=Paper=
{{Paper
|id=Vol-1900/paper23
|storemode=property
|title=Investigation of methods for the formation of multicolored images reconstructed with protective holograms
|pdfUrl=https://ceur-ws.org/Vol-1900/paper23.pdf
|volume=Vol-1900
|authors=Ludmila A. Nayden,Ivan K. Tsyganov,Sergey B. Odinokov
}}
==Investigation of methods for the formation of multicolored images reconstructed with protective holograms ==
https://ceur-ws.org/Vol-1900/paper23.pdf
Investigation of methods for the formation of multicolored images
reconstructed with protective holograms
L.A. Nayden1, I.K. Tsyganov1, S.B. Odinokov1
1
Moscow State Technical University named after N. U. Bauman, ul. Baumanskaya 2-ya, 5, 105005, Moscow, Russia
Abstract
Dot-matrix holograms contain diffraction gratings with different periods and orientations. Grating parameters (period and orintation) are
calculated according to input data, which is graphic raster file. Traditionally image uses additive color model RGB, which involves limited
color range. To increase color range International Illumination Commission (ICI) color model is considered. In this paper methods for
calculating the parameters of diffraction gratings with different periods and orientations for ICI graphic files are investigated and analyzed.
Keywords: Diffraction gratings; Colored holograms; Color chart; Dot-Matrix; Colorimetric system
1. Introduction
Result of the calculation dot-matrix hologram is a set of diffraction gratings. Color, displayed from hologram pixel, should be
close to the color of the corresponding pixel of the input image. The following grating parameters are used to set hologram pixel
color:
The period of the holographic grating;
Angular orientation of the holographic grating;
Relief parameters - depth and profile type.
2. Methods for calculating holographic pixel parameters
The period of the holographic diffraction grating determines the wavelength of the radiation diffracted on it. The the varying
grating orientation angular orientation determines the angle of rotation when a certain pattern is restored. It is possible to
achieve a smooth color change in the image when the hologram is rotated. Relief parameters: namely the depth and type of the
profile, which determine the brightness of the radiation diffracted from a particular pixel. The brightness of diffracted radiation
is determined by profile depth and type and grating area. The parameters of the diffraction gratings can be simply described in
the HSB colorimetric system, where the grating period corresponds to the Hue coordinate, and the brightness of the diffracted
radiation corresponds to the coordinates of the Saturation and Brightness.
The original image for rainbow holograms in most cases can be created using image editors on the computer. The result is a
raster image file, in which the image is represented as a finite set of pixels [2]. Image dot form a graphic pixel with diffraction
gratings located at a very small distance from each other. The perceived color of a pixel is coming result of diffraction in
different holographic gratings. Pixels contain information about the color described in the RGB colorimetric system [3-4]. There
are known formulas for converting color coordinates between colorimetric systems HSB and RGB. This fact allows us to
calculate the parameters of holographic diffraction gratings from the input image file.
Fig. 1. ICI color chart.
Although color acquisition using the RGB system is widely used in many areas, and the RGB system can be used display a
wide range of colors, but it still can not cover all possible colors in the ICI chart. To expand color range reproduction by means
3rd International conference “Information Technology and Nanotechnology 2017” 106
Computer Optics and Nanophotonics / L.A. Nayden, I.K. Tsyganov, S.B. Odinokov
of diffraction gratings, method of color reconstructing in the ICI colorimetric system (1931) is used. The ICI and RGB
colormaps are illustrated on Fig. 1.
Any three different diffraction dots representing three different wavelengths can form any color within the ICI diagram. X, Y,
Z are the color coordinates, the vertices of the triangle in which the color is formed. According to the ICI theory, as shown in
Fig. 2, the required color is the color having the coordinates x0 y0 and the intensity V0 denoted by [(x0, y0), Y0]. The three
selected points have the following coordinates (x1 y1), (x2 y2), (x3 y3). The intensity of the diffracted light at these three points
of light will be denoted by Y1, Y2, Y3. Then, knowing the coordinates of these points, through non-complex calculations, one
can come to the definition of the required coordinate.
Fig. 2. Forming a color at a point inside the triangle with vertices given by three diffraction points.
The intensity of the diffracted radiation (shown in Fig. 3.) depends on the number of points with diffraction gratings, the
more points, the greater the intensity, and, consequently, the brightness of the pixel.
Fig. 3. Schematic representation of a graphic pixel with different intensity of its constituent elements.
The required number of points of each previously defined color depends on the geometric distance in the ICI color chart
between the desired color and the three primary colors. In this case, the intensity of the reflected light corresponds to the number
of points used to represent the primary color.
3. Conclusion
Selecting a sufficient number of diffraction points that create colors close to the border of the ICI color chart, almost all the
colors located inside the diagram can be easily display by combining different diffraction pixels. Representation of the image in
the ICI colormap system allows to provide a larger color spectrum than RGB.
References
[1] Magnusson R, Gaylord TK. Diffraction efficiencies of thin phase gratings with arbitrary grating shape. J. Opt. Soc. Am. 1978; 68(6): 87–93.
[2] Frank SD. Holographic image conversion method for making a controlled holographic grating. U.S. patent 5262879 (16 nov. 1993).
[3] Kolyuchkin VV, Zlokazov EYu, Odinokov SB, Talalaev VYe, Tsyganov IK. A coherent measurement method for checking the surface microrelief depth in
holographic and diffractive optical elements. Computer Optics 2015; 39(4): 515–520. DOI: 10.18287/0134-2452-2015-39-4-515-520.
[4] Khomutov VN, Poleshchuk AG, Cherkashin VV. Measurement of diffraction efficiency of DOE in many diffractive orders. Computer Optics 2011; 35(2):
196–201.
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