beam is closed by Amici prism BS by the light of LCD, it
Pass through imaging len lens afterwardsiChromatic grating is imaged, H planes are imaged on, H is the position for placing modulation frame, is put on adjustment frame
Colored Fresnel hologram is set, colored Fresnel hologram is adjusted by adjusting frame so that colored Fresnel hologram and colour
The position of grating accurately matches, and realizes, red optical illumination colour Fresnel hologram red component, the colored luxuriant and rich with fragrance alunite of green optical illumination
That hologram green component, blue optical illumination colour Fresnel hologram blue portion, you can realize colored Fresnel hologram
Three-dimensional Display.F is imaging len lens in figureiNear back focal plane, since the color of three coloured light is different, chromatic grating is in lens
The convergent point position of back focal plane difference, the distance z of convergent point to holographic facet Hh, can be write as zr、zgAnd zb, have not
Same parameter.When convergent point is formation of hologram, the position where reference light.
Fig. 4 is the schematic diagram of the beam-expanding collimation system in Fig. 3, and beam-expanding collimation system has space Filter and lens
Composition, filter are located on the front focal plane of lens, can be directional light by the line laser beam-expanding collimation that laser is sent out.
Fig. 5 is the colored Fresnel holographic display system based on three three color single-chip LED illuminations.Three color mono-chip single-colours
LED is connected with LED controller LED controller, and LED controller can control the switch and brightness adjustment of each led.
Three mono-chip single-colour LED, that is, LEDr、LEDg、LEDbIt is located at lens lens1、lens3、lens5The first two times of focal plane,
Lens lens1、lens3、lens5Two times of focal planes place filter Filter respectively afterwards1、Fliter2、Filter3, control
The size of LED luminous points.In Filter1,Fliter2,Filter3Place lens respectively afterwards2,lens4,lens6, Filter1,
Fliter2,Filter3It is located at lens2,lens4,lens6Previous times of focal length at, from Filter1,Fliter2,Filter3
The light sent out passes through lens respectively2,lens4,lens6Back lighting lcdr,lcdg,lcdb, three amplitude type LCD are connected with computer,
Three Color Channels of the colored raster images of design can be loaded into respectively in three LCD.By the light of LCD by light splitting rib
Mirror BS closes beam, passes through imaging len lens lateriChromatic grating is imaged, H planes are imaged in, H is the position for placing modulation frame,
Colored Fresnel hologram is placed on adjustment frame, is matched with the size of chromatic grating, you can realizes colored Fresnel hologram three
Dimension display.Wherein F is imaging len lensiNear back focal plane, since the color of three coloured light is different, chromatic grating is after the lens
The convergent point position of focal plane difference, the distance z of convergent point to holographic facet Hh, can be write as zr、zgAnd zb, there is difference
Parameter.When convergent point is formation of hologram, the position where reference light.
There are two types of equivalent light paths for the making of hologram：
1>When object and hologram distance farther out when, corresponding equivalent light path is as shown in Figure 6.The wherein luminous point of reference light
In the center of the back focal plane of imaging, for different colors, center difference, hologram is symmetrical about optical axis,
The width of hologram is set as L, and object is z at a distance from hologramo.In order to meet the display condition of off-axis gaussian beam, object with
There are an offset x for optical axisoshift=xominThe width of+△, object are wo.As seen from the figure, reference light and object light maximum angle
αromaxThe light sent out by object up contour point connects in holographic facet lower edge line and reference light luminous point with hologram down contour point
The angle of line determines, can be expressed as：
Maximum spatial frequency on holographic facet is：
Spatial frequency on hologram is determined as f by holographic output systemh, in order to meet sampling thheorem, have：
fh≥2fxmax (16)
It is as follows using cloud algorithm come computed hologram after determining dimension of object and calculating parameter：
Wherein N is the points of three-dimension object, AnFor n-th point of amplitude, φonFor the phase of object light, φrFor reference light
Phase, RnFor the distance of object coordinates to holographic facet；
After the completion of trichromatic three holograms of color body calculate, it can be spliced according to method shown in FIG. 1,
Colored Fresnel hologram is obtained, is exported later by holographic output system, then is placed on Fig. 3 or system shown in fig. 5
The positions H of system, are aligned, and colored Fresnel holographic Three-dimensional Display can be realized in illumination.
2>When object distance holographic facet is close, carrying out hologram calculating according to Fig. 6 modes will become no longer feasible, former
Because being, for one and the comparable object of hologram size, line and reference of the object edge to hologram other edge
The very big of change is had very high spatial frequency by the angle of light on hologram, it will be difficult to meet holographic output system
Requirement.
