A low-coherence interferometer for optical information hiding that ensures security of an optical image by hiding the image behind a light-scattering medium is demonstrated. The interferometer has a distinctive feature in that modulation of the optical-path difference between the object and reference arms is performed with a manual operation. The main advantage of the operation method is the absence of expensive optomechanical parts in the interferometer.
© 2006 Optical Society of America
Data security is an important issue in information communication technology. Sensitive or confidential data must be protected from unauthorized access at every stage of information processing, including input, transmission, and output of the data. Both encryption techniques and hiding techniques are used to ensure data security. Encryption involves encoding the data itself to make it secret, without hiding its existence. On the other hand, information hiding involves hiding the existence of the data. Higher security can be achieved by combining the two techniques. When data are treated as two-dimensional images, optical image processing techniques are very useful, because of their advantages such as high spatial resolution, parallel processing, free-space (non-contact) parallel communication, and direct visual presentation to human users. Therefore, encryption techniques based on optical systems have been demonstrated as data protecting methods [1–8]. These encryption techniques prevent unauthorized access to confidential information on optical memories [9–11] and displays [12, 13].
An information hiding method based on optical techniques has been demonstrated [14–16]. This optical-information hiding involves covering an optical intensity image with a light scattering medium, and reading it out using low-temporal-coherence interferometry [17–21] and a contrast discrimination method . In contrast discrimination, a threshold operation is applied to the contrast of interference fringes. A phase image (relief object) placed behind a light-scattering medium can be read out with low-coherence phase-shifting digital holography . Imaging an object through a light scattering medium also performed with speckle ensemble method using a micro lens array . Low-coherence interferometry is a powerful tool for cross-sectional imaging of micrometer-scale structures embedded in light-scattering media, especially for observing the inner structure of biological tissues [19, 21]. The merits of optical-information hiding include the ability to prevent falsification and tampering of the data because the data is protected behind a light-scattering medium, and the ability to prevent unauthorized persons from peeping at the data because the data cannot be observed at large distances.
In this paper, we demonstrate readout of image data hidden behind a light-scattering medium using a simple low-coherence interferometer. The operating principle of the low-coherence interferometer is based on modulation of the optical path difference produced when the interferometer is pushed with the hand. This manual operation in the interferometer is, to our knowledge, the first demonstration of such a feature. The main advantage of this method is the absence of expensive optomechanical parts in the interferometer. In Section 2, we describe the principles of reading out a digital image hidden behind a light-scattering medium using low-coherence interference. In Section 3, we describe our experimental readout system. In Section 4, we describe readout experiments and evaluate the performance of the readout system. In Section 5 concludes our report.
2. Principles of reading out a digital image hidden behind a light-scattering medium
A Michelson interferometer with a low-coherence light source used for readout of a digital intensity-image data hidden behind a light-scattering medium is shown in Fig. 1. Details the components are described in Sec. 3. An interference signal I(x, y, ΔL) at a position (x, y) on a charge-couple device (CCD) image sensor for an optical-path difference (OPD) between an object-beam path length L obj and a reference-beam path length L ref, ΔL=L obj -L ref, is given by
where I r and Is(x, y) are the intensities of the reference light and the object light on the CCD image sensor, respectively, k is the wave number, and V tc(ΔL) is the temporal coherence function, where 0<V tc(ΔL)<1.20) Also, ΔL=ΔLi+ΔL om, where ΔLi is an initially-given OPD, which is positive, and ΔL om is a negative change in length of the object path given by pushing the optical system towards the object. Here, ΔLi is set for ΔL to pass the condition of ΔL=0 while the interferometer is pushed.
Here, we briefly describe the principle of the contrast discrimination method for reading out digital intensity-image data hidden behind a light-scattering medium. The details are described in Ref. . We consider an image with binary reflectance behind a light-scattering medium in the object beam of the interferometer. The binary values 0 (low) and 1 (high) are represented by reflectances r l and rh (0<rl<rh<1). When ΔL is changed by the movement of the optical system around zero, the maximum value and the minimum value of the interference signals are respectively I max(x, y)=Is(x, y)+Ir+2(IsIr)1/2|V tc(0)| and I min(x, y)=Is(x, y)+Ir - 2(IsIr)1/2|V tc(π/k)|, where |V tc(ΔL)| has the highest central peak at ΔL=0 and monotonically decreases as |ΔL| increases. The normalized contrast of the detected signals is defined as
where Is(x, y)=r(x, y)pIr, where r(x, y) is the reflectance at (x, y) in the image, which is r l or r h, and p is an intensity of the object beam after the beam is divided by a beam splitter when an intensity of the reference beam is 1, and we assumed |V tc(0)|=|V tc(π/k)|.
