Hans M. Pedersen

Theory of speckle dependence on surface roughness

The theory of speckle in partially coherent, monochromatic light is extended to cover the entire range of object roughness. For “almost white-noise” objects it is shown how the speckle statistics are related to a Gaussian approximation of the object statistics. Within this approximation, general relations are derived for the spatial speckle correlation and the spatial Wiener spectrum. The theory is applied to calculate rms speckle contrast as function of object roughness, coherence of the illumination, and receiver plane defocusing.

The roughness dependence of partially developed, monochromatic speckle patterns

Abstract The theory of partially developed speckle patterns is reviewed. Exact solutions for the speckle contrast as function of surface roughness are calculated for two different surface models. A linear approximation for small roughnesses is found to be valid if the phase deviations due to roughness are less than one. Applications to surface roughness measurements are discussed.

Object-roughness dependence of partially developed speckle patterns in coherent light

Abstract For a class of simple models, exact solutions are obtained for the surface roughness dependence of the speakle contrast. A recent gaussian-field approximation to the speckle statistics is generalized, and shown to give results in good agreement with the exact results obtained. The speckle contrast is found to be strongly dependent on the specific form of the objects profile height distribution, a feature which makes the effect less attractive for roughness measurement applications.

Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?

Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.

Measurement of small vibrations using electronic speckle pattern interferometry: Theory

A theoretical analysis of a recently published method for measurement of small vibrations using electronic speckle pattern interferometry is given. From the general description of the signal processing in electronic speckle pattern interferometry, we derive a theory that applies to ideal operation of the system. For two special cases, including the small-amplitude limit, the theory is extended to include nonideal effects. The calculated response functions show good agreement with experimental results also beyond the linear small-amplitude range.

Exact geometrical theory of free-space radiative energy transfer

An exact theory of free-space radiative energy transfer is given in terms of a generalized specific intensity that is constant along geometrical rays. General and explicit relations are derived for the generalized specific intensity expressed in terms of the field variables. Such relations are also derived for the cross-spectral density function of the field expressed in terms of the generalized specific intensity. For an arbitrary, freely propagated field, the theory is shown to reproduce the exact results of wave theory by transfer equations that are almost identical to the classical ones. The description reduces to the classical theory within a quasi-homogeneous field approximation. Similarly, it reduces to the geometrical-optics energy expressions in that approximation. For two-wave interference, additional ray contributions to the energy transport are found along the interference fringes. These interference rays serve only to describe the effects of the interference on the local energy transport.

Tomographic reconstruction of sound fields using TV holography

Combining TV holography recording with acoustic phase stepping and image processing, we measure the integrated density distribution in sound fields that propagate in air. We record a given number of two-dimensional cross sections that are tomographically backprojected to give the amplitude and phase distributions of the emitted sound field. The validity of the procedure is demonstrated.

Holographic vibration measurement using a tv speckle interferometer with silicon target vidicon

Abstract A basic realization of a TV speckle interferometer applying a silicon target vidicon is described. The increased detectivity compared with other vidicons reduces the laser power requirements. This enables stroboscopic operation in a fairly straightforward manner with a He-Ne laser source. Time average- and stroboscopic fringe patterns for a vibrating test object are presented.

Comparing roughness dependent contrasts of polychromatic speckle patterns in light of different spectral densities

Abstract An exact solution is obtained for the roughness dependent speckle contrast in the case of a rectangular spectrum. This is compared to the simple formula previously obtained for a gaussian spectrum. The agreement is shown to be good if the formulas are fitted to the same asymptotic dependence in the incoherent limit. From this we conclude that the simple gaussian formula may be a useful approximation even for other non-gaussian spectra, and a fitting procedure is indicated.

Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing.

We separately measure the higher harmonics vibration patterns of a periodic vibrating object by using time-average TV holography and phase modulation. During measurements the frequency of the phase modulation is adjusted to each harmonic component while the excitation of the object is set low enough to record all components on the linear part of the fringe function. Using acoustical phase stepping and calibration of the fringe function, we compute the amplitude and phase distributions of the frequency component. We measure components up to the 65th harmonic by using square-wave excitation.