Measurement of residual wedge angle with a reversal shear interferometer
Introduction
There are standard techniques for measurement of residual wedge angle of high optical quality transparent parallel plates as given in Refs. [1], [2], [3], [4], [5]. Fizeau interferometer is the most common instrument for this purpose. By measuring the spacing of the Fizeau fringes formed due to the interference of laser beams reflected from the two plane surfaces of the parallel plate, one can determine the residual wedge angle [3]. Measurement uncertainty arises when the fringe spacing is greater than the diameter of the parallel plate or the beam aperture. For instance, with He–Ne () laser, Fizeau fringes has limitations for residual wedge angle below 1 arc sec for parallel plate with clear apertures diameter. A technique which has no such limitations and which is suitable for the measurement of low residual wedge angle in sub arc sec regime has been presented in Ref. [6]. An interferometric technique to simultaneously test both surface flatness and parallelism of parallel plates has been reported [7]. Hibino et al. [8] reported a wavelength scanning Fizeau interferometer for testing a nearly parallel plate.
In the present paper, we describe a new technique for determination of residual wedge angle of high optical quality transparent parallel plate from the measurement of angular tilt of the two beam interference fringes of a reversal shear interferometer [9], [10], [11] (RSI) caused by the residual wedge angle of the parallel plate, which is placed in the path of the incident beam of the RSI, with its wedge orthogonal to the beam folding axis of the RSI.
Section snippets
Principle
Optical schematic of the set up used in the present experiment is shown in Fig. 1. Light from a He–Ne () laser source is allowed to pass through a spatial filtering arrangement consisting of a microscope objective (MO) and an appropriate pinhole (PH) placed at the front focal plane of the microscope objective. Pinhole is also situated at the back focal plane of a well-corrected telescope objective (TO) and thus an expanded collimated beam is produced. The plane wave-front corresponding
Theoretical analyses
We define sensitivity of measurement () as the rate of change of angular displacement w.r.t. the wedge angle . Differentiating Eq. (5) w.r.t. we obtainAccuracy of measurement of would depend upon the measurement accuracies of and , i.e., . The differentiation of giveswhere represent the measurement inaccuracy of and represent measurement inaccuracies of angular displacement and initial
Results and discussion
Optical schematic of the experimental set up used for the measurement of residual wedge angle of high optical quality transparent nearly parallel plate is shown in Fig. 1. Results obtained for a sample plate of diameter 50.0 mm are presented. Fringes obtained without the parallel plate and that with parallel plate are shown in Fig. 7(a), (b), respectively. Plate beam splitters have been used in our experiment.
The hollow roof prism used in the experiment has been obtained by using plane glass
Conclusion
A reversal shear interferometer-based technique for determination of residual wedge angle of high optical quality transparent parallel plate has been presented.
Though the principle of measurement is apparently similar to that of the Fizeau technique [6], there is significant improvement of sensitivity and measurement accuracy and a maximum of two-fold increase can be obtained for small residual wedge angle with the present technique.
An estimate of the order of magnitude of the lower limit of
Acknowledgements
We thank scientific and technical staffs of our Optical Workshop for their technical support.
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Cited by (14)
Measuring the wedge of flat optical windows
2021, Optics CommunicationsCitation Excerpt :Refractive index of the substrates needs to be known with a minimum accuracy for precisely determining the wedge angle. If the refractive index is known, the wedge angle can be determined by using autocollimators [1–3], diverse interferometers methods such as Twyman Green [4], Haidinger [5,6], and, specially, Fizeau [7–10] and shearing interferometers [11–14], or holographic methods [15,16]. Techniques for simultaneous measurement of refractive index and wedge angle have been also proposed [10,17–19].
Low-coherence phase-shifting shearing interferometer for measuring parallelism of parallel surfaces of transparent samples
2020, Optics and Laser TechnologyCitation Excerpt :To ensure their quality, examinations of thickness and parallelism between the two opposite surfaces are in great demand [1–5], of which the latter is particularly complicated and this motivates the researchers to develop appropriate instruments capable of undertaking the task. Up to date, three types of instruments have been proposed, they are mechanical probes, beam-direction examiners, and optical interferometers; where the mechanical probes, which can be micrometers or dial-gauges, examine the parallelism by inspecting the thickness distribution of the sample; the beam-direction examiners, which can be auto-collimators [6–9] or similar apparatus [10], examine the parallelism by detecting the angle between the beams reflected from the surfaces of the plate [6–9] or the angle deviation of the beam transmitting through the plate [6–10]; and the optical interferometers, which are based on the theory of Fizeau [11–14], Lau [15], cyclic [16,17], or reversal shear interferometry [18], measure the parallelism by recognizing the characteristic of the interference pattern, e.g. pattern fringe spacing or pattern centroid location. The beam-direction examiners and optical interferometers are with the features of no-contact and high measurement sensitivity, they are therefore more acceptable than the mechanical probes.
Measurement of wedge angle of a transparent parallel plate using quasi-monochromatic light source and phase shifting interferometry
2011, Optics CommunicationsCitation Excerpt :In the reflection methods, using Fizeau fringes (FF) [1], which is most common, the RWA is measured from the spacing of the two beam FF formed due to the interference of collimated light beams (Fresnel) reflected from the two surfaces of the PP, while in Haidinger fringe technique [2], parallelism is determined by measuring the shift of the center of the circular fringe system (formed due to the interference of divergent laser beams (Fresnel) reflected from the two surfaces of the PP) from the real or virtual point source. In the transmission methods, angular deviation suffered by the collimated beam passing through the PP is interferometrically measured [3,4]. A technique for the measurement of RWA of a PP using a multi-pass optical configuration is discussed in ref. [5].
Simple measurement of a wedge angle based on subwavelength grating
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