1. Introduction

Optical security technologies are one of the most demanded fields of research in optics. The key task of modern security technologies is the development of new visual security features. Optical security technologies allow security elements to be manufactured in hundreds of millions [1]. The key stage in the production of optical security elements is origination. Originals (master shims) are produced using various techniques: optical recording [2], dot matrix [3], and electron-beam technology. Optical recording of originals is an analog process, which is performed with interfering laser beams using a physical object. Dot-matrix and electron-beam technologies operate with computer-synthesized holograms. The overwhelming majority of companies that develop security technologies use optical or dot-matrix technologies to record the originals. Only a few companies worldwide produce master shims using electron-beam lithography.

Modern electron-beam lithography systems can record microrelief with a very high precision. The minimum beam size in modern lithography system can be as small as 5 nm [4]. E-beam lithography allows creating binary structures, blazed gratings [5], Fresnel lenses [6], and kinoforms [7] with high precision. E-beam technology allows synthesizing optical elements to form beam-shaping structures [8]. This technology can be used to produce not only reflective, but also transmitting elements [9].

E-beam lithography allows achieving breakthrough results in optical security technologies. It can be used to synthesize optical security elements that cannot be forged or imitated with standard holographic techniques [10, 11]. E-beam technology is knowledge intensive and by no means widespread. Only a few companies worldwide work in the field of the synthesis of flat optical security elements using e-beam technology. All these factors safely protect the optical security features developed using e-beam technology against counterfeiting. An example of the development of an optical element based on e-beam technology, which produces the visual effect of the change two 2D-images when turned by 180° [12]. This security feature is impossible to forge or imitate by means of optical origination techniques.

In this paper we propose a fundamentally new security feature – the vertical 3D/3D switch effect. In this paper we develop methods for computing and synthesizing a DOE to create this security feature. This security feature is based on e-beam technology. The feature is easy to control visually and is safely protected against counterfeit.

2. Formulation of the problem of the synthesis of a diffractive optical element with vertical 3D/3D switch effect

Computer generated 3D images are produced using well-known approaches involving sets of 2D frames of the 3D object recorded from different viewing directions. When each eye of the observer sees an image from the set of 2D frames that corresponds to the viewing direction, the observer perceives the image of the object as three-dimensional. In our case two sets of 2D frames have to be used to produce the vertical switch effect of the change of two 3D images. Let us denote the frames of the first 3D image by the letters K₀…K _{± N}, and those of the second 3D image, by the letters R₀…R _{± N}. The total number of frames for each 3D image is equal to 2N + 1. Figure 1 shows schematically the formation of the vertical switch effect.

 

Fig. 1 Scheme of the formation of the vertical 3D/3D switch visual security feature.

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Daylight source S illuminates diffractive optical element Q (hereafter referred to as DOE) located in the x = 0 plane with white light. As a result of diffraction on the DOE microrelief light becomes scattered so that the given 2D image forms on the DOE surface when observed from certain viewing directions. More precisely: points K₀…K _{± N} and R₀…R _{± N} in Fig. 1 indicate the positions of the observer’s eye from which the corresponding frame from the set of 2D frames is seen. We assume that the eyes of the observer are located at the same height, i.e., that the head is not tilted either to the right or to the left. The first 3D image is seen when observed from the positions K₀…K _{± N}. The second 3D image is seen from the positions R₀…R _{± N}. The angle between the viewing directions for the end frames R_-N and R_N determines the view angle of the security feature. For stable stereoscopic perception of the 3D image it is important for both eyes to receive the corresponding visual information, and hence the angle considered should be appreciably greater than the angular distance between the eyes of the observer. Figure 2 shows the cross section passing through the Oz and Ox axes and the light source S. This section crosses optical element Q along the Oz axis. The rays L₁ and L₂ directed toward the central frames are inclined at different angles to the Oz axis.

 

Fig. 2 Schematic arrangement of the optical security element, source, and observer.

