High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry
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Abstract:
We show that using multiple shears in spectral shearing interferometry is a powerful technique for improving precision, thus enabling the measurement of more complex pulses and resolving phase ambiguities. We derive an efficient and robust optimal phase reconstruction algorithm for extracting the spectral phase from interferograms taken at an arbitrary number of different shears. We show that if the shear is easily adjustable then a multishear measurement always offers a superior precision, even when considering the loss of precision of the raw data necessitated by multiple acquisitions. We present numerical examples and demonstrate an experimental implementation of the measurement of a double pulse using two shears.Keywords:
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The measurement of a positioning stage with high precision is usually based on a laser interferometer.According to the principle of measurement,the measuring error of the interferometer should be about 1/3 to 1/2 of that in the positioning stage,so that the measuring results are believable only in this condition.Analyses show that there are different factors which influence the precision of the interferometer.The error calculation based on the analyses gives results that show the synthetic error of the laser interferometer measuring system is 12.3 nm,which is sufficient to meet requirements of the positioning stage because both of them are completely matched in precision.
Accuracy and precision
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A laser synthetic wavelength interferometer that is capable of achieving large displacement measurement with nanometer accuracy is developed. The principle and the signal processing method of the interferometer are introduced. The displacement measurement experiments and the comparisons with a commercial interferometer both in small and large ranges are performed in order to verify the performance of the interferometer. Experimental results show that the average errors and standard deviations of the interferometer are in accordance with those obtained from the commercial interferometer. The resolution and the nonlinearity of the interferometer are also discussed in detail. These results show that the development of the interferometer is reasonable and feasible.
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In order to obtain quantitative phase distributions from interferograms, phase retrieval composed of phase extracting and unwrapping is adopted in quantitative interferometric microscopy. However, phase unwrapping often requires a long time, limiting applications such as high-speed phase observations and measurements. In order to accelerate the processing speed, a phase unwrapping free Hilbert transform (HT)-based phase retrieval method is proposed. Though another background interferogram without a sample is needed, phase unwrapping can be omitted, saving a large amount of time for phase recovery. Additionally, the proposed HT-based method can maintain more sample details, thus providing high-accurate quantitative phase imaging. Considering its fast speed and high accuracy in phase retrieval, it is believed that the unwrapping free HT-based phase retrieval method can be potentially applied in high throughput cellular observations and measurements.
Phase Unwrapping
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In this work we present a parallel polarizing phase shifting interferometer based in a Double Cyclic Interferometer (DCSI) to analyze transparent samples. This system has the advantage of generating four beams that can interfere properly; this can reduce the number of captures needed in phase shifting interferometry. The interferometric system generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. For the processing of the optical phase data map, a parallel phase shift can be generated by placing a linear polarizer covering two patterns. We analyze the cases of four patterns with arbitrary shifts captured in two shots. The unwrapped phase is processed by Kreis methods. Experimental results obtained by the proposed interferometer are presented.
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Phase Unwrapping
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Principles and types of radial shearing interferometer are presented, and the advantages, disadvantages and problems existing are analyzed. Developments of radial shearing interferometer are reviewed and its important role in measurement of optical information is discussed.
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