Haidinger Fringes Research Articles

Determination of optical constants for thin-walled glass cell based on Haidinger fringes

A validated method based on Haidinger fringes has been proposed to measure the optical constants for thin-walled glass cells. The method can significantly enhance measurement accuracy by utilizing the reflected spectrum to determine the optical constants of the sample. The reflected light off the inner and the outer surfaces of the cell combined together and formed the interferential pattern (Haidinger fringes) detected by the photodiodes. Taking into account that the sample in our experiment is a sealed cell, we deliberately set the incident angle to a non-zero value. First, the measurement principle has been analyzed, and subsequently, the relevant experimental platform has been established. To reduce random errors, we recalibrated the relationship between the frequency of the laser and the operating temperature. Furthermore, the incident angle has been accurately estimated using the method of non-linear least squares. Finally, the weighted average, considering correlated uncertainties for all measurements, is 1.873 ± 0.005 016 mm, which showcases clear advantages over conventional mechanical methods that risk potential damages.

An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes.

An interferometric system is proposed for measuring the thickness of parallel glass plates by analyzing Haidinger fringes. Although a conventional Haidinger interferometer can measure thickness without 2π ambiguity using positions of peak and valley points in the interferogram, measurement accuracy is directly affected by the number of these points involved in the calculation. The proposed method obtains phase values over the entire interferogram by analyzing the quadrature Haidinger fringes generated by a current modulated laser diode. Therefore, it can achieve high speed measurement and nanometric resolution without mechanical rotation and thickness limitation of specimens. In the experiments, the standard deviation of repeated thickness measurement was evaluated as less than 0.3 nm, and the measured thickness profile of the proposed system agreed with that of a conventional thickness interferometer within ±15 nm. We also discussed the required accuracy of refractive index of specimens to implement the proposed method successfully and presented an exemplary measurement result of a multi-layer coated sample having a discontinuous thickness profile.

Measurement of thickness profiles of glass plates by analyzing Haidinger fringes.

We report what we believe is a novel method for measuring the thickness profiles of plane parallel plates by analyzing their Haidinger fringes. When an extended monochromatic source is viewed through a ∼1-mm-thick plate, concentric transmission-type Haidinger fringes can easily be observed. Small variations in the plate thickness result in changes in the radii of the ring fringes. In this study, we scanned 20-mm-diameter fused silica and BK7 plates while tracing a specific ring in each fringe pattern to measure the thickness profiles of the plates, achieving an uncertainty of 2nm in the measurements of the thickness differences between two locations on each plate.

Simple technique for the generation of white-light Haidinger fringes with cyclic optical configuration

What we believe to be a new technique for the generation of white-light Haidinger's-type fringes using a cyclic path optical configuration is presented. Differences of the fringes with common Haidinger fringes have been discussed, and the result obtained with a white-light source is presented.

Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates

A quick estimation of the thickness of thin films deposited on glass plates is described in this paper. The principle of the method is based on the measurement of the Haidinger fringes generated by the film. For ease of observation and measurement, a commercial Fizeau-type interferometer such as a Zygo interferometer using a large angle of illumination has been used. The simple modification to observe the Haidinger fringes with the Fizeau-type interferometer is also described. The thickness of the film is related to the diameters of the Haidinger fringes. It is possible to estimate the thickness quickly by counting the number of fringes. A more accurate estimate can be obtained by the measurement of the diameters of the fringes and using these data in a formula that relates these two to the thickness of the film. The method is found to be useful for measuring the thickness of dichromated gelatin films (DCG) coated on a substrate to make holographic optical elements. The accuracy in estimating the thickness of the film is of the order ± 1 μ m . The method is entirely non-destructive and works well in the thickness range of 5– 150 μ m .

Low cost method for subarcsecond testing of a right angle prism

This paper describes a method for testing a right angle prism, or any other optical component having a right angle, to subarcsecond accuracy. The method makes use of Haidinger fringes and is simple to use. Unlike autocollimation and Fizeau interferometer methods, it does not involve an expensive optical setup and has no aperture restriction. The sensitivity of the method can be suitably modified by changing the test setup parameters.

Measurement of elastic deformation of rotating objects by using holographic interferometry

Double-exposure holographic interferometry is applied to measure the elastic deformation of rotating objects. The first exposure is made in the rotating state and the second in the static state. The precise positioning of the object between the two exposures is obtained by using holographically produced Haidinger's fringes.

Surfaces of Constant Order for Parallel-plane Interferometers

Two-dimensional curves of constant order, revolved to give three-dimensional surfaces, are presented as a simple and unified way of visualizing many of the properties of parallel-plane interferometers. Sections of these curves and surfaces give the locations of interference fringes, and constructions on the two-dimensional diagrams give many of the properties of these fringes in quantitative detail. Instruments considered are the Fabry-Perot interferometer, using both Haidinger and Edser-Butler fringes, interference filters, and the Michelson interferometer in its parallel gap configuration, including its use as a Fourier spectrograph.

Cube-Corner Fabry-Perot Interferometer

Polarized Haidinger fringes have been observed in a Fabry-Perot interferometer with one flat replaced by a cube-corner prism. Orientation of the polarization planes of the fringes and their relative phase shifts have been measured. Some applications are suggested.

Haidinger Fringes in a Basal Section of Calcite

Haidinger fringes were obtained with a partly silvered basal section of calcite. Two sets of fringes were observed: one associated with the ordinary ray, and one with the extraordinary ray. With a linear polarizer the two series are separated on the pattern diameters parallel to the polarizer axes. The oppositely polarized fringes periodically coincide and give rise to beats or a Moiré. An analysis is made to show that this coincidence occurs when the ratio of the fringe numbers of the coinciding fringes is the ratio of the squares of the two principal refractive indices.

A New Interference Effect

IN the course of a class experiment demonstrating the circular Haidinger fringes produced by monochromatic illumination of a thin film between silvered surfaces, it was noticed that coloured circular fringes could be seen if white light illumination was used. The effect is best seen by looking through the film (for example, a thin air film between silvered glass plates, or a thin mica film silvered on both sides) with the eye accommodated for infinity, at a strong point source such as a 'Pointolite'. For normal illumination, the point source is seen surrounded by several rainbow fringes, as in Fig. 1, while for oblique illumination, a sharp circular white-light fringe is seen passing through the source, with concentric rainbows inside and outside, as in Fig. 2. Unlike the usual monochromatic fringes, these fringes are not influenced by lack of accurate parallelism of the silvered surfaces. The sharpness of the white-light fringe improves with increase of the reflexion coefficient of the surfaces; with plates heavily silvered by the Tolansky technique1, the fringe width is limited only by the size of the source.

Newton's Rings and Haidinger's Fringes by Reflection from Platinum-Sputtered Surfaces

Newton's Rings and Haidinger's Fringes by Reflection from Platinum-Sputtered Surfaces