3d Technology And Holographics Computer Science Essay

Holography [ 1, 2 ] is a 3-dimensional ( 3D ) show technique that reconstructs the wave front of visible radiation reflected or scattered by objects. Unlike other 3D show techniques that reconstruct beams reflected or scattered by objects, such as multi-view show and built-in imagination show, holography reconstructs light from objects with greater physical truth. Therefore, holography is free from several jobs peculiar to ray-reconstruction type 3D shows, such as ocular weariness caused by adjustment & A ; gt ; vergence struggle, discontinuous gesture parallax, the marionette theatre consequence, and the composition board consequence.

However, spots are generated in 3D images reconstructed by holography, because coherent visible radiation is used during the recording and Reconstruction procedures. The spots significantly degrade the quality of 3D images. Because the coherent visible radiation does non be of course, we see objects under incoherent light light. A wavefront Reconstruction technique that does non bring forth spots is required. In the present survey, we propose a time-multiplexing technique to extinguish spots in hologram Reconstruction.

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Several techniques have been proposed to cut down spots in the reconstructed images for both optical and electronic holography [ 3-10 ] . Almost all of these techniques decrease the temporal or spacial coherency of the Reconstruction visible radiation. The temporal coherency is decreased utilizing incoherent light beginnings such as a light breathing rectifying tube [ 10 ] , changing the stages of light utilizing a revolving stage home base [ 5 ] , and clip averaging several reconstructed images [ 7, 9 ] . The spacial coherency is decreased by diverging the visible radiation utilizing a stage grating [ 4 ] and a diffusor [ 6, 8 ] . These techniques average out the spots temporally or spatially, i.

e. , the spots are blurred. Therefore, the reconstructed images are besides blurred. The spots are non extinguished by diminishing the coherency of visible radiation. Holography records the intervention form of an object moving ridge and a mention moving ridge ; spots are recorded in holograph because the object moving ridge contains the spots. Therefore, a holographic show technique that does non per se generate spots is required to avoid blurring of the reconstructed images. In digital holography, research workers have proposed several clip averaging techniques to cut down the spots in reconstructed images calculated by a computing machine [ 11 ] .

In add-on to the job of spot coevals, electronic holography has important restrictions on the sing zone and show screen size. An ultrafine pel pitch is required for

a spacial visible radiation modulator ( SLM ) to obtain a big sing zone: the sing zone angle is reciprocally relative to the pel pitch. An highly high-resolution is required for an SLM to obtain a big show screen, because the pixel pitch can non be enlarged to increase the screen size. For case, a holographic show with a sing zone angle of 30 & A ; gt ; and a 10-inch screen requires an SLM with a pixel pitch of 1? m and a declaration of 203,200 & A ; gt ; 152,400 pels. Several techniques have been proposed to get the better of these jobs [ 12-23 ] . However, their image quality is non satisfactory ; the spots degrade the image quality. Furthermore, the grayscale representation of the reconstructed images is unsatisfactory, because a high dynamic scope is required for the SLM to expose the intervention peripheries of holographs. The dynamic scope required for the SLM to expose the intervention forms is higher than that required for the reconstructed images. The grayscale representation of holographic shows should be comparable to that of the modern planar shows. Several surveies have been performed to better the grayscale representation of hologram Reconstruction [ 24, 25 ] .

In the present survey, a time-multiplexing holographic show technique is proposed that non merely eliminates spots from the reconstructed images but besides improves the grayscale representation of the reconstructed images.

2. Theory

2.1 Speckle riddance

First, we explain speckle riddance in hologram Reconstruction utilizing a time-multiplexing technique.

In the present survey, we assumed that a reconstructed image consists of an sum of object points, as shown in Fig. 1. Speckle coevals can be considered as intervention between these object points. To extinguish spots, the object points are divided into object point groups, denoted by Gt, which consist of sparse object points. The distances between object points in each group are made sufficiently big so as to non interference among the points in each group. All the object point groups are consecutive displayed in a time-multiplexing mode. Therefore, intervention does non happen between different object point groups because they are displayed at different times. Hence, no intervention occurs during hologram Reconstruction, and speckle-free holograph Reconstruction can be achieved. This technique generates practically incoherent object points, so 3D scenes illuminated by incoherent visible radiation can be reconstructed.

Fig. 1. 3D image consisting of object point groups Gt.

