Digital holography is the process where an object's phase and intensity information is retrieved from intensity images obtained using a digital camera (CCD or CMOS sensor). Unlike off-axis holography, object information is not modulated onto carrier fringes, thus in-line digital holography makes optimum use of the recording device's sampling bandwidth resulting in higher resolution digital holograms. However, reconstructed images are obscured by the linear superposition of the unwanted out of focus twin images. In addition to this, speckle noise degrades overall quality of the reconstructed images. The speckle effect is an optical phenomenon arising when laser sources are used in digital holographic systems. Minimizing the effects due to speckle noise, removal of the twin image and using the full sampling bandwidth of the capture device, aids overall reconstructed image quality. Using interferometric techniques, it is possible to record whole field information about an object. Digital processing of the reconstructed holograms can remove or suppress the twin image while effects from speckle noise can also be reduced numerically. Machine vision techniques can then be applied to segment and distinguish objects of interest in the hologram. Coding the resulting phase information onto a spatial light modulator (SLM), real world, three dimensional images of objects can be reconstructed using the computer generated hologram.
An optical implementation of the amplitude encoded double random phase encryption/decryption technique is implemented, and both numerical and experimental results are presented. In particular, we examine the effect of quantization in the decryption process due to the discrete values and quantized levels, which a spatial light modulator (SLM) can physically display. To do this, we characterize a transmissive SLM using Jones matrices and then map a complex image to the physically achievable levels of the SLM using the pseudorandom encoding technique. We present both numerical and experimental results that quantify the performance of the system.
We examine the Amplitude-Encoding (AE) case of the Double Random Phase Encoding (DRPE) technique. A cost function is the function we use to evaluate an attempted decryption with our original input image. For systems with a relatively small key-space we can evaluate the output of every key to get an overall idea of the spread of these keys in key-space. However for larger systems this is not practical. Based on a normalised root mean squared cost function we wish to identify expressions for the mean and variance of the output (decrypted) intensity for a sample set of keys in a large system (256x256 pixels).
The main advantage of the double random phase encryption technique is its physical implementation however to
allow us to analyse its behaviour we perform the encryption/decryption numerically. A typically strong encryption
scheme will have an extremely large key-space, which will make the probable success of any brute force attack on
that algorithm miniscule. Traditionally, designers of optical image encryption systems only demonstrate how a small
number of arbitrary keys cannot decrypt a chosen encrypted image in their system. We analyse this algorithm from a
key-space perspective. The key-space of an encryption algorithm can be defined as the set of possible keys that can
be used to encode data using that algorithm. For a range of problem instances we plot the distribution of decryption
errors in the key-space indicating the lack of feasibility of a simple brute force attack.
We consider a Double Random Phase Encoding (DRPE) Encryption/Decryption system in which the image encryption/decryption process is performed numerically. In this paper we present a key-space analysis of the (DRPE) algorithm which is used to encrypt two dimensional (2-D) images. We map the assiocated error for every phase-key in the key-space of a particular system to get a visual representation of the spread of phase-keys for the system and so assess its security from a key-space perspective.
Digital holography can be used to capture the whole Fresnel field from a reflective or transmissive object. Applications
include imaging and display of three-dimensional (3D) objects, and encryption and pattern recognition
of two-dimensional (2D) and 3D objects. Often, these optical systems employ discrete spatial light modulators
(SLMs) such as liquid-crystal displays. In the 2D case, SLMs can encode the inputs and keys during encryption
and decryption. For 3D processing, the SLM can be used as part of an optical reconstruction technique for 3D
objects, and can also represent the key during encryption and decryption. However, discrete SLMs can represent
only discrete levels of data necessitating a quantisation of continuous valued analog information. To date, many
such optical systems have been proposed in the literature, yet there has been relatively little experimental evaluation
of the practical performance of discrete SLMs in these systems. In this paper, we characterise conventional
phase-modulating liquid-crystal devices and examine their limitations (in terms of phase quantisation, alignment
tolerances, and nonlinear response) for the encryption of 2D and 3D data. Finally, we highlight the practical
importance of a highly controlled discretisation (optimal quantisation) for compression of digital holograms.
We consider a double random phase encoding Encryption/Decryption system in which the image encryption/decryption process is performed numerically. In this paper we look at the effect of quantisation in the decryption process due to the discrete values which a spatial light modulator can display. We look at the characterisation of a transmissive spatial light modulator and we present results from simulations of the system.
We report on recent advances made in the area of holographic image processing of three-dimensional (3D) objects. In particular, we look at developments made in the areas of encryption, compression, noise removal, and 3D shape extraction. Results are provided using simulated objects and real-world 3D objects captured using phase- shift digital holography.
The availability of high quality Spatial Light Modulators (SLMs) and high-resolution cameras have made it technologically feasible to perform many optical signal-processing functions in a relatively inexpensive manner. Furthermore, recent fast algorithms have been proposed to compute Linear Canonical Transforms (LCTs), which may be used to simulate paraxial optical systems. Optical Encryption offers the possibility of high-speed parallel encryption of image data. Such encryption/decryption may involve the capture of full field information, i.e. phase and intensity. Applications of Digital Holography go beyond applications to optical encryption. They include Holographic Interferometry (metrology) and Holographic displays. In this paper we discuss the design and analysis of systems used in the capture, encryption/decryption and display of 2-D (image) data and present our recent experimental and theoretical results.
Proc. SPIE. 5827, Opto-Ireland 2005: Photonic Engineering
KEYWORDS: Image encryption, Optical signal processing, Digital holography, Free space, Transform theory, Spatial light modulators, Data processing, Signal processing, Quantization, Wigner distribution functions
Coherent optical signal processors, due to their ability to process and relay information in two dimensions, have been receiving increasing attention in recent years. These systems involve a coherent field being propagated through some bulk optical system consisting of thin lenses and sections of free space (such paraxial systems being described mathematically using the Linear Canonical Transformation). A Spatial Light Modulator (SLM) may be used to modulate the input digital data onto a coherent wave-field as well as to modulate the amplitude and/or phase of the complex wave-field at any desired plane. The complex field (amplitude and phase) at any desired plane may be recorded quantitatively using a CCD camera, using digital holographic techniques allowing the further processing of data digitally. Such hybrid optoelectronic systems have applications for 2D and 3D data processing covering fields as diverse as data storage, data security and pattern recognition. But devices such as SLMs and CCD cameras can represent only discrete levels of data necessitating a quantisation of continuous valued analog information. In this paper, we take the example of an optical system used to encrypt 2D and 3D data and evaluate the effect of the finite discrete levels of an SLM on the encryption/decryption process.