High precision refractometry based on Fresnel diffraction from phase plates

Abstract

When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.

Fresnel Diffraction from Phase Steps and Its Applications

“…A parallel beam of light illuminates a transparent plate mounted on goniometer G. A detector mounted perpendicular to the transmission beam, records the diffraction fringes of the plate edge. As it has been shown in references [17,18], by rotating the plate and recording the repetition of the visibility, one can measure the plate refractive index, plate thickness, light wavelength with high precision, provided one or two of the mentioned parameters are given [17,18]. Installing the plate inside a cell containing a liquid, and rotating the cell, permits one to measure the refractive index of the liquid [18].…”

“…6(a), the visibility of the three central fringes [11]: [11]. We emphasize that the accurate specification of 0  , which is possible by precision of / 200  , allows us to measure the step height, the refractive index of the plate, and the wavelength of the incident light very accurately, provided one or two of the referred parameters are given [17][18][19]. So far, considering the diffraction effect, we studied the interference of two parallel wavefronts with common border plane that do not overlap in ray optics approach.…”

Applications of Fresnel diffraction from the edge of a transparent plate in transmission

“…Therefore, the visibility range remains between 0 and 1 at any incident angle. This kind of transparent step can be replaced by the plate used in [17] for more precise measurement of the refractive indices of liquids and gases. Also, by coating a transparent film in a step shape on a transparent substrate, the technique can be applied to the measurements of the film thickness and its refractive index.…”

“…But recently the Fresnel diffraction from phase steps have been studied rather in detail [10][11][12], and it has been shown that, by modest optics, the effect can be applied to accurate and reliable measurements of refractive index [13], film thickness [14], index profile of optical fiber [15], and nanometer displacements [16]. In our previous work, applying Fresnel diffraction from the edge of a transparent plane-parallel plate, we measured the refractive indices of transparent solids and liquids [17]. In the continuation of the work, we show that the technique is very adequate for the measurement of dispersion in plate shape samples in a wide range of thicknesses-less than 1 μm up to several millimeters.…”

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].…”