The field of optics, too, has been touched by the virtual. For example, if we go way back to Gabor’s Nobel–prize-winning holographic notion of imaging as a two-step process (recording followed by reconstruction) and couple it with the fact that nowadays holograms are typically reconstructed digitally rather than optically, we have a classic example of virtual optics at work: that is, an optical imaging system of which the computer forms an intrinsic part. Thus, rather than using lenses and masks and coherent photons and free-space diffraction as an analog optical computer to reconstruct a Gabor hologram, one can use the digital computer equivalent to the same end. Note that this is not “merely” generic image processing, but rather a digital computer processing coherent optical information at the complex-field level.
Other examples of the use of the virtual in an optical setting include the computational implementation of filtered backprojection in the context of phase-amplitude tomography, Fourier-optics coherent spatial filtering done digitally using Fast Fourier transforms, several different forms of digital interferogram analysis, and digital reconstruction of off-axis holograms.
The problem of optical encryption has also been touched by the virtual, with many workers over the years considering the problem of how one may use a digital computer to implement virtual-optics analogs of hardware-optics encryption schemes. The spotlighted article by Mosso et al. (from Universidad Nacional de La Plata, Argentina and Universidad de Antioquia, Colombia) presents a very nice example of virtual optics at work in the context of parallelized encryption, by developing and implementing a virtual-optics procedure for encrypting a series of grayscale frames in a movie.
Before going into more detail regarding the specifics of the spotlighted paper, we briefly revise two prerequisite concepts: (i) 4f double random phase encoding of a two-dimensional pixellated grayscale image involves multiplying it by a random phase mask, then Fourier transforming and multiplying by another random phase mask, and then inverse Fourier transforming; (ii) Theta-modulation multiplexing involves multiplying each member of a sequence of low-frequency, two-dimensional grayscale images by a distinct linear-grating mask (each mask having a different angular orientation), before adding together all of the mask-modulated images to give a single multiplexed image (which can then be decoded using Fourier-space filters since the individual overlapping fringe-modulated images will be nonoverlapping in Fourier space).
Mosso et al. take a sequence of pixellated grayscale images that form the consecutive frames of a movie, encrypt each of them separately using a 4f double-random phase-encoding architecture (with all frames being encrypted using the same random key), and then multiplex the resulting sequence of images using theta-modulation. This parallelized all-optical movie-encryption procedure may then be inverted using a virtual-optics decryption procedure that reverses the above coding process. A particular benefit of the theta-modulation is a reduction in the crosstalk between distinct images, in the context of the necessarily nonideal signals that will be obtained in practice.
The fascinating study by Mosso et al. immediately suggests a variety of experimental implementations and extensions that could form the subject of future work. Future experimental implementations might include multiple-exposure multiplexed encryption using both visible light and hard x-rays. Possible extensions include the use of unitary transformations other than the Fourier transform in Fig. 1, incorporation of watermarks, an additional level of encryption due to appropriate choice of nonuniform theta-modulation angles, a systematic study of the stability of the encryption-decryption procedure with respect to noise, the incorporation of phase-retrieval concepts into the analysis, and an investigation of the role of partial coherence.
I heartily commend this article to your attention and look forward to future works on this topic, both by the workers on the present paper and by other optics researchers who are stimulated by the results of this insightful investigation.
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