Dual-wavelength image-plane digital holography for dynamic measurement
Introduction
Since 1960s, various optical non-contact techniques have been applied for whole-field, non-contact dynamic measurement. Among them, the time-average method [1] is a typical technique for objects vibrating at a sinusoidal frequency whose period is many times smaller than the exposure time. The use of a twin-cavity double-pulsed laser in interferometry [2] has also been reported as an alternative to obtain transient parameters. Because of the rapid development of high-speed cameras, it is possible to record a sequence of interferograms with high capturing rates. High-speed phase-shifting [3] and temporal phase analysis [4], [5] were techniques introduced to retrieve the phase variation during the deformation or vibration of the objects. The former technique requires a high-speed phase shifter synchronized with a high-speed camera, while the latter technique analyzes each pixel of the interferograms independently as a function of time. Different processing algorithms including phase scanning [6], Fourier transform (FT) [7], windowed Fourier transform (WFT) [8], [9] and continuous wavelet transform (CWT) [10], [11] have been applied temporally or spatially to retrieve the phase from these two techniques.
In the past decade, a novel computer-aided optical technology, digital holography [12], has been successfully applied to different types of measurement. With a high-resolution CCD or CMOS sensor, one can record holograms directly with a camera and reconstruct the object digitally by computer simulation. The phase of the object can be retrieved from the digital reconstruction of one hologram. This advantage makes digital holography more suitable for dynamic measurement. In addition, no phase ambiguity problem exists in the further processing of the reconstructed phase. Different dynamic measurement techniques based on digital holography combined with a pulsed laser [13], a time-average method [14], and a temporal analysis [15] have been reported. A previous report [16] described a method for the measuring kinematic parameters of a vibrating object by image-plane digital holography. Digital holograms of a vibrating object were recorded on a high-speed sensor and the phase of the wavefront, recorded at different instants, was calculated from the recorded intensity using a two-dimensional (2-D) FT method. By processing the phase maps with a one-dimensional (1-D) WFT in the temporal domain, it is possible to obtain the instantaneous displacement, velocity and acceleration of the vibrating object.
One problem involved in dynamic measurements is that the imaging rate of the camera should be high enough so that the phase change on each pixel, between two adjacent images, should be less than π. This is equivalent to the path-length change of λ/2. It is impossible to bypass the Nyquist sampling theorem. However, we can enlarge the measurement range by two-wavelength interferometry (TWI) [17], [18]. Different types of TWI have been reported during the past several decades. The phases at a synthetic wavelength have been determined from the difference between two phases at a single wavelength by the use of different methods, such as the heterodyne technique [19], the time-multiplexed technique [20], the phase-shifting technique [21], the three-color method [22], the sinusoidal phase-demodulated technique [23], [24], the fractional fringe technique [25] or the Fourier-transform method [26]. A typical application of TWI is the measurement of a surface profile with height steps [27]. The concept of TWI can also be used with digital holography for surface profiling where the phase at single wavelength can be reconstructed from separately recorded digital holograms [28], [29]. However, it is not suitable for dynamic measurement because two holograms need to be recorded and reconstructed individually. In this paper, we propose TWI combined with image-plane digital holography to achieve a dynamic measurement on a vibrating object. The object was simultaneously illuminated by two lasers with different wavelengths, and a sequence of digital holograms was captured by a CCD camera. For each instant, two wrapped phase maps were reconstructed from one digital hologram [30], [31]. A new phase distribution with a synthetic wavelength was then obtained by subtracting these two wrapped phase maps. However, the new phase map is much noisier [32], and needed a robust algorithm to retrieve the temporal phase values and the phase derivatives. In this application, a windowed Fourier analysis was applied spatially and temporally to retrieve the instantaneous displacement and velocity of a vibrating object.
Section snippets
Two-wavelength image-plane digital holography
A schematic layout of an image-plane digital holography configuration, sensitive to out-of-plane displacement, is shown in Fig. 1. Two lasers with different wavelengths are used. Light from the first laser is split into an object beam and a reference beam. This object beam illuminates a vibrating specimen with a diffuse surface along a direction ei1. Some light is scattered in the observation direction eo where an image-plane hologram is formed on the CCD sensor, as a result of the interference
Experimental illustration
Fig. 1 shows the experimental setup for the measurements. The specimen tested in this study was a copper cantilever beam with a diffuse surface. A weight is fixed at the free-end of the beam. The distance between the weight and the clamping end was 80 mm. The width and thickness of the beam were 10 and 0.3 mm, respectively. The natural frequency of the beam was around 2 Hz. The first laser used was a He–Ne laser with a power of 15 mW and with a wavelength of λ1=632.8 nm. The second laser used was a
Results and discussion
One hundred and twenty holograms are captured during an 8 s period. Fig. 2(b) shows a typical Fourier spectrum of digital holograms captured by the CCD camera. The shadow of the fiber ends can be observed on the spectrums of both digital holograms. When filtering window A is selected, the reconstructed phase difference between the two instants represents the out-of-plane displacement for the wavelength 632.8 nm (Fig. 2(c)). When filtering window B is selected, the reconstructed phase between the
Concluding remarks
In this paper we have presented a novel dual-wavelength image-plane digital holography on a vibration measurement. Two lasers with different wavelengths were used to illuminate the test object simultaneously, and the two interferograms were superimposed on the CCD sensor. A sequence of digital holograms was captured by a CCD camera. At each instant, two wrapped phase maps were reconstructed from one digital hologram. The subtraction of these two phase maps yielded a new phase distribution with
Acknowledgements
Y. Fu gratefully acknowledges the financial support of the Alexander von Humboldt Foundation. This work is also supported by the German Science Foundation, DFG, Grant no. OS. 111/22-1, the MULTI-ENCODE project (006427 (SSPI)) funded by the European Union, and the National Science Foundation of China (NSFC) under Contract no. 10772171.
References (34)
Phase measurement in temporal speckle pattern interferometry using the Fourier transform method with and without a temporal carrier
Opt Commun
(2003)- et al.
Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry
Opt Laser Technol
(2001) - et al.
Digital double pulse-TV-holography
Opt Laser Eng
(1997) - et al.
Time-multiplex two-wavelength heterrodyne interferometer with frequency-ramped laser diodes
Opt Commun
(1999) Vibration measurement using phase-shifting time-average holographic interferometry
Appl Opt
(1986)- et al.
Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry
Appl Opt
(1998) - et al.
Phase-shifted dynamic speckle pattern interferometry at 1 kHz
Appl Opt
(1999) - et al.
Speckle interferometry with temporal phase evaluation for measuring large-object deformation
Appl Opt
(1998) - et al.
Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry
J Opt Soc Am
(1982) Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations
Opt Laser Eng
(2007)
Phase-shifting windowed Fourier ridges for determination of phase derivatives
Opt Lett
Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry
Opt Eng
Digital image formation from electronically detected holograms
Appl Phys Lett
Amplitude and phase analysis in digital dynamic holography
Opt Lett
High-speed digital holographic interferometry for vibration measurement
Appl Opt
Vibration measurement by temporal Fourier analyses of digital hologram sequence
Appl Opt
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