Now showing 1 - 6 of 6
  • Publication
    Role of phase key in the double random phase encoding technique : an error analysis
    We perform a numerical analysis of the double random phase encryption–decryption technique to determine how, in the case of both amplitude and phase encoding, the two decryption keys (the image- and Fourier-plane keys) affect the output gray-scale image when they are in error. We perform perfect encryption and imperfect decryption. We introduce errors into the decrypting keys that correspond to the use of random distributions of incorrect pixel values. We quantify the effects that increasing amounts of error in the image-plane key, the Fourier-plane key, and both keys simultaneously have on the decrypted image. Quantization effects are also examined
      1265Scopus© Citations 39
  • Publication
    Noninterferometric phase retrieval using a fractional Fourier system
    The signal extraction method based on intensity measurements in two close fractional Fourier domains is examined by using the phase space formalism. The fractional order separation has a lower bound and an upper bound that depend on the signal at hand and the noise in the optical system used for measurement. On the basis of a theoretical analysis, it is shown that for a given optical system a judicious choice of fractional order separation requires some a priori knowledge of the signal bandwidth. We also present some experimental results in support of the analysis.
      473Scopus© Citations 27
  • Publication
    Cryptanalysis of optical security systems with significant output images
    The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.
      543Scopus© Citations 87
  • Publication
    Generalized in-line digital holographic technique based on intensity measurements at two different planes
    In-line digital holography based on two-intensity measurements [Zhang et al. Opt. Lett. 29, 1787 (2004)], is modified by introducing a π shifting in the reference phase. Such an improvement avoids the assumption that the object beam must be much weaker than the reference beam in strength and results in a simplified experimental implementation. Computer simulations and optical experiments are carried out to validate the method, which we refer to as position-phase-shifting digital holography.
      1104Scopus© Citations 60
  • Publication
    Statistical investigation of the double random phase encoding technique
    The amplitude-encoding case of the double random phase encoding technique is examined by defining a cost function as a metric to compare an attempted decryption against the corresponding original input image. For the case when a cipher–text pair has been obtained and the correct decryption key is unknown, an iterative attack technique can be employed to ascertain the key. During such an attack the noise in the output field for an attempted decryption can be used as a measure of a possible decryption key’s correctness. For relatively small systems, i.e., systems involving fewer than 5x5 pixels, the output decryption of every possible key can be examined to evaluate the distribution of the keys in key space in relation to their relative performance when carrying out decryption. However, in order to do this for large systems, checking every single key is currently impractical. One metric used to quantify the correctness of a decryption key is the normalized root mean squared (NRMS) error. The NRMS is a measure of the cumulative intensity difference between the input and decrypted images. We identify a core term in the NRMS, which we refer to as the difference parameter, d. Expressions for the expected value (or mean) and variance of d are derived in terms of the mean and variance of the output field noise, which is shown to be circular Gaussian. These expressions assume a large sample set (number of pixels and keys). We show that as we increase the number of samples used, the decryption error obeys the statistically predicted characteristic values. Finally, we corroborate previously reported simulations in the literature by using the statistically derived expressions.
      1024Scopus© Citations 18
  • Publication
    Holography : an interpretation from the phase-space point of view
    (Optical Society of America, 2007-12-15) ;
    The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phaseretrieval techniques.
      562Scopus© Citations 28