Self-focusing hidden bar code Zhiqiang Zhong, Jianping Ding, Zhou Jin, Peiying Liang, and Gao Wenqi
A new type of diffractive optical bar code produced by computer-generated holographic technology is proposed. The message in the proposed bar code is hidden in the diffracted light of the bar code element and can be read from the first diffraction order. In contrast to the conventional hidden bar code, which needs a lens to focus the diffracted light, the proposed hidden bar code has a property of self-focusing. This self-focusing ability is achieved by modulating a function of the Fresnel zone plate into the bar code format. Consequently, the read-out process for the information in this hidden bar code avoids the use of a lens. Experiments have shown the feasibility of the proposed bar code and confirmed that it can perform better than the conventional hidden bar code. © 2002 Optical Society of America OCIS codes: 070.4560, 090.1970, 090.1760, 100.5010.
1. Introduction
Bar codes are used worldwide because of high efficiency, accuracy in management, and convenience in data information acquisition. A bar code commonly consists of a series of alternate black bars and white spaces, in which a bar means bit 1 and a space corresponds to bit 0. Several consecutive bars and spaces represent an alphanumber, and bars are organized according to specific rules into various patterns that represent letters, numbers, and other symbols.1 Hence the total product information is embedded in the bar code. To obtain the meaning of the bar code, a laser beam scans across the bar code tag, and the reflective signal is collected and translated into decimal numbers.2,3 Ordinary bar codes are large enough to be easily reproduced by duplicate machines or printers. A bar code cannot be applied on an article that is smaller than the bar code itself. A diffractive optical bar code, however, uses diffracted light rather than reflected light to read the information.4 Because the information cannot be seen by directly viewing the bar code tag, this kind of bar code is called a hidden bar code. A hidden bar code ele-
When this research was performed, the authors were with the Department of Physics, Nanjing University, Nanjing 210093, China. Z. Zhong is now with the Department of Basic Courses, East China Shipbuilding Institute, Zhenjiang 212003, China. The e-mail address of the corresponding author, J. Ding, is
[email protected]. Received 27 June 2001. 0003-6935兾02兾020308-04$15.00兾0 © 2002 Optical Society of America 308
APPLIED OPTICS 兾 Vol. 41, No. 2 兾 10 January 2002
ment is of small dimensions and can be produced by computer-generated holographic techniques.5 Its Fraunhofer diffraction yields a sequence of stripes 共or a bar兲. Accordingly, the hidden bar code is small in size compared with ordinary bar codes and has a specific purpose of application. For the labeling of miniature products, such as a biochip, the diffractive bar code is preferable to the ordinary bar code. The diffractive bar code also provides more security because it is difficult to duplicate and its information cannot be directly viewed by the eye. According to diffraction theory, the smaller the diffracting object is, the bigger the diffraction pattern is. Hence, although the size of a hidden bar code is small, its information can be detected easily and accurately in the diffraction pattern. In the diffraction image, a bright area denotes 1 and a blank space denotes 0. In this way, the diffraction image of a hidden bar code contains the information in a binary bit format, which can be converted into alphanumbers and letters. To read the information in a hidden bar code, a lens should usually be placed behind the bar code to focus the diffracted light into the back focal plane. In this paper we propose a new hidden bar code that has a property of self-focusing. The proposed hidden bar code is formed by a modulation of a Fresnel zone plate 共FZP兲 with a diffractive bar code. Because the FZP can play the role of a lens, the readout process for the information in this bar code avoids the use of a lens. Experiments have shown the feasibility of the proposed hidden bar code and confirmed that it can achieve satisfactory performance.
