Rene Skov Hansen

Laser-speckle angular-displacement sensor: theoretical and experimental study

A novel, to our knowledge, method for the measurement of angular displacement for arbitrarily shaped objects is presented in which the angular displacement is perpendicular to the optical axis. The method is based on Fourier-transforming the scattered field from a single laser beam that illuminates the target. The angular distribution of the light field at the target is linearly mapped on a linear image sensor placed in the Fourier plane. Measuring this displacement facilitates the determination of the angular displacement of the target. It is demonstrated both theoretically and experimentally that the angular-displacement sensor is insensitive to object shape and target distance if the linear image sensor is placed in the Fourier plane. A straightforward procedure for positioning the image sensor in the Fourier plane is presented. Any transverse or longitudinal movement of the target will give rise to partial speckle decorrelation, but it will not affect the angular measurement. Furthermore, any change in the illuminating wavelength will not affect the angular measurements. Theoretically and experimentally it is shown that the method has a resolution of 0.3 mdeg ( approximately 5 murad) for small angular displacements, and methods for further improvement in resolution is discussed. No special surface treatment is required for surfaces giving rise to fully developed speckle. The effect of partially developed speckle is considered both theoretically and experimentally.

Modeling of the nonlinear response of the intrinsic HgCdTe photoconductor by a two-level rate equation with a finite number of carriers available for photoexcitation

A description of the nonlinear response of a HgCdTe photoconductor on the incident optical radiation is derived from a two-level rate equation for the photoexcited carriers. The model accounts for a limited number of electrons available for photoexcitation, and the possibility of photostimulated relaxation of an already excited photoelectron. The detector response as well as the level of incident optical power where saturation occurs is directly related to the physical constants of the detector material. The saturation of the detector is the same phenomenon as is known for the saturable absorbers-the detector material becomes transparent when the incident optical power exceeds the saturation power. Even though the description given here is applied to the HgCdTe detector, the general model can be applied to other detector materials as well. The parameters for the model are fitted to a thermoelectrically cooled HgCdTe detector and afterwards employed to predict the detector noise performance in a heterodyne setup. Unlike for liquid-nitrogen-cooled detectors, shot-noise-limited detection cannot be obtained with use of only thermoelectrical cooling (226 K) of the detector. However, the detector performance can be optimized to be able to perform Doppler measurements from aerosol backscatter by use of the model presented to optimize the applied optical power in the reference wave.

Three-dimensional speckles: static and dynamic properties

A discussion of the static and dynamic 3D behavior of a speckle pattern is given. The discussion is based on general theoretical results, which are valid within the paraxial approximation for a general optical system using the concept of complex ABCD-matrices. Especially, we examine the 3D nature of speckles, which are formed in free-space, in Fourier transform geometry and in imaging systems. The dynamic evolution of these speckles is derived from the space/time-lagged intensity covariance that results from an in-plane translation of a diffuse scattering object, which is illuminated by a Gaussian shaped laser beam in a back- scattering configuration. In particular, the origin of speckle decorrelation will be investigated. Speckles are commonly analyzed in a plane where decorrelation can arise either from true speckle decorrelation or due to a frozen 3D speckle pattern being translated through the plane of observation, i.e. subjective speckle decorrelation. The presentation will be concluded with illustrative experimental results. The implications of the 3D dynamic properties for measurement systems based on speckle correlation will be considered.

Statistics for partially developed speckles: the impact on speckle-based measurements

The treatment of first- and second order intensity statistics of light scattered from surfaces not giving rise to fully developed speckles will be presented. Analytical expressions will be given for speckle size, first-order intensity moments and intensity variance within the framework of using the Huygens-Fresnel integral with the complete optical system included by the complex valued system ray ABCD-matrix. Various surface models will be presented, all being based on a Gaussian height distribution with various lateral length scale(s). For the sake of simplicity, only rotationally symmetric optical systems will be treated and no depolarization effects during scattering will be included.

Impulse response function for common-path interferometers

The concept of an impulse response function (IRF) for interferometers - and especially for common-path mterferometers - will be introduced as a tool for depicting fringe appearance in ESPI systems based on the shearing effect-1.The impulse response function relates the measured phase change at an arbitrary position in the detector plane with a displacement in the object plane. Thus the TRY depicts the function of a specific filter placed in the Fourier plane ofthe common-path interferometer. A suite of filters will be introduced to show the specific way in which the filter will control the fringe interpretatio

Fourier plane filters and common path interferometry in vibrometers and electronic speckle interferometers

In the present paper it will be shown how the introduction of a Fourier plane filter can create various types of common path interferometers for measuring changes in surface tilt or curvature of an object surface. This is obtained by placing a holographic optical element in the Fourier plane of a 4-f optical system. The interferometers are analyzed by using the paraxial approximation of the Huygens-Fresnel integral formalism, and the interferometer functions are given by a novel formalism using impulse response functions. Based on this technique, an interferometer for measuring dedicated changes in surface deflection is presented. This interferometer is insensitive to rigid surface rotations and displacements. The interferometer can be embedded in systems based on single point measurement of a time dependent deflection, i.e. vibrometers, as well as in full-field measurements such as electronic speckle interferometers.

Compact optical sensors for measuring linear and angular velocities

In this paper, we present a suite of novel speckle based displacement sensors. A laser beam illuminates the optically rough object and the light scattered off the object is collected and processed by various optical elements and, finally, the speckle pattern is detected. A new theoretical tool has been developed in which the speckle dynamics at the detector plane is described for an arbitrary complex optical system simply by means of the ABCD ray-transfer matrix elements for the optical system. Armed with the general theoretical tool, this paper discusses the correlation between object displacement and the speckle dynamics observed at the detector. In particular, the general theoretical tool allows trade-of analyses that are very important for industrial applications. As an example, all the sensors presented here are designed such that they are independent on variations in object distance. A new method is introduced in which rapid prototype optical sensors can be realized with standard optical elements. This facilitates a way of rapid realization of very compact optical sensors.

Compact system for measuring rotational speed in two dimensions

A simple system for detecting the rotation in two directions of a reflective ball is presented. The primary goal for the set-up is to realize a simple and compact concept that can be used for PC-cursor control, yet having an adequate precision for cursor control. A slightly diverging beam from a Vertical Surface Cavity Emitting Laser (VCSEL) mounted on a pcb-board with a diameter of 6.8 mm illuminates a reflective ball (0 4 mm) placed at a distance of 15 mm. Light scattered off the rotating ball produces a speckled field, which sweeps across two pairs of elongated photo detectors arranged perpendicular to each other. The four photo detector signals are digitized and fed into an ASIC, which determines the rotation of the ball in two directions including the sign of the rotation.

Effects of system apertures and defocus on the measured phase shift in interferometric displacement measurements

The difference between the phase shift occurring at the objectsurface owing to displacement and the phase shift occurring at theobservation plane of the imaging system of the interferometer isstudied. Analytical expressions for the phase shift for a number ofsurface displacements are found. From these expressions it is foundthat the difference between the phase shifts at the object and theobservation planes depends on the number of speckle-correlation modesin the observation plane and the product between the relative apertureand the relative defocus of the imaging system. For generaldisplacement the results indicate that the accuracy of a phase-shiftmeasurement with a small-aperture interferometer is limited only by thenumber of speckle-correlation modes at the observation plane for thecase of a focused system. For a large-aperture interferometer thephase shift at the observation plane becomes sensitive to defocusing ofthe imaging system. Agreement between theory and experiments is observed.