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Optics Letters

Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram

Eliot Bolduc, Nicolas Bent, Enrico Santamato, Ebrahim Karimi, Robert W. Boyd

Published Sep 4, 2013• 380 citations
Publisher

Abstract

A phase-only hologram applies a modal transformation to an optical transverse spatial mode via phase encoding and intensity masking. Accurate control of the optical field crucially depends on the method employed to encode the hologram. In this Letter, we present a method to encode the amplitude and the phase of an optical field into a phase-only hologram, which allows the exact control of spatial transverse modes. Any intensity masking method modulates the amplitude and alters the phase of the optical field. Our method consists in correcting for this unwanted phase alteration by modifying the phase encryption accordingly. We experimentally verify the accuracy of our method by applying it to the generation and detection of transverse spatial modes in mutually unbiased bases of dimension two and three.

DOI
10.1364/ol.38.003546

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A phase-only hologram applies a modal transformation to an optical transverse spatial mode via phase encoding and intensity masking. Accurate control of the optical field crucially depends on the method employed to encode the hologram. In this Letter, we present a method to encode the amplitude and the phase of an optical field into a phase-only hologram, which allows the exact control of spatial transverse modes. Any intensity masking method modulates the amplitude and alters the phase of the optical field. Our method consists in correcting for this unwanted phase alteration by modifying the phase encryption accordingly. We experimentally verify the accuracy of our method by applying it to the generation and detection of transverse spatial modes in mutually unbiased bases of dimension two and three.
The scalar attributes of the optical field are considered as an approach to enhancing bit rates in quantum key distribution over free-space optical links. The implications of spatial-mode encoding to system aperture requirements are considered for rectilinear and azimuthal bases of phase modulation. Diffractive-optics-based approaches to generating and discriminating photons based on spatial mode characteristics are quantified through analysis and experimentation. Spatial modes based on phase modulation are generated via modulo-2π phase modulation with a liquid-crystal spatial light modulator (LC SLM). The phase and amplitude modulation associated with superpositions of phase modulated fields are achieved via computer-generated holography with single LC SLM. Transmission volume holograms are evaluated as a technique for de-multiplexing phase modulated modes and cascaded volume holograms are considered as an approach to performing projective measurements on optical fields.
There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.
A phase-only encryption/decryption scheme with the readout based on the zeroth-order phase-contrast technique (ZOPCT), without the use of a phase-changing plate on the Fourier plane of an optical system based on the 4f optical correlator, is proposed. The encryption of a gray-level image is achieved by multiplying the phase distribution obtained directly from the gray-level image by a random phase distribution. The robustness of the encoding is assured by the nonlinearity intrinsic to the proposed phase-contrast method and the random phase distribution used in the encryption process. The experimental system has been implemented with liquid-crystal spatial modulators to generate phase-encrypted masks and a decrypting key. The advantage of this method is the easy scheme to recover the gray-level information from the decrypted phase-only mask applying the ZOPCT. An analysis of this decryption method was performed against brute force attacks.
Interference-based optical encryption schemes have an inherent silhouette problem due to the equipollent nature of the phase-only masks (POMs) generated using an analytical method. One of the earlier methods suggested that removing the problem by use of exchanging process between two masks increases the computational load. This shortcoming is overcome with a noniterative method using the jigsaw transformation (JT) in a single step, with improved security because the inverse JT of these masks, along with correct permutation keys that are necessary to decrypt the original image. The stringent alignment requirement of the POMs in two different arms during the experiment is removed with an alternative method using a single spatial light modulator. Experimental results are provided to demonstrate the decryption process with the proposed method.
A new scheme for parallel optical decryption and the display of encrypted image information is presented. The scheme is based on a common path interferometer configuration providing a simple and robust optical setup. Images are encrypted directly during recording by use of a combined phase encoding and phase scrambling method. The encoding and encryption does not require sophisticated, iterative and time consuming optimization algorithms. Pixels are independently encoded and encrypted by use of a simple look-up table technique that can be performed in milliseconds on a standard personal computer. Optical decryption can subsequently be implemented in the common path interferometer by use of single phase or if desired a combined phase/amplitude key. An advantage of the presented method is that the encrypted image may selectively require recording and decryption of phase values or amplitude values or a combination thereof. Another advantage is that decryption is performed in a plane adjacent to the encrypted mask or an equivalent plane whereby generation of speckles in the decrypted image is strongly suppressed. Finally, there is no requirement of positioning a decrypting mask or spatial light modulator in the optical Fourier plane whereby an accurate three dimensional positioning requirement can be avoided.
Abstract For the purpose of alleviating the vulnerability of double random phase encryption system in the linear canonical transform domain, a novel approach for optical security and cryptographic systems is presented. This proposed system uses a fully phase encoding technique to augment the security of encryption system in the linear canonical transform. The first step in this system involves phase encoding of the initial amplitude image to be ciphered and then modulated by the phase masks. The decryption process of image is the reversal operation of the encryption method. The effectiveness and sensitivity of our proposed cryptosystem for the encryption secret keys are verified. The resistance of our method against occlusion attacks is investigated. Moreover, the results demonstrate that the fully phase-based optical cryptosystem is more secure and robust than the amplitude-based scheme in a linear canonical domain.