**2. Synthetic holography**

In this section, the basics of synthetic image holography are discussed. According to the above described principles of autostereoscopy, it is desirable to exploit the directionality of the diffraction of light on the hologram (or more generally on the diffractive structure) for creating the spatially separated image channels in space. The problem consists of two main tasks, first the acquisition of image data for recording of particular channels and the second dealing with the recording process itself. Thus in Section 2.1 the general ideas of decomposition of the three-dimensional signal to the set of two-dimensional views are described. In Section 2.2 two particular approaches to the multiplexing of the 2D information within a single holographic element are presented. In the last part (Section 2.3), more detailed aspects of the recording and reconstruction processes are analyzed such as the true-color mixing based on holographic elements, various spatial properties of the reconstructed image, and possible synthesis of the holograms with kinetic behavior.

### **2.1 3D image as a set of 2D views**

The analysis of human vision (Section 1.1) showed that three-dimensional image perception can be artificially generated by creating the spatially separated discrete image channels in space. It has been also mentioned, that due to the inability of the human eye to register the phase properties of the incident optical wave (except for the directionality of the wave), the real image signal can be substituted by two-dimensional intensity views. The question is, how the discretization of the spatial channels should be done to create a satisfactory

remains perpendicular to the direction of movement. In this case, taking the snapshots with a real camera would require a special objective, so-called shifted-lens camera. However, this method is more often used in the case of capturing the virtual 3D object in a PC. Therefore, the need for a special objective can be bypassed by using "wide angle" capturing and cropping the recorded image. A big advantage of this method is a relatively simple recording setup for the master-hologram - with only linear translations. This is the method used in the experiments

Synthetic Image Holograms 215

The other possible setup for a single parallax case is the equiangular method with the circular movement of the camera. This method is the simplest from the capturing point of view, since the camera can be static while the object rotates around a vertical axis. It is also the closest approach to the viewing setup when the observer holds the hologram and tilts it around the vertical axis. However, if the recording medium is not coated on a cylindrical surface, this method demands sophisticated image preprocessing of the 2D images to match the flat surface

The closest method to the viewing setup is the one when the camera makes equidistant steps on a straight line and the camera axis tilts towards the object. It resembles the case when the hologram is hanging on a wall and the observer moves around, turning his head towards the hologram. Nevertheless, it is much more complicated from the capturing point of view and, similarly to the equiangular method, the images would have to be processed in a computer before recording the master-hologram. The above mentioned methods are the ones that are

If the final hologram should include both the horizontal parallax and vertical parallax, the process of camera movement should also include the vertical parallax. There are again several ways how to capture the spatial information. Similarly to the equiangular method with the circular movement of the camera, there is a "spherical" method for capturing the two parallaxes. In such a case the object turns around its vertical axis and the snapshots for the horizontal parallax are taken. The next horizontal "row" of exposures is taken after the object is turned about a small angle around its horizontal axis. In this manner the required range of angles in both parallaxes is taken. In Fig. 3, the planar method of capturing the two parallaxes is also provided - the "single parallax" line of capturing is repeated in the vertical direction.

This is how the continuous 3D information is sampled into a set of discrete 2D views. The following sections describe how various synthetic holograms are created from such a set of

In this section the basic approaches to the multiplexing of angular views obtained in the previous section are presented. There are many different ways how to realize different spatial channels but only those based on holographic or, more generally, on diffractive principles will be analyzed. As has been already mentioned, the decomposition of the 3D information into the two-dimensional channels is conditioned by the limited performance of the human eye. The first of the presented methods, named "synthesis at the hologram plane" is based on the limited resolution of the human eye in the image plane. The next approach, called commonly "synthesis at the eye-pupil plane" is based on the limited (finite) pupil size of the human eye which limits the monocular 3D perception. Both methods exploit holographic principles for

The axis of the camera is again kept perpendicular to the plane of movement.

described in this chapter.

of the hologram plate.

views.

image creation.

the most widely used for the 2D data capturing.

**2.2 Multiplexing views within a single hologram**

undisturbed 3D view. The method is obviously based on imperfections of the detecting system (in this case the human eye) in terms of a pupil size and limited resolution. It has also been denoted, that classical holography is the most perfect autostereoscopic method, as it reconstructs the signal wavefront in its full complexity. The interesting question arises if limiting the viewing channel size by the synthesis of the hologram from 2D views will converge to the "analogue" optical hologram. From the point of view of intensity distribution the classical hologram is apparently the limiting case of the synthetic construction, but there is a huge difference in phase properties of the reconstructed optical field. Although the phase behavior of the reconstruction must possess certain resemblance to that of the "ideal" hologram as the signal directional distribution is similar, particular spatial views are not mutually phase-synchronized as they would be from the classical hologram. This effect in principle does not affect the observation by human eye, but can cause problems when using the element for other applications.

### **Acquiring the source data**

Both approaches presented in this chapter need to somehow capture the set of 2D images before the synthesis can be processed. These images can be obtained using a real camera taking pictures of a real object or using a virtual camera capturing a virtual 3D object in a PC. There is a variety of methods that can be used for this sampling of an object. The methods can be classified according to the shape of the trajectory of the camera and according to the direction of the optical axis of the camera. The way of capturing also depends on the demands on the 3D behavior of the reconstruction - if the final hologram should be composed of both parallaxes or if it should be single parallax only (Section 2.3.2). Fig. 3 shows one of the possible capturing setups for both the single-parallax and the full parallax case.

Assuming the single parallax case, the above figure shows the method in which the camera is moved through equal length steps on a straight line, while the optical axis of the camera

Fig. 3. **(a)** Capturing of the 2D images. The figure shows the equidistant capturing with linear movement of the camera. The blue line represents the single parallax case - in each "square" one snapshot is taken. The whole array represents the case of capturing both parallaxes when the camera moves in two mutually perpendicular directions. **(b)** The positions of the viewing zones are coincident with the positions of a camera during the capturing process.

6 Will-be-set-by-IN-TECH

undisturbed 3D view. The method is obviously based on imperfections of the detecting system (in this case the human eye) in terms of a pupil size and limited resolution. It has also been denoted, that classical holography is the most perfect autostereoscopic method, as it reconstructs the signal wavefront in its full complexity. The interesting question arises if limiting the viewing channel size by the synthesis of the hologram from 2D views will converge to the "analogue" optical hologram. From the point of view of intensity distribution the classical hologram is apparently the limiting case of the synthetic construction, but there is a huge difference in phase properties of the reconstructed optical field. Although the phase behavior of the reconstruction must possess certain resemblance to that of the "ideal" hologram as the signal directional distribution is similar, particular spatial views are not mutually phase-synchronized as they would be from the classical hologram. This effect in principle does not affect the observation by human eye, but can cause problems when using

Both approaches presented in this chapter need to somehow capture the set of 2D images before the synthesis can be processed. These images can be obtained using a real camera taking pictures of a real object or using a virtual camera capturing a virtual 3D object in a PC. There is a variety of methods that can be used for this sampling of an object. The methods can be classified according to the shape of the trajectory of the camera and according to the direction of the optical axis of the camera. The way of capturing also depends on the demands on the 3D behavior of the reconstruction - if the final hologram should be composed of both parallaxes or if it should be single parallax only (Section 2.3.2). Fig. 3 shows one of the possible

Assuming the single parallax case, the above figure shows the method in which the camera is moved through equal length steps on a straight line, while the optical axis of the camera

(a) (b)

Fig. 3. **(a)** Capturing of the 2D images. The figure shows the equidistant capturing with linear movement of the camera. The blue line represents the single parallax case - in each "square" one snapshot is taken. The whole array represents the case of capturing both parallaxes when the camera moves in two mutually perpendicular directions. **(b)** The positions of the viewing zones are coincident with the positions of a camera during the capturing process.

capturing setups for both the single-parallax and the full parallax case.

the element for other applications.

**Acquiring the source data**

remains perpendicular to the direction of movement. In this case, taking the snapshots with a real camera would require a special objective, so-called shifted-lens camera. However, this method is more often used in the case of capturing the virtual 3D object in a PC. Therefore, the need for a special objective can be bypassed by using "wide angle" capturing and cropping the recorded image. A big advantage of this method is a relatively simple recording setup for the master-hologram - with only linear translations. This is the method used in the experiments described in this chapter.

The other possible setup for a single parallax case is the equiangular method with the circular movement of the camera. This method is the simplest from the capturing point of view, since the camera can be static while the object rotates around a vertical axis. It is also the closest approach to the viewing setup when the observer holds the hologram and tilts it around the vertical axis. However, if the recording medium is not coated on a cylindrical surface, this method demands sophisticated image preprocessing of the 2D images to match the flat surface of the hologram plate.

The closest method to the viewing setup is the one when the camera makes equidistant steps on a straight line and the camera axis tilts towards the object. It resembles the case when the hologram is hanging on a wall and the observer moves around, turning his head towards the hologram. Nevertheless, it is much more complicated from the capturing point of view and, similarly to the equiangular method, the images would have to be processed in a computer before recording the master-hologram. The above mentioned methods are the ones that are the most widely used for the 2D data capturing.

If the final hologram should include both the horizontal parallax and vertical parallax, the process of camera movement should also include the vertical parallax. There are again several ways how to capture the spatial information. Similarly to the equiangular method with the circular movement of the camera, there is a "spherical" method for capturing the two parallaxes. In such a case the object turns around its vertical axis and the snapshots for the horizontal parallax are taken. The next horizontal "row" of exposures is taken after the object is turned about a small angle around its horizontal axis. In this manner the required range of angles in both parallaxes is taken. In Fig. 3, the planar method of capturing the two parallaxes is also provided - the "single parallax" line of capturing is repeated in the vertical direction. The axis of the camera is again kept perpendicular to the plane of movement.