At this point, carrying out hologram calculating using equivalent model shown in Fig. 7.The lighting system of reference light is identical as Fig. 6, object
Displacement is not present in body in the X direction, sets the light emitting angle having the same of every bit on object, p (x as shown in the figureo,yo)
One object point, light emitting angle is in θx1And θx2Between, in order to meet off-axis gaussian beam condition, it is desirable that θx1The corresponding space frequency of angle
Rate is higher than the spatial frequency of reference light, hasObject light and reference light maximum angle on hologram are sent out by object point
Light lower edge light and the angle of reference light lower edge light determine, can be expressed as：
Maximum spatial frequency on holographic facet is：
It will be apparent that it can be seen from the figure that a regional area of the light that sends out of object point on holographic facet, can calculate
On holographic facet, P points send out light COMPLEX AMPLITUDE directions x on holographic facet range xhp：
xo+zotan(θx1)≤xhp≤xo+zotan(θx2) (21)
As object point light emitting angle θ on the given directions yy1And θy2Afterwards, the COMPLEX AMPLITUDE that P points send out light can equally be calculated
The range y in the directions y on holographic facethp:
yo+zotan(θy1)≤yhp≤yo+zotan(θy2) (22)
After sampling and parameter determine, the calculating of hologram can be carried out according to formula (16), difference is only each object
Distributed areas of the point on holographic facet are determined by formula (20) and formula (21).When the trichromatic three hologram meters of color body
After the completion of calculation, it can be spliced according to method shown in FIG. 1, obtain colored Fresnel hologram, be exported later by holography
System is exported, then is placed on the positions H of Fig. 3 or system shown in fig. 5, and contraposition is adjusted using adjustment frame, illumination
Colored Fresnel holographic Three-dimensional Display can be realized in hologram.
Embodiment 2
The present embodiment is illustrated by specific parameter setting on the basis of embodiment 1.
According to the schematic diagram of Fig. 5, optical system is devised, the centre wavelength of three monochromatic LEDs is respectively λr=630nm, λg
=521nm, λb=468nm, spectral half width are respectively △ λr=17nm, △ λg=38nm, △ λb=28nm.It is used
The power of three-color LED is respectively：Red LED power is 5w, green LED power 3w, blue led power 3w.lens1、lens3With
lens5For the cemented doublet of identical parameters, bore 25.4mm, focal length 30mm.Filter1、Filter2And Filter3For
Adjustable rectangular aperture, diaphragm adjustable range are 0.1mm to 12mm, are located at lens1、lens3And lens5Afterwards at two times of focal lengths.
LEDr、LEDgAnd LEDbFor the single-chip LED light source used, it is located at lens1、lens3And lens5At the first two times of focal length.LED
By lens at etc. big picture, image planes position be arranged diaphragm, to control the size of LED luminous points.lens2、lens4And lens6
Be focal length it is 60mm, the cemented doublet of bore 25.4mm with identical parameters.Three diaphragms are located at lens2、lens4
And lens6Front focal plane on, lcd is illuminated by filtered light respectively by lens forming almost plane waver、lcdgWith
lcdb。lcdr、lcdgAnd lcdbIt is preceding to place orthogonal polarizing film, realize amplitude modulation.The resolution ratio of used 0.55 cun of LCD
It is 1024 × 768.By LCD light by lens lens after Amici prism BS closes beam7Imaging, used in an experiment two it is tight
The Fourier transform lens combination suffered is used as imaging len lens7, the bore of Fourier transform lens is 50mm, and focal length is
300mm。
First, the colored Fresnel hologram of a complicated colorful three-dimensional model, size X × Y × Z=are calculated
16.85mm × 27.65mm × 14.37mm, zr=372mm, zg=364mm and zb=360mm.Each color component when calculating
Wavelength is the centre wavelength of LED, and hologram size is 30mm × 30mm, and resolution ratio is 94208 × 94208.Between holographic surface sample
It is divided into 0.318um.The distance of object center to holographic facet is 100mm, raster size wr=0.14mm, wg=0.133mm, wb
=0.136mm, the gap being arranged between two adjacent cells holograms are 60 Pixel Dimensions, corresponding physical size wp=
0.019mm.Offset of the object in the directions x is 10mm.Fig. 8 is that a view of the example original three-dimension object and three reproduce
Picture.
Furthermore using the computational methods of Fig. 7 devise object distance holographic facet it is close when colored Fresnel holographic display side
The experiment two of case.The parameter of parallactic angle design is 40 ° of the directions x, and 20 ° of objects are set as 20mm at a distance from hologram on the directions y,
Other calculating parameters are identical as experiment one.Fig. 9 provides the reproduction effects of the experiment.
