Optical phase singularities in detection of laser beam collimation

Optical phase singularities, also called optical vortices, are known to have applications in various branches of optics. Here the role played by optical vortices in collimation testing is explained. Interference and a diffractive experimental setup in which the presence of an optical vortex permits collimation testing are presented. It is shown that the moire fringes that aid in collimation detection are due solely to the presence of vortices and not to the accompanying phase factors that are involved in producing a grating structure.     

Wedge-plate shearing interferometers for collimation testing: use of a moiré technique

Various optical arrangements of a double-wedge-plate shearing interferometer are presented for checking laser beam collimation. The use of moiré fringes is found to be advantageous for setting the shear fringes parallel to the direction of shear in order to obtain a well-collimated laser beam. The experimental procedure and various details of the interferometer are discussed. A brief summary of a few methods for collimation testing that use a wedge plate is also given. The accuracies achievable with shearing interferometers that use a parallel plate, a wedge plate of small angle, a double wedge having a large wedge angle, a wedge plate of large angle along with two flat mirrors, and a wedge plate having a large angle are compared and summarized.     

Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry

In this paper, we report an automated technique for collimation testing by incorporating Fourier fringe analysis of the recorded interferograms in Talbot interferometry. The triangular profile of Talbot interferometric fringes has been recorded using a CCD and computer system. The interferograms corresponding to the in-focus, at-focus, and out-of-focus positions of the collimating lens have been recorded. Direct phase measurement using the Fourier transform method has been used for detection of collimation positions. Good accuracy and precision in measurement have been achieved.     

Focal-length measurement by multiple-beam shearing interferometry

The application of multiple-beam shearing interferometry to lens focal-length measurement is described. A coated shearing plate interferometer was used in transmission to produce sharp multiple-beam fringes that rotate as the collimation of the incoming wave front from the lens under test changes. The test lens was used to collimate light from a point source that was translated longitudinally, and the focal length was determined from the rate of rotation of the fringes as the source moved. This method is simple, accurate, and lends itself to automatic determination of focal length.     

Effects of unparallel grating planes in Talbot interferometry

The properties of moiré fringes in Talbot interferometry are analyzed when the angle between the two grating planes is small. The results indicate that the tilt angle of the moiré fringes, observed just behind the test grating, is sensitive to the small angle. Based on this sensitivity, several features of parallelism of the two grating planes are presented, and the influence of the small angle when checking the beam collimation of a lens is also discussed. The validity of the theoretical analysis is illustrated by experiment.     

Lau effect and beam collimation

Abstract

We report a new phenomenon in showing that the rotation sensitivity of Lau fringes depends not only on spatial coherence of the illumination used but also on its convergence or divergence. This finding could be usefully applied to beam collimation and focal length measurement.     

Phase Measurement by Differentiating Interferometric Fringes

Abstract

In this paper we discuss a method of wavefront phase detection by differentiation of the interferometric fringes. We show that only one phase step is required to determine the wavefront phase. In the process of differentiation, Moiré fringes are formed. Conditions on the angle of tilt introduced between the interfering beams to overcome the formation of Moiré fringes are also presented. The method is shown to be suitable for techniques such as null optical testing or interferometric methods where comparison is made between a master and a test. We present in this paper the theory of the method and experimental results obtained for both specular and speckle interferometric fringes.     

Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.     

平板剪切干涉法检验激光准直性的改进

本文提出了利用平板剪切干涉法检验激光束准直性的一种改进方案。以两组干涉条纹的平行作为准直性判据,既简化了检测过程,又可使检验灵敏度提高一倍。     

Improved collimation testing technique

Laser collimation is an essential part of many experimental setups including optical coherent processors, image transformers, Fourier transform generators, and 4f-based optical systems. A device is required to test the collimation of lasers in such experiments. We are proposing a modification in the existing two-lens-system (TLS)-based collimation testing technique in which a combination of a convex and a concave lens is placed in space between the collimating lens and the first grating of the conventional setup. In the proposed method, we change the position of the second TLS component, placing it between the two gratings. The proposed idea not only reduces the size of the system but also gives improved results. Theoretical modeling and simulated and experimental results are presented to support our idea.     

