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Hennelly, Bryan M.
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Hennelly, Bryan M.
Official Name
Hennelly, Bryan M.
Research Output
Now showing 1 - 10 of 13
- PublicationOptical image encryption by random shifting in fractional Fourier domainsA number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.
1242Scopus© Citations 427 - PublicationSpeckle photography : mixed domain fractional Fourier motion detection(Optical Society of America, 2006-01-01)
; ; ; ; ; A reflection-based optical implementation of two simultaneous scale-invariant fractional Fourier transforms (FRTs) is used to develop a novel compact speckle photographic system. The system allows the independent determination of both surface tilting and in-plane translational motion from two sequential mixed domain images captured using a single camera526Scopus© Citations 26 - PublicationAdditional sampling criterion for the linear canonical transformThe linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its samples. To achieve this, an additional sampling criterion has been developed for sampling both the input and the output wave fields.
474Scopus© Citations 43 - PublicationWavelength-controlled variable-order optical fractional Fourier transformThe relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths.
350Scopus© Citations 9 - PublicationGeneralized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture(Optical Society of America, 2006-12-01)
; ; ; ; ; In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.489Scopus© Citations 15 - PublicationGeneralizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transformsBy use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadraticphase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
704Scopus© Citations 172 - PublicationMagnitude and direction of motion with speckle correlation and the optical fractional Fourier transformThe optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body’s motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions
479Scopus© Citations 29 - PublicationParaxial speckle-based metrology systems with an aperture(Optical Society of America, 2006-11-01)
; ; ; ; ; Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [D. P. Kelly et al. Appl. Opt. 44, 2720 (2005)] it has been shown that optical fractional Fourier transforms (OFRTs) can be used to vary the range and sensitivity of speckle-based metrology systems, allowing the measurement of both the magnitude and direction of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. This requires two bulk optical systems. We extend the OFRT analysis to more general LCT systems with a single limiting aperture. The effect of a limiting aperture in LCT systems is examined in more detail by deriving a generalized Yamaguchi correlation factor. We demonstrate the benefits of using an LCT approach to metrology design. Using this technique, we show that by varying the curvature of the illuminating field, we can effectively change the output domain. From a practical perspective this means that estimation of the motion of a target can be achieved by using one bulk optical system and different illuminating conditions. Experimental results are provided to support our theoretical analysis.482Scopus© Citations 24 - PublicationMotion detection, the Wigner distribution function, and the optical fractional Fourier transformIt is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.
375Scopus© Citations 29 - PublicationOptical wave propagation simulation, Wigner phase-space diagrams, and wave energy confinement(Optical Society of America, 2005-10-16)
; ; The number of samples required for efficient numerical simulation of wave propagation can be determined by a combination of Wigner phase-space techniques, wave energy confinement arguments, and a theorem relating energy confinement to accuracy.356