Determination of refractive indices of liquids by Fresnel diffraction

doi:10.1016/j.optlastec.2009.02.007

Optics & Laser Technology

Volume 41, Issue 7, October 2009, Pages 892-896

https://doi.org/10.1016/j.optlastec.2009.02.007 Get rights and content

Abstract

We demonstrate an easy, reliable, applicable, and sensitive method to measure refractive index of liquids by using Fresnel diffraction. In this method a cylindrical glass rod, in general, or an optical fiber in special case, is immersed into a liquid. Physical parameters of the rod, like radius and refractive index, should be well known. Then, the normalized intensity distribution on the Fresnel diffraction pattern of a plane wave diffracted from the immersed fiber is measured. Thereafter, refractive index of the liquid is evolved by the least-square method. This method applied to determine the refractive index of four liquids; pure water, 2-propanol (isopropanol), acetone and methanol. Index of refraction of each one has been acquired for four visible wavelengths. A theoretical approach and experimental results is presented.

Introduction

Refractive index is one of the important optical parameters of material. Its accurate measurement plays an important role in physical and chemical applications. Precise determination of refractive index gives an insight into purity and reproducibility of the material for instrumentation. Accurate knowledge of refractive index and its variation with concentration leads to identification of material in chemical proceedings. Nowadays, there are different techniques to determine the refractive index of liquids and dispersion. Interferometric methods [1], [2], [3], [4], [5], [6], [7], [8], minimum angle of deviation and autocollimation methods [9], [10], [11], liquid–prism interface methods [12], [13], ellipsometry methods [14], [15] are some of these methods. Abbe refractometers are applied as a standard tool for measuring the refractive index of liquids [16]. They are designed to give refractive indices of the yellow light of sodium D line ( $λ = 589.3 nm$ ) without using a sodium lamp. This type of instrument has a prism with known refractive index with a face to which the sample is presented. To calibrate the measurement in the required range, standard liquids are needed.

Recently, phase diffraction due to changing of the phase of a wavefront traversed across a phase object has been considered to reconstruct the index of refraction of optical fibers [17]. In this method an optical fiber is immersed into an arbitrary liquid perpendicular to the laser beam. By fitting the theoretically normalized intensity distribution on the experimentally obtained normalized intensity of a diffracted plane wave from the fiber, refractive index of the fiber's core, could be reconstructed. This method is sensitive to the refractive index difference between the surrounding medium-cladding. Considering the latter leads to measure the refractive index of the surrounding medium, provided that, refractive index of the rod (or the fiber cladding) to be well known.

This paper is organized as follows. In Section 2 theoretical approach and simulation study are presented. In Section 3 experimental procedure and results are covered. Conclusions are included in Section 4.

Section snippets

Theoretical approach

Our approach is based on diffraction of a plane wave from a cylindrical glass rod. Since, we could not find a rod glass with an optical quality better than the optical fiber, therefore, a single-mode optical fiber was used.

In Fig. 1(a), a monochromatic parallel beam of light impinges an optical fiber perpendicular to its axis. The amplitude of the diffracted wave in the observation plane at an arbitrary point Q in Fig. 1(b) is given by [17] $U (Q) = \frac{K^{'} \exp (- i ϕ_{Su})}{B} (1 + C (α) - C (β) + i [1 + S (α) - S (β)] + B \{\int_{- b}^{- a} \exp [-$

Experimental procedure and results

A schematic of the experimental set up is sketched in Fig. 3. A laser beam is expanded into a parallel beam of the diameter $40 mm$ . He–Ne laser of wavelength 632.8 nm and ${Ar}^{+}$ at lines 514.5, 488.0, and 457.9 nm are sources were used. The beam strikes the immersed optical fiber into a liquid, perpendicular to its axis. The intensity distributions are recorded before and after installing the fiber by an astronomical CCD of pixel size $9 \times 9 μ m$ , specified by “sbig ST-7E”, which is passed to a computer for

Conclusions

1.
This study shows that the Fresnel diffraction from cylindrical glass (transparent) rod has high potential in evaluating refractive indices of liquids. It provides large volumes of reliable data in a relatively simple way.
2.
We demonstrated that the optical rod could be replaced by a single-mode optical fiber as long as fiber-to-CCD distance is greater than 40 cm.
3.
Another way to do this experiment is to use a phase strip instead of a rod or an optical fiber. This phase object may be created into a

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Determination of refractive indices of liquids by Fresnel diffraction

Abstract

Introduction

Section snippets

Theoretical approach

Experimental procedure and results

Conclusions

Opt Laser Technol

Refractive indices of water vapor and carbon dioxide at low pressure

J Opt Soc Am

Principles of optics

Liquid refractometer based on interferometric fringe projection

Opt Commun

Using interference in frequency domain for precise determination of thickness and refractive indices of dispersive material

J Opt Soc Am

Refractive index of liquid solution at low temperatures: an accurate measurement

Appl Opt

Stepwise interferometric method of measuring the refractive index of liquid samples

Appl Opt

Folded Jamin interferometer: a stable instrument for refractive index measurement

Opt Lett