Optical refractometry based on Fresnel diffraction from a phase wedge

Abstract

A method that utilizes the Fresnel diffraction of light from the phase step formed by a transparent wedge is introduced for measuring the refractive indices of transparent solids, liquids, and solutions. It is shown that, as a transparent wedge of small apex angle is illuminated perpendicular to its surface by a monochromatic parallel beam of light, the Fresnel fringes, caused by abrupt change in refractive index at the wedge lateral boundary, are formed on a screen held perpendicular to the beam propagation direction. The visibility of the fringes varies periodically between zero and 1 in the direction normal to the wedge apex. For a known or measured apex angle, the wedge refractive index is obtained by measuring the period length by a CCD. To measure the refractive index of a transparent liquid or solution, the wedge is installed in a transparent rectangle cell containing the sample. Then, the cell is illuminated perpendicularly and the visibility period is measured. By using modest optics, one can measure the refractive index at a relative uncertainty level of 10(-5). There is no limitation on the refractive index range. The method can be applied easily with no mechanical manipulation. The measuring apparatus can be very compact with low mechanical and optical noises.

Fresnel Diffraction from Phase Steps and Its Applications

“…When a parallel beam of light strikes a step of height h at angle of incidence , Fig. 3(a), the phase difference of the reflected wavefronts is [15]:…”

Measurement of thickness of thin film by fitting to the intensity profile of Fresnel diffraction from a nanophase step

“…Using this technique, i.e., the visibility method, the step heights in the range of few tens nanometers up to several millimeters have been measured [23,24]. Also, the visibility change versus step height or incident angle in 1D FD from PS has been applied to the measurements of plate thickness, wavelength, and dispersion relation [23], nano displacement [25], refractive indices of solids and liquids [26][27][28], specification of the temperature profile around a very thin hot wire [29], refractive index of fiber [30], spectral modification by singular line [31], coherence length, correlations and shape of the spectrum [32], nonlinear refractive index [33] and refractive index of the transparent films [34], phase step diffractometer [35] and its application to wavemetery [36], focal/back-focal length measurement [37,38], measurement of thickness of thin film by white light diffractometry [39] and phase singularity [40]. Also, the FD from a step with two different materials on its both sides in the reflection mode has been theoretically formulated [41].…”

Quantitative phase imaging based on Fresnel diffraction from a phase plate

“…Thus far, Fresnel diffraction from a phase step is studied [27][28][29] and widely considered in the context of different metrological applications, e.g., the measurement of refractive indices of solids and liquids [30][31][32], thickness of films and plates [33], focal length of an imaging system [34], etching rate of glass steps [35], and determination of the off-axis angle and the wavelength of light [36].…”