2. Theory A.
Table 1. Relation between Decimal Digits and Binary-Coded Decimal Code
Fresnel Zone Plate Modulation
A FZP is composed of a series of alternately transparent and opaque concentric circular rings, and the radius of the nth circle is given by Rn,6 R n2 ⫽ nR 12,
(1)
where R1 represents the radius of the first circular zone. The transmittance t共r兲 of the FZP can be described as7 t共r兲 ⫽ 12 ⫹ 12 兵sgn关sin共r 2兾R 12兲兴其,
(2)
Decimal Number
BCD Code
Decimal Number
BCD Code
0 1 2 3 4
0000 0001 0010 0011 0100
5 6 7 8 9
0101 0110 0111 1000 1001
cipal focal plane Z ⫽ f1 ⫽ R12兾, resulting from the converging wave of the order 1 of the FZP, is given by9 U共 x, y, f 1兲 ⫽ ⫺
冋
⫻ exp j
where r is the radial distance from the center of the FZP, and the function sgn共 兲 is defined by
再
(3)
It is evident that the transmittance expressed in Eq. 共2兲 is a period function of r. Hence the function may be expanded in a Fourier series as8 t共r兲 ⫽
1 1 ⫹ 2 j
兺
m⫽⫺⬁
冉
2
冊
r 1 exp jm 2 . m R1
(4)
Under the illumination of a plane light wave, each term in the sum will produce a spherical wave, plus an undiffracted plane wave that is the dc term corresponding to the 1兾2 in Eq. 共4兲. The converging waves 共positive m兲 will come to a focus after propagating a distance of fm given by 2
fm ⫽
R1 , m
(5)
where is the wavelength of incident light, and the diverging waves 共negative m兲 appear to merge from virtual foci located before the FZP at distances fm that are also given by Eq. 共5兲. The FZP thus acts as a series of lenses; its converging property will be used in our research. The focus corresponding to m ⫽ 1 is referred to as the principal focus, having a maximal convergence of light energy. We are interested in the corresponding principal focal plane in which a light signal is detected; it is thus also called the output plane. Now we use a FZP to modulate a window containing the bar code information. Let 共x, y兲 denote the window function, 共x, y兲 ⫽ 1 denote inside the window, and 共x, y兲 ⫽ 0 denote outside the window. If the window modulated by the FZP is placed in the plane Z ⫽ 0 and illuminated normally with a planewave amplitude A, the light distribution in the prin-
冊
共 x 2 ⫹ y 2兲 f 1
⫻ F兵共 x, y兲其
⫹1, x ⱖ 0 sgn共 x兲 ⫽ . ⫺1, x ⬍ 0
⬁
冉
A 2 exp j f1 f 1
冏
u⫽
册
x y , ⫽ f1 f1
,
(6)
where F兵 其 represents Fourier transformation. Equation 共6兲 shows that, in the principal focal plane of the zone plate, the complex amplitude U is proportional to the Fourier transformation of the window , and the corresponding irradiance is I共 x, y, f 1兲 ⫽
冉 冊冏 A f 1
冏
2
2
F兵共 x, y兲其兩u⫽ x
y , ⫽ f1 f1
.
(7)
If the window modulated by the FZP is a rectangle with a dimension of a ⫻ b, the irradiance in the principal focal plane 共also the output plane兲 of the FZP becomes I共 x, y, f 1兲 ⫽ I 0 sinc2
冉 冊 冉 冊
ax by sinc2 , f 1 f 1
(8)
where I0 is a constant factor. Equation 共8兲 means that, if a is much bigger than b, the diffraction pattern in the central maximum region is similar to a bright stripe. So we can use such a diffractive stripe to represent 1 in a way similar to an ordinary bar code. Owing to FZP modulation, such a diffractive bar code is self-focused in the output plane, without the use of converging lens. B. Diffractive Bar Code by Use of the Fresnel Zone Plate Modulation
In computer science a decimal number is usually expressed in a binary-coded decimal 共BCD兲, which contains four binary bits that are 0 or 1. The relation between a decimal digit and the BCD code is shown in Table 1. In optics the BCD code can be easily realized by the use of a bright strip to represent 1 and a space to represent 0. For instance, the BCD code of decimal number 49 is 01001001. Figure 1 shows how to represent it by an optical method, in which black stripes mean brightness and blank spaces mean darkness. Hence every four positions represents a BCD code of a decimal digit. 10 January 2002 兾 Vol. 41, No. 2 兾 APPLIED OPTICS
309
number can be written in a series of BCD codes as follows: 0000000100100011010001010110 011110001001100001110110. Fig. 1. Optical bar representation of decimal number 49. Black stripes mean brightness, and blank spaces mean darkness.
From the above analysis, we know that the center of the diffraction pattern of the rectangle window modulated by a FZP is just the coordinate origin of the FZP. If the length of the rectangle is much bigger than its width, the diffraction pattern is similar to a slim stripe that is perpendicular to the longer side of a modulated rectangle. We can combine a series of rectangles modulated by the FZP. If the centers of all FZPs are aligned in a straight line and separate from each other, then in the principal focal plane of the FZP the diffraction pattern is a sequence of parallel bright stripes. We can use these stripes to represent decimal digits in BCD code. Figure 2 illustrates the combination of two rectangles modulated by the FZP and the diffraction of the two rectangles. The undiffracted plane wave that is the dc term corresponding to the 1兾2 in Eq. 共4兲 may cause remarkable background noise. To avoid the effect of that noise on a bar code signal, we adopt an off-axis FZP, the center of which is outside the rectangle, as shown in Fig. 2. There are many bar code encoding schemes 共also called symbology by the bar code industry兲, one of which is the European Article Number system that uses 13 decimal digits to represent product information 共EAN-13兲. We accept the EAN-13 symbology in the design of self-focusing diffractive bar codes. In our experiment a 13-digit decimal number, 0123456789876, is used for testing. This decimal
Fig. 2. Diffraction of the self-focusing hidden bar code element. 310
APPLIED OPTICS 兾 Vol. 41, No. 2 兾 10 January 2002
To mark the beginning and the ending of this BCD code, a beginning sign of 1111 and an ending sign of 1011 need to be added. Accordingly, there are 60 binary bits shown below: 11110000000100100011010001010110 0111100010011000011101101011. To make a self-focusing hidden bar code, 60 points with equal space between them are arranged in a straight line with each point corresponding to one bit. All points that correspond to 1’s are chosen as the center to draw a FZP contained in a rectangle window, and nothing is drawn for 0’s. All rectangle windows have the same dimensions and are combined one by one along the direction perpendicular to the longer dimension of rectangles. The entire pattern composed of these FZP-modulated rectangle windows will form a self-focusing hidden bar code. 3. Manufacture of Self-Focusing Hidden Bar Codes
Two types of self-focusing hidden bar code elements, reflective and transmissive, are made in our experiments. We assume a decimal number encoded by a bar code to be 0123456789876 and take the radius of the first circular zone in the FZP as R1 ⫽ 50 mm.
