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.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

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.

Encrypting three-dimensional information with digital holography

We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.

Image formation in phase-shifting digital holography and applications to microscopy

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

Two-step phase-shifting interferometry and its application in image encryption.

Information security and authentication are important challenges facing society. Recent attacks by hackers on the databases of large commercial and financial companies have demonstrated that more research and development of advanced approaches are necessary to deny unauthorized access to critical data. Free space optical technology has been investigated by many researchers in information security, encryption, and authentication. The main motivation for using optics and photonics for information security is that optical waveforms possess many complex degrees of freedom such as amplitude, phase, polarization, large bandwidth, nonlinear transformations, quantum properties of photons, and multiplexing that can be combined in many ways to make information encryption more secure and more difficult to attack. This roadmap article presents an overview of the potential, recent advances, and challenges of optical security and encryption using free space optics. The roadmap on optical security is comprised of six categories that together include 16 short sections written by authors who have made relevant contributions in this field. The first category of this roadmap describes novel encryption approaches, including secure optical sensing which summarizes double random phase encryption applications and flaws [Yamaguchi], the digital holographic encryption in free space optical technique which describes encryption using multidimensional digital holography [Nomura], simultaneous encryption of multiple signals [Perez-Cabre], asymmetric methods based on information truncation [Nishchal], and dynamic encryption of video sequences [Torroba]. Asymmetric and one-way cryptosystems are analyzed by Peng. The second category is on compression for encryption. In their respective contributions, Alfalou and Stern propose similar goals involving compressed data and compressive sensing encryption. The very important area of cryptanalysis is the topic of the third category with two sections: Sheridan reviews phase retrieval algorithms to perform different attacks, whereas Situ discusses nonlinear optical encryption techniques and the development of a rigorous optical information security theory. The fourth category with two contributions reports how encryption could be implemented at the nano- or micro-scale. Naruse discusses the use of nanostructures in security applications and Carnicer proposes encoding information in a tightly focused beam. In the fifth category, encryption based on ghost imaging using single-pixel detectors is also considered. In particular, the authors [Chen, Tajahuerce] emphasize the need for more specialized hardware and image processing algorithms. Finally, in the sixth category, Mosk and Javidi analyze in their corresponding papers how quantum imaging can benefit optical encryption systems. Sources that use few photons make encryption systems much more difficult to attack, providing a secure method for authentication.

http://diposit.ub.edu/dspace/bitstream/2445/118388/1/664334.pdf

Roadmap on optical security

A technique that combines the high speed and the high security of optical encryption with the advantages of electronic transmission, storage, and decryption is introduced. Digital phase-shifting interferometry is used for efficient recording of phase and amplitude information with an intensity recording device. The encryption is performed by use of two random phase codes, one in the object plane and another in the Fresnel domain, providing high security in the encrypted image and a key with many degrees of freedom. We describe how our technique can be adapted to encrypt either the Fraunhofer or the Fresnel diffraction pattern of the input. Electronic decryption can be performed with a one-step fast Fourier transform reconstruction procedure. Experimental results for both systems including a lensless setup are shown.

Optoelectronic information encryption with phase-shifting interferometry

The performance of fully phase- and amplitude-based encryption processors is analyzed. The effects of noise perturbations on the encrypted information are considered. A thresholding method of decryption that further reduces the mean-squared error (MSE) for the fully phase- and amplitude-based encryption processes is provided. The proposed thresholding scheme significantly improves the performance of fully phase- and amplitude-based encryption, as measured by the MSE metric. We obtain analytical MSE bounds when thresholding is used for both decryption methods, and we also present computer-simulation results. These results show that the fully phase-based method is more robust. We also give a formal proof of a conjecture about the decrypted distribution of distorted encrypted information. This allows the analytical bounds of the MSE to be extended to more general non-Gaussian, nonadditive, nonstationary distortions. Computer simulations support this extension.

Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption

A novel photon-based proton model is developed. A proton’s ground state is assumed to be coherent to the degree that all of its mass-energy precipitates into a single uncharged spherical structure. A quantum vortex, initiated by the strong force, but sustained in the proton’s ground state by the circular Unruh effect and a spherical Rindler horizon, is proposed to confine the proton’s mass-energy in its ground state. A direct connection between the circular Unruh effect, the zitterbewegung effect, spin, and general relativity is proposed. Such a structure acts as an uncharged zitterbewegung fermion, and may explain neutrino mass. A ground-state proton’s central zitterbewegung fermion is assumed to be surrounded by a halo of charge shells of both signs. Virtual photon standing waves are assumed to synchronize the inner shell with the central zitterbewegung fermion. The charge shells are proposed to be associated with isospin and proton g-factor. There are only two model inputs—proton mass and quantized electronic charge—and just one adjustable parameter. The adjustable parameter, reduced only by about 0.4% from an initial estimate, provides the proton’s experimentally determined magnetic moment to arbitrary precision. The resulting modeled proton charge radius agrees very well with the 2018 CODATA value. Magnetic moment and charge radius are calculated algebraically in a manner easily understood by undergraduate physics students. This proposed ground-state proton model could be considered a low-energy approximation to a full quantum chromodynamical proton model. 

https://www.researchsquare.com/article/rs-2008624/latest.pdf

Steven C. Verrall

Papers

Optoelectronic information encryption with phase-shifting interferometry

Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption

Ground State Quantum Vortex Proton Model