Wang-Tsung Wu

An alternative bend-testing technique for a flexible indium tin oxide film

The two-dimensional refractive index distribution of a flexible indium tin oxide film deposited on a PET layer is measured before/after the bend-testing with an alternative technique based on Fresnel equations and the heterodyne interferometry. Their standard deviations are derived and they vary more obviously than the resistance variations measured in the conventional method. Hence the standard deviation of the refractive index can be used as the indicator to justify the durability of a flexible indium tin oxide film. The validity is demonstrated.

High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique

In a modified Twyman-Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.

Alternative method for measuring the full-field refractive index of a gradient-index lens with normal incidence heterodyne interferometry

A linearly/circularly polarized heterodyne light beam coming from a heterodyne light source with an electro-optic modulator in turn enters a modified Twyman-Green interferometer to measure the surface plane of a GRIN lens. Two groups of periodic sinusoidal segments recorded by a fast complementary metal-oxide semiconductor camera are modified, and their associated phases are derived with the unique technique. The data are substituted into the special equations derived from the Fresnel equations, and the refractive index can be obtained. When the processes are applied to other pixels, the full-field refractive-index distribution can be obtained similarly. Its validity is demonstrated.

Method for measuring the refractive index distribution of a GRIN lens with heterodyne interferometry

Based on the Fresnels equations and the heterodyne interferometry, an alternative method for measuring the refractive index distribution of a GRIN lens is presented. A light coming from the heterodyne light source passes through a quarterwave plate and is incident on the tested GRIN lens. The reflected light passes through an analyzer and an imaging lens; finally it enters a CMOS camera. The interference signals produced by the components of the s- and the p-polarizations are recorded and they are sent to a personal computer to be analyzed. In order to measure the absolute phases of the interference signals accurately, a special condition is chosen. Then, the interference signals become a group of periodic sinusoidal segments, and each segment has an initial phase ψ with the information of the refractive index. Consequently, the estimated data of ψ are substituted into the special equations derived from Fresnels equations, and the refractive index distribution of the GRIN lens can be obtained. Because of its common-path optical configuration, this method has both merits of the common-path interferometry and the heterodyne interferometry. In addition, the phase can be measured without reference signals.

Two-wavelength full-field heterodyne interferometric profilometry

An alternative full-field interferometric profilometry is proposed by combining two-wavelength interferometry and heterodyne interferometry. A collimated heterodyne light is introduced into a modified Twyman–Green interferometer, the full-field interference signals are taken by a fast CMOS camera. The sampled intensities recorded by each pixel are fitted to derive a sinusoidal signal with the least-square sine wave fitting algorithm, and its phase can be obtained. Comparing the phase of the reference point, the relative phase of the pixel can be calculated. Next, the same measurement is made again at a different wavelength. The relative phase with respect to the effective wavelength can be calculated and the profile of the tested sample can be derived with the two-wavelength interferometric technique. Its validity is demonstrated. It has merits of both two-wavelength interferometry and heterodyne interferometry.

Optimal sampling conditions for a commonly used charge-coupled device camera in the full-field heterodyne interferometry

The processes to derive the associated phase of an interference signal from the data of a series of recorded frames are performed, and we find that the sampling frequency being lower than the Nyquist sampling rate can also be applied to the full-field heterodyne interferometry. Two optimal sampling conditions for a commonly used CCD camera are proposed based on the relation between the heterodyne frequency and the contrast of the interference signal under the condition that the phase error is set to be 0.05 deg.

Method for gauge block measurement with the heterodyne central fringe identification technique

In a modified Michelson interferometer, the top face of the wringing platen is first identified using the heterodyne central fringe identification technique. Then the reference mirror located in the other arm is moved by a precision translation stage until the top face of the tested gauge block is also identified with the same technique. The displacement of the mirror is exactly equivalent to the length of the tested gauge block. The measurable range of the interferometer relates to the maximum travel range of the translation stage and its uncertainty depends on the uncertainty of the heterodyne central fringe identification method and the resolution of the translation stage.

Nano-roughness measurements with a modified Linnik microscope and the uses of full-field heterodyne interferometry

A collimated heterodyne light enters a modified Linnik micro- scope, and the full-field interference signals are taken by a fast CMOS camera. The sampling intensities recorded at each pixel are fitted to derive a sinusoidal signal, and its phase can be obtained. Next, the 2-D phase unwrapping technique is applied to derive the 2-D phase distribu- tion. Then, Ingelstams formula is used to calculate the height distribu- tion. Last, the height distribution is filtered with the Gaussian filter, the roughness topography and its average roughness can be obtained and its validity is demonstrated.

Two-dimensional refractive index distribution measurement of a GRIN lens

Based on the Fresnels equations and the phase-shifting method, an alternative method for measuring the refractive index distribution of a GRIN lens is presented. A linearly/circularly polarized light in order enters a modified Twyman-Green interferometer, in which an electro-optical modulator is used as a phase shifter. In the interferometer, the light beam is divided by a beam-splitter into two beams, a reference beam and a test beam. After they are reflected by a plane mirror and the tested GRIN lens, respectively, they are combined together and pass through an analyzer. The analyzer extracts the same polarized components to interfere each other, and the full-field interference signals produced by the components of the s- and the p-polarizations can be obtained. The full-field interference signals are taken by a CMOS camera. The phase differences can be obtained by using the four-step phase-shifting interferometric method. Substituting these two groups of data into special equations derived from Fresnel equations, and the two-dimensional refractive index distribution of the GRIN lens can be calculated. Its validity is demonstrated and has some merits such as simple optical configuration, easy operation and high resolution.

Step height measurement by using heterodyne central fringe identification technique

A simple method for measuring a step-height sample is presented with the heterodyne central fringe identification technique and a precision translation stage. This method can accurately point out the zero optical path difference position such that the optical path lengths of two arms of the interferometer are absolutely equivalent. Thus, the two surfaces of the step-height sample can be identified sequentially with the translation stage. The displacement of the translation stage is equal to the step-height of the test sample. The feasibility of the technique is demonstrated. The measurable range is not limited by the coherence length of the light source. The measurement accuracy depends on the uncertainties of the heterodyne central fringe identification method and the translation stage. In our setup, we have a 100 mm measurable range and a 4 nm uncertainty. The wavelength stability of the light source has a minor effect on the measurement.