This is how the continuous 3D information is sampled into a set of discrete 2D views. The following sections describe how various synthetic holograms are created from such a set of views.

### **2.2 Multiplexing views within a single hologram**

In this section the basic approaches to the multiplexing of angular views obtained in the previous section are presented. There are many different ways how to realize different spatial channels but only those based on holographic or, more generally, on diffractive principles will be analyzed. As has been already mentioned, the decomposition of the 3D information into the two-dimensional channels is conditioned by the limited performance of the human eye. The first of the presented methods, named "synthesis at the hologram plane" is based on the limited resolution of the human eye in the image plane. The next approach, called commonly "synthesis at the eye-pupil plane" is based on the limited (finite) pupil size of the human eye which limits the monocular 3D perception. Both methods exploit holographic principles for image creation.

namely the 0-th order with *α*<sup>0</sup> = *α<sup>i</sup>* and the first diffraction order with *α*<sup>1</sup> ≈ 0◦. When the light is polychromatic, there will be one "white" 0-th order and many 1*st* orders, one for each spectral color. They will slightly differ in direction according to the equation (1). If we specify the direction of observation to be the normal to the hologram at its midpoint, one will observe only a narrow spectral band of colors and, in our example, he will see the grating as green (∼ 530nm). The described principle is used in synthetic holography for generation of the different colors from a single white light source. Namely if the grating period changes within the range from 600nm to 950nm, an observer looking in the direction perpendicular to the hologram will perceive the wavelengths from 430nm to 670nm, which is approximately the range of the visible light. Of course, if he changes his viewing direction, the perceived color will change according to the grating equation. Each image point can in principle change its color from blue to red through all rainbow colors; this is why such holograms are also called rainbow holograms [Benton, 1969]. The rainbow hologram can be observed in correct color composition only under the defined geometry (relative position of the light source, hologram, and observer). Otherwise the colors are shifted according to the equation (1). If there is more than one color in the image, particular colors will maintain their relative relations, but they will be all shifted in the same manner when the geometry is changed (e.g. when the hologram

Synthetic Image Holograms 217

It has been shown that the period of the elementary grating on the hologram surface determines the color observed from the particular direction if the hologram is illuminated with white light in the defined geometry. The next important parameter of the grating is the orientation of the grating lines. In the above example they were perpendicular to the plane of incidence of the reconstructing light beam. In general, the grating orientation can be rotated

Based on this analysis we can suggest the method for generating a synthetic 3D hologram from 2D views. As has been mentioned, in the given geometry 3D imaging requires the ability of the particular point on the hologram surface to send different signal in the different directions. Such a functionality can be accomplished using the elementary point segmentation according

within the range of 360◦. The effect of such a change is demonstrated in Fig. 4b.

Fig. 5. Basic idea of generating the spatial image channels using diffraction gratings.

Each distinguishable point on the hologram surface (further called a macro-dot) is divided into a set of smaller units (further called micro-dots). Each micro-dot is filled with a regular grating with appropriate period and orientation. As shown earlier, the number of micro-dots with dimensions sufficient to contain a functional grating, which could fit within a single macro-dot, is several hundreds, so there is plenty of space for representing a high number of angular views of an object. In fact, it is not necessary to use such a high number of

is vertically tilted).

to Fig. 5.

### **2.2.1 Data synthesis at the hologram plane**

In optical holography, the relative positions of the object and the final hologram (the physical plate on which the recording has been made) can be arbitrary. However, during the copying process the object is usually placed in the close neighborhood of the final hologram for several reasons. The most important are dispersion and sensitivity to the imperfections of the reconstructing light source. When the image is formed close to the hologram, the blurring caused by the dispersion effects is negligible as is the blurring caused by the spatial incoherence of the light source. If we suppose such a geometry, we can assume that the image points and their projections to the hologram plane are approximately of the same size.

When the hologram is observed from the conventional distance ∼ 25 cm, the approximate resolution limit of the human eye is ∼ 0.1 mm. On the other hand, from the point of view of diffractive structures such a dimension is large enough for carrying much more than just the information about a single point. As a rough estimate, if we assume an elementary diffraction grating with period ∼ 800 nm and area 4 × 4*μ* m (which contains 5 periods of such a grating), we can place more than 600 different gratings within the area of 0.1 <sup>×</sup> 0.1 mm2. The main idea of image multiplexing at the hologram plane is based exactly on this calculation.

To understand the method one has to realize how the principle of stereoscopy applies for the given geometry. Let us assume the situation according to Fig. 3. If the observer sees the 3D image floating in the neighborhood of the hologram plane, it means, that each point on the hologram should send different information to the different directions (meaning that the visibility of the particular point on the hologram surface in terms of color and intensity is dependent on the observation angle). It is impossible to achieve such an angular functionality from conventional photography, where the angular luminosity is a smooth function. On the other hand, the idea of realizing an angularly selective image on the base of diffraction is pretty straightforward. Let us assume the diffraction of white light by the elementary regular diffraction grating according to Fig. 4a.

Fig. 4. Diffraction of white light on the thin diffraction grating under the common geometry for horizontal grating **(a)** and rotated grating **(b)**.

Let the diffraction grating have the period 750 nm, the incidence angle is 45◦, and the grating lines are perpendicular to the plane of incidence. If the light is monochromatic (with wavelength in the middle of the visible region, e.g. *λ* = 530 nm), there will be only two diffracted beams according to the grating equation

$$
\sin \alpha\_m = \sin \alpha\_i + m \frac{\lambda}{\Lambda'} \tag{1}
$$

8 Will-be-set-by-IN-TECH

In optical holography, the relative positions of the object and the final hologram (the physical plate on which the recording has been made) can be arbitrary. However, during the copying process the object is usually placed in the close neighborhood of the final hologram for several reasons. The most important are dispersion and sensitivity to the imperfections of the reconstructing light source. When the image is formed close to the hologram, the blurring caused by the dispersion effects is negligible as is the blurring caused by the spatial incoherence of the light source. If we suppose such a geometry, we can assume that the image points and their projections to the hologram plane are approximately of the same size.

When the hologram is observed from the conventional distance ∼ 25 cm, the approximate resolution limit of the human eye is ∼ 0.1 mm. On the other hand, from the point of view of diffractive structures such a dimension is large enough for carrying much more than just the information about a single point. As a rough estimate, if we assume an elementary diffraction grating with period ∼ 800 nm and area 4 × 4*μ* m (which contains 5 periods of such a grating), we can place more than 600 different gratings within the area of 0.1 <sup>×</sup> 0.1 mm2. The main idea

To understand the method one has to realize how the principle of stereoscopy applies for the given geometry. Let us assume the situation according to Fig. 3. If the observer sees the 3D image floating in the neighborhood of the hologram plane, it means, that each point on the hologram should send different information to the different directions (meaning that the visibility of the particular point on the hologram surface in terms of color and intensity is dependent on the observation angle). It is impossible to achieve such an angular functionality from conventional photography, where the angular luminosity is a smooth function. On the other hand, the idea of realizing an angularly selective image on the base of diffraction is pretty straightforward. Let us assume the diffraction of white light by the elementary regular

(a) (b)

Fig. 4. Diffraction of white light on the thin diffraction grating under the common geometry -

Let the diffraction grating have the period 750 nm, the incidence angle is 45◦, and the grating lines are perpendicular to the plane of incidence. If the light is monochromatic (with wavelength in the middle of the visible region, e.g. *λ* = 530 nm), there will be only two

sin *α<sup>m</sup>* = sin *α<sup>i</sup>* + *m*

*λ*

<sup>Λ</sup>, (1)

of image multiplexing at the hologram plane is based exactly on this calculation.

**2.2.1 Data synthesis at the hologram plane**

diffraction grating according to Fig. 4a.

for horizontal grating **(a)** and rotated grating **(b)**.

diffracted beams according to the grating equation

namely the 0-th order with *α*<sup>0</sup> = *α<sup>i</sup>* and the first diffraction order with *α*<sup>1</sup> ≈ 0◦. When the light is polychromatic, there will be one "white" 0-th order and many 1*st* orders, one for each spectral color. They will slightly differ in direction according to the equation (1). If we specify the direction of observation to be the normal to the hologram at its midpoint, one will observe only a narrow spectral band of colors and, in our example, he will see the grating as green (∼ 530nm). The described principle is used in synthetic holography for generation of the different colors from a single white light source. Namely if the grating period changes within the range from 600nm to 950nm, an observer looking in the direction perpendicular to the hologram will perceive the wavelengths from 430nm to 670nm, which is approximately the range of the visible light. Of course, if he changes his viewing direction, the perceived color will change according to the grating equation. Each image point can in principle change its color from blue to red through all rainbow colors; this is why such holograms are also called rainbow holograms [Benton, 1969]. The rainbow hologram can be observed in correct color composition only under the defined geometry (relative position of the light source, hologram, and observer). Otherwise the colors are shifted according to the equation (1). If there is more than one color in the image, particular colors will maintain their relative relations, but they will be all shifted in the same manner when the geometry is changed (e.g. when the hologram is vertically tilted).

It has been shown that the period of the elementary grating on the hologram surface determines the color observed from the particular direction if the hologram is illuminated with white light in the defined geometry. The next important parameter of the grating is the orientation of the grating lines. In the above example they were perpendicular to the plane of incidence of the reconstructing light beam. In general, the grating orientation can be rotated within the range of 360◦. The effect of such a change is demonstrated in Fig. 4b.