A phase-conjugate Twyman-Green interferometer with increased sensitivity for laser beam collimation

Abstract

A Twyman-Green interferometer having a phase-conjugate mirror in one arm and double mirror in another arm is described to measure divergence and to check the collimation of a laser beam. It uses an internally self-pumped phase conjugation in BaTiO₃ crystal as phase-conjugate mirror. The use of double mirror gives a dual interference field which results in improved sensitivity in collimation testing. The dual-field interferogram is also useful in easily distinguishing between the divergent and convergent nature of the test beam. Measurement results are presented.     

用同步辐射实现X射线干涉技术的实验研究

根据Ｘ射线干涉的特点，制出ＬＬＬ型Ｘ射线干涉仪器。Ｘ射线源选用同步辐射光，充分利用其强度大，波长丰富和准直性好的优点，在北京同步辐射实验室利用４Ｗ１Ａ束线进行了Ｘ射线干涉实验，在拍摄的底片上比较清楚地观察到了Ｘ射线霈条纹。     

General inclination effects produced by a beam-splitter grating in talbot interferometry with crossed gratings

The effects of an arbitrary small inclination between the two crossed gratings on moiré fringes in Talbot interferometry are discussed. The small inclination is formed by the rotation by a small angle gamma of the beam splitter's grating about the axis that is on the plane of the grating and has an arbitrary angle delta with respect to the lines of the grating. The results indicate that the small inclination has a great influence on measurements for which Talbot interferometry is applied, such as beam collimation and measurement of the focal length of a lens. The theoretical analyses are proved by experimental results. Some methods for judging the size of a small inclination are also proposed.     

Effects of a Small Inclination Misalignment in Talbot Interferometry by Use of Gratings with Arbitrary Line Orientation. II. Experimental Verification

The theoretical results of the effects of a small inclination misalignment, which is formed by rotation of the beam-splitter grating around the axis on the grating plane when the axis has an arbitrary angle with respect to the line direction of the grating, between the two grating planes on the moiré fringes in the Talbot interferometry are verified by experiment. The experimental results coincide well with theoretical ones. Consequently, the effect of the small arbitrary inclination on practical measurements based on the Talbot interferometry is further explained by an example that examines the beam collimation of a lens, and the advantages and limitations of the effect are also discussed.     

Collimation testing with circular gratings

We investigate the testing of collimation by Talbot interferometry with circular gratings. Circular gratings are immune to misalignment owing to rigid body rotations in a plane perpendicular to the optic axis. Experimental results of the investigation are presented, and they are in good agreement with the theoretical predictions. Experimental results verify that collimation testing with circular gratings can be superior to that with linear dual-field gratings.     

Collimation testing with linear dual-field, spiral, and evolute gratings: a comparative study

A comparative study of the performance of linear dual-field, spiral, and evolute gratings for collimation testing with Talbot interferometry is reported.     

Modified double-wedge-plate shearing interferometer for collimation testing

A modified configuration of the double-wedge-plate shearing interferometer for collimation testing is described. Results of the measurements to determine the setting sensitivity with this configuration are presented.     

Offset of coherent envelope position due to phase change on reflection

Different materials with different phase changes on reflection affect the surface-height measurement when interferometric techniques are employed for testing objects constructed of different materials that are adjacent to one another. We test the influence of this phase change on reflection when vertical scanning interferometry with a broadband source is used. We show theoretically and experimentally that the strong linear dependence of the dispersion of the phase change on reflection preserves the shape of the coherence envelope of the fringes but shifts it along the optical axis by approximately 10-40 nm for metallic surfaces.     

Wave-front analysis method of circular aperture sampling for collimation testing

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence.     

Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry

We describe an electronic speckle-pattern interferometry system for analyzing addition fringes generated by the transient deformation of a test object. The system is based on a frequency-doubled twin Nd:YAG laser emitting dual pulses at a TV camera field rate (50 Hz). The main advance has been the automatic, quantitative analysis of dual-pulse addition electronic speckle-pattern interferometry data by the introduction of carrier fringes and the application of Fourier methods. The carrier fringes are introduced between dual pulses by a rotating mirror that tilts the reference beam. The resulting deformation-modulated addition fringes are enhanced with a deviation filter, giving fringe visibility close to that of subtraction fringes. The phase distribution is evaluated with a Fourier-transform method with bandpass filtering. From the wrapped phase distribution, a continuous phase map is reconstructed with an iterative weighted least-squares unwrapper. Preliminary results for a thin plate excited by an acoustic shock show the suitability of the system for the quantitative evaluation of transient deformation fields.