Image encryption and the fractional Fourier transform

A number of method have been recently proposed in the literature for the encryption of 2-D information using optical systems based on the fractional Fourier fransform, FRT. In this paper a brief review of the methods proposed to date is presented. A measure of the strength/robustness of the level of encryption of the various techniques is proposed and a comparison is carried out between the methods. Optical implementations are discussed. Robustness of system with respect to misalignment and blind decryption are also discussed

Optimal Choice of Sample Substrate and Laser Wavelength for Raman Spectroscopic Analysis of Biological Specimen

Raman spectroscopy is an optical technique based on the inelastic scattering of monochromatic light that can be used to identify the biomolecular composition of biological cells and tissues. It can be used as both an aid for understanding the etiology of disease and for accurate clinical diagnostics when combined with multivariate statistical algorithms. This method is nondestructive,potentially non-invasive and can be applied in vitro or in vivo directly or via a fiber optic probe. However, there exists a high degree of variability across experimental protocols, some of which result in large background signals that can often overpower the weak Raman signals being emitted. These protocols need to be standardised before the technique can provide reliable and reproducible experimental results in an everyday clinical environment. The objective of this study is to investigate the impact of different experimental parameters involved in the analysis of biological specimen. We investigate the Raman signals generated from healthy human cheek cells using different source laser wavelengths; 473 nm, 532 nm, 660 nm, 785 nm and 830 nm, and different sample substrates; Raman-grade calcium fluoride, IR polished calcium fluoride, magnesium fluoride, aluminium (100 nm and 1500 nm thin films on glass), glass, fused silica, potassium bromide, sodium chloride and zinc selenide, whilst maintaining all other experimental parameters constant throughout the study insofar as possible

Introducing secure modes of operation for optical encryption

We analyze optical encryption systems using the techniques of conventional cryptography. All conventional block encryption algorithms are vulnerable to attack, and often they employ secure modes of operation as one way to increase security. We introduce the concept of conventional secure modes to optical encryption and analyze the results in the context of known conventional and optical attacks. We consider only the optical system “double random phase encoding,” which forms the basis for a large number of optical encryption, watermarking, and multiplexing systems. We consider all attacks proposed to date in one particular scenario. We analyze only the mathematical algorithms themselves and do not consider the additional security that arises from employing these algorithms in physical optical systems

Quantifying the 2.5D imaging performance of digital holographic systems

Digital holographic systems are a class of two step, opto-numerical, three-dimensional imaging techniques. The role of the digital camera in limiting the resolution and field of view of the reconstructed image, and the interaction of these limits with a general optical system is poorly understood. The linear canonical transform describes any optical system consisting of lenses and/or free space in a unified manner. Expressions derived using it are parametrised in terms of the parameters of the optical system, as well as those of the digital camera: aperture size, pixel size and pixel pitch. We develop rules of thumb for selecting an optical system to minimise mean squared error for given input and digital camera parameters. In the limit, our results constitute a point spread function analysis. The results presented in this paper will allow digital holography practitioners to select an optical system to maximise the quality of their reconstructed image using a priori knowledge of the camera and object

Using Commodity Graphics Hardware for Real-Time Digital Hologram View-Reconstruction

View-reconstruction and display is an important part of many applications in digital holography such as computer vision and microscopy. Thus far, this has been an offline procedure for megapixel sized holograms. This paper introduces an implementation of real-time view-reconstruction using programmable graphics hardware. The theory of Fresnel-based view-reconstruction is introduced, after which an implementation using stream programming is presented. Two different fast Fourier transform (FFT)-based reconstruction methods are implemented, as well as two different FFT strategies. The efficiency of the methods is evaluated and compared to a CPU-based implementation, providing over 100 times speedup for a hologram size of 2048 x 2048

Using Commodity Graphics Hardware for Real-Time Digital Hologram View-Reconstruction

View-reconstruction and display is an important part of many applications in digital holography such as computer vision and microscopy. Thus far, this has been an offline procedure for megapixel sized holograms. This paper introduces an implementation of real-time view-reconstruction using programmable graphics hardware. The theory of Fresnel-based view-reconstruction is introduced, after which an implementation using stream programming is presented. Two different fast Fourier transform (FFT)-based reconstruction methods are implemented, as well as two different FFT strategies. The efficiency of the methods is evaluated and compared to a CPU-based implementation, providing over 100 times speedup for a hologram size of 2048 x 2048