The reproduction image of above-mentioned two experiment shoots to obtain by slr camera, and practical to watch color reduction accurately, three-dimensional is vertical
Body-sensing is strong.
It is above the preferred embodiment of the present invention, protection scope of the present invention is not limited, for people in the art
The deformation and improvement that member's mentality of designing according to the present invention is made, all should be considered as within protection scope of the present invention.
Claims (10)
1. a kind of large scale high-resolution color Fresnel holographic production method, which is characterized in that include the following steps：
Step 1 analyzes the influence that space samples reproduce Fresnel hologram picture point, it is real to give colored Fresnel holographic
Existing Parameter Conditions；
Step 2 calculates separately three primary colors Fresnel hologram to 3 D color object,
Step 3, by chromatic grating formed by the unit hologram dimensional parameters of colored Fresnel hologram and display system as
Dimensional parameters are set as consistent, according to Parameter Conditions, design the size of each color cell hologram, adjacent two color lists
It is designed with gap between first hologram size；It is adjacent by three primary colors hologram according to the size of each color cell hologram
Two color cell hologram gaps, are split and are recombinated, and large scale high-resolution color Fresnel hologram is formed.
2. a kind of large scale high-resolution color Fresnel holographic production method according to claim 1, which is characterized in that institute
Step 1 is stated to specifically include：
1.1 obtain sampled-grating parameter, calculate the COMPLEX AMPLITUDE after space samples；
1.2 hologram transmissivities are space samples Fresnel hologram, are calculated accordingly on holographic facet comprising with reference to optical information
Under COMPLEX AMPLITUDE, Fresnel approximation and ignore the constant phase factor, finally obtains the light field complex amplitude point after spatial sampling
Cloth；
1.3 are reproduced with former reference light, obtain the light field complex amplitude of hologram outgoing, the light field in image plane, light intensity, again
The dimension limit of the multistage picture point of phenomenon, the extension width of picture point, spatial sampling hologram.
3. a kind of large scale high-resolution color Fresnel holographic production method according to claim 2, which is characterized in that institute
Step 1.1 is stated specifically, sampled-grating g (xh) can be expressed as：
Wherein WhxFor the length of hologram in the x direction, a is light transmission part, and d is the period of sampled-grating, xhIt is hologram in x
Coordinate on direction；
Assuming that hologram COMPLEX AMPLITUDE is τh(xh), then the COMPLEX AMPLITUDE after space samples can be written as：
4. a kind of large scale high-resolution color Fresnel holographic production method according to claim 3, which is characterized in that institute
Stating step 1.2 is specially：It can be expressed as comprising the COMPLEX AMPLITUDE with reference to optical information on holographic facet：
τh(xh)=o (xh)exp{i[φo(xh)-φr(xh)]} (3)
Wherein o (xh) be object light amplitude, φo(xh) be object light phase, φr(xh) reference light phase；
Under Fresnel approximation, only considers that object is a luminous point, send out divergent spherical wave, and reference light is another luminous point, hair
Go out spherical wave, ignores the constant phase factor, have：
Wherein (xo,zo) be object point coordinate, (xr,zr) be reference light luminous point coordinate,For wave number, λ is light wave wave
It is long；
Formula (3) can be brought into formula (4) and obtained by the light field COMPLEX AMPLITUDE after spatial sampling：
It can be expressed as after bringing formula (4) into formula (5) expansion：
5. a kind of large scale high-resolution color Fresnel holographic production method according to claim 4, which is characterized in that institute
Stating step 1.3 is specially：
When the reconstruction of hologram, the identical light of reference light used when being recorded with hologram is reproduced, that is, it is that a point is sent out to reproduce light
The coordinate of the divergent spherical wave gone out, the luminous point is (xr,zr), it is identical with former reference light,
I.e.The light field complex amplitude being then emitted from hologram can be expressed as：
It can be written as in the light field of image plane：
WhereinIndicate object point and the distance with reference to light coordinate；
Light intensity can be expressed as：
Wherein n is the diffraction time of diffraction light.xiFor the coordinate of the picture point of reproduction；
Reproduction image is multistage picture point, and the coordinate of multistage picture point is：
Wherein xoOriginal point coordinates, that is, ideal image point coordinate, the intensity of multistage picture point byTune
System；When a=± 1 (n/d), picture point amplitude is 0, at this time nc=± (d/a), ncIndicate the level of the positive and negative level-one picture point of political affairs；It is other high
The amplitude very little of level can be ignored；When the sampling period, d was larger, the extension for the multistage picture point that formula (10) indicates cannot
It is being spatially separating, but energy is concentrated mainly in the range of ± 1 grade of picture point, i.e.,Within in range；Therefore it can incite somebody to action
The range regards the equivalent picture point of a diffusion as, if the size of the picture point in the viewing demand that disclosure satisfy that human eye, as
The extension of point is negligible to the fuzzy of reproduction image；
The extension width of picture point is：
△xi=2 λ zo/a (11)
IfMeet：
Wherein δEFor the angle of minimum resolution of human eye, 1.5 ' (4.35 × 10 are traditionally arranged to be in engineering-4rad)；Formula (11) takes
Number, the dimension limit of spatial sampling hologram can be found out：
Formula (13) is exactly the minimum dimension of unit hologram.