Fig. 3. Diagram of the manufacture of the self-focusing hidden bar code element.
Fig. 4. Diffraction pattern of the proposed self-focusing diffractive bar code and the corresponding digital message. The contained information is a decimal number sequence of 13 digits: 0123456789876.
The bar code element is fabricated in the manner of producing a computer-generated hologram. We use a laser printer to draw the pattern calculated by computer. The length of the rectangle is 300 mm, and the width is 20 mm. The size of the original pattern is 560 mm ⫻ 300 mm, and the final size is 5.6 mm ⫻ 3 mm after photoreduction in Kodak high-resolution film. In our experiments the wavelength of the illuminating light is 633 nm, so the first focal length of the FZP is designed to be 40 mm. The pattern formed in the film becomes a transmissive selffocusing hidden bar code. This transmissive bar code element can also be transformed into a reflective one by use of photolithography, ion etching, and aluminium coating. Figure 3 illustrates the manufacturing process of the reflective bar code element. The resulting relief pattern can also be used as a mother mask, which could be transferred onto metal foil, such as aluminium foil, by use of mold pressing, thereby forming a trademark tag that is attached to a product. In this way, the massive production of reflective self-focusing bar code elements become possible. The diffraction pattern of a self-focusing bar code element in our experiments is shown in Fig. 4. The pattern is captured by a one-dimensional CCD sensor and translated into a series of decimal digits by computer. To avoid the influence of background noise, a threshold is set during data acquisition and processing. If the measured intensity is larger than the threshold value, it is regarded as 1, and otherwise it is regarded as 0. 4. Conclusions
The proposed diffractive optical bar code takes advantage of the converging property of the FZP, thus avoiding use of a lens that is required by the conventional diffractive bar code when the message in the
bar code is read. Consequently, the proposed diffractive bar code makes the readout setup simpler and more compact. The bar code also provides more security because its information is hidden in the diffracted light of the element and cannot be directly viewed by the eye. The bar code element is produced by use of a computer-generated holographic technique and is thus difficult to duplicate and counterfeit. Although the size of the hidden bar code element is small, the information in it can be detected easily and accurately in the diffracted light. The small size of the proposed diffractive bar code element makes it especially suitable for miniature product labeling. Experiments have shown the feasibility of the proposed hidden bar code and confirmed that it can perform satisfactorily. References 1. D. Tsi, K. Marom, J. Katz, and J. Swartz, “System analysis of CCD-based bar code readers,” Appl. Opt. 32, 3504 –3512 共1993兲. 2. J. M. Eastman and A. M. Quinn, “Diffraction analysis of beams for bar code scanning,” in High-Speed Inspection Architectures, Barcoding, and Character Recognition, M. J. Chen, ed., Proc. SPIE 1384, 185–194 共1990兲. 3. D. J. Reiley, “Polarization of barcode readers,” Opt. Eng. 37, 688 – 695 共1998兲. 4. S. J. Bever and J. P. Allebach, “Synthesis of diffractive optical barcode,” in Computer and Optically Formed Holographic Optics, I. Cindrich and S. H. Lee, Proc. SPIE 1211, 38 – 49 共1990兲. 5. W-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. 共Elsevier, Amsterdam, 1978兲, Vol. 16, pp. 126 –133. 6. E. Hecht and A. Zajac, Optics 共Addison-Wesley, Reading, Mass., 1979兲, pp. 375–376. 7. H. H. Barrett, F. A. Horrigan, “Fresnel zone plate imaging of gamma rays; theory,” Appl. Opt. 12, 2686 –2702 共1973兲. 8. A. R. Shulman, Optical Data Processing 共Wiley, New York, 1970兲, p. 387. 9. J. W. Goodman, Introduction to Fourier Optics 共McGraw-Hill, New York, 1968兲, pp. 83– 88.
10 January 2002 兾 Vol. 41, No. 2 兾 APPLIED OPTICS
311