The binary output image P(x, y) is obtained by applying a threshold operation at the value V th, that is, P(x, y)=0 if V max(x, y)<V th, and P(x, y)=1 otherwise. In practice, there are spatial variations in the density of the light scattering medium and the reflectance of the binary data. To theoretically determine the threshold value V th, here we assume that the object beam intensity on the CCD image sensor has a maximum variation of δ according to the spatial variations of the density and reflectance. Therefore, the object beam intensities at the CCD image sensor of pixels with the reflectances rh and r l are between prh(1-δ)Ir and prh(1+δ)Ir, and between prl(1-δ)Ir and prl(1+δ)Ir, respectively. Substituting the minimum contrast obtained by the object beam from a pixel with reflectance r h, namely, prh(1-δ)Ir, and the maximum contrast obtained by the object beam from another pixel with reflectance r l, namely, prl (1+δ)Ir, in Eq. (2), gives
If V l≤V th≤V h, there are no bit errors. The condition V l=V h gives the largest allowable variation δmax=(r h - r l)/(r h+r l). Substituting r h(1-δmax) for r(x, y) in Eq. (2), the threshold contrast value is
Thus, V th reduces as |V tc(0)| decreases and as p increases, that is, as the density of the light-scattering medium increases.
The advantages of the contrast discrimination method include its robustness not only for changes and spatial variations in the light-intensity and deformation of the interference pattern caused by the shape of the medium, but also for spatial variations in the light scattering medium and binary data, as shown by Eq. (2). Furthermore, the contrast discrimination method is performed with a low-complexity computational process, including selection of I max(x, y) and I min(x, y) and calculation of the maximum contrast image V max(x, y).
3. Experimental setup
Figures 1 and 2 show a schematic diagram and a photograph of the Michelson interferometer, which included a superluminescent diode (SLD). The SLD had a center wavelength λ of 790 nm and a spectral width Δλ of ~19 nm, corresponding to a coherence length Lc of ~26 µm. The beam from the SLD was collimated with a lens and divided into the reference and object beams by a beam splitter (BS) after a polarizer. A rubber sheet with a beam-passing hole was placed on the surface of the prism box containing the BS in the object beam. The length of the object-beam arm was changed using elasticity of the rubber sheet. The interferometer was placed on an object composed of a light-scattering medium and a binary image on a mirror and was pushed. The intensity of the reference beam was regulated with a variable attenuator. The object beam and the reference beam were superimposed, and their resultant interference pattern was detected by a CCD image sensor after an analyzer. The CCD image sensor had square pixels with a side length of 10.3 µm, and the signals were transferred to a computer through a frame grabber. The transmission axes of the polarizer and the analyzer were set in the same direction. Together, they acted as a polarization gate for removing scattered light that loses the image information. The computer selected I max(x, y) and I min(x, y) and calculated V max(x, y).
A binary image was made of a photographic film on a mirror. The light-scattering medium was thermosetting epoxy resin containing titanium oxide powder sandwiched between a slide glass and a cover glass separated by 100 µm with glass beads. The density of the light-scattering medium was controlled by the amount of titanium oxide powder. The optical density (OD) was experimentally obtained from OD=-log[(I 2-I 2’)/I 1], where I 1 is the light intensity reflected from the mirror without the light-scattering medium, I 2 is the light intensity reflected from the mirror with the light-scattering medium in place, and I 2’ is the light intensity reflected from the light scattering medium without the mirror.
4. Experimental Results
Figure 3 shows experimental results of reading out the binary image behind the light-scattering medium. The binary image as directly observed by the CCD image sensor without the light-scattering medium is shown in Fig. 3(a). The binary image behind the light scattering medium with OD=1.15 was perfectly hidden when the reference beam was obstructed, as shown in Fig. 3(b). As shown in Fig. 3(c), the interference fringes could be observed when the OPD was within the coherence length of the SLD. While pushing the interferometer toward the object some times, V max(x, y) was calculated at each pixel. The output binary image P(x, y) shown in Fig. 3(d) was obtained by the threshold processing of V max(x, y). It was substantially the same as the original image, even in the presence of a distortion of the interference signals caused by the surface shape and the spatial variations of the light-scattering medium, the digital data, and the illumination light.
Figure 4 shows the temporal variation of the interference signals when the interferometer was pushed and released. The interference signals were detected by a photodetector placed on the image plane instead of the CCD image sensor. In this experiment, an initial OPD, ΔLi, was set across the coherence region. When the interferometer was pushed, the change in the optical path length of the object beam was about 100 µm. Around the OPD where the interference signal appeared, the average speed of the optical system was 45 µm/s. After releasing pressure from the optical system, the optical path length of the object beam gradually increased.
The average speed of 45 µm/s was too fast for the CCD image sensor, whose frame rate was 30 frames/s, because an OPD change of 1.5 µm occurred within one frame exceeds the center wavelength of the SLD. Therefore, the OPD was set to be around 0 when the optical system was at its lowest point because the speed of the optical system was low at the lowest point. Figure 5 shows the interference signals at a pixel of the CCD image sensor with this OPD setting when the interferometer was pushed and released. The upper trace and the lower trace are the interference signals obtained on the pixel with r h and r l, respectively. The interference signals on the pixel with r h exhibited large changes and the contrast calculated from the maximum and the minimum values was high. In contrast, the interference signals on the pixel with r l exhibited only small changes, equivalent to the noise level, and the contrast was low. The setting of the initial OPD, which is regulated with the reference mirror, is important to obtain a high contrast.