A high-velocity SLM is used to expose the object point groups. As shown in Fig. 2 ( a ) , each group consists of every bit spaced object points in the horizontal and perpendicular waies. The object points are divided into M groups horizontally and N groups vertically. All the object points are divided into M & A ; gt ; N object point groups, denoted by Gmn ( 0 = m = M? ? 1, 0 = n = N - ? 1 ) . We use a half-zone home base to bring forth an object point, because the usage of the half-zone

home base enables easy remotion of the coupled image from the holograph Reconstruction [ 26-28 ] . Figure 2 ( B ) shows the manner in which the half-zone home bases are displayed on the SLM to bring forth the object point groups Gmn. The SLM & A ; gt ; s expose screen is divided into many rectangular countries aligned two-dimensionally, and one zone home base is displayed in one rectangular country. The places of the rectangular countries are shifted both horizontally and vertically to expose different object point groups. Figure 2 shows the instance in which M = 4 and N = 2.

The declaration of the SLM is represented by X & A ; gt ; Y pels. The size of the rectangular country for exposing the half-zone home base is represented by S & A ; gt ; ( S/2 ) pels. The tallness of the zone home base is half of its breadth because the sing zone is halved in the perpendicular way to extinguish the conjugate image [ 28 ] . Therefore, each object point group consists of ( X/S ) & A ; gt ; ( 2Y/S ) object points. The holograph forms are shifted by S/M pels horizontally and S/2N pels vertically to bring forth different object point groups. The entire figure of object points representing the reconstructed image is ( MX/S ) & A ; gt ; ( 2NY/S ) .

Fig. 2. Speckle-free coevals of object points utilizing high-velocity SLM: ( a ) agreement of object point groups and ( B ) holograph forms for bring forthing object point groups.

2.2 Grayscale representation

The grayscale representation of the reconstructed images is besides improved by a time-multiplexing technique.

For the grayscale representation, each object point group is produced by exposing multiple holograph forms on the high-velocity SLM. As shown in Fig. 3, an object point group with grayscale values is represented by multiple spot forms. The spot flat decomposition method is used. The binary form matching to the q-th spot plane is denoted by Gmnq. Binary degree object points are generated by exposing the half-zone home bases on the high-velocity SLM mentioning to the binary form Gmnq, as described in Sec. 2.1. When the binary form Gmnq is generated, the SLM is illuminated by a optical maser visible radiation whose strength is relative to 2q. When each object point group is decomposed into Q binary forms ( 0 = Q = Q? ? 1 ) , the reconstructed images with 2Q grey degrees can be produced.

The strength of the light optical maser visible radiation can be modulated utilizing light strength modulators, such as an acousto-optic modulator and an electro-optic modulator. The strength can besides be modulated by pulse width transition of a optical maser, e.g. , utilizing direct current transition of a optical maser rectifying tube.

Fig. 3. Grayscale representation by time-multiplexing technique.

3. Speckle-free show conditions

A holograph show status that does non bring forth spots is considered.

Each half-zone home base, after go throughing through the 4f imagination system, generates a spherical moving ridge meeting to an object point. The topographic point size of the object point must be smaller than the interval between the object points in each object point group in order to stamp down intervention among the object points. When we assume that the half-zone home base provides a perfect spherical moving ridge by pretermiting the effects of trying caused by the pel construction of the SLM and the effects of the light amplitude quantisation caused by the SLM, the topographic point size is reciprocally relative to the size of the half-zone home base. From the trying theorem, the breadth and tallness of the half-zone home base are? z/p and? z/2p, severally, where? is the wavelength of the visible radiation, omega is the deepness of the object point, and P is the pixel pitch of the SLM [ 28 ] . When the size of the half-zone home base is smaller than the rectangular country, the horizontal and perpendicular topographic point sizes are p and 2p, severally. When the zone home base size is larger than the rectangular country, the topographic point sizes are reciprocally relative to the rectangular country, the horizontal and perpendicular topographic point sizes are? z/Sp and 2? z/Sp, severally. The horizontal and perpendicular topographic point sizes are illustrated in Fig. 4. The topographic point sizes addition as the deepness of the object points increases. Therefore, the intervention between object points becomes stronger when the object points are displayed further from the screen. The perpendicular topographic point size is twice every bit big as the horizontal topographic point size, and the perpendicular interval of the object points, given by Sp/2, is half of the horizontal interval, given by Sp. Therefore, the perpendicular intervention must be considered. In this survey, we assume that the perpendicular interval should be at least K times larger than the perpendicular topographic point size to avoid intervention, as illustrated in Fig. 5. With this premise, the needed deepness of the object point is z = 4S2p2/K? . This means that spots might non be generated when the object points are displayed within the maximal deepness zmax = 4S2p2/K? . Proper finding of the value of K is of import for effectual speckle riddance. In this survey, the value of K is by experimentation determined, as described in Sec. 4.2.