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Angle θ between rays L₁ and L₂ determines how “clear” is the image switch effect. In the case of small angles θ the images will blend because of the spectral decomposition of white light by the diffractive structures of the DOE. When choosing angle θ one should also bear in mind that under real observing conditions the element may be illuminated by a nonpoint source with a significant spatial extent. Hence to ensure better stability of the effect, angle θ should be chosen to be sufficiently large to take into account the angles of the decomposition of white light into a spectrum and the extent of the light source. On the other hand, if angle θ is too large, the formation of the first 3D image will require the use of diffraction gratings with large periods (the first 3D image will have to be located near zero diffraction order). As a result, the image will be inconvenient to observe, and its contrast and saturation will be reduced appreciably. In the case of our sample angle θ is equal to about 24 degrees.

We used a 3D computer simulation software to obtain sets of «shots» of the 3D scene from given directions. In the case of our chosen 3D effect viewing width of 30 degrees and 16-20 2D frames are usually sufficient to obtain a quality 3D image. We used 17 frames to produce each 3D image. The first 3D image is formed by sets of frames K₀…K _{± 8}, and the second observable 3D image is formed by another own set of frames R₀…R _{± 8}, the viewing directions for the «frames» of the 3D scene are as shown in the schematic layout in Fig. 1. Figure 3 shows five selected frames from each set. Each 2D image in Fig. 3 consists of pixels and there are about 150 000 pixels per frame.

 

Fig. 3 Set of 2D frames for the formation of 3D images.

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Stereo effect, and hence the 3D/3D switch, is observed while the eyes of the observer remain in positions K _{± N} or R _{± N} as shown in Fig. 1. In practice the effect of the alternation of 3D images can also be observed in the scheme where the observer and light source are fixed and the only motion allowed is the tilt of the optical element in the vertical plane about the Oy axis. Thus by tilting the DOE up/down, the observer sees at a certain position the first 3D image, which transitions into the second 3D image when the tilt angle of DOE is changed.

3. Method of computation and fabrication

To shape the internal structure of the DOE we subdivide the optical element into elementary areas in the form of equal rectangles. Let the number of elementary areas be equal to M x N. The idea of partitioning the DOE into elementary areas with different microrelief recorded in each area is well known and widely used in security technologies [1]. The maximum size of such area is determined by the resolution of human eye. The observer must not see that the DOE consists of elementary areas and therefore their size should be no greater than 80 micrometers. On the other hand, the size cannot be too small. The directivity diagram produced by a single elementary area has a rather complex structure, and the quality of synthesized 3D images degrades substantially if elementary areas are smaller than 30 micrometers. The sizes of elementary areas in this study range from 40 to 80 micrometers.

Hereafter we assume that each 2D frame consists of M x N image pixels and hence the number of pixels in a frame coincides with that of elementary areas in the DOE. Let us consider a 2D-frame pixel with the coordinates (i, j), where i and j are the row and column number of the pixel, respectively. The geometric location of the center of each elementary area at position (i, j) inside the DOE corresponds to the geometric position of the center of image pixel with the same coordinates (i, j) for each 2D frame. The optical element is synthesized so that when observed from any given direction the color of the elementary area with coordinates (i, j) matches that of the frame pixel with coordinates (i, j) corresponding to this direction. For example, the color of the pixel with coordinates (i, j) in 2D frame R₀ is synthesized by only one elementary area with coordinates (i, j) when observed from point R₀.

Thus the DOE is so constructed that each elementary area participates in the synthesis of all 2D frames. Each elementary area of the DOE synthesizes the pixels of both the first and second 3D images. All these are color frames, and the 2D images have therefore to be synthesized in three colors (RGB). Hence computing the microrelief in each elementary area is a rather difficult task because the radiation diffracted from the microrelief participates in the synthesis of many color pixels. This problem would be unsolvable if each elementary area were filled with only one grating.

That is why each elementary area is subdivided into diffraction pixels, and in each such pixel a diffraction grating is recorded with the given period and orientation. Figure 4 shows schematically a fragment of the elementary area. The letters “K” denote the diffraction pixels that synthesize the first 3D image (shown by yellow color), and the letter “R” denotes the diffraction pixels that synthesize the second 3D image.

