Analysis of Mechanical Oscillations by Speckling

Tiziani, Hans J.

doi:10.1364/ao.11.002911

Cited by 38 publications

(7 citation statements)

References 12 publications

(6 reference statements)

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“…However, these chaotic and speckle phenomena have applications in various uses, such as coupling high pump power into chaotic double-clad EDFA's [20], mechanical models of Chua's circuit [22], cryptography based on chaotic systems [23], algorithmic trading [24], measurements of coherence [25], surface roughness [26], and displacement of an object [27], among others. This paper is organized as follows: Section 2 introduces an integral method to calculate the field intensities of an infinite optical waveguide based on the ideas of Ref.…”

Section: Introductionmentioning

confidence: 99%

Disordered Field Patterns in a Waveguide With Periodic Surfaces

Pérez-Aguilar¹,

Mendoza-Suárez²,

Tututi³

et al. 2013

PIER B

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Abstract-This paper considers an electromagnetic waveguide composed of two periodic, perfectly conducting, rippled surfaces. This periodic system has a band structure given by a dispersion relation that allows us characterize eigenmodes of the system. We considered the cases of both smooth and rough surfaces, using an integral numerical method to calculate field intensities corresponding to eigenmodes over a wide frequency range. Under certain conditions, the system presents disordered patterns of field intensities with smooth surfaces. We believe that the explanation of disordered patterns is the following: for smooth surfaces, the phenomenon of electromagnetic chaos; and for rough surfaces, the speckle phenomenon. Since it is well known that the surfaces of materials always have a certain degree of roughness, it can be concluded that both chaos and speckle contribute to the presence of disordered field patterns.

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Section: Introductionmentioning

confidence: 99%

Disordered Field Patterns in a Waveguide With Periodic Surfaces

Pérez-Aguilar¹,

Mendoza-Suárez²,

Tututi³

et al. 2013

PIER B

View full text Add to dashboard Cite

show abstract

“…A speckle field carries information about the surface it originates from, so much so that changes to the surface profile through applied stress [1,2], motion [3][4][5][6][7], or object surface slopes [8] can be detected by monitoring the resultant variation in the field. While an imaging system is often used for speckle metrology, alternative optical systems [described by using the linear canonical transform (LCT)], have been shown to be useful for estimating simultaneous in-plane translation and surface tilting [3][4][5][6][7], as well as allowing the user greater control over sensitivity and dynamic range of the measuring system. Speckle decorrelation [4,5] effects can also be minimized.…”

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confidence: 99%

Controlling speckle using lenses and free space

et al. 2007

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“…1,2 In-plane translation measurement involves the capture of the intensity of the field reflected from the surface both before and after motion. Numerically calculating the Fourier transform (FT) of the sum or difference of the two sequential images yields a cosinusoidal fringe pattern with spacing inversely proportional to the surface displacement and fringe normal to the direction of motion.…”

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confidence: 99%

Speckle photography: mixed domain fractional Fourier motion detection

et al. 2006

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A reflection-based optical implementation of two simultaneous scale-invariant fractional Fourier transforms (FRTs) is used to develop a novel compact speckle photographic system. The system allows the independent determination of both surface tilting and in-plane translational motion from two sequential mixed domain images captured using a single camera. © 2006 Optical Society of America OCIS codes: 070.2580 Speckle photography (SP) is a practical means of measuring in-plane translation and tilting motion of optically rough surfaces. 1,2 In-plane translation measurement involves the capture of the intensity of the field reflected from the surface both before and after motion. Numerically calculating the Fourier transform (FT) of the sum or difference of the two sequential images yields a cosinusoidal fringe pattern with spacing inversely proportional to the surface displacement and fringe normal to the direction of motion. In the measurement of tilting, the optical Fourier transform (OFT) of the reflected surface fields is captured and the FT of the sum or difference results in fringe spacing inversely proportional to the magnitude of the rotation. While the imaging technique is insensitive to tilting motion, the OFT technique is insensitive to translation, and thus two systems are required to capture both components of surface motion. Neither technique allows the user to determine the direction of motion.The fractional Fourier transform 3,4 (FRT) is a linear transform, of which the imaging operation and the FT are special cases. [5][6][7][8][9][10] Combining the optical implementation of the FRT (OFRT) with SP allows the simultaneous measurement of mixed translation and tilting motions.11 Using an OFRT system, 12 termed a "fake-zoom lens," variation of both the minimum resolution and the dynamic range of measurement has been demonstrated. 13 Separation of both motion components can be achieved, using images captured in a single FRT domain, if a linear relationship exists between the two types of motion. Otherwise, capture in two different fractional domains is necessary 14 and has been demonstrated. 15 The technique involves the capture of two images first in one domain (OFRT order a1) and then two more in the second (OFRT order a2), by using a two-lens, scaleinvariant OFRT. 16 Correlating these images numerically allows the direction of motion to be determined and also allows decorrelation effects to be observed. In summary this technique requires the capture of four sequential images at a single camera, with a change of OFRT order during capture or the use of two parallel optical systems with different OFRT orders and two cameras, each of which captures two sequential images.The use of reflective elements in OFRT systems has been discussed theoretically.17 Light, after crossing a system made up of free-space distances and refracting elements, may be reflected back through the same system by a plane mirror. The effect of the "back" transit can be described by the concatenation of the system components in reve...

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Analysis of Mechanical Oscillations by Speckling

Cited by 38 publications

References 12 publications

Disordered Field Patterns in a Waveguide With Periodic Surfaces

Disordered Field Patterns in a Waveguide With Periodic Surfaces

Controlling speckle using lenses and free space

Speckle photography: mixed domain fractional Fourier motion detection

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