When the object point groups are displayed within the deepness zmax, the interval of the object points is at least K times larger than their topographic point size in the perpendicular way in each object point group. Therefore, the figure of object point groups aligned in the perpendicular way should be K or less from Sparrow & A ; gt ; s standard. In this survey, we use N = K. The horizontal interval of the object points is twice the perpendicular interval in each object point group,

and the horizontal topographic point size of the object points is half the perpendicular topographic point size. To do the horizontal interval of the object points equal to the perpendicular one in the reconstructed images, M must be 2K, although Sparrow & A ; gt ; s standard allows M to be every bit big as 4K. Therefore, the entire figure of object points in the reconstructed images is ( 2KX/S ) & A ; gt ; ( 2KY/S ) .

The frame rate of holograph coevals depends on the figure of object point groups and the figure of spot planes used for the grayscale representation. When the frame rate of the high-velocity SLM is denoted by f Hz, the frame rate of holograph coevals is given by f/MNQ Hz.

Fig. 4. Dependence of horizontal and perpendicular topographic point sizes of an object point on its deepness.

Fig. 5. Topographic point size and interval of object points to avoid intervention.

4. Experiments

Experiments were conducted to research the show conditions that enable the riddance of spots. Speckle-free grayscale holograph Reconstruction was verified.

4.1 Experimental system

The experimental system is shown in Fig. 6. A 4f imagination system was used for hologram Reconstruction ; it consists of two Fourier-transform lenses and has a single-sideband filter on its Fourier plane. The combination of the 4f imagination system and the usage of half-zone home bases efficaciously eliminate the conjugate image and zero-order diffraction visible radiation from the holograph Reconstruction [ 24-26 ] . A high-velocity SLM is placed on the object plane, and a holograph that does non bring forth a conjugate image and zero-order diffraction visible radiation is obtained on the image plane.

A digital micromirror device ( DMD ) ( DiscoveryTM 3000, Texas Instruments ) was used as the high-velocity SLM. The declaration was 1,024 & A ; gt ; 768, the pel pitch was 13.68? m, and the screen size was 0.69 inches. The figure of grey degrees represented by the DMD decreases when the frame rate additions. We used binary image manner, which yields a maximal frame rate of 13,333 Hz. Therefore, the half-zone home bases were displayed as binary images. A optical maser rectifying tube with a wavelength of 635 nanometer was used as a light beginning. The focal length of the two Fourier-transform lenses was 150 millimeter. Pulse width transition was used to modulate the strength of the optical maser rectifying tube. An H8 personal computer running at 2.5 MHz was used to command the pulsation breadth. The personal computer receives an image update signal from a DMD driver and

generates pulsations to modulate the optical maser rectifying tube. The maximal pulse breadth corresponds to 128 clock rhythms. The time-averaged optical power of the pulse-modulated visible radiation was measured by an optical power metre and found to be additive harmonizing to the figure of clock rhythms. The grayscale image was decomposed into eight spot planes ( Q = 8 ) .

Fig. 6. Experimental 4f imagination system.

4.2 Speckle-free show conditions

The value of K, which is the ratio of the interval between the object points and their topographic point size, is by experimentation determined for speckle suppression.

Table 1 shows the maximal deepness zmax of the object points calculated for K = 1, 2, 3, 4, and 5. The rating was conducted for several sizes of rectangular country in which the zone home base is displayed: S = 16, 32, 48, and 64. The object points were displayed at the five maximal deepnesss zmax, and intervention between the object points was evaluated. In an object point group, 13 & A ; gt ; 13 object points were generated at the centre. The graylevel of the generated object points was 255. The stages of the object points were the same because it was easier to measure the constructive intervention than the destructive intervention. The detector plane of a cooled CCD camera was placed at the plane where the reconstructed images were generated, i.e. , at a distance zmax from the screen. Photographs of the object point groups are shown in Fig. 7. The exposure show the cardinal 5 & A ; gt ; 10 object points. The strength distributions along the perpendicular axis are shown in Fig. 8. Constructive intervention was observed when K = 3. For all values of S, no intervention was observed when K = 4. Therefore, in the staying portion of this survey, K = 4 is used.