 

Fig. 4 Scheme of the microrelief formation of a fragment of a flat optical element.

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Each elementary area contains about several dozen pixels. The total number of diffraction pixels in an optical element amounts to about 1 million. Elementary areas consist not only of diffraction pixels, but also contain empty places. The total number of parameters used for the inverse problem is of about 2 million. Such a parameter set size is quite sufficient for synthesizing not just one 3D image, but also for producing the effect of the switch of two 3D images. It turns out that constructive methods can be proposed for computing the periods and orientations of the diffraction gratings in each diffraction pixels.

We further assume that each diffraction pixel is responsible for the synthesis of one color channel of a single frame as seen by the observer. Thus the parameters of the diffraction grating of each diffraction pixel are computed for the given wavelength and given direction toward the observer. Diffraction of obliquely incident light by gratings has been thoroughly studied even in the case of complex models with polarization [13]. The situation simplifies substantially in the scalar wave model that we use in this paper. There is a well-known formula that relates the components of the wave vectors of the incident and diffracted waves [14]:

In our case vector ${\overrightarrow{k}}_i$ is collinear to vector $\overrightarrow{\mathrm{SO}}$, and vector ${\overrightarrow{k}}_m$ is collinear to the observing direction of the corresponding frame:${\overrightarrow{\mathrm{OK}}}_j$ for the first image and ${\overrightarrow{OR}}_j$ for the second image (see Fig. 1). The absolute values of vectors ${\overrightarrow{k}}_i$ and ${\overrightarrow{k}}_m$ are equal to $2\pi /\lambda$. The coordinates of vectors ${\overrightarrow{k}}_i$ and ${\overrightarrow{k}}_m$ are known and therefore it is easy to compute the coordinates of their projections ${\overrightarrow{k}}_{Q,i}$ and ${\overrightarrow{k}}_{Q,m}$ onto the optical element plane x = 0. In our case we synthesize images in the first order of diffraction and hence m = 1. It follows from formula (1) that $\overrightarrow{D}={\overrightarrow{k}}_{Q,m}-{\overrightarrow{k}}_{Q,i},$ and this vector determines both the direction of the lines of the diffraction gratings in each pixel and the period of the diffraction grating for each wavelength corresponding to the red, green, and blue colors.

We chose to partition the elementary area into rectangular diffraction pixels with sizes ranging from 5 to 15 micrometers. Each diffraction pixel is responsible for the formation of one color channel of a single frame as seen by the observer. For the first and second 3D image we used monochrome frames (i.e., one color channel) and full-color RGB images, respectively. The elementary area can be filled with diffraction gratings not only completely, but also partly. To synthesize the visual switch 3D/3D effect, here we use diffraction gratings with periods ranging from 0.6 to 1.4 micrometers. The first 3D image is generated by gratings with periods from 1.2 to 1.4 micrometers, and the second 3D image, by gratings with periods from 0.6 to 0.85 micrometers. The range of periods of the gratings that form each image translates into the range of colors of the resulting 3D images. The second 3D image is a full-color picture of a rose. The 0.25 micrometer range of diffraction grating periods is sufficient to generate the image in true colors from red to blue.

Red (0.62 micrometer wavelength) image fragments are produced by diffraction gratings with the periods of 0.79 – 0.85 micrometer depending on the departure of the frame angle from zero. Blue (0.47 micrometer wavelength) image fragments are produced by diffraction gratings with the periods of 0.6 – 0.65 micrometer. Green (0.547 micrometer wavelength) image fragments are produced by gratings with the periods in the 0.7 – 0.75 micrometer interval. Such parameters ensure that red, green, and blue image fragments are seen simultaneously from the same observing angle.

A 3D image is formed because the left and right eyes of the observer see different frames. If the observer’s eyes are at the same height and the nose bridge is at position K₀, the observer sees a 3D image of the key. This image remains three-dimensional even when the optical element is tilted left/right as far as the eyes of the observer remain between frames K_-8 – K₊₈. If the eyes of the observer are at the same height and the nose bridge is at the center of zero frame R₀ then the observer sees a 3D image of the rose. This image remains three-dimensional even when the optical element is tilted left/right as far as the eyes of the observer remain between frames R_-8 – R₊₈. The switching of the key and rose images occurs when the optical element is tilted up/down.