Numerical sampling rules for paraxial regime pulse diffraction calculations

Sampling rules for numerically calculating ultrashort pulse fields are discussed. Such pulses are not monochromatic but rather have a finite spectral distribution about some central (temporal) frequency. Accordingly, the diffraction pattern for many spectral components must be considered. From a numerical implementation viewpoint, one may ask how many of these spectral components are needed to accurately calculate the pulse field. Using an analytical expression for the Fresnel diffraction from a 1-D slit, we examine this question by varying the number of contributing spectral components. We show how undersampling the spectral profile produces erroneous numerical artifacts (aliasing) in the spatial–temporal domain. A guideline, based on graphical considerations, is proposed that determines appropriate sampling conditions. We show that there is a relationship between this sampling rule and a diffraction wave that emerges from the aperture edge; comparisons are drawn with boundary diffraction waves. Numerical results for 2-D square and circular apertures are presented and discussed, and a potentially time-saving calculation technique that relates pulse distributions in different z planes is described

Numerical sampling rules for paraxial regime pulse diffraction calculations

Sampling rules for numerically calculating ultrashort pulse fields are discussed. Such pulses are not monochromatic but rather have a finite spectral distribution about some central (temporal) frequency. Accordingly, the diffraction pattern for many spectral components must be considered. From a numerical implementation viewpoint, one may ask how many of these spectral components are needed to accurately calculate the pulse field. Using an analytical expression for the Fresnel diffraction from a 1-D slit, we examine this question by varying the number of contributing spectral components. We show how undersampling the spectral profile produces erroneous numerical artifacts (aliasing) in the spatial–temporal domain. A guideline, based on graphical considerations, is proposed that determines appropriate sampling conditions. We show that there is a relationship between this sampling rule and a diffraction wave that emerges from the aperture edge; comparisons are drawn with boundary diffraction waves. Numerical results for 2-D square and circular apertures are presented and discussed, and a potentially time-saving calculation technique that relates pulse distributions in different z planes is described

A multivariate statistical investigation of background subtraction algorithms for Raman spectra of cytology samples recorded on glass slides

Traditional preparation methods for cytology samples pose a significant problem for Raman microspectroscopy, with long-established clinical techniques depositing cells on glass slides. Unfortunately, both the signal from the glass slide and the baseline signal from the cell itself obscure the Raman cell spectrum. The intensity of the glass signal varies from cell to cell depending on morphology, and although smooth, the signal is more complex within the fingerprint region than the baseline, and cannot be easily removed from the Raman spectrum using polynomial fitting techniques. It is difficult to accurately remove both background signals, and therefore, the use of standard glass slides compromises the capability of pre-processing methods to extract reliable and reproducible spectra from biological cells. To avoid this signal, Raman spectra are often recorded from cells on expensive substrates, such as calcium fluoride (CaF2) or quartz, but this practice is impractical for large scale applications of Raman cytology for diagnostics or screening purposes. This study investigates the potential of a number of background subtraction algorithms to remove both the glass signal and the baseline, and investigates the effect of these algorithms on subsequent multivariate analysis for the purpose of cell classification. This study demonstrates that the well-known extended multivariate signal correction (EMSC) algorithm is particularly effective in this regard, and that the results of subsequent multivariate statistical analysis are independent of the reference cell spectrum used in the algorithm. Matlab code is provided for the implementation of the EMSC algorith

Fresnel and Fourier digital holography architectures: a comparison.

In this manuscript we examine the characteristics of holograms that are captured using both Fresnel and lens-less Fourier digital holographic systems. We begin by introducing some of the fundamental equations describing the intensity distribution captured by the camera. Naturally this captured intensity will vary depending on whether the system used is a Fourier or a Fresnel due to the different reference field in each case, however as we shall see with appropriate numerical processing it is possible to obtain similar performance from both systems. We discuss a reconstruction algorithm for changing the focus depth in Fourier holograms and examine how it effects the twin image and dc terms. A theoretical comparison with Fresnel holograms is made. Experimental results are provided to support our analysis. We finish with a brief conclusion