Table 1. Maximal depth zmax [ millimeter ] for several values of K

K

Size of zone home base country

16 & A ; gt ; 8

32 & A ; gt ; 16

48 & A ; gt ; 24

64 & A ; gt ; 32

1

18.9

75.4

170

302

2

9.43

37.7

84.9

151

3

6.26

25.1

56.6

101

4

4.72

18.9

42.4

75.4

5

3.77

15.1

34.0

60.4

Fig. 7. Reconstructed images of object point groups: ( a ) S = 16, ( B ) S = 32, ( degree Celsius ) S = 48, and ( vitamin D ) S = 64.

Fig. 8. Vertical strength distributions of reconstructed images of object point groups shown in Fig. 7: ( a ) S = 16, ( B ) S = 32, ( degree Celsius ) S = 48, and ( vitamin D ) S = 64.

4.3 Resolution of reconstructed images

The declaration of 3D images generated by the proposed technique was evaluated. The proposed method can bring forth a limited figure of object points. In this survey, the declaration is defined as the figure of object points generated in the horizontal and perpendicular waies.

Table 2 shows the declaration of the reconstructed images for several sizes of the rectangular country for the half-zone home base when K = 4. The allowable maximal deepnesss of the reconstructed images are besides shown. To verify the declaration of the reconstructed images, the separation of the object points in the reconstructed images was evaluated. In the reconstructed images, 16 & A ; gt ; 16 object points with a grey degree of 255 in the cardinal country were generated. Figure 9 shows exposure of the reconstructed images when they were displayed at distances of 75.4 millimeter ( zmax ) , 56.6 millimeter ( 3zmax/4 ) , 37.7 millimeter ( zmax/2 ) , and 18.9 millimeter ( zmax/4 ) from the screen. The cooled CCD camera, whose detector plane was placed where the reconstructed images were generated, was besides used to capture the images. The reconstructed 16 & A ; gt ; 16 object points are shown. The strength distributions of the reconstructed images along the perpendicular and horizontal axes are shown in Fig. 10. The separation between the object points disappeared in the perpendicular way when the image was displayed at the maximal deepness of 75.4 millimeter. Under Sparrow & A ; gt ; s standard, the declaration of the reconstructed images was 128? 96 when they were displayed at distances of less than 75.4 millimeter.

Table 2. Number of object points in the reconstructed image

Size of rectangular country

Number of object points

Maximum deepness zmax [ millimeter ]

16 & A ; gt ; 8

512 & A ; gt ; 384

4.72

32 & A ; gt ; 16

256 & A ; gt ; 192

18.9

48 & A ; gt ; 24

170 & A ; gt ; 128

42.4

64 & A ; gt ; 32

128 & A ; gt ; 96

75.4

Fig. 9. Reconstructed images of 16 & A ; gt ; 16 object points displayed at distances of ( a ) 75.4 millimeter ( zmax ) , ( B ) 56.6 millimeter ( 3zmax/4 ) , ( degree Celsius ) 37.7 millimeter ( zmax/2 ) , and ( vitamin D ) 18.9 millimeter ( zmax/4 ) .

Fig. 10. Vertical strength distribution of reconstructed images of 16 & A ; gt ; 16 object points displayed at distances of ( a ) 75.4 millimeter ( zmax ) , ( B ) 56.6 millimeter ( 3zmax/4 ) , ( degree Celsius ) 37.7 millimeter ( zmax/2 ) , and ( vitamin D ) 18.9 millimeter ( zmax/4 ) .

4.4 Grayscale holograph Reconstruction

Next, the grayscale representation by the proposed time-multiplexing technique was verified.

The declaration of the reconstructed images was 128 & A ; gt ; 96 ( M = 8, N = 4, and S = 64. ) The grayscale image was decomposed into eight spot planes ( Q = 8 ) , so the figure of grey degrees was 256. The frame rate for holograph coevals was 52 Hz.

A trial form was displayed. Eight filled rectangles dwelling of 8 & A ; gt ; 8 object points with grey degrees of 1, 3, 7, 15, 31, 63, 127, and 255 were generated at a distance of 37.0 millimeter. The grey degrees were chosen so that they were represented by the add-on of different spot planes, i.e. , 1 = 0000 0001b, 3 = 0000 0011b, 7 = 0000 0111b, 15 = 0000 1111b, 31 = 0001 1111b, 63 = 0011 1111b, 127 = 0111 1111b, and 255 = 1111 1111b. Figure 11 shows the reconstructed image captured by a cooled CCD camera holding its detector plane at the plane where the image was reconstructed. The cardinal 32 & A ; gt ; 16 object points are shown. The mean strengths in the eight rectangles were measured along the two horizontal lines shown in Fig. 11 ; the consequences are shown in Fig. 12. The consequences show that the proposed technique outputs good one-dimensionality in the grayscale representation.

