Now showing 1 - 10 of 14
  • Publication
    Measuring optical phase digitally in coherent metrology systems
    (Society of Photo-optical Instrumentation Engineers (SPIE), 2017-04-09) ; ; ;
    The accurate measurement of optical phase has many applications in metrology. For biological samples, which appear transparent, the phase data provides information about the refractive index of the sample. In speckle metrology, the phase can be used to estimate stress and strains of a rough surface with high sensitivity. In this theoretical manuscript we compare and contrast the properties of two techniques for estimating the phase distribution of a wave field under the paraxial approximation: (I) A digital holographic system, and (II) An idealized phase retrieval system. Both systems use a CCD or CMOS array to measure the intensities of the wave fields that are reflected from or transmitted through the sample of interest. This introduces a numerical aspect to the problem. For the two systems above we examine how numerical calculations can limit the performance of these systems leading to a near-infinite number of possible solutions.
  • Publication
    Speckle orientation in paraxial optical systems
    (Optical Society of America, 2012-02) ; ; ;
    The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.
      532Scopus© Citations 12
  • Publication
    Three-dimensional speckle size in generalized optical systems with limiting apertures
    (Optical Society of America, 2009-08-01) ; ;
    Correlation properties of speckle fields at the output of quadratic phase systems with hard square and circular apertures are examined. Using the linear canonical transform and ABCD ray matrix techniques to describe these general optical systems, we first derive analytical formulas for determining axial and lateral speckle sizes. Then using a numerical technique, we extend the analysis so that the correlation properties of nonaxial speckles can also be considered. Using some simple optical systems as examples, we demonstrate how this approach may be conveniently applied. The results of this analysis apply broadly both to the design of metrology systems and to speckle control schemes
      680Scopus© Citations 11
  • Publication
    Wavelength-controlled variable-order optical fractional Fourier transform
    (Optical Society of America, 2004-03-01) ; ;
    The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths.
      354Scopus© Citations 9
  • Publication
    Three-dimensional static speckle fields. Part I. Theory and numerical investigation
    (Optical Society of America, 2011-09-01) ; ;
    When monochromatic light is scattered from an optically rough surface a complicated three-dimensional (3D) field is generated. These fields are often described by reference to the 3D volume (extent) of their speckles, leading to the definition of lateral (x; y) and longitudinal speckle sizes (z). For reasons of mathematical simplicity the longitudinal speckle size is often derived by examining the decorrelation of the speckle field for a single point lying on axis, i.e., x=y=0, and this size is generally assumed to be representative for other speckles that lie further offaxis. Some recent theoretical results, however, indicate that in fact longitudinal speckle size gets smaller as the observation position moves to off-axis spatial locations. In this paper (Part I), we review the physical argument leading to this conclusion and support this analysis with a series of robust numerical simulations. We discuss, in some detail, computational issues that arise when simulating the propagation of speckle fields numerically, showing that the spectral method is not a suitable propagation algorithm when the autocorrelation of the scattering surface is assumed to be delta correlated. In Part II [J. Opt. Soc. Am. A 28, 1904 (2011)] of this paper, experimental results are provided that exhibit the predicted variation of longitudinal speckle size as a function of position in x and y. The results are not only of theoretical interest but have practical implications, and in Part II a method for locating the optical system axis is proposed and experimentally demonstrated.
      737Scopus© Citations 25
  • Publication
    Motion detection, the Wigner distribution function, and the optical fractional Fourier transform
    (Optical Society of America, 2003-06-01) ; ;
    It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.
      390Scopus© Citations 29
  • Publication
    Fundamental diffraction limitations in a paraxial 4-f imaging system with coherent and incoherent illumination
    (Optical Society of America, 2007-07-01) ; ;
    In the usual model of an imaging system, only the effects of the aperture stop are considered in determining diffraction-limited system performance. In fact, diffraction at other stops—those associated with different lens elements, for example—can also affect system performance and cause the imaging to be space variant, even in the absence of vignetting in the conventional ray optics sense. For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops. If the diameters of the lenses are equal, the aperture of the first lens has a greater effect on system performance than does that of the second.
      480Scopus© Citations 14
  • Publication
    Spread-space spread-spectrum technique for secure multiplexing
    A novel technique for multiplexing complex images is proposed in which each image may be demultiplexed only if a set of random encryption keys is known. The technique utilizes the ability of the double random phase encoding method to spread a signals’ energy in both the space and the spatial frequency domains in a controlled manner. To multiplex, images are independently encrypted with different phase keys and then superimposed by recording sequentially on the same material. Each image is extracted by using the particular key associated with it. During decryption the energy from the other images is further spread, making it possible to minimize its effects by using suitable filters. Wigner analysis is applied to the technique, and numerical results are presented.
      486Scopus© Citations 51
  • Publication
    Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform
    (Optical Society of America, 2005-05-10) ; ;
    The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body’s motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions
      492Scopus© Citations 29
  • Publication
    Three-dimensional static speckle fields. Part II. Experimental investigation
    (Optical Society of America, 2011-09-01) ; ;
    In Part I [J. Opt. Soc. Am. A 28, 1896 (2011) of this paper, the physical model for fully developed speckle is examined based on two critical assumptions. (i) It is assumed that in the object plane, the speckle field is delta correlated, and (ii) it is assumed that the speckle field in the observation plane can be described as a Gaussian random process. A satisfactory simulation technique, based on the assumption that spatial averaging can be used to replace ensemble averaging, is also presented. In this part a detailed experimental investigation of the three dimensional speckle properties is performed using spatial averaging. The results provide solid verification for the predictions presented in Part I. The results are not only of theoretical interest but have practical implications. Techniques for locating and aligning the optical system axis with the camera center, and for measuring out-of plane displacement, are demonstrated.
      447Scopus© Citations 17