Talbot Interferometry for Focal Length Measurement Using Linear and Circular Gratings
Several methods for measurement of focal length of a positive lens involve the measurement of distances of the object and image planes from principal planes, which are mathematical planes; the positions of which are difficult to figure out accurately. The
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Abstract Several methods for measurement of focal length of a positive lens involve the measurement of distances of the object and image planes from principal planes, which are mathematical planes; the positions of which are difficult to figure out accurately. The Talbot method for focal length measurement is a method, which does not require the distances from the principal planes. Further Talbot interferometry can be used to measure focal length variation over the surface of a progressive power lens. A technique for the measurement of focal length using Talbot interferometry and moiré effect has been described. The Talbot image of a Ronchi grating placed just after a test lens is superimposed on the second grating to give us the moiré fringes. The angle of tilt of the moiré fringes can be used to find out the focal length. The effect of unequal pitches of the gratings on moiré formation is also investigated. The investigation is also carried out using binary gratings having equidistant circular rings (circular gratings). The theory and experimental results obtained with both types of gratings have been discussed.
1 Introduction A number of methods have been proposed and used for the measurement of focal length [1]. Combination of Talbot [2] and moiré phenomena [3] provides a method that is suited for the measurement of long focal length of a lens and large radius of curvature of a mirror. There has been large number of publications on this subject [4–12]. Use of both linear and circular gratings is made for the measurement of focal length.
R.K. Choudhary (&) S.M. Hazarika R.S. Sirohi Department of Physics, Tezpur University, Tezpur, Assam, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 I. Bhattacharya et al. (eds.), Advances in Optical Science and Engineering, Springer Proceedings in Physics 194, DOI 10.1007/978-981-10-3908-9_80
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2 Theory When a linear grating is placed in a collimated beam of monochromatic light of wavelength k, it images itself, due to diffraction, at equidistant planes from the grating: the separation between two consecutive self-image planes is the Talbot distance given by d2/k, where d is the pitch of the grating. When the illumination of the grating is by a spherical wave, the Talbot planes are not equidistant. The position of the nth Talbot plane is given by Sirohi [1] zsn ¼
k d2
n Rn
ð1Þ
where R is the radius of curvature of the wave at a plane where the linear grating is placed: here + sign stands for convergent spherical wave and − sign stands for divergent spherical wave. For the convergent wave illumination, the separation between consecutive Talbot planes keeps on decreasing while for divergent illumination, it keeps on increasing. Further the pitch at the Talbot plane is such as if the grating is projected, implying that the pitch decrease in convergent illumination and increases in divergent illumination. Figure 1 shows an experimental set-up for measuring focal length of a lens. There are two situations: in on
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