**3.2.3 Qualifying displacements**

98 Microelectromechanical Systems and Devices

 (a) Bright field image (b) Interferometric field image

The optical flow algorithms used by the MMA work for in-plane or out-of-plane measurements. For out-of-plane measurements, image sequences can be collected at different planes of focus (optical sectioning). In this way, brightness gradients can be sampled along the optical axis and then used in a manner identical to in-plane sequences.

Figure 8(b) is the interference field image, which is formed by the reflected light from the tested sample and the reference mirror in the optics module. The interferogram in the picture is sensitive to the optical path change of the sample, which can be used to calculate

The final result of the computation is an extremely powerful tool capable of measuring motions of magnified targets well below the resolution of human vision. Although, the resolution of a single static image is limited in a theoretical sense by the wavelength of the light used to generate the image, the resolution of a motion measurement is limited by the sensitivity of the CCD camera as shown in figure 9. Sub-pixel motion of an object or region

Fig. 8. Images of the tested micro-resonator

**3.2.1.2 Interference field image** 

**3.2.2 Sub-pixel displacements measurement** 

Fig. 9. In-plane motion measurement using optical flow algorithm

the height of the sample and the out-of-plane motion between images.

In order to quantify in-plane or out-of-plane displacements, the algorithms need a length scale. It means that different measurements need corresponding length scale.

For bright field images (in-plane measurements and optical sectioning), an in-plane length standard such as a grating (a target with a ruling of known spacing) is used to calibrate the length per pixel for a given magnification. The algorithms then convert the calculated displacements from pixels to micrometers.

Interference images have a more convenient length scale available. In this case, measurements are quantified using the known wavelength of the illumination source. This length standard is independent of magnification.
