Nanoscale tilt measurement using a cyclic interferometer with polarization phase stepping and multiple reflections.

High-accuracy tilt or roll angle measurement is required for a variety of engineering and scientific applications. A cyclic interferometer with multiple reflections has been developed to measure small tilt angles. To accomplish this task, a novel and simple method, phase shift by polarization, was developed. The results of these studies show that the multiple reflection cyclic interferometers can be used to measure object tilts on the order of 0.2 nano-radians. We develop the theory for polarization phase step and show that accurate measurements can be made with the cyclic interferometer.

Vibration fringes by phase stepping on an electronic speckle pattern interferometer: an analysis.

A detailed analysis of the vibration fringes obtained by phase stepping on a time-averaged electronic speckle pattern interferometer is presented. It is shown that the contrast of the fringes remains relatively high for any phase step between 30 degrees and 180 degrees for low electronic noise and fringe density. Also, for the four-phase-stepped method, the vibration fringes have the same contrast as that of the pi-phase-shift method except that the high-frequency speckles are smoothed. The contrast of the fringes obtained with extra phase steps along with incoherent superimposition is shown to be higher than the single- or four-phase-step method. Both theory and experimental results are presented.

Phase-measuring interferometry: new methods and error analysis.

New methods that can be used to determine phase in phase-stepping interferometry are presented. It is shown that a combination of some of these methods can be used to reduce the error introduced by phase-stepper miscalibration and nonlinearity. Moreover these new algorithms can also be used to detect the presence of miscalibration or phase-shifter nonlinearity. A simplified approach to understanding the error introduced by miscalibration and nonlinearity of the phase stepper and its reduction in phase-shifting interferometry is also presented.

Modified electronic speckle pattern interferometer employing an off-axis reference beam.

A new arrangment for an electronic speckle pattern interferometer is reported in which an off-axis reference beam is used, thereby eliminating alignment problems.

Simple electronic speckle-shearing-pattern interferometer.

A simple electronic speckle-shearing-pattern interferometer, in which the image of an object is focused and sheared with a split lens onto a diffuser, is described. The sheared images on the diffuser are focused by a television camera and then digitized and processed in a host computer. The results obtained for two basic types of shearing, lateral and radial, are presented.

Quasi-equal-path electronic speckle pattern interferometric system.

Limitations of a quasi-equal-path electronic speckle pattern interferometric system are discussed. We show that by replacement of the reference glass plate with a plano-concave lens the quasi-equal-path electronic speckle pattern interferometric system can be made more versatile. An arrangement to reduce the aberration in the reference beam is also presented.

Diameter measurement of single-mode fiber by using interferometric and imaging techniques.

Two methods to measure the cladding diameter of single-mode fibers are presented. The first method is based on an interference fringe measurement technique. Interference fringe spacing at two different planes is measured to determine the cladding diameter of the fiber. The theory of the fringe formation in the interferometeric arrangement using single-mode fibers is discussed. It is theoretically shown that the far-field overlapping Gaussian field distribution from the fibers shifts the position of the fringe maxima and minima. As a special case of unit fringe visibility the minima positions do not shift, whereasthe maxima positions are shifted. In the case of a Lloyd mirror arrangement it is shown that fringes can be obtained from a rough surface as well. A lens is used in the second method to image the two identical point sources that cause the interference. Through the use of the magnification and spacing of the images, the cladding diameter is estimated. It is shown that the accuracy of the fiber cladding-diameter measurement can be enhanced by generating multiple point sources. Consistent results of the fiber cladding diameter have been obtained with the proposed methods. Fiber cladding-diameter measurements with a standard error of less than 0.15 µm can be achieved.

Contrast of the vibration fringes in time-averaged electronic speckle-pattern interferometry: effect of speckle averaging.

This paper presents a detailed investigation of the effect of speckle averaging in electronic speckle-pattern interferometric fringes. The theory states that the constrast of the resultant smoothed fringes increases as the number of frames is increased. It is shown that the contrast of the fringes is optimized with a limited number of superpositions, and further addition results in the reduction of speckle noise with the contrast remaining almost the same. The contrast of the fringes obtained with pi and pi/2 phase-stepping methods with speckle averaging is also discussed. Both theoretical and experimental results are presented in this paper.

Increased sensitivity to in-plane displacements in electronic speckle pattern interferometry.