6. a kind of high-resolution colored Fresnel hologram display system of large scale, which is characterized in that including,
Light source, for generating illumination light；
Lens system, the light for sending out light source are converted into approximate planar light；
Imaging system, for the chromatic grating of Computer Design to be imaged；
Diaphragm is used for the size of limiting light source luminous point, reduces since the size that shines is big caused as fuzzy；
Computer for designing chromatic grating, and chromatic grating is transferred in optical projection system and is imaged；
Adjustment frame carries out position for the position of the whole colored Fresnel hologram of tune with chromatic grating formed by imaging system
Matching realizes colored Fresnel holographic Three-dimensional Display when location matches are consistent.
7. a kind of high-resolution colored Fresnel hologram display system of large scale according to claim 6, feature
It is, the lens system includes that the diverging light that LED is sent out is converged to the lens of a bit, in the space filtering that the convergent point is placed
Device, the size for limiting convergent point only allow a tuftlet light to enter follow-up system；And the lens placed at rear, space
Filter is located on the front focal plane of postposition lens, and the light beam sent out after being limited by spatial filter collimates, and is formed flat
Face light illuminates subsequent LCD.
8. a kind of high-resolution colored Fresnel hologram display system of large scale according to claim 6, feature
It is, the laser or single-chip LED that the light source corresponds to red, green, blue light wave using three.
9. a kind of high-resolution colored Fresnel hologram display system of large scale according to claim 8, feature
It is, when the light source uses tri-color laser, the light that red, green, blue tri-color laser is sent out passes through three beam-expanding collimations respectively
System forms plane wave, illuminates three amplitude type LCD respectively, and three amplitude type LCD are connected with computer, the computer
Three Color Channels of the colored raster images of design are loaded into respectively in three amplitude type LCD, what three amplitude type LCD were sent out
Light closes Shu Houzai by Amici prism BS and passes through imaging len lensiChromatic grating is imaged, H planes are imaged in, H planes are to put
The position of modulation frame is set, colored Fresnel hologram is placed on adjustment frame, is matched with the size of chromatic grating, realizes colored luxuriant and rich with fragrance alunite
That hologram Three-dimensional Display；
Alternatively, when the light source is using three single-chip LED for corresponding to red, green, blue light wave, three color mono-chip single-colour LEDr、
LEDg、LEDbIt is connected with controller, controller is used to control the switch and brightness adjustment of each monochromatic single-chip LED, three color
Mono-chip single-colour LEDLEDr、LEDg、LEDbIt is located at three lens lens1、lens3、lens5The first two times of focal plane, three
A lens lens1、lens3、lens5Two times of focal plane difference placement space filter Filter afterwards1、Fliter2、Filter3,
Spatial filter is used to limit the size of the light beam sent out by lens rear focal point, only one, center zonule is allowed to send out
Light beam enters follow-up system, the quality for entering follow-up lighting system light is improved, in spatial filter Filter1、Fliter2、
Filter3Lens lens is placed respectively in rear2、lens4、lens6, spatial filter Filter1、Fliter2、Filter3Respectively
Positioned at lens lens2、lens4、lens6Previous times of focal length at, through three spatial filter Filter1,Fliter2,Filter3
The light sent out passes through lens respectively2、lens4、lens6Three amplitude type LEDlcd of back lightingr、lcdg、lcdb, three amplitude types
LCD is connected with computer, and three Color Channels of the colored raster images of design are loaded into respectively in three amplitude type LCD, leads to
The light for crossing three amplitude type LCD closes beam by Amici prism BS, passes through imaging len lens lateriChromatic grating is imaged, at
As in placing modulation frame in H planes, H planes, colored Fresnel hologram, the size with chromatic grating are placed on adjustment frame
Match, realizes colored Fresnel hologram Three-dimensional Display.
10. a kind of high-resolution colored Fresnel hologram display system of large scale according to claim 9, feature
It is, the orthogonal polarizing film in the front and back placement polarization direction of each amplitude type LCD of three amplitude type LCD is used for amplitude
Modulation.
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