Spiral Phase Transform Research Articles

Optical cryptosystem scheme for hyperspectral image based on random spiral transform in gyrator domains

A novel chaotic cryptosystem for hyperspectral image, in this paper, is proposed by using a 4D hyperchaotic system in gyrator transform domains. In encryption process, a random spiral phase function (RSPF) is designed to generate variable spiral phase mask, which can be used for phase encoding with the hyperspectral image. Subsequently, the 4D hyperchaotic system is utilized to generate the chaotic sequences and these chaotic data is employed in designing RSPF, scrambling the hyperspectral image and synthesizing complex ciphertext, respectively. Finally, an improved spiral phase transform (SPT) in gyrator domains is implemented to obtain the ciphertext. To enhance the security of the encryption scheme, the ciphertext is reorganized according to the hyperchaotic attractor. Theoretical simulation analysis is given to demonstrate the validity and robustness of the proposed cryptosystem.

An asymmetric color-image cryptosystem based on spiral phase transformation and equal modulus decomposition

In this paper, we propose an asymmetric color-image cryptosystem based on spiral phase transform (SPT) and equal modulus decomposition (EMD). The original image is divided into three-channel components of R, G and B firstly. Then we encrypt these components by two random phase mask (RPMs) modulations, two spiral phase transformations, and an equal modulus decomposition. Finally, we obtain four encryption keys which are RPM1, RPM2, an EMD’s angle and the order q of the SPT, and produce two private keys (PKs) which are PK1 and PK2. The proposed method has enhanced the key sensitivity of the order q with 100 times, while it maintains the advantages of simple structure, high speed and less data amount. The proposed method is highly robust to iteration attack and other attacks. Numerical simulation results show the effectiveness and feasibility of the proposed cryptosystem.

Wavelets Teager–Kaiser Hilbert approach for AM–FM signal demodulation: application in the field of speckle metrology

In this work, we propose a combination of the Teager–Kaiser energy operator (TKEO) and the spiral phase transform (SPT) for robust instant energy estimation of amplitude-modulated and frequency-modulated (AM–FM) signals, where the energy extraction is followed by a high-frequency component, generally considered as noise. We demonstrate that this noise component can be subtracted mathematically using the SPT transformation applied to the AM–FM signal. The improvement in demodulation is tested using a simulated AM–FM image and evaluated by the image quality index. An experimental speckle fringe pattern obtained by digital speckle pattern interferometry on a hard disk is denoised using a multiband approach and demodulated using the proposed method.

Optical colour image encryption using spiral phase transform and chaotic pixel scrambling

ABSTRACTIn this study, we propose a new optical colour image encryption technique using spiral phase transform and chaotic pixel scrambling. For encryption, three channels of the colour image i.e. red, green and blue are first separated and modulated with three different structured phase masks. Spiral phase transform (SPT) with a particular order of modified spiral phase function (MSPF) is utilized for further processing. Random modulus decomposition is applied to the complex output after SPT to generate the private key for decryption. The pixels of the image are scrambled by using the chaotic Tinkerbell map for enhanced security. The order of MSPF, three structured phase masks, parameters of Tinkerbell mapping, and the private key generated during the encryption process serve as the security keys. The robustness of the proposed method is checked against various potential attacks. A series of numerical simulation results are presented to validate the proposed colour image encryption method.

Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition

In this study, we propose a quick response (QR) code based nonlinear optical image encryption technique using spiral phase transform (SPT), equal modulus decomposition (EMD) and singular value decomposition (SVD). First, the primary image is converted into a QR code and then multiplied with a spiral phase mask (SPM). Next, the product is spiral phase transformed with particular spiral phase function, and further, the EMD is performed on the output of SPT, which results into two complex images, Z1 and Z2. Among these, Z1 is further Fresnel propagated with distance d, and Z2 is reserved as a decryption key. Afterwards, SVD is performed on Fresnel propagated output to get three decomposed matrices i.e. one diagonal matrix and two unitary matrices. The two unitary matrices are modulated with two different SPMs and then, the inverse SVD is performed using the diagonal matrix and modulated unitary matrices to get the final encrypted image. Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise attack, specific attack, and brutal force attack. Simulation results are presented in support of the proposed idea.

