Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry

Abstract

We propose and demonstrate a novel technique for simultaneous measurement of the phase index, n(p) , the group index, n(g) , and the thickness, t , of transparent plates by use of a low-coherence interferometer. The output light from a superluminescent diode is focused upon the front plane of a transparent plate that is used as the sample. The sample stage is subsequently moved until the light is focused upon the rear plane of the plate. Measurement of the stage movement distance and the corresponding optical path difference allows us to determine both n(p) and n(g) . By placing the sample between two glass plates, we measured n(p) , n(g) , and t simultaneously, with an error of 0.3% or less, for nearly 1-mm-thick transparent plates, including glass and electro-optic crystals.

Digital Gradient Sensing Method to Evaluate Thermal Stress at Elevated Temperatures

“…We obtained in-plane stresses of the ZnS specimen at elevated temperatures using equation (5). illustrates the full-field variation of the in-plane stresses at 100 to 400°C with the room-temperature state as a reference.…”

“…Consequently, imaging systems used to monitor objects in environments at elevated temperatures have to contend with the non-uniformity of the refractive index of both air (caused by air convection) and the optical lens material (caused by thermal stress) [5,6].…”

Dual Interferometer System for Measuring Index of Refraction

“…Individually, each of these techniques falls short of the list of requirements shown in Table 1.1; they require prior knowledge of thickness, they measure the group index instead of the phase index (Hirai, 2003;Hirai, 2006;Murphy, 2000), they have insufficient accuracy (Fukano, 1999), they assume a dispersion curve (Hopler, 1991), the sample must be at least 1 mm thick (Haruna, 1998), or they are incapable of measuring a sample that must be in solution (Maruyama, 2002). Rather then discuss all of the various techniques and pointing out where they fall short of our measurement parameters, the novel technique used will be presented.…”

High-sensitivity surface-profile measurements by heterodyne white-light interferometer

“…White-light interferometry with a low-coherence light source has potential for measurement of the complex surface profile of 3-D objects with high accuracy and high sensitivity. [1][2][3] However, the homodyne technique is limited to normalsensitivity measurements because the visibility of the interference fringe is very poor in the case of interference between very weak probe light and strong reference light, which is usual in practical applications such as in the case of surfaces with very low reflectivity. Therefore, in whitelight interferometry, the heterodyne technique was developed by using the Doppler shift of light frequency, for example to study a living body with a high level of sensitivity and a resolution of several micrometers.…”