Figure 6 shows the contrast of the interference signals versus OD. Light-scattering media with OD=0.09, 0.24, 0.64, 1.15, 1.66, and 1.94 were used. The binary image had 100×100 pixels, including r h pixels in the left half and r l pixels in the right half, as indicated in the inset of the graph. The filled circles on the solid line indicate the average of the contrasts measured on the pixels with r h, that is, the average of V h. The filled squares on the solid line indicate the average of the contrast measured on the pixels with r l, that is, the average of V l. The two-headed arrows indicate the minimum and the maximum contrasts. The light intensity of the reference beam was set to be same as that of the object beam, that is, p=1. When the binary image was not hidden with the light-scattering medium, the average of V h was 0.68, and the maximum V h and the minimum V h were 0.72 and 0.60, respectively. This dispersion was mainly caused by a spatial variation of the illumination light. Because V l=~0.06, V th can be determined so as to produce a bit error of 0. As the OD increased, the difference between V h and V l decreased, because the increased OD caused a decrease of |V tc(0)| and an increase of δ due to the increase of the scattered light from the light-scattering media. When OD=1.15, the average of V h was 0.27, and the maximum V h and the minimum V l were 0.37 and 0.21, respectively. V th was carefully selected for zero-error, because the difference between V h and V l was small. When OD=1.66, the average of V h was 0.17, and the maximum V h and the minimum V h were 0.28 and 0.09, respectively. Because the average of V l was 0.09, and V h and V l overlapped, a bit error was generated for any V th. When OD=1.94, the amplitude of the interference signal was below the noise level. The dashed line indicates the theoretical threshold value obtained from Eq. (3). The binary image had r h=0.84 and r l=0.06. |V tc(0)| spatially varied, because the light-scattering medium was slightly nonuniform. Therefore, V th was also nonuniform and was calculated from the average value of |V tc(0)| in 10 pixels at the respective ODs. V th was slightly larger than the minimum value of V h when OD=0.64, and some bit errors were counted, but Vh and Vl could be well separated at other values of V th.
The spatial resolution of the constructed optical system was measured with U.S. Air Force test chart 1951 behind the light-scattering media with OD=0.09, 0.24, 0.64, 1.15, 1.66, and 1.94. The spatial resolution was 22.62 lp/mm when the test chart was directly observed without a light-scattering medium. The resolution had a small dependence on the increase of OD in the measured OD range. When OD=1.94, no interference signal was observed. Because the magnification of the optical system was 0.47, that is, the corresponding square pixel size on the object plane had a side length of 21.9 (=10.3/0.47) µm, the theoretical maximum resolvable spatial frequency of the optical system is 22.8 lp/mm. This value is in good agreement with the experimental value.
We have demonstrated the readout of a digital image hidden behind a light-scattering medium by using a low-coherence interferometer. The method is based on the contrast difference of interference signals due to the reflectance of a digital image in low-coherence interference and threshold processing of the contrast. The distinctive feature of the low-coherence interferometer is that modulation of the optical path difference for obtaining the contrast of the interference signals is achieved by a manual operation. To the best of our knowledge, this is the first demonstration of such a feature in the field of interference measurement. The low-coherence interferometer did not require expensive optomechanical parts. The spatial resolution of the low-coherence interferometer was 22.6 lp/mm. The interferometer successfully read out a digital image hidden behind a light-scattering medium with OD=1.66. To improve the performance of the low-coherence interferometer to read out images hidden behind media with higher ODs, it will be necessary to remove unnecessary background light reflected from optical parts, and to use an image sensor with a higher sensitivity and higher dynamic range We believe that our technique will be useful for optical information hiding where image data used for physical distribution of products, for example, two-dimensional barcodes, is hidden behind a medium such as a label.
This work is supported by the Venture Business Incubation Laboratory of The University of Tokushima, the Nakatani Electronic Measuring Technology Association of Japan, and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) #16360035.
References and links
2. R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996). [CrossRef]
3. N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999). [CrossRef]
4. S. Fukushima, T. Kurokawa, and Y. Sakai, “Image encipherment based on optical parallel processing using spatial light modulators,” IEEE Trans. Photonics Tech. Lett. 3, 1133–1135 (1991). [CrossRef]
5. S. Zhang and M. A. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999). [CrossRef]
6. P. C. Mogensen and J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000). [CrossRef]
8. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000). [CrossRef]
9. T. Nomura, S. Mikan, Y. Morimoto, and B. Javidi, “Secure optical data storage with random phase key codes by use of a configuration of a joint transform correlator,” Appl. Opt. 42, 1508–1514 (2003). [CrossRef] [PubMed]
10. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998). [CrossRef]
11. O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785–6790 (1999). [CrossRef]
14. J. Rosen and B. Javidi, “Hidden images in halftone pictures,” Appl. Phys. 40, 3346–3353 (2001).
15. Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004). [CrossRef] [PubMed]
16. S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt. 45, 953–959 (2006). [CrossRef] [PubMed]
18. K. Takada, I. Yokoyama, K. Chiba, and J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1063–1606 (1987). [CrossRef]
19. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef] [PubMed]