Optical image encryption in Fresnel domain using spiral phase transform

In this study, we propose a new nonlinear optical image encryption technique using spiral phase transform (SPT). First, the primary image is phase encoded and multiplied with a random amplitude mask (RAM), and using power function, the product is then powered to m. This powered output is Fresnel propagated with distance z1 and then modulated with a random phase mask (RPM). The modulated image is further Fresnel propagated with distance z2. Similarly, a security image is also modulated with another RAM and then Fresnel propagated with distance z3. Next, the two modulated images after Fresnel propagations, are interfered and further Fresnel propagated with distance z4 to get a complex image. Finally, this complex image is SPT with particular spiral phase function (SPF), to get the final encrypted image for transmission. In the proposed technique, the security keys are Fresnel propagation distances, the security image, RPM, RAMs, power order, m, and order of SPF, q. Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise and brutal force attacks.

Using composite sinusoidal patterns in structured-illumination reflectance imaging (SIRI) for enhanced detection of apple bruise

Structured-illumination reflectance imaging (SIRI) provides a new means for enhanced detection of defects in horticultural products. Implementing the technique relies on retrieving amplitude images by illuminating the object with sinusoidal patterns of single spatial frequencies, which, however, are limited in interrogating the tissues at different depths. This study presented a first exploration of using composite sinusoidal patterns that integrated two and three spatial frequencies of interest, in SIRI for enhanced detection of defects in food (e.g., bruises in apples). Three methods based on Fourier transform were proposed to retrieve amplitude images at different frequencies by using either phase shifting with or without spiral phase transform (SPT) or frequency-domain filtering. The phase-shifting method involves solving a linear system that is composed of multiple phase-shifted pattern images in the Fourier space, and SPT that acts as a two-dimensional quadrature transform operator is used to reduce the images needed for amplitude retrieval; while the filtering-based method directly extracts different frequency components from only one pattern image that are then subjected to SPT processing. The three methods were tested for dual-frequency and triple-frequency patterns through numerical simulations and experiments on the detection of fresh bruises in apples by SIRI. The phase-shifting methods showed good performance in terms of small demodulation errors and strong image contrast for bruise detection; the filtering-based method, although viable in numerical simulation, needed improvement due to the worst practical performance. In addition, more frequency components introduced in the pattern would deteriorate the performance of these methods, and grid composite patterns were superior over the fringe ones due to reduced interactions between different frequency components.

Fast demodulation of pattern images by spiral phase transform in structured-illumination reflectance imaging for detection of bruises in apples

A structured-illumination reflectance imaging (SIRI) system was recently developed in our laboratory for enhanced quality evaluation of horticultural products. It was implemented using a digital camera to acquire reflectance images from food products subjected to sinusoidal patterns of illumination, instead of conventional diffuse or uniform illumination. The reconstruction of amplitude images is a key step in implementing SIRI technique. Conventional methods require acquisition and subsequent demodulation of three phase-shifted pattern images, which limits the speed of image acquisition. This study proposed the use of spiral phase transform (SPT) for demodulation of pattern images acquired by SIRI. Three SPT-based methods involving only one or two images were investigated through numerical simulation, followed with experiments on the detection of fresh bruises in apples. Compared to conventional three-phase based and two-phase based Gram-Schmidt (GS) orthonormalization demodulation methods, the two-phase SPT method achieved the same or even higher demodulation accuracy, which applies to two pattern images that can be arbitrarily phase-shifted. SPT also allowed single-image based demodulation, although its performance still needs to be improved. This study demonstrated that SPT for amplitude demodulation can increase the imaging speed of SIRI by using one or two pattern images, which is a significant step towards real-time implementation of the technique.

Two-dimensional discrete wavelets transform for optical phase extraction: application on speckle correlation fringes

A method for optical phase extraction based on two-dimensional discrete wavelets transform (2-DWT) decomposition is shown. From modulated fringe pattern, phase distribution is extracted by the ratio between detail and approximation. Modulation process is realized digitally by introducing high-frequency spatial carrier, and this process needs two π /2 -shifted fringe patterns. We propose to use only single fringe and generate its quadrature by spiral phase transform (SPT). After validation by computer simulation, we apply the 2-DWT algorithm on experimental speckle fringe correlation taken for hard disk surface. The extracted phase using SPT quadrature was compared with that given using this time experimental quadrature, and we show a good performance by multiscale structural similarity metric.

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].