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Journal ArticleDOI

Encrypting three-dimensional information with digital holography

10 Dec 2000-Applied Optics (Optical Society of America)-Vol. 39, Iss: 35, pp 6595-6601
TL;DR: A method for optical encryption of three-dimensional (3D) information by use of digital holography using a phase-shifting interferometer and an intensity-recording device.
Abstract: A method for optical encryption of three-dimensional (3D) information by use of digital holography is presented. A phase-shifting interferometer records the phase and amplitude information generated by a 3D object at a plane located in the Fresnel diffraction region with an intensity-recording device. Encryption is performed optically by use of the Fresnel diffraction pattern of a random phase code. Images of the 3D object with different perspectives and focused at different planes can be generated digital or optically after decryption with the proper key. Experimental results are presented.
Citations
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Journal Article
TL;DR: In this article, a self-scanned 1024 element photodiode array and a minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100.
Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

1,300 citations

Journal ArticleDOI
TL;DR: The principles and major applications of digital recording and numerical reconstruction of holograms (digital holography) are described, which are applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media.
Abstract: This article describes the principles and major applications of digital recording and numerical reconstruction of holograms (digital holography). Digital holography became feasible since charged coupled devices (CCDs) with suitable numbers and sizes of pixels and computers with sufficient speed became available. The Fresnel or Fourier holograms are recorded directly by the CCD and stored digitally. No film material involving wet-chemical or other processing is necessary. The reconstruction of the wavefield, which is done optically by illumination of a hologram, is performed by numerical methods. The numerical reconstruction process is based on the Fresnel–Kirchhoff integral, which describes the diffraction of the reconstructing wave at the micro-structure of the hologram. In the numerical reconstruction process not only the intensity, but also the phase distribution of the stored wavefield can be computed from the digital hologram. This offers new possibilities for a variety of applications. Digital holography is applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media. Further applications are imaging and microscopy, where it is advantageous to refocus the area under investigation by numerical methods.

1,171 citations


Cites methods from "Encrypting three-dimensional inform..."

  • ...• improvements in the experimental techniques and reconstruction algorithm [31–50], • applications in deformation analysis and shape measurement [51–55, 71, 111], • the development of phase-shifting digital holography [56– 64], • applications in imaging, particle tracking and microscopy [65–70, 73, 104], • measurement of refractive index distributions within transparent media [72, 74, 75], • applications in encrypting information [76, 77], • the development of digital light-in-flight holography [78– 83], • the development of comparative digital holography [84]....

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Journal ArticleDOI
TL;DR: Optical processing methodologies, based on filtering, are described that are applicable to transmission and/or data storage and the advantages and limitations of a set of optical compression and encryption methods are discussed.
Abstract: Over the years extensive studies have been carried out to apply coherent optics methods in real-time communications and image transmission. This is especially true when a large amount of information needs to be processed, e.g., in high-resolution imaging. The recent progress in data-processing networks and communication systems has considerably increased the capacity of information exchange. However, the transmitted data can be intercepted by nonauthorized people. This explains why considerable effort is being devoted at the current time to data encryption and secure transmission. In addition, only a small part of the overall information is really useful for many applications. Consequently, applications can tolerate information compression that requires important processing when the transmission bit rate is taken into account. To enable efficient and secure information exchange, it is often necessary to reduce the amount of transmitted information. In this context, much work has been undertaken using the principle of coherent optics filtering for selecting relevant information and encrypting it. Compression and encryption operations are often carried out separately, although they are strongly related and can influence each other. Optical processing methodologies, based on filtering, are described that are applicable to transmission and/or data storage. Finally, the advantages and limitations of a set of optical compression and encryption methods are discussed.

463 citations

Journal ArticleDOI
TL;DR: A technique to recover the exact keys with only two known plain images is described, and this technique is compared to other attacks proposed in the literature.
Abstract: Several attacks are proposed against the double random phase encryption scheme. These attacks are demonstrated on computer-generated ciphered images. The scheme is shown to be resistant against brute force attacks but susceptible to chosen and known plaintext attacks. In particular, we describe a technique to recover the exact keys with only two known plain images. We compare this technique to other attacks proposed in the literature.

444 citations

Journal ArticleDOI
TL;DR: This Letter shows how computational ghost imaging can be used to encrypt and transmit object information to a remote party and important features, such as key compressibility and vulnerability to eavesdropping, are experimentally analyzed.
Abstract: Ghost imaging is an optical technique in which the information of an object is encoded in the correlation of the intensity fluctuations of light. The computational version of this fascinating phenomenon emulates, offline, the optical propagation through the reference arm, enabling 3D visualization of a complex object whose transmitted light is measured by a bucket detector. In this Letter, we show how computational ghost imaging can be used to encrypt and transmit object information to a remote party. Important features, such as key compressibility and vulnerability to eavesdropping, are experimentally analyzed.

416 citations

References
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Journal ArticleDOI
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Abstract: An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices, where m is proportional to log N. This results inma procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form. Attention is given to the choice of N. It is also shown how special advantage can be obtained in the use of a binary computer with N = 2' and how the entire calculation can be performed within the array of N data storage locations used for the given Fourier coefficients. Consider the problem of calculating the complex Fourier series N-1 (1) X(j) = EA(k)-Wjk, j = 0 1, * ,N- 1, k=0

11,795 citations

Journal ArticleDOI
TL;DR: A new optical encoding method of images for security applications is proposed and it is shown that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.
Abstract: We propose a new optical encoding method of images for security applications. The encoded image is obtained by random-phase encoding in both the input and the Fourier planes. We analyze the statistical properties of this technique and show that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

2,361 citations

Journal ArticleDOI
TL;DR: A new method is proposed in which the distribution of complex amplitude at a plane is measured by phase-shifting interferometry and then Fresnel transformed by a digital computer, which can reconstruct an arbitrary cross section of a three-dimensional object with higher image quality and a wider viewing angle than from conventional digital holography using an off-axis configuration.
Abstract: A new method for three-dimensional image formation is proposed in which the distribution of complex amplitude at a plane is measured by phase-shifting interferometry and then Fresnel transformed by a digital computer. The method can reconstruct an arbitrary cross section of a three-dimensional object with higher image quality and a wider viewing angle than from conventional digital holography using an off-axis configuration. Basic principles and experimental verification are described.

1,813 citations

Journal ArticleDOI
TL;DR: The principle of recording holograms directly on a CCD target is described and a real image of the object is reconstructed from the digitally sampled hologram by means of numerical methods.
Abstract: The principle of recording holograms directly on a CCD target is described. A real image of the object is reconstructed from the digitally sampled hologram by means of numerical methods.

1,444 citations

Journal Article
TL;DR: In this article, a self-scanned 1024 element photodiode array and a minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100.
Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

1,300 citations