We describe an optical arrangement that increases the sensitivity to in-plane displacement in an electronic speckle-pattern interferometric system. This is accomplished by oblique illumination and observation along the direction of illumination. An anamorphic prism placed in front of the object is used to correct for the eccentricity in the image caused by the oblique observation. The sensitivity to in-plane displacement can be increased to a maximum of approximately λ/2. Experimental results including phase stepping are presented.

Contouring by speckle interferometry.

An optical method of generating high-constrast contours by using speckle interferometry has been proposed. To demonstrate the use of this technique the conventional dual-index immersion method has been adopted.

Pulsed lasers in speckle photography: error owing to pulse width.

The effect of the pulse width of a pulsed laser in the studies of speckle velocimetry and transient vibration analysis is discussed. Because of the motion of the object during an exposure, a sine function is obtained by using the pointwise filtering method. This function modulates the halo along with the Young's fringes. It is shown that for high object velocities the sinc function modifies the halo distribution; as a result, the error in calculating the fringe position increases. An aperture geometry for which the autocorrelation halo is made constant in certain regions is proposed in which the intensity variation in this region is the result of the modulating sinc function only. A closed-form solution for the shift in the position of the fringes in this region is obtained. Experimental results of the simulation are presented.

Contouring by electronic speckle pattern interferometry employing dual beam illumination.

In this paper we extend and study the method for generating contours of diffuse objects employing a dual beam illumination coupled with electronic speckle pattern interferometry. The sensitivity and the orientation of the contour planes are analyzed. A novel method for tilting the planes of contours and experimental results incorporating phase shifting and fringe analysis are also presented. The theoretical and the experimental results show good agreement.

Oblique incidence and observation electronic speckle-pattern interferometry.

In this paper we discuss an oblique incidence and observation electronic speckle-pattern interferometer, in which we use an anamorphic prism in front of the object. A collimated beam traveling through the prism is partly reflected at the base of the prism. The reflected light is the reference beam and the transmitted light illuminates the diffuse object, thereby generating the object beam. In this scheme the object and the reference beams are collinear. A new scheme that uses two prisms and permits phase stepping is also presented.

Quasi-equal-path electronic speckle pattern interferometric system.

A quasi-equal-path electronic speckle pattern interferometric system that uses the polarization property of a diffusing object is presented. The fringe pattern is extremely stable with high visibility. Phase stepping in this arrangement is accomplished by translating the glass plate used for obtaining the reference beam. The only alignment that is necessary is that for obtaining a uniform field of view. This experimental arrangement demonstrates high efficiency of laser power usage. An equation for longitudinal alignment tolerance is also obtained.

Speckle interferometry with temporal phase evaluation for measuring large-object deformation.

We propose a new method for measuring large-object deformations byusing temporal evolution of the speckles in speckleinterferometry. The principle of the method is that by deformingthe object continuously, one obtains fluctuations in the intensity ofthe speckle. A large number of frames of the object motion arecollected to be analyzed later. The phase data for whole-objectdeformation are then retrieved by inverse Fourier transformation of afiltered spectrum obtained by Fourier transformation of thesignal. With this method one is capable of measuring deformationsof more than 100 mum, which is not possible using conventionalelectronic speckle pattern interferometry. We discuss theunderlying principle of the method and the results of theexperiments. Some nondestructive testing results are alsopresented.

Shape Measurement by use of Temporal Fourier transformation in Dual-Beam Illumination Speckle Interferometry.

We outline a novel method for determining the shape of an object by use of temporal Fourier-transform analysis in dual-beam illumination speckle interferometry. The object whose shape is to be determined is rotated about an axis, and a number of frames of the image of the object motion are acquired. Temporal in-plane displacement that is due to the object rotation is related to the shape of the object and is retrieved from this large set of data by Fourier transformation. With this method one can determine the absolute height of the object with variable resolution, thereby allowing shapes of objects with large and small slopes to be determined. The theory of the method along with experimental results is presented.

Speckle interferometric methods of measuring small out-of-plane displacements.

We present two new methods for measuring small out-of-plane displacement. These methods are descendents of Leendertz's method in speckle interferometry but provide fringes of good contrast.

Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera.

Recently, a new method to measure object shape and deformation with temporal evolution of speckles in speckle interferometry was reported. In this method, certain parameters, sensitive to shape or deformation are changed continuously, and the fluctuations in the irradiance of each speckle is recorded. The information over the whole object deformation is retrieved by Fourier-transformation techniques. We present a detailed theory and analyze the influence of decorrelation due to longitudinal and lateral size of the speckles. It is also shown that the method can be used to measure small deformations (less than 5 microm) with higher resolution. Further, the nonlinearity of the camera is shown to enhance the sensitivity.