Browsing by Author "Su, D. C."

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A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry
(2008)
Hsieh, H. C.
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Jian, Z. C.
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Chen, Y. L.
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Hsieh, P. J.
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Su, D. C.
Based tin Fresnel equations and the phase-shifting interferometry, an alternative method for measuring the two-dimensional refractive index distribution of a material is presented. A linearly polarized light passes through a quarter wave-plate and is incident on the tested material. The reflected light propagates through an analyzer, and then the interference signal can be obtained. The special equations to estimate the phase of the interferometric signal can be derived by using Fresnel equations. Next, the associated two-dimensional phase distribution is measured by the four-step phase-shifting interferometry. Then, the measured data are substituted into the special equations derived previously, and the two-dimensional refractive index distribution of the tested material can be obtained.
An alternative method for measuring the index profile of a gradient-index lens
(2011)
Hsieh, H. C.
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Wu, W. C.
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Chang, W. Y.
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Hsu, F. S.
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Su, D. C.
An alternative method for measuring the index profile of the GRIN lens is proposed based on Fresnel's equations and the common-path phase-shifting interfermetry. A light beam composing of the right- nd the left- ircularly polarized components is obliquely incident on the tested GRIN lens and the reflected light passes through an analyzer. The light is collected and imaged by an imaging lens to a CMOS camera. Four interferograms under different additional phases are taken and Carre's phase-shifting method is used to calculate the full-field phase distribution. Next, the estimated data are substituted into the special equations derived from the Fresnel's equations, and the index profile of the GRIN lens can be obtained. Its validity has been demonstrated. It has both merits of the common-path interferemetry and the phase-shifting interferemetry.
Full-field absolute phase measurements in the heterodyne interferometer with an electro-optic modulator
(2009)
Chen, Y. L.
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Hsieh, H. C.
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Wu, W. T.
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Su, D. C.
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光電工程學系
A novel method for full-field absolute phase measurements in the heterodyne interferometer with an electro-optic modulator is proposed in this paper. Instead of the commonly-used half-wave voltage to drive the electro-optic modulator, a saw-tooth voltage signal with the amplitude being lower than its half-wave voltage is used. The interference signals become a group of periodical sinusoidal segments. The initial phase of each sinusoidal segment depends on the phase difference induced by the test sample. In real measurements, each segment is taken by a fast camera and becomes discrete digital points. After a series of operations, the starting point of the sampled sinusoidal segment can be determined accurately. Next, the period of the sampled sinusoidal segments is lengthened and they can be modified to a continuous sinusoidal wave by using a least-square sine fitting algorithm. The initial phase of the continuous sinusoidal wave can also be estimated. Subtracting the characteristic phase of the modulator from the initial phase, the absolute phase measured at the pixel can be obtained without the conventional reference signals. These operations are applied to other pixels, and the full-field absolute phase measurements can be achieved. The phase retardation of a quarter-wave plate is measured to show the validity of this method.
Method for measuring the refractive index distribution of a GRIN lens with heterodyne interferometry
(2009)
Hsieh, H. C.
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Chen, Y. L.
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Wu, W. T.
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Su, D. C.
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光電工程學系
Based on the Fresnel's 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 quarter-wave 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 psi with the information of the refractive index. Consequently, the estimated data of psi are substituted into the special equations derived from Fresnel's 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.
Step Height Measurement by Using Heterodyne Central Fringe Identification Technique
(2010)
Wu, W. T.
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Hsieh, H. C.
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Chen, Y. L.
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Chang, W. Y.
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Su, D. C.
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.
Two-dimensional refractive index distribution measurement of a GRIN lens
(2010)
Hsieh, H. C.
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Chen, Y. L.
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Wu, W. T.
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Chang, W. Y.
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Su, D. C.
Based on the Fresnel's 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.