Based on this analysis we can suggest the method for generating a synthetic 3D hologram from 2D views. As has been mentioned, in the given geometry 3D imaging requires the ability of the particular point on the hologram surface to send different signal in the different directions. Such a functionality can be accomplished using the elementary point segmentation according to Fig. 5.

Fig. 5. Basic idea of generating the spatial image channels using diffraction gratings.

Each distinguishable point on the hologram surface (further called a macro-dot) is divided into a set of smaller units (further called micro-dots). Each micro-dot is filled with a regular grating with appropriate period and orientation. As shown earlier, the number of micro-dots with dimensions sufficient to contain a functional grating, which could fit within a single macro-dot, is several hundreds, so there is plenty of space for representing a high number of angular views of an object. In fact, it is not necessary to use such a high number of

The described synthesis at the hologram plane has many advantages but also several disadvantages in comparison with other hologram synthesis techniques. Because of the direct calculation of properties of each image point, the approach is very flexible. It enables us to calculate full 3D holograms with true-color RGB color mixing (see Section 2.3.1), kinetic behavior (see Section 2.3.3), and high contrast with low noise. There is one more aspect which should be mentioned, namely the possibility to fully adjust the luminosity of each image point. The overall luminosity of the micro-grating is given by its area and diffraction efficiency. To manage the luminosity continuously, either of these two parameters can be used. If the area of micro-dot is maintained, the diffraction efficiency can be changed by tuning the profile shape or the depth of the modulation (usually the depth of the modulation is tuned as it can be done easily by changing the exposure dose for the particular micro-grating). Unfortunately, it is relatively tricky to maintain the proper luminosity relations as the dependency of the depth of the modulation on the exposure dose can be highly nonlinear, apart from the potential problems with changing the dose independently for each grating within the chosen recording setup. Thus, the luminosity is usually driven by changing the micro-dot area and simultaneous maintaining of other parameters of the grating (shape and depth of the modulation). The micro-dot is divided into two parts, one filled with grating and the second unexposed (see Fig. 6a). This allows one to perfectly (linearly) tune the luminosity and set the desired luminosity relations over the hologram area. The main drawback is the further segmentation of the micro-dots, which enhances the diffraction effects on the grating aperture (which is now even smaller) and can lead to higher noise levels in reconstruction. Thus the proper choice of the dot size as a kind of trade off between the mentioned effects crucially

Synthetic Image Holograms 219

In the previous case, the area of the hologram is divided into the macro- and micro-dots, where the primary gratings are finally directly recorded using one of the approaches described in Section 3.1. In the case of synthesis at the eye-pupil plane, the microstructure of the final synthetic hologram is continuous without any segmentation. The discretization of the spatial information is achieved using holographic principles - an interference pattern of one reference beam and multiple signal beams is recorded to the synthetic hologram. Each of the signal waves would represent one particular viewing zone (see Fig. 3). To achieve this effect, the data synthesis at the eye-pupil plane consists of two steps. First, the synthetic master-hologram is created, where the particular 2D views are recorded and then the master-hologram is transferred into the final hologram. The name of the method is derived from the fact that the position of the former master-hologram coincides with the eye-pupil plane when viewing

The most instructive one and probably the most known method is the one shown in Fig. 7. There are four main steps included in this type of synthesis: **1.** sampling of the 3D object (obtaining the set of 2D views - Fig. 3a), **2.** recording of these 2D views (spatially separated) into the synthetic master-hologram (Fig. 7a), **3.** transferring these recorded views into the final

The 2D images are sequentially displayed on the ground glass screen shown in Fig. 7a. The holographic plate is placed in front of the screen approximately within the plane, where the snapshots were taken from. The plate is covered with a shade with a vertical slit, so that only a narrow stripe of the same width (or smaller than the width) of eye pupil is exposed at each shot. The reference wave is incident from the same side as the signal wave. When the stripe

hologram by a single shot (Fig. 7b), and **4.** viewing the final hologram (Fig. 3b).

influences the final quality of the reconstructed image.

**2.2.2 Data synthesis at the eye-pupil plane**

the final hologram.

micro-dots for two reasons. First, most holograms synthesized using this method are of rainbow type, thus the vertical parallax is omitted and angular views are captured only in the horizontal direction. This significantly reduces the number of necessary micro-dots. Second, the finite angular resolution of the human eye and the finite eye-pupil size limit the number of horizontal views (of course this number is also influenced by the desired angular range). In practice, only a relatively small number of horizontal views is needed to create a satisfactory 3D perception. Usually 9-16 angular channels are used.

At this point it is necessary to mention that the spatial separation of the micro-dots within the elementary resolvable macro-dot is not the only method of multiplexing the elementary gratings. Depending on the holographic recording techniques, particular gratings can also partially or fully overlap within the macro-dot area. The multiple exposure of a single macro-dot area can record all gratings while maintaining their particular properties. However, it can be shown, that the potential drawbacks of this method have more serious consequences than those of the spatial multiplexing. Moreover, the exposure parameters are dependent on the particular grating parameters and the number of multiplexed gratings when exposing the same area multiple times, whereas they are completely independent when the gratings are separated spatially.

Unfortunately, the spatial separation also brings several unwanted effects to the image reconstruction, the fragmentation of the microstructure to the micro-dots being the worst of them. In practice, the often used dimension of the micro-dot is below 10*μ*m. Thus the diffraction by the grating is affected with the diffraction by the aperture of the grating. Mathematically, the diffraction pattern consists of the convolution of the diffraction by the grating and by the rectangular aperture. This leads to the spreading of the diffraction order, introduces noise, and decreases the observed luminosity of the point. As a consequence, the micro-dot size must be chosen as a trade off between resolution and luminosity of the image. In Fig. 6 there are examples of the desired and real microstructure which has been synthesized

Fig. 6. Example of the macro-dot segmentation **(a)** and the corresponding real micro-structure **(b)**.

using the described technique. The micro-dots are clearly visible together with the gratings inside them which have a periodicity of ∼ 600 − 950nm depending on particular micro-dot and the dimension of micro-dots is ∼ 13*μ*m. The macro-dot (or the observable image point) has a dimension of ∼ 39*μ*m and is segmented into 9 micro-dots (there are 9 angular views distributed in horizontal direction, the hologram is of rainbow type).

10 Will-be-set-by-IN-TECH

micro-dots for two reasons. First, most holograms synthesized using this method are of rainbow type, thus the vertical parallax is omitted and angular views are captured only in the horizontal direction. This significantly reduces the number of necessary micro-dots. Second, the finite angular resolution of the human eye and the finite eye-pupil size limit the number of horizontal views (of course this number is also influenced by the desired angular range). In practice, only a relatively small number of horizontal views is needed to create a satisfactory

At this point it is necessary to mention that the spatial separation of the micro-dots within the elementary resolvable macro-dot is not the only method of multiplexing the elementary gratings. Depending on the holographic recording techniques, particular gratings can also partially or fully overlap within the macro-dot area. The multiple exposure of a single macro-dot area can record all gratings while maintaining their particular properties. However, it can be shown, that the potential drawbacks of this method have more serious consequences than those of the spatial multiplexing. Moreover, the exposure parameters are dependent on the particular grating parameters and the number of multiplexed gratings when exposing the same area multiple times, whereas they are completely independent when the gratings are

Unfortunately, the spatial separation also brings several unwanted effects to the image reconstruction, the fragmentation of the microstructure to the micro-dots being the worst of them. In practice, the often used dimension of the micro-dot is below 10*μ*m. Thus the diffraction by the grating is affected with the diffraction by the aperture of the grating. Mathematically, the diffraction pattern consists of the convolution of the diffraction by the grating and by the rectangular aperture. This leads to the spreading of the diffraction order, introduces noise, and decreases the observed luminosity of the point. As a consequence, the micro-dot size must be chosen as a trade off between resolution and luminosity of the image. In Fig. 6 there are examples of the desired and real microstructure which has been synthesized

(a) (b)

using the described technique. The micro-dots are clearly visible together with the gratings inside them which have a periodicity of ∼ 600 − 950nm depending on particular micro-dot and the dimension of micro-dots is ∼ 13*μ*m. The macro-dot (or the observable image point) has a dimension of ∼ 39*μ*m and is segmented into 9 micro-dots (there are 9 angular views

Fig. 6. Example of the macro-dot segmentation **(a)** and the corresponding real

distributed in horizontal direction, the hologram is of rainbow type).

3D perception. Usually 9-16 angular channels are used.

separated spatially.

micro-structure **(b)**.

The described synthesis at the hologram plane has many advantages but also several disadvantages in comparison with other hologram synthesis techniques. Because of the direct calculation of properties of each image point, the approach is very flexible. It enables us to calculate full 3D holograms with true-color RGB color mixing (see Section 2.3.1), kinetic behavior (see Section 2.3.3), and high contrast with low noise. There is one more aspect which should be mentioned, namely the possibility to fully adjust the luminosity of each image point. The overall luminosity of the micro-grating is given by its area and diffraction efficiency. To manage the luminosity continuously, either of these two parameters can be used. If the area of micro-dot is maintained, the diffraction efficiency can be changed by tuning the profile shape or the depth of the modulation (usually the depth of the modulation is tuned as it can be done easily by changing the exposure dose for the particular micro-grating). Unfortunately, it is relatively tricky to maintain the proper luminosity relations as the dependency of the depth of the modulation on the exposure dose can be highly nonlinear, apart from the potential problems with changing the dose independently for each grating within the chosen recording setup. Thus, the luminosity is usually driven by changing the micro-dot area and simultaneous maintaining of other parameters of the grating (shape and depth of the modulation). The micro-dot is divided into two parts, one filled with grating and the second unexposed (see Fig. 6a). This allows one to perfectly (linearly) tune the luminosity and set the desired luminosity relations over the hologram area. The main drawback is the further segmentation of the micro-dots, which enhances the diffraction effects on the grating aperture (which is now even smaller) and can lead to higher noise levels in reconstruction. Thus the proper choice of the dot size as a kind of trade off between the mentioned effects crucially influences the final quality of the reconstructed image.

