Measurement of small rotation angles by using a parallel interference pattern

Littrow angle based autocollimation method for precision online monitoring three-dimensional angular drifts of chirped-pulse compression-gratings

A simple optical method for online precisely monitoring three-dimensional (3D) angular drifts of chirped-pulse compression-gratings in chirped-pulse amplification (CPA) lasers is proposed. Monitoring objects include all dimensional angular drifts of a grating, especially the grating groove in-plane-rotation. Monitoring contents contain direction and amount. And monitoring results are obtained by detecting the direction and the amount of 2D relative offsets of three focal spots formed by a ternary monitoring beam line. The theoretical model of the proposed method is set up using a matrix ray-tracing method, and a simplified monitoring equation is concluded based on numerical simulations. And the validity of this method is verified by a simple demonstration experiment. Besides, monitoring error and reliability discussion of the method are presented, as well.

A heterodyne interferometer for angle metrology

We have developed a compact, high-resolution, angle measurement instrument based on a heterodyne interferometer. Common-path heterodyne interferometer metrology is used to measure displacements of a reflective target surface. In the interferometer set up, an optical mask is used to sample the laser beam reflecting back from four areas on a target surface. From the relative displacement measurements of the target surface areas, we can simultaneously determine angular rotations around two orthogonal axes in a plane perpendicular to the measurement beam propagation direction. The device is used in a testbed for a tracking telescope system where pitch and yaw angle measurements of a flat mirror are performed. Angle noise measurement of the device shows 0.1 nrad/square root of Hz at 1 Hz, at a working distance of 1 m. The operation range and nonlinearity of the device when used with a flat mirror is approximately +/-0.15 mrad, and 3 microrad rms, respectively.

Measurement of angle and axis of rotation in a carousel interferometer: a detailed analysis

A detailed analysis of a carousel interferometer is presented for the measurement of an unknown angle and axis of rotation. The technique exploits a set of compensator glass plates and a right-angle prism that is placed in each of the two arms of the interferometer. The two sets are placed at the same rotational stage, while the end mirrors of the interferometer are static. When rotation takes place, individual and relative optical path differences are generated in the two beams of the interferometer. The generated phase differences contribute toward finding the angle and axis of rotation. The analysis is presented for any initial position of the interferometer, i.e., the radial vector from the axis of rotation to the apex of one of the prisms used. The results show the slight variations in the error and nonlinearity when different parameters are manipulated. Moreover, the trade-off between the maximum size of the prisms and the radial distances are also presented.

Optical measurements of angle and axis of rotation

A carousel interferometer is designed to find the unknown angle and axis of rotation simultaneously. A set consisting of a compensator glass plate and a right-angle prism is placed in each of the two arms of the interferometer while located at the same rotational stage. When rotation takes place individual and relative optical path differences are generated in the beams that contribute toward finding out the angle and axis of rotation. Computer simulation shows that error remains less than a nanometer for a 1 m length of unknown radius and rotation range of +/-15 degrees .

Use of the circular Dammann grating in angle measurement

We describe a novel method of angle measurement by borrowing the concept of the circular Dammann grating (CDG). A three-order CDG is employed in this experiment. The displacement of the tilted angle can be determined accurately by measuring the projection from the distorted CDG image. This method is controlled only by the initial radius of the image and the converging ratio of the lens. Compared with conventional techniques, this technique has the advantages of a simple design with superior resolution to within 1 degree, low cost, and compactness. A theoretical analysis together with experimental results is presented.

Measurement of two-dimensional small angle deviation with a prism interferometer

A new technique for the measurement of two-dimensional small angular deviation is presented. A compound prism, which effectively produces a combination of two right-angled prisms in orthogonal directions, and plane reference surfaces have been utilized for the measurement of the orthogonal components of the angular tilt of an incident plane wavefront. Each orthogonal component of the angular tilt is separately measured from the angular rotation of the resultant wedge fringes between two plane wavefronts generated due to splitting of the incident plane wavefront by the corresponding set of right-angled prism and plane reference surface. The technique is shown to have high sensitivity for the measurement of small angle deviation. A monolithic prism interferometer, which is practically insensitive to vibration, is also proposed. Results obtained for the measurement of a known tilt angle are presented.

Optimization of linearity by use of a glass plate in carousel interferometers

Carousel interferometers are compact swinging interferometers, but their popularity is limited because of significant nonlinearity in rotational measurements. Introducing a glass plate in a rotating interferometer and optimizing its thickness has improved the linearity drastically. Computer simulations show reductions in nonlinearity of several orders of magnitude.

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.

High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns

Based on the idea of measuring small rotation angles with a parallel interference pattern (PIP), a method is developed to measure large rotation angles accurately. Two parallel PIP's that have different periods are used to measure a rotation angle of an object. The measurement made with a small-period PIP provides a high accuracy, and the measurement made with a large-period PIP provides a wide range. An accurate measurement for wide-range angles is made by combining the two measured values. The accuracy of the phase detection is determined by the periods of two PIP's. Rotation angles from approximately -30 to 30 arc min can be measured with an accuracy of 0.2 arc sec. Analytical results are supported by experimental results.

Simple wide-range method for angle measurement with a point fiber-optic output

We propose a simple optical method for precise, wide-range angle measurement based on the use of a single-mode optical fiber as a registration scheme output. Because of its micrometric core dimensions, the fiber serves as a point receiver that is highly sensitive to angular displacements of focused laser emission. The method allows the independent photoelectric measurement of both rotation and spatial angles of various optical elements, combining a wide angular dynamic range (from 0 degrees to 360 degrees ) with high accuracy (exceeding 3 arcsec).

Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns

Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Δθ and Δφ by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 × 1.5 mm(2) are achieved in the measurement. Theoretical analysis and experimental results show that error ε(1) in the measurement of Δφ is almost equal to -0.01Δθ and error ε(2) in the measurement of Δθ is almost equal to -0.01Δφ. For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.