Apparent nonlinear effect of the microscope on the laser Doppler vibrometer

One powerful method for measuring the motion of microelectromechanical systems (MEMS) relies on a Laser Doppler Vibrometer (LDV) focused through very an optical microscope. Recent data taken under a simple and common condition demonstrate that the velocity signal produced by the LDV with an optical microscope may be different from the velocity signal produced by the LDV without a microscope. This is especially important if one wishes to estimate acceleration by differentiating velocity. In this study, the time derivatives of LDV signals are compared against the signal from an accelerometer when the LDV is focused through an optical microscope and without the microscope system. The signal from the LDV without the microscope is almost identical to the accelerometer signal. In contrast. the signal from the LDV with the microscope exhibits a nonlinear relationship with the accelerometer signal. Both the LDV and the accelerometer were measuring a sinusoidal velocity generated by all electromechanical shaker. The Fourier transform of the acceleration from the LDV with the microscope shows a multitude of high harmonics of the excitation frequency, which have much higher amplitudes than the harmonics present in the accelerometer signal. Without the microscope, the LDV gives a much less distorted sinusoidal signal, even after time differentiation. The distortion of the signal from the LDV is periodic, with the same period as the sinusoidal drive signal. The largest distortion occurs near points of maximum negative acceleration, corresponding to the positive displacement peak of the sinusoidal oscillation. Because the measured oscillation is out of plane, pseudo-vibrations caused by speckle noise do not explain the distortion. Instead, the distortion appears to be caused by the optics of the microscope.