### **2.2.2 Data synthesis at the eye-pupil plane**

In the previous case, the area of the hologram is divided into the macro- and micro-dots, where the primary gratings are finally directly recorded using one of the approaches described in Section 3.1. In the case of synthesis at the eye-pupil plane, the microstructure of the final synthetic hologram is continuous without any segmentation. The discretization of the spatial information is achieved using holographic principles - an interference pattern of one reference beam and multiple signal beams is recorded to the synthetic hologram. Each of the signal waves would represent one particular viewing zone (see Fig. 3). To achieve this effect, the data synthesis at the eye-pupil plane consists of two steps. First, the synthetic master-hologram is created, where the particular 2D views are recorded and then the master-hologram is transferred into the final hologram. The name of the method is derived from the fact that the position of the former master-hologram coincides with the eye-pupil plane when viewing the final hologram.

The most instructive one and probably the most known method is the one shown in Fig. 7. There are four main steps included in this type of synthesis: **1.** sampling of the 3D object (obtaining the set of 2D views - Fig. 3a), **2.** recording of these 2D views (spatially separated) into the synthetic master-hologram (Fig. 7a), **3.** transferring these recorded views into the final hologram by a single shot (Fig. 7b), and **4.** viewing the final hologram (Fig. 3b).

The 2D images are sequentially displayed on the ground glass screen shown in Fig. 7a. The holographic plate is placed in front of the screen approximately within the plane, where the snapshots were taken from. The plate is covered with a shade with a vertical slit, so that only a narrow stripe of the same width (or smaller than the width) of eye pupil is exposed at each shot. The reference wave is incident from the same side as the signal wave. When the stripe

various types of final holograms (full parallax, color, etc.). The following section shows the possibilities of creating such types of holograms using the two discussed synthetic

Synthetic Image Holograms 221

The following paragraphs provide information about the most common types of synthetic holograms and their properties, that can be created using the discussed methods. It is

Since the reconstruction of the hologram is based on the diffraction of the light on the hologram structure, the observed colors are spectral ones. If a non-spectral color is required

Additive color mixing is based on the colorimetric theory. It can be described by the means of CIE 1931 color space. The CIE defines a so called standard colorimetric observer and the color sensation experienced by the observer is determined by the spectral sensitivity of his eye cells (the cone cells). There are three peaks of their sensitivity. Hence, the sensation can be described using three parameters (X, Y, and Z), so called tristimulus values. These values can be used for computing the coordinates of a color in the well known CIE xy chromaticity

The most common way of achieving a mixed color is to use two or three spectral colors, usually red, green, and blue (RGB), although the color mix can be achieved from another colors. As was stated the hologram is a diffractive structure, thus these three colors are

Considering the data synthesis at the hologram plane, these gratings are created directly in each particular dot. The true-color dot is divided into three smaller areas, each filled with one grating. The relative areas of these three gratings control the contributions of each of the

(a) (b)

Fig. 8. Macro-dot segmentation for RGB color mixing **(a)** theoretical idea and **(b)** image of a

diagram. More details of colorimetry can be found e.g. in [Wyszecki and Stiles, 2000].

colors to the true-color mix. Such an array of "mixed" dots can be seen in Fig. 8.

concerned with color holograms, full parallax holograms and kinetic holograms.

approaches.

**2.3 Advanced properties of synthetic holograms**

(e.g. white), the additive color mixing must be introduced.

**2.3.1 Color mixing in synthetic holography**

obtained by the means of diffraction gratings.

real microstructure.

Fig. 7. Hologram synthesis in the eye pupil: **(a)** The 2D views are sequentially displayed on a ground glass screen and recorded as elementary holograms in the form of narrow stripes. This means that the master-hologram is composed of a number of these elementary holograms placed next to each other. **(b)** The transfer scheme. All the stripes from the master-hologram are replayed at once using a conjugate "reference wave" from (a). All the reconstructed images overlap in the former ground glass plane and the final hologram is recorded.

is exposed, the image on the ground glass is changed to the next view, the shade is shifted to the next position and the next exposure is taken. In this manner, all the views of the object are processed.

After developing the plate, this synthetic master is placed into the transfer scheme (Fig. 7b). All the recorded stripes are reconstructed at once and all the 2D views overlap in the former plane of the ground glass screen. The final hologram plate is placed exactly in this plane and the hologram is exposed. When viewing the final hologram, the stripes of the synthetic master-hologram are reconstructed in the exact position where the master was placed during the transfer process. The plane of the observer's eyes coincide with these stripes and each eye perceives only the view of the object from the correct direction (Fig. 3).

The main advantage of this method over the method of synthesis at the hologram plane is in the achievable size of the final hologram. Unlike the directly written synthetic holograms, there is no high demand on accuracy of the positioning of the recorded stripes (let us say about 0.1 mm). Therefore there are no big constraints on the recording device. Furthermore, the size of the final image is not limited by the size of the master-hologram, but by the size of the image on the screen. There are, of course, also several disadvantages depending on the particular setup. For example the main disadvantage of the setup in Fig. 7 is wasting the energy on the slit aperture. Although the energy loss can be lowered by shaping the reference beam, the reference beam must be shifted along with the shade, which makes the exposure complicated. There are, however, ways how to make the synthesis more efficient in a simpler setup (Section 3.2). The general disadvantage of these methods is in lower contrast compared to the directly written synthetic holograms.

The hologram described in the above section lacks vertical parallax. Therefore, it is used for creating a single-parallax rainbow hologram. The setup can be modified to create 12 Will-be-set-by-IN-TECH

(a) (b)

recorded.

processed.

Fig. 7. Hologram synthesis in the eye pupil: **(a)** The 2D views are sequentially displayed on a ground glass screen and recorded as elementary holograms in the form of narrow stripes. This means that the master-hologram is composed of a number of these elementary holograms placed next to each other. **(b)** The transfer scheme. All the stripes from the master-hologram are replayed at once using a conjugate "reference wave" from (a). All the reconstructed images overlap in the former ground glass plane and the final hologram is

is exposed, the image on the ground glass is changed to the next view, the shade is shifted to the next position and the next exposure is taken. In this manner, all the views of the object are

After developing the plate, this synthetic master is placed into the transfer scheme (Fig. 7b). All the recorded stripes are reconstructed at once and all the 2D views overlap in the former plane of the ground glass screen. The final hologram plate is placed exactly in this plane and the hologram is exposed. When viewing the final hologram, the stripes of the synthetic master-hologram are reconstructed in the exact position where the master was placed during the transfer process. The plane of the observer's eyes coincide with these stripes and each eye

The main advantage of this method over the method of synthesis at the hologram plane is in the achievable size of the final hologram. Unlike the directly written synthetic holograms, there is no high demand on accuracy of the positioning of the recorded stripes (let us say about 0.1 mm). Therefore there are no big constraints on the recording device. Furthermore, the size of the final image is not limited by the size of the master-hologram, but by the size of the image on the screen. There are, of course, also several disadvantages depending on the particular setup. For example the main disadvantage of the setup in Fig. 7 is wasting the energy on the slit aperture. Although the energy loss can be lowered by shaping the reference beam, the reference beam must be shifted along with the shade, which makes the exposure complicated. There are, however, ways how to make the synthesis more efficient in a simpler setup (Section 3.2). The general disadvantage of these methods is in lower contrast compared

The hologram described in the above section lacks vertical parallax. Therefore, it is used for creating a single-parallax rainbow hologram. The setup can be modified to create

perceives only the view of the object from the correct direction (Fig. 3).

to the directly written synthetic holograms.

various types of final holograms (full parallax, color, etc.). The following section shows the possibilities of creating such types of holograms using the two discussed synthetic approaches.

### **2.3 Advanced properties of synthetic holograms**

The following paragraphs provide information about the most common types of synthetic holograms and their properties, that can be created using the discussed methods. It is concerned with color holograms, full parallax holograms and kinetic holograms.

### **2.3.1 Color mixing in synthetic holography**

Since the reconstruction of the hologram is based on the diffraction of the light on the hologram structure, the observed colors are spectral ones. If a non-spectral color is required (e.g. white), the additive color mixing must be introduced.

Additive color mixing is based on the colorimetric theory. It can be described by the means of CIE 1931 color space. The CIE defines a so called standard colorimetric observer and the color sensation experienced by the observer is determined by the spectral sensitivity of his eye cells (the cone cells). There are three peaks of their sensitivity. Hence, the sensation can be described using three parameters (X, Y, and Z), so called tristimulus values. These values can be used for computing the coordinates of a color in the well known CIE xy chromaticity diagram. More details of colorimetry can be found e.g. in [Wyszecki and Stiles, 2000].

The most common way of achieving a mixed color is to use two or three spectral colors, usually red, green, and blue (RGB), although the color mix can be achieved from another colors. As was stated the hologram is a diffractive structure, thus these three colors are obtained by the means of diffraction gratings.

