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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 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 ȥ with the information of the refractive index. Consequently, the estimated data of ȥ 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.

Based on 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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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.