# Computer-Generated Holograms Application in Security Printing
## 3 Printed Hologram  
One of the simple ways to realize CGH-based informative elements is its printing on film using so called Computer-to-Film technology (Ctf) and even on paper using an office printer. The main drawback of this approach is the limitation to binary amplitude modulation. In ref. [20], film-printed CGHs were implemented for complex Fourier filter holographic realization in 4-f correlator. It was shown that different screening techniques such as stochastic screening or diamond screening can be applied for grayscale patterns realization and distribution of spatial noise caused by quantization error can be controlled. However, the spatial resolution of the fringe pattern increases proportionally to the square root of the grayscale levels number. Binarization of CGH fringe pattern model does not affect the spatial resolution, but it causes the rise of quantization error in the restored field. In refs. [21; 22], it was demonstrated that binarized CGHs that form hidden 3D images can be imprinted onto a grayscale image by the use of Ctf technology. Each element of the image was presented by binary sub-hologram, which forms a single-perspective 2D view of a hidden 2D or 3D object. Halftone levels of image elements are encoded by the selection of a threshold level of corresponding sub-hologram fringe pattern binarization algorithms. Restoration of hidden image can be performed with the use of coherent light sources such as laser diodes or even LEDs. The problem of film-printed CGHs implementation in security applications is the complexity of restoring hidden objects using the same smartphone as both a light source and image detector due to the transmissive nature of such an optical element. In ref. [23], it was shown that amplitude Fourier off-axis CGHs, designed according Equations (3a) and (6), can be printed on paper using thermal-transfer printing equipment or even an office printer and used as protective visible marks, named \"Holocode\", on products. These marks can be captured by smartphone cameras and encoded data objects or text can be numerically decoded. No coherent optical setup is used to read out the element as soon as the fringe pattern is captured by camera and subjected to post-processing using the algorithms based on scalar diffraction theory. The object image is restored numerically, which makes this method similar to the digital holography method, where the fringe pattern of a hologram is captured by a digital camera in a coherent interferometric scheme on a first step and the image is numerically restored on a second. The only difference is that we capture the fringe pattern of the printed Fourier CGH. A Holocode as a marking method has fundamental differences from the well-known and widely used methods of marking, such as QR codes or DataMatrix codes. Experiments with attempts to distort the Holocodes showed that even in the case of up to 70% of surface distortions, a hidden image can be restored and analyzed. Moreover, different encryption techniques can be implemented in order to protect the authenticity of such a mark [24]. With the selected encoding algorithm, a sufficient quality of encoded data read-out and high computational speed, comparable to the speed of streaming printing, are provided. As an example, Figure 2 shows the process of converting the original logo \"K\" into a CGH and the subsequent read-out of this logo when the CGH fringe pattern image is captured with a smartphone camera. In addition to higher reliability indicators, a Holocode may be used either with an internet and database connection or as an independent tool for read-out of the total volume of information. The obtained method of Holocode generation and read-out may be used for marking any goods and may be applied to tamper-evident sealing labels or just to self-adhesive labels and contain manufacturer details, serial number, or any other official information.