Considering the data synthesis at the hologram plane, these gratings are created directly in each particular dot. The true-color dot is divided into three smaller areas, each filled with one grating. The relative areas of these three gratings control the contributions of each of the colors to the true-color mix. Such an array of "mixed" dots can be seen in Fig. 8.

Fig. 8. Macro-dot segmentation for RGB color mixing **(a)** theoretical idea and **(b)** image of a real microstructure.

(a) (b)

Fig. 10. **(a)** Photograph of the "RGB color" master-hologram. The three color channels can be clearly seen. **(b)** Photograph of the final color synthetic rainbow hologram, that was obtained

Synthetic Image Holograms 223

magnification for the three wavelengths that actually compose this particular point. This issue can be solved by a proper "pre-distortion" of the image data before the recording process.1 The described techniques for color mixing utilized the rainbow effect (diffraction of white light by the volume transmission or thin grating). However, the color can be synthesized also in volume reflection holograms, where all steps are complicated by the Bragg condition (the dispersion cannot be used for generation of whole spectral range of colors as the grating recorded with the given geometry will not work for other than the design color). Nevertheless, a reflection color hologram can be synthesized using special techniques [Hariharan, 1996].

In general, the classical hologram can record the complete 3D properties of the object including both horizontal and vertical parallaxes. However, the parallax perpendicular to the fringes on the hologram surface can potentially suffer from strong dispersion effects. If the reconstructing light source is monochromatic, the dispersion will not apply and full three-dimensionality can be easily achieved. In a case of polychromatic reconstruction (which is the usual demand), the dispersion effects can lead to unacceptable rainbow blurring of the

Let us assume the common geometry of reconstruction according to Fig. 4a. The reconstruction beam is coming from the top and the observer is viewing the image from the front of the holographic plate. Thus the main direction of the fringes is horizontal. Besides

<sup>1</sup> The position of the non-compensated reconstructed color point differs from the original object point due to the different axial magnification for the particular reconstruction wavelengths. In the case of green recording wavelength (*λ<sup>G</sup>* = 532 nm), assuming the reference and reconstruction waves are planar, the axial magnifications for the particular color channels are *α<sup>R</sup>* = 0.84, *α<sup>G</sup>* = 1, and *α<sup>B</sup>* = 1.13 (for the red wavelength *λ<sup>R</sup>* = 633 nm and blue wavelength *λ<sup>B</sup>* = 470 nm). Since the hologram is mostly synthesized from the 2D views obtained from the computer, this distortion can be compensated by pre-distorting the 3D model on the computer in the opposite manner. To overlap in the plane of the hologram the red point has to be located on the "beam" coming from the red channel and the blue point on the beam coming from the blue channel. To compensate for the distortion in the z direction, the red "object" has to be axially magnified by the ratio 1/*α<sup>R</sup>* and the blue one shrank by the ratio 1/*αB*. During the 2D images processing, the proper pre-distortion can be introduced to each color channel. When reconstructed, the spectral deformation causes all the three channels to overlap in the position of

using the master from step (a).

image.

the green channel.

**2.3.2 Single and full parallax synthetic holograms**

The area of the dot is divided into two major parts - one filled with grating and the second empty. The ratio of these areas defines the overall luminosity of the image point. The grating part is further segmented into three parts each of them filled with one basic grating for color mixing. In principle, the color can be mixed from two, three or more gratings, but the most common is the three-color mix. The particular basic gratings are chosen individually for each mixed color as the closest components in the colorimetric triangle. In a case of a true-color 3D synthetic hologram, each dot is divided into micro-dots corresponding to the spatial channels (see Section 2.2.1), where each such micro-dot is further segmented into the color components. As already mentioned, such complicated fragmentation can negatively affect the efficiency of the hologram and overall noise level, so the dot size must be carefully chosen.

In the case of the eye-pupil synthesis, the area of the final hologram is not composed of any elementary dots. Thus the color mixing must be synthesized during the recording of the master hologram. If three different lasers are used for synthesis (with proper wavelengths corresponding to the desired RGB mix), the synthesis is relatively simple, all angular channels are exposed three times (once for each color) within the same area of the recording medium. For each exposure, the recorded 2D view contains only particular color channel of the image. However, three-laser synthesis is relatively rare, usually the complete recording process is performed using a single laser (including the copying of the master to the final hologram). Thus the master hologram for color mixing (in a case of color rainbow hologram synthesis) consists of three independent vertically shifted rows of exposures. The shift between the three rows (color channels) can be calculated from analysis of the dispersion effects accompanying the diffraction by the final hologram [Saxby, 1994]. Each of the signal waves coming from the three channels carries the same spatial information about the object. The correct true-color mix is achieved by controlling the relative intensities of these waves. Fig. 9a shows copying of such an RGB synthetic master into the final hologram. Fig. 9b shows the diffraction of white light by the final rainbow hologram.

Fig. 9. **(a)** Transfering three color masters into final RGB color rainbow hologram. **(b)** Reconstruction of the final hologram from the step (a) with white light replay beam. Only the orders that are diffracted in the direction of the observer are indicated in the figure.

In Fig. 10a there is an example of the RGB color master for a rainbow hologram synthesized using the method described in Section 3.2. The final hologram (copy of the master) is displayed in Fig. 10b.

Color mixing as shown in Fig. 9a is exactly correct for the plane of the final hologram. If the color point is outside of the hologram plane, it gets distorted due to the different axial 14 Will-be-set-by-IN-TECH

The area of the dot is divided into two major parts - one filled with grating and the second empty. The ratio of these areas defines the overall luminosity of the image point. The grating part is further segmented into three parts each of them filled with one basic grating for color mixing. In principle, the color can be mixed from two, three or more gratings, but the most common is the three-color mix. The particular basic gratings are chosen individually for each mixed color as the closest components in the colorimetric triangle. In a case of a true-color 3D synthetic hologram, each dot is divided into micro-dots corresponding to the spatial channels (see Section 2.2.1), where each such micro-dot is further segmented into the color components. As already mentioned, such complicated fragmentation can negatively affect the efficiency of

In the case of the eye-pupil synthesis, the area of the final hologram is not composed of any elementary dots. Thus the color mixing must be synthesized during the recording of the master hologram. If three different lasers are used for synthesis (with proper wavelengths corresponding to the desired RGB mix), the synthesis is relatively simple, all angular channels are exposed three times (once for each color) within the same area of the recording medium. For each exposure, the recorded 2D view contains only particular color channel of the image. However, three-laser synthesis is relatively rare, usually the complete recording process is performed using a single laser (including the copying of the master to the final hologram). Thus the master hologram for color mixing (in a case of color rainbow hologram synthesis) consists of three independent vertically shifted rows of exposures. The shift between the three rows (color channels) can be calculated from analysis of the dispersion effects accompanying the diffraction by the final hologram [Saxby, 1994]. Each of the signal waves coming from the three channels carries the same spatial information about the object. The correct true-color mix is achieved by controlling the relative intensities of these waves. Fig. 9a shows copying of such an RGB synthetic master into the final hologram. Fig. 9b shows the diffraction of white

(a) (b)

**(b)** Reconstruction of the final hologram from the step (a) with white light replay beam. Only the orders that are diffracted in the direction of the observer are indicated in the figure.

In Fig. 10a there is an example of the RGB color master for a rainbow hologram synthesized using the method described in Section 3.2. The final hologram (copy of the master) is

Color mixing as shown in Fig. 9a is exactly correct for the plane of the final hologram. If the color point is outside of the hologram plane, it gets distorted due to the different axial

Fig. 9. **(a)** Transfering three color masters into final RGB color rainbow hologram.

the hologram and overall noise level, so the dot size must be carefully chosen.

light by the final rainbow hologram.

displayed in Fig. 10b.

Fig. 10. **(a)** Photograph of the "RGB color" master-hologram. The three color channels can be clearly seen. **(b)** Photograph of the final color synthetic rainbow hologram, that was obtained using the master from step (a).

magnification for the three wavelengths that actually compose this particular point. This issue can be solved by a proper "pre-distortion" of the image data before the recording process.1 The described techniques for color mixing utilized the rainbow effect (diffraction of white light by the volume transmission or thin grating). However, the color can be synthesized also in volume reflection holograms, where all steps are complicated by the Bragg condition (the dispersion cannot be used for generation of whole spectral range of colors as the grating recorded with the given geometry will not work for other than the design color). Nevertheless, a reflection color hologram can be synthesized using special techniques [Hariharan, 1996].

### **2.3.2 Single and full parallax synthetic holograms**

In general, the classical hologram can record the complete 3D properties of the object including both horizontal and vertical parallaxes. However, the parallax perpendicular to the fringes on the hologram surface can potentially suffer from strong dispersion effects. If the reconstructing light source is monochromatic, the dispersion will not apply and full three-dimensionality can be easily achieved. In a case of polychromatic reconstruction (which is the usual demand), the dispersion effects can lead to unacceptable rainbow blurring of the image.

Let us assume the common geometry of reconstruction according to Fig. 4a. The reconstruction beam is coming from the top and the observer is viewing the image from the front of the holographic plate. Thus the main direction of the fringes is horizontal. Besides

<sup>1</sup> The position of the non-compensated reconstructed color point differs from the original object point due to the different axial magnification for the particular reconstruction wavelengths. In the case of green recording wavelength (*λ<sup>G</sup>* = 532 nm), assuming the reference and reconstruction waves are planar, the axial magnifications for the particular color channels are *α<sup>R</sup>* = 0.84, *α<sup>G</sup>* = 1, and *α<sup>B</sup>* = 1.13 (for the red wavelength *λ<sup>R</sup>* = 633 nm and blue wavelength *λ<sup>B</sup>* = 470 nm). Since the hologram is mostly synthesized from the 2D views obtained from the computer, this distortion can be compensated by pre-distorting the 3D model on the computer in the opposite manner. To overlap in the plane of the hologram the red point has to be located on the "beam" coming from the red channel and the blue point on the beam coming from the blue channel. To compensate for the distortion in the z direction, the red "object" has to be axially magnified by the ratio 1/*α<sup>R</sup>* and the blue one shrank by the ratio 1/*αB*. During the 2D images processing, the proper pre-distortion can be introduced to each color channel. When reconstructed, the spectral deformation causes all the three channels to overlap in the position of the green channel.

