Optical implementation of the Bode transform

The Bode transformation is a useful tool for determining and analyzing the frequency response of a system. It has a special importance for detecting the resonance frequencies of a linear system that, because of its linearity, can be totally characterized by its impulse response. An optical configuration that implements the Bode transformation of a function is suggested and demonstrated experimentally.     

Color image security system using double random-structured phase encoding in gyrator transform domain

A novel method for encoding color information based on a double random phase mask and a double structured phase mask in a gyrator transform domain is proposed. The amplitude transmittance of the Fresnel zone plate is used as structured phase-mask encoding. A color image is first segregated into red, green, and blue component images. Each of these component images are then independently encrypted using first a random phase mask placed at the image plane and transmitted through the first structured phase mask. They are then encoded by the first gyrator transform. The resulting information is again encrypted by a second random phase mask placed at the gyrator transform plane and transmitted through the second structured phase mask, and then encoded by the second gyrator transform. The system parameters of the structured phase mask and gyrator transform in each channel serve as additional encryption keys and enlarge the key space. The encryption process can be realized with an electro-optical hybrid system. The proposed system avoids problems arising from misalignment and benefits of a higher space-bandwidth product. Numerical simulations are presented to confirm the security, validity, and possibility of the proposed idea.     

Image encryption by encoding with a nonuniform optical beam in gyrator transform domains

Based on an optical gyrator transform system, an image encryption algorithm is designed and studied. An original secret image is regarded as the output intensity of the second gyrator transform. A coherent nonuniform optical beam is converted into the input of the first gyrator transform. A Gerchberg-Saxton phase retrieval algorithm is employed for obtaining the compensation phases in the first gyrator transform pair. The compensation phases are regarded as the encrypted image and key in this algorithm. The parameters of the laser beam and gyrator transform can serve as the additional key of encryption method. The decryption process of this encryption algorithm can be achieved with an optical system. Numerical simulations are performed to test the validity and capability of the encryption algorithm.     

Optical implementation of the continuous wavelet transform

A simple optical implementation for the one-dimensional wavelet transform (WT) is proposed. In contrast with previous WT optical implementations, the obtained WT is continuous along both axes (dilation and shift). An optical implementation to the inverse WT is proposed as well. Thus an optical continuous WT processor can be implemented.     

One-step implementation of the optical hit-miss transform

A spatial-encoding scheme for the one-step implementation of the optical hit-miss transform (HMT) is presented. The rank-order HMT, which yields better performance in the presence of noise and clutter, can also be carried out by the use of this scheme. Numerical simulations and experimental results have proved the scheme to be feasible.     

Fractional fourier transform: photonic implementation

The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features. We show how it is possible to implement the fractional Fourier transform on time signals by using optoelectronic modulators and optical fibers with suitable dispersion. We also show how a fractional-Fourier-transform-based photonic signal-processing system could be composed.     

Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain

This paper proposes a method of double image encryption based on hybrid structured phase mask (HSPM) in the gyrator transform (GT) domain. The scheme becomes more secure by parameters used in the HSPM. These HSPMs are generated by using the combination of the optical vortex phase masks and secondary images after taking Fourier transform (FT). The input images are encrypted and recovered with correct values of HSPMs, rotation angles of GT and their keys used during the encryption. The use of an HSPM-based phase mask increases the security and key space for encryption. It can also be implemented opto-electronically. The mean square error calculated between the input and retrieved images shows the efficacy of scheme. The proposed method has also been investigated for its sensitivity to encryption parameters and its security against occlusion and noise attacks under a number of iterations. A set of numerical simulation results support the feasibility and security of the proposed scheme.     

Wiener filter in the gyrator domain

The Wiener filter is the optimal filter according to the minimal mean square error criterion. For data distorted by noise with given spectral density, the Wiener filter is the optimal filter for restoring the noisy image. In this paper we will define a gyrator convolution operator and its optical implementation. The new generalized gyrator Wiener filter was defined using the new operator. The new filter was compared to the conventional Wiener filter and showed improved performance. An improvement of up to 40?dB in the mean square error at the optimal rotation angle in comparison to the conventional Wiener filter is demonstrated.     

