Fig. 1. Optical design of FMSI. The light-emitting diode (LED) array is 32 × 16 pixels, and each pixel is 5 mm × 5 mm. Power sensor: S130C, Thorlabs; power meter console: PM100USB, Thorlabs.

Fig. 2. Simulations of the vibration measurement with FMSI. (a) The original binary sample (64 × 64), (b) Fourier transformation of the signal when all the objects are stable, (c) single-pixel image when all the objects are stable, (d) Fourier transformation of the signal when object 1 is vibrating horizontally, (e) single-pixel image when object 1 is vibrating horizontally, and (f) single-pixel image of vibrating area.

Fig. 3. Frequency distribution of transmittance when the amplitude of the vibration is larger than one pixel. (a) The edge of the object vibrating between pixel 1 and pixel 2. Pixel 1 and pixel 2 are the two pixels affected by the vibration edge, where the amplitude of the vibration is 1.6 times the length of the pixel. (b) and (c) Change of transmittance at the pixel 1 and pixel 2, (d) frequency of the vibration, (e) and (f) frequency of transmittance of pixel 1 and pixel 2.

Fig. 4. Experiments of the vibration measurement with FMSI. The signals of the stable object and vibrating object, and mirror signal are shown.

Fig. 5. Experiments of the vibration measurement with FMSI. (a) Fourier transformation of the signal when all the objects are stable, (b) single-pixel image when all the objects are stable, (c) single-pixel image of the same area as (f), (d) Fourier transformation of the signal when the cylinder is vibrating horizontally, (e) single-pixel image when the cylinder is vibrating horizontally, and (f) single-pixel image of the vibrating area.