(a) (b)

Synthetic Image Holograms 225

Fig. 12. **(a)** Photograph of full parallax master-hologram. The holopixels are recorded in both the horizontal and the vertical direction. **(b)** Photograph of reconstructed image from

The second possible approach to synthesizing a volume reflection hologram directly at the hologram plane is based on using a volume material already for the primary recording. However, in such a case the elementary micro-gratings must be recorded as volume reflection elements. The method requires full control over the direction of the recording beam and in the case of color holograms also the possibility to change the reference beam direction. Recording of this kind is very complicated and most of the advantages of the synthetic approach will be suppressed. In Fig. 13, there is an example of the rainbow 3D hologram with true-color RGB

The above described methods demonstrated the ability of the diffractive structures to create a system of spatially separated image channels in observation space. Such a system can be used not only for simulating the three-dimensional behavior of the object, but also for introducing dynamic effects into the viewed scene. The main idea of the synthesis of holographic animation is straightforward. Instead of the different angular views of the object, particular channels can contain the views of the object at the different time instants. However, it is necessary to analyze how the dynamic effect will influence another parameters of the reconstructed image, particularly how can the dynamic behavior be combined with the three-dimensional effects. There are in principle two main groups of dynamic effect which can be synthesized. The first is the continuous animation when the same scene is observed from all viewing directions but with some continuous incremental changes between neighboring channels. The second group consists of effects when the observed scene completely changes if the observer moves his head or tilts the hologram - such effects are usually called flip-flop. When the continuous holographic animation is to be synthesized, the crucial problem can arise from interference between the animation and the 3D effects. If the time development is introduced in the horizontal plane, each eye of the observer will perceive a different object (taken at the different time instant). Such disproportion can rapidly disturb the observation. To remove the problem, the reconstruction can be observed with one eye only, which means

reflection hologram, that was created using the synthetic master from (a).

mix recorded at the hologram plane using a dot-matrix writer.

**2.3.3 Kinetic behavior and holographic animations**

the reconstruction by the monochromatic source (which is also possible today thanks to the wide availability of semiconductor laser sources) there are two principal solutions of this problem. The first is to use volume reflection holograms which can be highly selective to the reconstruction wavelength - it means the holographic reconstruction will appear only for a narrow band of wavelengths also in a case when the light source is polychromatic. The second approach exploits the idea of rainbow holography - the vertical parallax is omitted and the object maintains its 3D properties only in horizontal plane. When observing such a hologram from different directions in vertical plane, the object is seen in different "rainbow" colors. However, such a single parallax hologram can offer a very truthful 3D perception thanks to the geometry described in Fig. 4a and the horizontal position of human eyes. The missing vertical parallax disrupts the observation less than one might expect.

In Fig. 11, there is an example of the recorded master for the rainbow hologram created using

Fig. 11. Photograph of single parallax master-hologram. Each "shining" holopixel represents one view of the object.

the synthesizing method described in Section 2.2.2. Each of the "shining" spots in the figure represents recorded interference pattern of signal and reference wave. These spots are further denoted "holopixels". As it is seen, the process is very simple as only a small number of exposures is needed. Also the data acquisition from the object or computer model is much simpler than in the general full parallax case. The "single row" master is copied to the final plate in the transfer scheme and the rainbow hologram is created. The final hologram can be thin or thick, white light reconstruction is possible and the dispersion effects will only create the rainbow reconstruction under different directions of observation in the vertical plane. By contrast the monochromatic reconstruction is undesirable, in such case the reconstruction is visible only in a narrow stripe.

The full parallax hologram can be also synthesized at the eye-pupil plane. In such a case, the views must be acquired in both vertical and horizontal directions and recorded in a two-dimensional field. In Fig. 12a, there is a typical full parallax master recorded using the method described in Section 2.2.1. The exposed area corresponds to the future region where the observer's eyes will move. Finally, the recorded master must be copied to the reflection copy in the classical holographic transfer setup. In Fig. 12b there is an example of the image reconstructed from a full parallax reflection hologram fabricated using the described method. When using the synthesis at the hologram plane, usually rainbow holograms (single parallax) are synthesized. The rainbow effect is used for achieving proper color composition and white light diffraction is essential for proper image synthesis. The common techniques for recording such holograms are also usually capable of recording thin gratings only, so the volume reflection hologram cannot be easily recorded. However, the volume recording is theoretically possible using one of the following methods.

If the hologram is designed for monochromatic reconstruction, it can maintain both parallaxes and, based on the thin gratings of various period and orientation, the full 3D images can be constructed. Such a "master" can be copied in laser light to a different plane and then again back to the original plane using volume recording materials and a reflection holographic recording setup. This method gives the desired result, but the complexity of the approach is pretty high and most advantages of the direct recording at the hologram plane will vanish. 16 Will-be-set-by-IN-TECH

the reconstruction by the monochromatic source (which is also possible today thanks to the wide availability of semiconductor laser sources) there are two principal solutions of this problem. The first is to use volume reflection holograms which can be highly selective to the reconstruction wavelength - it means the holographic reconstruction will appear only for a narrow band of wavelengths also in a case when the light source is polychromatic. The second approach exploits the idea of rainbow holography - the vertical parallax is omitted and the object maintains its 3D properties only in horizontal plane. When observing such a hologram from different directions in vertical plane, the object is seen in different "rainbow" colors. However, such a single parallax hologram can offer a very truthful 3D perception thanks to the geometry described in Fig. 4a and the horizontal position of human eyes. The

In Fig. 11, there is an example of the recorded master for the rainbow hologram created using

Fig. 11. Photograph of single parallax master-hologram. Each "shining" holopixel represents

the synthesizing method described in Section 2.2.2. Each of the "shining" spots in the figure represents recorded interference pattern of signal and reference wave. These spots are further denoted "holopixels". As it is seen, the process is very simple as only a small number of exposures is needed. Also the data acquisition from the object or computer model is much simpler than in the general full parallax case. The "single row" master is copied to the final plate in the transfer scheme and the rainbow hologram is created. The final hologram can be thin or thick, white light reconstruction is possible and the dispersion effects will only create the rainbow reconstruction under different directions of observation in the vertical plane. By contrast the monochromatic reconstruction is undesirable, in such case the reconstruction is

The full parallax hologram can be also synthesized at the eye-pupil plane. In such a case, the views must be acquired in both vertical and horizontal directions and recorded in a two-dimensional field. In Fig. 12a, there is a typical full parallax master recorded using the method described in Section 2.2.1. The exposed area corresponds to the future region where the observer's eyes will move. Finally, the recorded master must be copied to the reflection copy in the classical holographic transfer setup. In Fig. 12b there is an example of the image reconstructed from a full parallax reflection hologram fabricated using the described method. When using the synthesis at the hologram plane, usually rainbow holograms (single parallax) are synthesized. The rainbow effect is used for achieving proper color composition and white light diffraction is essential for proper image synthesis. The common techniques for recording such holograms are also usually capable of recording thin gratings only, so the volume reflection hologram cannot be easily recorded. However, the volume recording is

If the hologram is designed for monochromatic reconstruction, it can maintain both parallaxes and, based on the thin gratings of various period and orientation, the full 3D images can be constructed. Such a "master" can be copied in laser light to a different plane and then again back to the original plane using volume recording materials and a reflection holographic recording setup. This method gives the desired result, but the complexity of the approach is pretty high and most advantages of the direct recording at the hologram plane will vanish.

missing vertical parallax disrupts the observation less than one might expect.

one view of the object.

visible only in a narrow stripe.

theoretically possible using one of the following methods.

Fig. 12. **(a)** Photograph of full parallax master-hologram. The holopixels are recorded in both the horizontal and the vertical direction. **(b)** Photograph of reconstructed image from reflection hologram, that was created using the synthetic master from (a).

The second possible approach to synthesizing a volume reflection hologram directly at the hologram plane is based on using a volume material already for the primary recording. However, in such a case the elementary micro-gratings must be recorded as volume reflection elements. The method requires full control over the direction of the recording beam and in the case of color holograms also the possibility to change the reference beam direction. Recording of this kind is very complicated and most of the advantages of the synthetic approach will be suppressed. In Fig. 13, there is an example of the rainbow 3D hologram with true-color RGB mix recorded at the hologram plane using a dot-matrix writer.

