Speckle-Interferometer Based Electro-Optic Displacement Sensor

Speckle- interferometer based electro -optic displacement sensorC.P. Grover and A.K. AgarwalDivision of Physics, National Research Council of CanadaOttawa, Ontario, Canada K1A OR6AbstractAn analysis of the fringe visibility of a speckle interferometer has been given as afunction of the source position. The interferometer consists of a double exposurespeckle recording which, for an infinite aperture, produces in monochromatic light a setof unit visibility rectilinear fringes localized at infinity. In practice, the planeconjugate to that of the point source of light is taken to be the localization as well asthe observation plane of the fringes. A longitudinal displacement of the light sourcegives rise to a reduction in the fringe visibility which has been monitored bypositioning a line detector in the observation plane. The sensitivity of such a positionsensing device depends upon the size and location in reference to the fringe profile andit has been estimated to be of the order of 0.1 micrometer. This study has been appliedto the design and construction of a remote electro -optic displacement sensor. The rangeand the sensitivity of the device are mutually complementary and one could only beincreased at the loss of the other or vice -versa. Furthermore, a study of the linearityof the sensor has been made as a function of the other sensor parameters.IntroductionThe determination of linear displacement is one of the most fundamental of allmeasurements. The most commonly used devices for this purpose include mechanical,pneumatic and optical comparators and sensors such as strain gauges, differentialtransformers, capacitive and pizoelectric transducersl. These low resolution devices aregenerally unsuitable for submicron measurements and the laser interferometry2 has so farbeen the only well developed technique for any precision measurement. However, its useis limited primarily for laboratory applications. Furthermore, several authors haveinvestigated the speckle interferometry3 which for real time applications could beimplemented in the form of electronic speckle pattern interferometry (ESPI)`'. Thecapability of electro optical systems to meet the present day fast production and qualitycontrol demands, has resulted in their rapid development in recent years. While, theoptical triangulations is the most common technique, other methods such as the use of aPockels ce116 or a position sensing diode have also been incorporated in these systems.This paper describes the development of a new electro optical displacement sensorbased on a simple speckle interferometer. The formation of Young's fringes from a doubleexposure recording of a speckle distribution is a well known phenomenon8'9. For aninfinite aperture these fringes are strictly localized at the infinity and have a unitvisibility. A longitudinal displacement of the light source produces a reduction in thefringe visibility in the observation plane, attributed mainly to the defocussing. Wepresent an analysis relating the object displacement to the fringe visibility and discussthe sensitivity of this method for the purpose of measuring micro displacements.TheoreticalConsider the optical arrangement of Figure 1 where S is a point source of light imagedby the lens system L at the point S' in the observation plane P2. The double exposurephotographic recording H of a speckle distribution is placed in the plane P1. Therectangular coordinate systems (x,y) and (u,v) characterize the planes P1 and P2respectively. The double exposure speckle recording was made with the speckledistribution undergoing a linear displacement E along the x -axis, in between theexposures. Let g(x,y) denote the irradiance of the speckle at the time of the recording.When illuminated by an infinite plane wave of monochromatic light of wavelength A, itproduces a complex amplitude in plane P2 given byA(u,v) = 0[(1 + exp i2nuE