4.5 Speckle-free and grayscale holograph Reconstruction

Finally, 3D images were generated by the proposed technique. The show conditions are indistinguishable to those in the experiment described in Sec. 4.4. The textures and deepnesss of the 3D images are shown in Fig. 13. Figure 14 shows exposure of the reconstructed images. The centres of the reconstructed images shown in Figs. 14 ( a ) and 14 ( B ) were located at the distances of 21.9 millimeters and 23.9 millimeter from the screen, severally. In contrast to the old experiments, which used a cooled CCD camera, a digital camera was used to capture the reconstructed images. The digital camera was placed in the observation infinite, and its focal point was adjusted suitably for the reconstructed images. No spots were observed in the reconstructed images. The reconstructed images had good grayscale representation, and no spark was observed.

Fig. 11. Reconstructed image of trial form dwelling of eight rectangles with different grey degrees.

Fig. 12. Measured characteristic of grayscale representation of the proposed technique.

Fig. 13. Datas of 3D images used for the experiment: ( a ) texture and ( B ) deepness of & A ; gt ; truck, & A ; gt ; and ( degree Celsius ) texture and ( vitamin D ) deepness of & A ; gt ; castle. & A ; gt ;

Fig. 14. Reconstructed 3D images: ( a ) truck and ( B ) palace.

5. Discussion

The value of the parametric quantity K was by experimentation determined, because the topographic point size of the object point is affected by the construction of the half-zone home base. Therefore, the intervention between the object points varied with S. Assuming that an object point is generated by a spherical moving ridge emitted from the rectangular country S & A ; gt ; S/2 and pretermiting the half-zone home base construction, the object point distribution is given by sinc ( Sx/ ? omega ) sinc ( Sy/2? omega ) , where ( x, y ) denotes the plane analogue to the show screen located at the deepness where the object points are generated. In this instance, the chief lobes of the sinc map of next object points do non superpose when K = 2, and the first side lobes do non superpose when K = 3, so that K = 2 or 3 might be sufficient. However, we by experimentation found that K = 4 was required because of the debasement of topographic point size caused by the construction of the half-zone home base.

The one-dimensionality of the grayscale representation shown in Fig. 12 was non perfect, because the strength of light lighting the DMD was different for the two measuring lines shown in Fig. 11.

The horizontal and perpendicular sing zone angles of the reconstructed images were merely 2.7 & A ; gt ; and 1.3 & A ; gt ; , severally, which are given by the equations 2sin-1 ( ? /2p ) and 2sin-1 ( ? /4p ) , severally. The holograph screen size was merely 0.69 inches, because it is indistinguishable to the SLM screen size. The technique proposed in this survey should be combined with the techniques [ 12-23 ] that have been developed to increase the sing zone angle and the screen size.

In the experimental consequences shown in Figs. 9 and 11, black countries exist between object points in the horizontal way, because the horizontal and perpendicular pitches of the object points were made equal by puting M = 2K. The pitch of the object points was 109? m, so the black country were non observed in the reconstructed images, as shown in Fig. 14. By puting M = 4K, the horizontal declaration can be doubled.

The proposed technique does non let imbrication of the half-zone home bases. Therefore, each holograph form has binary amplitudes. When the high-velocity SLM can modulate light with multiple amplitude degrees, overlapping of the half-zone home bases can be allowed, and the figure of object points in the reconstructed images can be increased. Because the DMD can execute pure binary amplitude transition, the highest frame rate manner was chosen in this survey.

6. Decision

A hologram show technique that does non bring forth spots and improves the grayscale representation of the reconstructed images was proposed. The object points representing the reconstructed image were divided into several groups dwelling of sparse object points. Then, each object point group was decomposed into multiple spot planes to stand for the grey degrees of the object points. Finally, binary holographs generated from the spot plane forms were consecutive displayed utilizing a time-multiplexing technique.

A DMD was used as a high-velocity SLM, and the speckle-free reconstructed images with 128 & A ; gt ; 96 object points with grey degrees of 255 were demonstrated. The frame rate for holograph coevals was 52 Hz.