Veselago’s lens consisting of left-handed materials with arbitrary index of refraction

We study Veselago’s lens with arbitrary index of refraction and characteristic impedance. Using a full wave optics calculation, we show that this lens can be considered as an imaging system and we derive the appropriate lens formula. The lens with arbitrary index and impedance retains some of the properties of the matched lens, such as the invariance of its optical axis, three-dimensional imaging and easy manufacturing, but it loses the property of sub-wavelength resolution. We also show that identical results can be obtained for the impedance matched lens in the framework of paraxial geometrical optics, from which it can be inferred that optical systems containing such a lens can be studied and designed using traditional ray-tracing tools.     

Three Gaussian beam heterodyne interferometer for surface profiling

A novel three Gaussian beam interferometric technique for profiling optical smooth surfaces is presented. The technique is based on the heterodinization of three Gaussian beams, two of them with the same temporal frequency. The first beam is used as a probe beam after being focused and reflected from the surface under test. The second beam is reflected from a reference surface. The third beam is obtained from the first diffraction order of a Bragg cell and thus, it is shifted in its temporal frequency. The three beams are coherently added at the sensitive plane of a photodetector that integrates the overall intensity of the beams. We show analytically that the electrical signal at the output of the photodetector consists of a temporal carrier whose amplitude is a sinusoidal function of the local topography. We include the measurement of the topography of a sample consisting in a blazed-reflecting grating calibrated by means of an atomic force microscope.     

Fourth order correction to a paraxial Gaussian beam in a rotationally symmetric system of non-spherical surfaces

We formulate the fourth order correction to a paraxial Gaussian beam propagating through a non-spherical surface system that is rotationally symmetric. First we represent the Gaussian beam by a complex-source-point spherical wave (CSPSW). Next we examine the evolution of the CSPSW through the non-spherical surface system by applying a Fresnel–Kirchhoff diffraction integral. We find a ray-optical solution to the diffraction integral in terms of both the conic constant and the aspheric coefficient of fourth order. Then we numerically evaluate the quality factor of the fourth order-corrected beam propagating through either an aspheric mirror or a thin lens made up of two non-spherical surfaces. The fourth order formulas derived here can be useful in determining the quality factor of the Gaussian beam degraded by a rotationally symmetric system of non-spherical surfaces.     

Application of Cosine Zone Plates to Image Encryption

We analyse the diffraction result of optical field after Cosine zone plate, and theoretically deduce its transform matrix. Under some conditions, its diffraction distribution is a mixture of fractional Fourier spectra. Then we use Cosine zone plate and its diffraction result to image encryption. Possible optical image encryption and decryption implementations are proposed, and some numerical simulation results are also provided.     

Real-time nondestructive imaging with THz waves

We present a real-time imaging measurement in the terahertz (THz) frequency region. The dynamic subtraction technique is used to reduce long-term optical background drift. The reflective images of two targets, a Nikon camera’s lens cap and a plastic toy gun, are obtained. For the lens cap, the image data were processed to be false-color images. For the toy gun, we show that even under an optically opaque canvas bag, a clear terahertz image is obtained. It is shown that terahertz real-time imaging can be used to nondestructively detect concealed objects.     

Optical color image encryption with redefined fractional Hartley transform

We propose a new method for color image encryption by wavelength multiplexing on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. A color image can be considered as three monochromatic images and then divided into three components and each component is encrypted independently with different wavelength corresponding to red, green or blue light. The system parameters of fractional Hartley transform and random phase masks are keys in the color image encryption and decryption. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.     

Optical Image Encryption with Simplified Fractional Hartley Transform

We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the advantage that it can also append fractional orders as additional keys for the purpose of improving the system security to some extent. With this method, one can encrypt an image with an intensity-only medium such as a photographic film or a CCD camera by spatially incoherent or coherent illumination. The optical realization is then proposed and computer simulations are also performed to verify the feasibility of this method.     

The use of a consumer grade photo camera in optical-digital correlator for pattern recognition and input scene restoration

In this work an optical-digital correlator for pattern recognition and input scene restoration is described. Main features of the described correlator are portability and ability of multi-element input scenes processing. The correlator consists of a consumer grade digital photo camera with a diffractive optical element (DOE) inserted as a correlation filter. Correlation of an input scene with a reference image recorded on the DOE are provided optically and registered by the digital photo camera for further processing. Using obtained correlation signals and DOE’s point spread function (PSF), one can restore the image of the input scene from the image of correlation signals by digital deconvolution algorithms.The construction of the correlator based on the consumer grade digital photo camera is presented. The software procedure that is necessary for images linearization of correlation signals is described. Experimental results on optical correlation are compared with numerical simulation. The results of images restoration from conventionally and specially processed correlation signals are reported. Quantitative estimations of accuracy of correlation signals as well as restored images of the input scene are presented.     

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular ?-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.     

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer-Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.     

