Elsevier

Optics Communications

Volume 482, 1 March 2021, 126602
Optics Communications

A new multiplexed system for the simultaneous measurement of out-of-plane deformation and its first derivative

https://doi.org/10.1016/j.optcom.2020.126602Get rights and content

Highlights

  • A new multiplexed system for the simultaneous measurement is proposed.

  • The carrier frequency and the shearing amount can be independently adjusted.

  • The spectrum distribution is simple.

  • The system structure is compact and suitable for practical applications.

Abstract

A new multiplexed system based on double imaging Mach–Zehnder interferometry is proposed in this study for the simultaneous measurement of out-of-plane deformation and its first derivative. A modified Mach–Zehnder interferometer is used in the proposed system as shearing device, which has two pairs of imaging lenses and apertures placed on its arms. Therefore, carrier frequency and shearing amount can be independently adjusted using different components. An optical fiber is used to introduce reference beam, which has orthogonal states of polarization with one of the object beams. Shearogram and hologram without cross interference can be obtained by interference with the unpolarized object beam. Experimental results are presented for two pressure-loaded circular plates.

Introduction

Deformation and its first derivative are both key parameters in analyzing mechanical properties of materials. The simultaneous and accurate measurement of these two parameters is urgently required for practical applications in automotive and aerospace industries [1], [2], [3], [4], [5]. Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are widely used optical measurement methods due to their real-time, full-field, noncontact, and high-sensitivity advantages [6], [7], [8], [9], [10]. The former is used to measure in-plane or out-of-plane deformation, while the latter is typically used to measure the first derivative of deformation. Therefore, developing a multiplexed system of DSPI and DS is necessary to meet practical requirements of simultaneous measurement of deformation and its first derivative.

In the past few years, various DSPI and DS multiplexed setups have been proposed. However, problems, such as complex systems, difficult spectrum separation, and poor image quality, still need further improvement.

Bhaduri first proposed a multi-aperture measurement system that can simultaneously measure out-of-plane deformation and slope [11], [12], [13]. A specially designed three-aperture mask is used to introduce three different spatial carrier frequencies, and the hologram and shearogram are then extracted from a single image by Fourier transform [14]. However, this system is limited in practical applications because of the requirement of redesigning the multi-aperture mask to adapt to different sizes of measured objects.

Xie subsequently proposed a Michelson-based multiplexed system for the simultaneous measurement of deformation and its first derivative [15]. An optical fiber is used to introduce the reference beam into the shearing device, and sheared reference and object beams then interfere with each other to obtain the hologram and the shearogram. Compared with the structure of the multi-aperture mask, the stability of this system is higher and the size of the measured object is unlimited, thus the system is more suitable for practical applications. However, an excessive number of beams make the separation of the Fourier-transformed spectrum difficult. And spots formed by reference beams coincide with the position of the shearing spectrum, which affect the measurement results of shearography. To this end, Zhao proposed an improved setup to change the introduction position of the optical fiber to reduce beams, thereby simplifying the spectrum and avoiding the influence of spots on the extraction of the shearing spectrum [16]. However, Michelson-based systems commonly require a large shearing amount to separate side spectra from the center spectrum and result in a small valid measurement area.

This study proposes a multiplexed measurement system based on double imaging Mach–Zehnder interferometry. A single wavelength laser and a single CCD camera are used to realize the simultaneous dynamic measurement of out-of-plane deformation and its first derivative. Compared with the Michelson-based structure, the proposed system can independently adjust the carrier frequency and the shearing amount to meet different measurement requirements. A small shearing amount can be selected when a large measurement area is required, and a large shearing amount can be selected when high measurement sensitivity is required. Shearing directions can also be simply changed. Polarization technology is used to separate object and reference beams, which simplifies the spectrum further and makes the spectrum separation easier. In addition, the compact structure of this system is suitable for instrumental design, which makes the system have high application value. Theoretical derivation and experimental results are described in detail.

Section snippets

Theory

The schematic of the double imaging Mach–Zehnder multiplexed measurement system is shown in Fig. 1. The laser is transformed from linear to circular polarization by a quarter wave plate and then divided into an object beam and a reference beam by a beam splitter (BS1). The object beam is extended by a beam expander (BE) to illuminate the measured object, and the scattered light is divided into two beams by a beam splitter (BS2): One beam passes through a mirror (M1), an aperture (AP1), an

Experiments and results

The corresponding experimental setup shown in Fig. 3 was built in accordance with the optical path to verify the performance of the double imaging Mach–Zehnder multiplexed measurement system. A round, edge-clamped, center-loaded metal plate with a diameter of 130 mm was used as the measured object. A solid state single longitudinal mode green laser (NewOpto Technology Corporation, Model# MSL-FN-532-200 mW, 532 nm, 200 mW) was used as the light source. A CCD camera (Basler, Model# acA2440-75 μm,

Conclusion

This study proposes a new multiplexed system based on double imaging Mach–Zehnder interferometry, which can easily obtain the measurement results of deformation and its first derivative under static or dynamic loading. One shearogram and one hologram can be generated combined with the polarization technology, while the carrier-frequency spatial phase shift method is used to extract the phase from the single speckle interferogram. The experimental results show that the system has several

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

National Key Research and Development Program of China (No. 2016YFF0101803); National Natural Science Foundation of China (No. 51805137).

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