Full-field refractive index distribution measurement of a gradient-index lens with heterodyne interferometry

Abstract

A light beam coming from a circular heterodyne light source with an electro-optic modulator is incident on a gradient-index lens obliquely. The reflected light passes through an analyzer and an imaging lens, and is recorded by a fast CMOS camera. A group of periodic sinusoidal segments recorded by each pixel is modified, and its associated phase is derived with a unique technique. The processes are applied to other pixels; the two-dimensional phase distribution can be obtained similarly. The estimated data are substituted into the special equations derived from Fresnel's equations, and the full-field refractive index distribution of the gradient-index lens can be obtained. This method has the merits of both common-path interferometry and heterodyne interferometry.

Designing Highly Precise Overlay Targets for Asymmetric Sidewall Structures Using Quasi-Periodic Line Widths and Finite-Difference Time-Domain Simulation

“…The incident light E 0 is linearly polarized with a wavelength of λ, and the polarization direction of 45 • with respect to the x-axis was divided into transmitted light E t and diffracted light E d by the top grating structure. According to the Jones matrix calculation [21,22], we can calculate the electric fields of E t and E d , and they can be written as…”

Glucose Concentration Measurement by All-Grating-Based System

“…)→AN1(45 • )→D1. According to the Jones matrix calculation [13][14][15], we can calculate the electric field of the lights passing through these two paths as 𝐸 , , and 𝐸 , , , and they can be written as…”

“…According to the arrangement of the optical configuration, the interference signal detected by detector D1 is composed of the p-polarization of the positive first-order diffracted light from G2 and the s-polarization of the positive first-order diffracted light from G1. After calculating the Jones matrix, this signal can be written as According to the Jones matrix calculation [13][14][15], we can calculate the electric field of the lights passing through these two paths as E t,G1+1,S and E r,G2+1,P , and they can be written as…”

“…In this study, a circular heterodyne interferometry [13] was used for the glucose concentration measurement. We simplify the configurations for convenience: (1) The BS we used in the experiment is ideal so that r P = 1 and r S = 1.…”