The original of the DOE was produced using a shaped beam system with a minimum beam size of 0.1 х 0.1 μm². Such a beam size is quite sufficient to generate high-quality 3D images. We used positive e-beam resist to record the microstructures. The DOE has a total size of 40 x 30 mm², and the size of the area occupied by the 3D effect is 25 x 18 mm².

Figure 5 shows a fragment of the microrelief of two 10 x 15 μm² diffraction pixels obtained with an AFM. The period of diffraction gratings is equal to about 0.6 micrometer. The image in Fig. 5 is that of the DOE master hologram. The microrelief depth is of about 100 nm. The depth accuracy of the shaping of the microrelief of diffraction gratings is 20 nm.

 

Fig. 5 AFM image of a DOE microrelief fragment.

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We used standard electroforming and recombination procedures to produce recombined master shims incorporating 20 DOE copies. We then used them to produce working shims, which served to make production samples of optical security elements on a 23-micrometer thick polyester film (self-adhesive labels) on standard embossing equipment.

Figure 6 shows the photos of a real sample optical element after replication. The left-hand image in Fig. 6 was obtained from the observing point corresponding to the central frame K₀ of the first 3D image A video of the same sample was recorded (Visualization 1) to demonstrate the switch effect. The absence of gratings with periods in the 0.85 – 1.2 micrometer interval provides the gap between the two observed 3D images to ensure clear switch between them even when the element is illuminated by a lamp with finite angular size of up to 8 degrees and not just by a point source.

 

Fig. 6 Photo of the optical element taken from a point K₀ (a) and R₀ (b) (see Visualization 1).

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As is evident from the video, the technology of the synthesis of the switch 3D/3D visual security effect produced using electron-beam technology allows mass replication with standard equipment.

4. Discussion

The purpose of optical security technologies is to develop new security features for visual control. Security features should be easy to identify visually. However, this is not enough. It is important to provide the strongest protection possible for the security feature against counterfeit or imitation. Optical elements with a 3D effect can be synthesized using optical recording [15, 16], Dot Matrix [17, 18] or e-beam technologies [19]. However, a 3D image as a visual security feature can no longer be considered as a sign of high level of protection. The same conclusion was reached by Naruse et al. [20] in their paper dedicated to the development of 3D image generating optical security elements.

One possible line of further development could be to create more complex 3D objects. The potential of computer synthesis can be used to build a very detailed model and produce an optical security element that would generate it. However, the authenticity of such an optical element could be identified only by illuminating it with ideal point source and with no other light sources present in a room. We suggest another way. In this paper we propose the switch effect of two 3D images. Of all possible options we have chosen the vertical 3D/3D switch effect as the most difficult to manufacture feature. At the same time, this effect is easy to control visually even by an inexperienced observer.

The resulting DOE allows one to reliably control the effect of the switch of two 3D images in the ± 10 degree interval of horizontal angles in the case of illuminated by a point source. The difference between the vertical observing angles of the two 3D images is 15 degrees when illuminated by a point source. In the video presented here, which demonstrates the 3D/3D switch effect, the angular size of the light source was equal to 8 degrees and the effect shows up successfully because of the sufficient angular gap between the 3D images.

One of the problems in the case of the synthesis of the switch effect of two 3D images is that with gratings we have not only the + 1 order of diffraction where the effect is produced, but also the zero, minus first, second, and minus second orders. Note, however, that the zero and all negative orders have no effect on the quality of synthesized 3D images, except for the partial loss of light energy into these orders. A serious problem in this case is posed by possible artifacts in the second 3D image (rose) due to the second order in the structures that synthesize the first 3D image (key). To address this problem, the microrelief of diffraction gratings has to be synthesized with high precision to minimize the intensity of the second order of diffraction on these structures. The video presented here demonstrates that this problem can be successfully solved.