A method for single-pass distortion correction using holography in rhodium-doped barium titanate

We present a holographic method of one-way image transmission with ‘real-time’ correction of distortion through an optical system. The technique is demonstrated using a crystal of photorefractive rhodium-doped barium titanate as the holographic medium and corrects for phase distortions imposed upon a US Air Force test chart. This technique is suitable for applications in both cw and pulsed regimes, and for either fixed or changing distortions. Received: 26 October 1998 / Revised version: 19 December 1998 / Published online: 12 April 1999     

Diffraction efficiency and signal-to-noise ratio of multiplexed volume phase holograms recorded in a photographic emulsion

The problems related to noise that arise during recording and reconstruction of holograms used in optical data storage or in massive optical interconnection systems are quite similar and can be analyzed in order to improve the quality of the images that these optical systems provide. In this paper, we will analyze noise in cases in which several coherent object waves are simultaneously stored in a phase recording material in a way that allows us to obtain information about the relationship that exists between the recording material and the number of waves that are being stored. The material used in this study is Agfa Gevaert 8E75 HD holographic film processed with a rehalogenating—type bleach bath without a fixation step. Additionally, we show experimentally that it is possible to holographically store more than 400 waves at the same time (in a coherent fashion) using the same storage geometry, with a signal-to-noise ratio larger than 20 and an average diffraction efficiency of 15%.     

Novel Ghost Imaging Method for a Pure Phase Object

We propose a novel ghost imaging scheme which is especially served to a pure phase object. A spatially incoherent beam is mixed with a coherent beam of the same frequency field by a beamsplitter. Then we perform the ghost imaging scheme using the mixed beam. Our theoretical result shows that this approach is capable of reconstructing a pure phase object in joint-intensity measurement. The visibility of the images is also analysed for two pure phase objects, an optical wedge and a phase grating.     

Enhancement of collapse threshold of two Gaussian beams of light with orthogonal polarization in a nonlinear defocusing shifted parabolic graded-index rod lens

Received: 22 December 1996/Revised version: 12 March 1997     

Prediction of negative index material lenses based on metallo‐dielectric nanotubes

We propose to assemble negative index materials (NIMs) from dielectric nanotubes with inner and outer surfaces covered by thin metallic films. The focusing properties of flat and concave lenses assembled from metallized titania nanotubes are compared with those of lenses made from nanorods with the refractive index n = –1 by performing numerical calculations using a multiple‐scattering approach. Focusing is proved for both types of lenses, however, the focusing properties of concave lenses are better. The lenses are shown to be tolerant to the introduction of disorder in the arrangement of nanotubes. Moreover, the disorder proves to improve the quality of the focal spot. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Color image encoding in dual fractional Fourier-wavelet domain with random phases

A new cryptology in dual fractional Fourier-wavelet domain is proposed in this paper, which is calculated by discrete fractional Fourier transform and wavelet decomposition. Different random phases are used in different wavelet subbands in encryption. A new color image encoding method is also presented with basic color decomposition and encryption respectively. All the keys, including random phases and fractional orders in R, G and B three channels, should be correctly used in decryption, otherwise people cannot obtain the totally correct information. Some numerical simulations are presented to demonstrate the possibility of the method. It would have widely potential applications in digital color image processing and protection.     

Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement

An approach to the wavelet multiresolution analysis is realized using Coiflet wavelets and a two-wave mixing arrangement via transmission gratings in a bismuth silicon oxide (BSO) crystal. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. 2-D wavelet bases are generated by a tensorial product of the 1-D Coiflet bases and are separable in x and y. Therefore, the 1-D band-pass property produces direction ability in the 2-D tensorial products. In this way, unlike the Mexican hat-based filters, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of an original image. The decomposition of a signal in two levels of multiresolution is experimentally demonstrated in this scheme. The original image is discomposed in an average image and several detail images depending on the level of multiresolution. Coif12 wavelets are used to achieve the multiresolution analysis. The photorefractive implementation of the wavelet analysis is numerically simulated and experimentally performed. An agreement between numerical and experimental results is obtained.     

Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift

An iterative algorithm to extract the arbitrary unknown phase shift in two-frame phase-shifting interferometry and then reconstruct the complex object wave is proposed. In combination with the least square principle and some calculation formulae we developed, this algorithm allows us to find the value of unknown phase shift by using only two interferograms without additional knowledge or measurement. Computer simulations have shown that this algorithm works well for both the smooth and diffusing objects to a very high accuracy over a wide range of the phase shift from 0.4 to 2.5 rad.     

Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens

Spectral changes of a twisted electromagnetic Gaussian Schell-model (EGSM) beam focused by a thin lens are investigated by using a tensor method. It is shown that the spectral shift is mainly determined by the degree of polarization, twist phase and correlation coefficients of the initial beam. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points.     

Imaging and post-processing of laser-induced fluorescence from NO in a diesel engine

Received: 11 July 1996/Revised version: 12 November 1996