### **2.3.3 Kinetic behavior and holographic animations**

The above described methods demonstrated the ability of the diffractive structures to create a system of spatially separated image channels in observation space. Such a system can be used not only for simulating the three-dimensional behavior of the object, but also for introducing dynamic effects into the viewed scene. The main idea of the synthesis of holographic animation is straightforward. Instead of the different angular views of the object, particular channels can contain the views of the object at the different time instants. However, it is necessary to analyze how the dynamic effect will influence another parameters of the reconstructed image, particularly how can the dynamic behavior be combined with the three-dimensional effects. There are in principle two main groups of dynamic effect which can be synthesized. The first is the continuous animation when the same scene is observed from all viewing directions but with some continuous incremental changes between neighboring channels. The second group consists of effects when the observed scene completely changes if the observer moves his head or tilts the hologram - such effects are usually called flip-flop. When the continuous holographic animation is to be synthesized, the crucial problem can arise from interference between the animation and the 3D effects. If the time development is introduced in the horizontal plane, each eye of the observer will perceive a different object (taken at the different time instant). Such disproportion can rapidly disturb the observation. To remove the problem, the reconstruction can be observed with one eye only, which means

similar to those discussed in Section 2.3.2 can arise when synthesizing the volume reflection

Synthetic Image Holograms 227

There are various techniques which can be used for recording of synthetic holograms. In principle, they can be divided into two major groups. The first group consists of approaches where the diffractive microstructure is recorded point-by-point with high resolution. The devices used are usually the commonly available direct writers such as electron beam or laser beam lithography writers. The second group comprises approaches based on classical holography where the microstructure is created "automatically" using exposure with an

When synthetic image holograms are calculated point-by-point, a recording device with very high resolution is needed. The typical periodicity of the hologram microstructure is for most holograms within the range 500 − 1000nm. In this case, direct-write lithography is usually used for recording. In principle, three different approaches can be chosen according to the particular application, namely the e-beam lithography, focused laser lithography, and matrix

The finest microstructure can be recorded using a focused electron beam. Very high resolution can be achieved using the e-beam writing technology, where feature size can be on the nanometric scale. However, for image holograms such extreme resolution is not necessary. As has been shown in Section 2.2.1, the typical synthetic image hologram consist of a set of regular microgratings with periodicity just below one micron and dimensions of several microns. The e-beam lithography can easily achieve these parameters, but with very high costs and several restrictions following from the principles of the technique. The strongest limitations are usually the overall size of the hologram which can hardly exceed several cm2 and complications connected with the fact, that the recording must take place in vacuum and on conductive recording material. In case of electron beam the interference effect cannot be exploited in order to simplify the exposure process. The exposure itself is usually extremely

A very similar technique to e-beam writing is laser lithography with a focused laser beam. The recording process is practically identical to the e-beam recording except that instead of an e-beam, a focused laser beam is used. Usually visible lasers with wavelength in the blue part of the spectrum are used. The biggest advantage of the process is operation in normal conditions (no vacuum is needed) and overall costs of the process. The biggest disadvantage is limited resolution given by the focusability of the laser beam (which depends on the recording wavelength and numerical aperture of the focusing system). The grating periodicity of hundreds of nanometers is more or less on the edge of capabilities of the technology. The most advanced technology for recording the optical microstructures is the matrix laser lithography. In these devices, the elementary grating is recorded as a pattern of interference between two focused laser beams. Thus the parameters of the grating (periodicity and orientation) are given by the angle between the beams and their plane of incidence (instead of the size of the focused spot). Moreover, a whole micro-grating with area of hundreds of *μ*m2 is exposed at once in a single exposure, which rapidly speeds up the recording process. The original so-called dot-matrix devices used two physical laser beams with mechanical alignment of their geometry. However, such an approach could not ensure

hologram at the hologram plane.

**3. Recording technology and materials**

interference field of two or more large laser waves.

long (many hours to days according to the area to be exposed).

**3.1 Direct-write lithography techniques**

laser lithography.

Fig. 13. Example of the real reconstruction of the true-color RGB synthetic 3D rainbow hologram designed using the synthesis at the hologram plane and fabricated using dot-matrix laser lithography (in scale).

the three-dimensionality will be perceived only through the movement parallax. Another solution could be based on introducing the time development in the vertical direction. Such an approach automatically suspends application of rainbow holograms as the rainbow effect occupies the vertical parallax. However, for full parallax holograms the approach is possible. The recording process is very similar to the one from Section 2.3.2 with the only difference in image contents for particular rows of exposures (while there the rows corresponded to different vertical views of the object, here each row corresponds to different time states of the scene). As known from rainbow holography, the vertical parallax is not crucial for 3D perception so this approach can offer satisfactory 3D reconstruction with dynamic behavior when moving the observer's head up and down.

Practically, because of the complicated process of recording of volume reflection holograms, many holographic animations are based on the combination of rainbow hologram with dynamic behavior. Both 3D effect and the time development are included in the horizontal direction and the observer eyes are forced to perceive a kind of unnatural view. However, if the time development of the scene is slow and smooth (there is no complete change of the objects but only small parts are moved), the reconstruction can be satisfactorily observed including both the 3D and the dynamic effects.

When the dynamic flip-flop behavior is desired, the above described problems will not apply. For example, if two different objects should be observed, one from the left and second from the right, all channels left of the normal will contain only angular views of the first object and all channels right from the normal will contain the views of the second one. The transition zone, when the left eye of the observer sees the left object and the right eye sees the right one, is usually ignored. In principle, several different objects can be recorded in a single hologram. Both approaches - full parallax (volume reflection holograms) and single parallax (rainbow holograms) can be used when appropriate requirements are met.

In principle, the analysis above is independent of the chosen recording technology. Both synthesis at the hologram plane and eye-pupil plane can be used. Of course, limitations 18 Will-be-set-by-IN-TECH

Fig. 13. Example of the real reconstruction of the true-color RGB synthetic 3D rainbow hologram designed using the synthesis at the hologram plane and fabricated using

the three-dimensionality will be perceived only through the movement parallax. Another solution could be based on introducing the time development in the vertical direction. Such an approach automatically suspends application of rainbow holograms as the rainbow effect occupies the vertical parallax. However, for full parallax holograms the approach is possible. The recording process is very similar to the one from Section 2.3.2 with the only difference in image contents for particular rows of exposures (while there the rows corresponded to different vertical views of the object, here each row corresponds to different time states of the scene). As known from rainbow holography, the vertical parallax is not crucial for 3D perception so this approach can offer satisfactory 3D reconstruction with dynamic behavior

Practically, because of the complicated process of recording of volume reflection holograms, many holographic animations are based on the combination of rainbow hologram with dynamic behavior. Both 3D effect and the time development are included in the horizontal direction and the observer eyes are forced to perceive a kind of unnatural view. However, if the time development of the scene is slow and smooth (there is no complete change of the objects but only small parts are moved), the reconstruction can be satisfactorily observed

When the dynamic flip-flop behavior is desired, the above described problems will not apply. For example, if two different objects should be observed, one from the left and second from the right, all channels left of the normal will contain only angular views of the first object and all channels right from the normal will contain the views of the second one. The transition zone, when the left eye of the observer sees the left object and the right eye sees the right one, is usually ignored. In principle, several different objects can be recorded in a single hologram. Both approaches - full parallax (volume reflection holograms) and single parallax (rainbow

In principle, the analysis above is independent of the chosen recording technology. Both synthesis at the hologram plane and eye-pupil plane can be used. Of course, limitations

dot-matrix laser lithography (in scale).

when moving the observer's head up and down.

including both the 3D and the dynamic effects.

holograms) can be used when appropriate requirements are met.

similar to those discussed in Section 2.3.2 can arise when synthesizing the volume reflection hologram at the hologram plane.

### **3. Recording technology and materials**

There are various techniques which can be used for recording of synthetic holograms. In principle, they can be divided into two major groups. The first group consists of approaches where the diffractive microstructure is recorded point-by-point with high resolution. The devices used are usually the commonly available direct writers such as electron beam or laser beam lithography writers. The second group comprises approaches based on classical holography where the microstructure is created "automatically" using exposure with an interference field of two or more large laser waves.

### **3.1 Direct-write lithography techniques**

When synthetic image holograms are calculated point-by-point, a recording device with very high resolution is needed. The typical periodicity of the hologram microstructure is for most holograms within the range 500 − 1000nm. In this case, direct-write lithography is usually used for recording. In principle, three different approaches can be chosen according to the particular application, namely the e-beam lithography, focused laser lithography, and matrix laser lithography.

The finest microstructure can be recorded using a focused electron beam. Very high resolution can be achieved using the e-beam writing technology, where feature size can be on the nanometric scale. However, for image holograms such extreme resolution is not necessary. As has been shown in Section 2.2.1, the typical synthetic image hologram consist of a set of regular microgratings with periodicity just below one micron and dimensions of several microns. The e-beam lithography can easily achieve these parameters, but with very high costs and several restrictions following from the principles of the technique. The strongest limitations are usually the overall size of the hologram which can hardly exceed several cm2 and complications connected with the fact, that the recording must take place in vacuum and on conductive recording material. In case of electron beam the interference effect cannot be exploited in order to simplify the exposure process. The exposure itself is usually extremely long (many hours to days according to the area to be exposed).

A very similar technique to e-beam writing is laser lithography with a focused laser beam. The recording process is practically identical to the e-beam recording except that instead of an e-beam, a focused laser beam is used. Usually visible lasers with wavelength in the blue part of the spectrum are used. The biggest advantage of the process is operation in normal conditions (no vacuum is needed) and overall costs of the process. The biggest disadvantage is limited resolution given by the focusability of the laser beam (which depends on the recording wavelength and numerical aperture of the focusing system). The grating periodicity of hundreds of nanometers is more or less on the edge of capabilities of the technology.

