Printed Graysale Security Elements for Product Labeling
• ability to quickly synthesize and change the encoded information of digital holograms; mass distribution of computer equipment, digital scanners and digital printers made it possible to obtain high-quality reproduction of images with such holograms  based on compact and cheap desktop equipment.
Typically, a digital hologram is a grayscale transparency, usually consisting of 256 shades of gray  and more . To display such a hologram on a physical medium, special laser image generators  are usually used, which today can provide an accurate transmission of only two gradations of the amplitude transmission coefficient.
The calculation of such security elements (without a reference beam) is based on the conjugation of the symmetric expansion of the amplitude-phase representation of the image, the calculation of the discrete Fourier transform (DFT) and the formation of a grayscale image. Thanks to this method, each pixel of the element contains all the information about the original image, which provides stability of such an element to mechanical or other damage. In connection with this, we considered the production of such elements in the form of a grayscale transparency consisting of 256 shades of gray and obtained with a digital printer. Reconstruction of the image was done using smartphone camera and special software.
In this regard, the creation of grayscale security elements on any objects (metal and non-metallic) will include the following technological stages:
• Selecting an encoding object
For example, such objects as shown in Fig. 1 or Fig. 2. The data page is an image (see Fig. 1), coded according to standard ECMA‑377. This kind of data page is used in holographic optical memory .
• Computer transformation of the object of coding into the structure of the grayscale picture.
To maintain the smoothness of tonal transitions when encoding images in digital form, it is necessary to ensure the proper number of signal levels for each hardware channel (either RGB-trichromatic, or luminance and color differential, or CMY, or CMYK). To ensure the perceptual uniformity of tonal transitions within the dynamic range of the system 90 levels of brightness are enough and, therefore, 90 levels of sampling of the brightness information.
Depending on the required resolution, coding objects, operating conditions, the method of printing (laser, offset, inkjet, etc.) is selected and printed on any physical media (paper, laser film, plastic).
Reconstruction of encoding objects is possible using a digital scanner or smartphone camera and special software. Examples of reconstructed images are shown below (Fig. 4, Fig. 6–7).
As seen from Fig. 3 the presence of a grayscale security element did not affect the overall perception of the given digital image.
For evaluation the stability of the recovery of encoded information, two types of damage to such structures were accepted: mechanical impact (crumpled paper) and direct impact by a ballpoint pen on paper.
The study was provided as a part of state assignments of The Ministry of education and science of Russian Federation № 3.2236.2017.