Optical implementation of the fractional Hilbert transform for two-dimensional objects

The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is pi-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.     

Incoherent fractional Fourier transform and its optical implementation

The fractional Fourier transform is redefined for working with incoherent light. As a real transformation, the incoherent fractional Fourier transform overcomes coherent system disadvantages such as the speckle effect and the need for incoherent-coherent conversion. It also might have some applications for digital image and signal processing owing to its decreased computing complexity. An incoherent optical implementation of the new transform based on the shearing interferometer is suggested. Laboratory experimental results are given.     

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens.     

White-light optical implementation of the fractional fourier transform with adjustable order control

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.     

Anamorphic fractional Fourier transform: optical implementation and applications

An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. Alaboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains are briefly suggested.     

Experimental implementation of the multifunctional compact two-photon state analyzer

We report on experimental implementation of a multifunctional two-photon state analyzer. The device aims to be compact and able to provide several important characteristics about any two-photon quantum state. It operates in two modes: first mode is the two-photon interference analysis giving the information about spectral properties of the photons and the degree of mutual indistinguishability. The second mode provides polarization analysis and complete two-photon state tomography. Density matrix estimated from the tomography data reveals namely the quantum state purity or negativity. This device was tested on the photon pairs generated by the Kwiat source.     

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.     

Dispersion implementation in optical filter design by the Fourier transform method using correction factors

The Fourier transform method to design graded-index optical filters, that relates the desired reflection spectrum and the index profile through the use of a Q function, has two important drawbacks: (1) It relies on approximate Q functions, and (2) it does not account for the dispersion of the index of refraction. The former is usually addressed by an iterative correction process. We propose to address the latter by scaling the wavelength in the Fourier transform by the optical thickness of the filter and to multiply the Q function by a wavelength-dependent correction factor. We demonstrate the high effectiveness of this approach by the performance of optical filters designed with such correction factors using the optical properties of SiO2/TiO2 mixtures.     

Experimental aspects of asynchronous rapid-scan fourier transform infrared imaging

In the asynchronous, rapid-scan approach to Fourier transform infrared (FT-IR) imaging, data sampling is not correlated with the zero crossings of the interference fringes of the HeNe reference laser. The success of this data collection scheme depends on the reproducibility of the clock signals driving the interferometer mirror and focal plane array data collection. In previous studies, it was shown that this implementation provides for markedly faster data acquisition without sacrificing data quality, as compared with stepscan imaging. This approach to data collection introduces some unique peculiarities to the acquisition and processing of imaging data. The purpose of this paper is to address a few of these concerns in terms of their effect on final data quality. Also, the practical aspects of implementing such an acquisition scheme are described in detail.     

Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators

We describe a nonlinear joint transform correlator-based two-layer neural network that uses a supervised learning algorithm for real-time face recognition. The system is trained with a sequence of facial images and is able to classify an input face image in real time. Computer simulations and optical experimental results are presented. The processor can be manufactured into a compact low-cost optoelectronic system. The use of the nonlinear joint transform correlator provides good noise robustness and good image discrimination.     

Experimental systems implementation of a hybrid optical-digital correlator

A high-speed hybrid optical-digital correlator system was designed, constructed, modeled, and demonstrated experimentally. This correlator is capable of operation at approximately 3000 correlations/s. The input scene is digitized at a resolution of 512 x 512 pixels and the phase information of the two-dimensional fast Fourier transform calculated and displayed in the correlator filter plane at normal video frame rates. High-fidelity reference template images are stored in a phase-conjugating optical memory placed at the nominal input plane of the correlator and reconstructed with a high-speed acousto-optic scanner; this allows for cross correlation of the entire reference data set with the input scene within one frame period. A high-speed CCD camera is used to capture the correlation-plane image, and rapid correlation-plane processing is achieved with a parallel processing architecture.