The most advanced technology for recording the optical microstructures is the matrix laser lithography. In these devices, the elementary grating is recorded as a pattern of interference between two focused laser beams. Thus the parameters of the grating (periodicity and orientation) are given by the angle between the beams and their plane of incidence (instead of the size of the focused spot). Moreover, a whole micro-grating with area of hundreds of *μ*m2 is exposed at once in a single exposure, which rapidly speeds up the recording process. The original so-called dot-matrix devices used two physical laser beams with mechanical alignment of their geometry. However, such an approach could not ensure

transfer copying. Concerning the first step - recording the synthetic master-hologram, there are various approaches [DeBitetto, 1969; Huff, 1981; Ratcliffe, 2003]. The one that we are going to present in more detail omits the ground glass with the focused image (Fig. 7a) and it also saves energy by shaping the reference beam and omitting the slit aperture. This particular setup differs from the one shown in Fig. 7 - the image wavefront is recorded before it actually

Synthetic Image Holograms 229

(a)

(b)

Fig. 15. **(a)** Recording a single 2D image near the output pupil of the objective. **(b)** While replaying with the "reference" wave, the magnified image is focused in the former image plane. The magnified image in the image plane is two-dimensional, lying in the plane perpendicular to the plane of paper (the correct projection of the "big cube" in the image

The recording process itself is in the following sequence. The 2D image, representing a particular view, is uploaded to a transparent SLM. The signal wave passes through the SLM and the 2D image is focused by the "writing" objective onto its image plane with some magnification. Near the output pupil of the objective, the pattern of interference between the signal and reference beam (the *holopixel*) is recorded onto a holographic plate. Then the plate is moved, the image on the SLM is switched for the next view and the next holopixel is

should be a line segment).

creates the image. The principle of the method is explained in Fig. 15.

sufficient resolution for shaping the micro-gratings, precise alignment of the gratings within larger areas, or massive segmentation needed by multi-channel RGB stereograms. Recently, the advanced devices have been developed based on the projection of a microstructure from the computer driven micro-display with large demagnification. The basic idea of such a device is depicted in Fig. 14.

Fig. 14. **(a)** Basic setup of the matrix laser writer. **(b)** Photograph of exposed photoresist.

The system of micro-gratings (with general parameters) is projected on a micro-display (usually a liquid crystal based spatial light modulator - SLM). The display is imaged on the recording material in laser light with large demagnification (several hundred times). In a single exposure a relatively large area is exposed at once, which can contain different gratings with arbitrary parameters. Micro-gratings within this area (typically <sup>∼</sup> 0.01 <sup>−</sup> 0.05 mm2 are perfectly phase-synchronized and also a completely aperiodic microstructure can be recorded. The exposure is performed multiple times and between subsequent exposures the recording material is moved. The device can operate in typical room environment and can easily reach a recording speed of several cm2 per hour. In Fig. 14b there is an example of the microstructure obtained using the described technology. Particular exposures in the form of rectangular tiles are clearly visible. Each tile contains a system of micro-gratings.

The advantages of the direct writing are high flexibility of the recorded microstructure and excellent properties of the reconstructed image (high contrast, low noise, true-color RGB, etc.). The main disadvantages are high costs of the technology and the area of the hologram, which rarely exceeds several tens of cm2.

### **3.2 Wide-beam interference based methods**

As has been stated in Section 2.2.2, the synthesis in eye-pupil plane requires two steps to create the final synthetic hologram. The second step is more or less the standard holographic 20 Will-be-set-by-IN-TECH

sufficient resolution for shaping the micro-gratings, precise alignment of the gratings within larger areas, or massive segmentation needed by multi-channel RGB stereograms. Recently, the advanced devices have been developed based on the projection of a microstructure from the computer driven micro-display with large demagnification. The basic idea of such a device

(a) (b)

The system of micro-gratings (with general parameters) is projected on a micro-display (usually a liquid crystal based spatial light modulator - SLM). The display is imaged on the recording material in laser light with large demagnification (several hundred times). In a single exposure a relatively large area is exposed at once, which can contain different gratings with arbitrary parameters. Micro-gratings within this area (typically <sup>∼</sup> 0.01 <sup>−</sup> 0.05 mm2 are perfectly phase-synchronized and also a completely aperiodic microstructure can be recorded. The exposure is performed multiple times and between subsequent exposures the recording material is moved. The device can operate in typical room environment and can easily reach a recording speed of several cm2 per hour. In Fig. 14b there is an example of the microstructure obtained using the described technology. Particular exposures in the form of rectangular tiles

The advantages of the direct writing are high flexibility of the recorded microstructure and excellent properties of the reconstructed image (high contrast, low noise, true-color RGB, etc.). The main disadvantages are high costs of the technology and the area of the hologram, which

As has been stated in Section 2.2.2, the synthesis in eye-pupil plane requires two steps to create the final synthetic hologram. The second step is more or less the standard holographic

Fig. 14. **(a)** Basic setup of the matrix laser writer. **(b)** Photograph of exposed photoresist.

are clearly visible. Each tile contains a system of micro-gratings.

rarely exceeds several tens of cm2.

**3.2 Wide-beam interference based methods**

is depicted in Fig. 14.

transfer copying. Concerning the first step - recording the synthetic master-hologram, there are various approaches [DeBitetto, 1969; Huff, 1981; Ratcliffe, 2003]. The one that we are going to present in more detail omits the ground glass with the focused image (Fig. 7a) and it also saves energy by shaping the reference beam and omitting the slit aperture. This particular setup differs from the one shown in Fig. 7 - the image wavefront is recorded before it actually creates the image. The principle of the method is explained in Fig. 15.

Fig. 15. **(a)** Recording a single 2D image near the output pupil of the objective. **(b)** While replaying with the "reference" wave, the magnified image is focused in the former image plane. The magnified image in the image plane is two-dimensional, lying in the plane perpendicular to the plane of paper (the correct projection of the "big cube" in the image should be a line segment).

The recording process itself is in the following sequence. The 2D image, representing a particular view, is uploaded to a transparent SLM. The signal wave passes through the SLM and the 2D image is focused by the "writing" objective onto its image plane with some magnification. Near the output pupil of the objective, the pattern of interference between the signal and reference beam (the *holopixel*) is recorded onto a holographic plate. Then the plate is moved, the image on the SLM is switched for the next view and the next holopixel is

for document security applications are often made in series of a million). Thus it is extremely important to look for a proper technology which could enable cost effective production of large series. In classical image holography the holograms are usually copied optically in an optical setup, which is still a relatively expensive process. Volume gratings could not be copied in any other way. However, if the grating is of the relief type, it can be also copied using some of the imprint techniques (like mechanical embossing, etc.). To make this possible, the hologram must be exposed in proper relief recording material. The light source used usually

Synthetic Image Holograms 231

For exposure of relief gratings photoresists are often used (if exposing with laser beam). For e-beam exposure the electron beam sensitive resists are used. Unfortunately, the gratings in photoresists are usually thin, so this material can be used only when the volume properties are not needed (theoretically, the relief gratings in resist can be "thick" and possess volume effects, but they can not be copied using an embossing technology). Photoresist can be used for all exposure steps or the hologram can be finally transfered to the resist material from a different recording medium. The spectral sensitivity is maximum in UV part of the spectrum so photoresists are usually exposed using short wavelength visible sources (such as semiconductor lasers with wavelength ∼ 400nm or gas lasers with wavelengths within the range 400 − 460nm). Because of their overall low sensitivity the photoresists are not perfectly

After the hologram is recorded in the relief material such as photoresist it is usually metalized and copied to a hard metal (usually Nickel) relief copy using the electro-forming process. Such

For recording of the volume gratings whole range of holographic materials can be used according to particular needs. Silver halide gelatin, dichromated gelatin, and some photopolymers can satisfy the requirements. In contrast to the resist materials, they can be easily sensitized for laser sources within the whole visible range. Recently, diode pumped solid state lasers are widely used in holography because of their high output power, very good coherence properties, high efficiency, and relatively low operational costs. Very common are 532nm sources based on the second harmonic from Neodymium doped active material. For further details concerning the recording materials and other components necessary for the

The synthetic image holograms can be constructed in various ways according to the particular application and other demands on the hologram properties. Within this chapter only the basic ideas have been presented. Within the Optical Physics Group at the Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University in Prague, various approaches to image synthesis are researched. Besides research in the field of holographic techniques, also recording materials are developed and automated recording devices are constructed. All samples presented in this text have been fabricated using the technology

Benton, S. A. (1969). A method of reducing the information content of holograms, *Journal of*

Bjelkhagen, H. I. (1993). *Silver-Halide Recording Materials for Holography and their Processing*,

depends on the requirements of the particular recording medium.

suitable for primary exposure of large areas.

available at the Optical Physics Group.

Springer-Verlag.

**4. References**

a matrix is then used for mechanical embossing.

recording process see [Bjelkhagen, 1993; Collier et al., 1971].

*the Optical Society of America*: -59–1545

recorded, and so on. The process is more complicated, since the movement of the holographic plate needs to be compensated by moving also the SLM.2 The scheme of the particular setup can be seen in Fig. 16. All the views obtained by sampling the object are recorded in this manner and the plate is developed and bleached. Since the reference wave is collimated, the replay beam can be a wide collimated wave that reconstructs all the recorded holopixels at once. The reconstructed images from all the holopixels overlap at the place where the object was situated during capturing. The final hologram plate is placed into this place and the final hologram is recorded (similar to Fig. 7b). The device is driven by a PC - the images are sequentially uploaded to the SLM and the two *x* − *y* stages are operated as shown in the figure.

Fig. 16. Scheme of the eye pupil synthesis device: **1** laser, **2** shutter, **3** mirror, **4** beam splitter, **5** microscope objective with spatial filter, **6** beam expander, **7** collimator, **8** holographic diffuser, **9** square aperture, **10** signal shade, **11** SLM, **12** special objective, **13** holographic plate.
