To reduce temporally uncorrelated noise, the mea- sured data in the time domain was first filtered and av- eraged by a Fourier transformation that is implemented in the PSV-Software。 Such techniques are common in dynamic measurements [18]。 A Hanning window was applied to the data prior to the FTT to minimize spec- tral leakage。 The frequency resolution for the Fourier analysis was set to 500 mHz which resulted in a sam- pling time of 2 s for each FFT。 A total 64 averages were taken at each measurement point with an overlap of 75%, taking approximately half a minute per point。 Ad- ditional to the actual measurement time for each point, some time (approximately 3 s) for the triangulation of the laser beams on the measurement object each time the lasers move to a new point have to be accounted for。 With these settings, a measurement with 1,000 data points takes almost 9 h。

The long measurement time is owing to the restric- tion to low frequencies due to the clamping apparatus as discussed in the previous section。 The measurement time could be significantly reduced, if the specimens were driven at a higher frequency, however this would have made comparisons with the quasi-static FEA model invalid。

All measurements were conducted at an ambient temperature of 23◦C。 The data  were  exported from the PSV-software to a universal file format and post- processed in Matlab。

The measurement were conducted on the two different  specimens  illustrated  in  Fig。  5   including

(a)Rectangular plate (b) Rectangular plate with

circular hole

Fig。 5 Schematics of the specimens and their meshes for the strain measurements

schematics of the meshes used for the measurement。 These meshes are predefined prior to the measurement。

Experimental Results

Effect of Mesh Density

Prior to conducting the main experiments detailed in this paper, it was necessary to identify the optimal mesh density suitable for the measurements。 Too fine and the method is sensitive to imprecisions in the laser beam position on the measurement object as is illustrated in Fig。 6。 When the distances between measurement points approach the error in position, the normalised error in the strain arising from the finite difference may become extremely large。 If the mesh is too coarse, then spatial resolution is compromised。

Fig。 6 Positioning imprecisions due to finite accuracy of the 3D alignment [11]

When preparing a scan the user first defines a nomi- nal grid。 The triangulation routine of the PSV-software then attempts to aim the three laser beams on the defined points。 As the accuracy of the triangulation is finite, the actual position of the beams differs slightly from the nominal position。 The effect of this imprecise positioning is illustrated in Fig。 7 for two different spac- ing intervals。 While the fine mesh exhibits a very noisy displacement field (compared to the regular nominal grid) and large relative errors in positioning, the coarse mesh shows a rather smooth displacement field on a relatively structured mesh。

The positioning for fine meshes can be  enhanced by zooming in the object as much as possible and satisfying results for meshes with the spacing of around

0。5 mm can be achieved。 Therefore, the measurement object should occupy the whole camera image to obtain optimal results ensuring that each pixel represents the smallest possible distance。

The measurement of a rectangular plate under ten- sile loading yields a constant strain field。  Therefore by evaluating the standard derivation σ of the strain from the mean value μ of the strain, one can obtain information on the possible refinement of the mesh and the filter coefficients used to estimate the strain。

Figure 8(a) gives the normalized variance coefficient cv = σ/μ in terms of the spacing intervals of the mesh for εxx and εyy with a uniaxial load in the y-direction。 The exact loading conditions are described more fully in the following sections。 The error in x-direction is much higher that the y-direction which is due to the significantly lower amplitudes of the strain signal in that direction。 In Fig。 8(b) the dependence of the filter strength is illustrated。 Given a stronger attenuation of the noise due to higher filter parameter m, the vari- ance coefficient decreases。 The figures are based on measurements that are performed on a mesh of 19 × 19 points at a constant camera zoom。 In all cases the rel- ative error of the measurements increases significantly for meshes with spacing intervals below 1。5 mm。