To produce the diffractive optical element, we used a shaped beam lithography system [4], which allows recording the microrelief not only with 0.1 x 0.1 μm² square spots, but also with various rectangular spots with sizes up to 6 microns. A distinguishing feature of the use of shaped beam lithography system is that inclined gratings are recorded by approximating them by a set of rectangular spots of fixed orientation. As is evident from Fig. 5, the resulting gratings have burrs with sizes no greater than 0.1 micrometer, which is several times smaller than the wavelength of visible light. Such microrelief features produce only minor noise on the synthesized 3D images, which, as is evident from the video, is practically indiscernible by the naked eye.

The well-known property of diffraction grating of changing their color with the change of observing angle in the white light leads to the change of the image color when the DOE is tilted. The degree of color change resulting from the tilt of the optical element can be estimated from the video (Visualization 1). The switch 3D visual security feature consists in observer being able to reliably identify each 3D image when the optical element is tilted. To ensure bona fide recognition of 3D images they should be sufficiently simple for human brain to easily and rapidly identify them as 3D objects.

A comparison of known technologies of recording holographic 3D images shows that the quality of optically recorded single 3D images is superior to that of each individual 3D image considered in this paper. This is a result of the pixel microstructure of the DOE. However, electron-beam technology allows producing optical elements with much higher level of protection against counterfeit and imitation. Visual 3D/3D switch effect is an example of such a development. Dot-matrix technology also uses pixel structure. Dot-matrix technology ranks below electron-beam technology in all technical parameters such as resolution, accuracy of profile recording, and pixel couplings. For dot-matrix technology to produce a DOE even for the synthesis a usual 3D image is a challenging task.

Mathematically, the problem of producing the diffraction effect for the synthesis of 3D/3D image is a typical inverse problem [21]. In this study we consider the problem of the computation of the DOE phase function for synthesizing the effect of the switch of 3D images. Solving the inverse problem is an extremely challenging task. This paper proposes an efficient method for computing the phase function of optical element in finite-dimensional representation. The optical element is subdivided into diffraction pixels, and a grating of given orientation and period is incorporated in each pixel. We proposed an efficient algorithm, which despite the large number of parameters in the inverse problem allows constructive computation of the orientation and period of gratings in each diffraction pixel from the given set of frames of the 3D image. Solving the synthesis problem in such approximation takes no more than 1 minute on an ordinary PC. The finite-dimensional parametric model employed is an approximation. Subjective perception of the effect by the observer and the video clip showing a real DOE prove that the proposed model is a good approximation.

5. Conclusion

Electron-beam technology opens up new prospects for the synthesis of flat optical elements. The development of security features for visual control is one of the most important and pressing tasks. Optical elements should be safely protected against counterfeit and imitation. An example of such a development is the Switch-180° security feature – the effect of alternation of 2D images when the element is turned by 180° [12]. The new security feature presented in this paper demonstrates that e-beam technology can be used to generate 3D images.

The 3D/3D vertical switch feature presented in this paper is easy to control visually. The optical security elements that produce it are fabricated using e-beam technology with a microrelief formation precision of 20 nm in depth. E-beam technology is knowledge intensive and by no means widespread. The new security element developed in this study is safely protected against counterfeit and allows mass replication.

We present the technology of the synthesis of 3D/3D vertical switch effect. Similarly, optical elements can be made to produce effects consisting of the alternation of two full-color 3D images when the element is tilted left/right or turned by 90 degrees. For example, to produce horizontal 3D/3D switch effect when the element is tilted left/right, it is sufficient to arrange the 2D frames of the first 3D image left of the zero frame, and the 2D frames of the second 3D image, right of the zero frame. Vertical 3D/3D switch effect is most protected against counterfeit and easiest to observe.

Modern e-beam lithography systems operate with plates covered with electron resist and having sizes of up to 20 x 20 cm². Hence they can be used to fabricate optical security features with the size of several square cm and as large as a passport page. The visual security feature that we developed – the vertical 3D/3D switch effect – can be used for protection of banknotes and documents.