Electrostatic comb drive for vertical actuation Page: 4 of 14
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and controlled displacements in the nanometer range are possible. Phase shifting interferometry involves the combination of a
test wavefront generated by an unknown optical component, such as a lens or mirror, with a known reference wavefront, allow-
ing for precise measurement of the unknown component's optical properties. The interference pattern generated by the test
and reference waves is recorded a number of times while the phase of the reference wavefront is shifted by a known amount
between measurements. By using a detector array, such as a CCD camera, and a computer, measurements can be made simul-
taneously at a large number of points covering the interference pattern. Given the properties of the reference wave, these time
sequenced measurements can be used to calculate the properties of the test wave26. However, to obtain accurate results, it is
necessary that the phase shift be accurately known. For this reason, the phase shifting component must yield an accurate and
repeatable phase shift over the entire range of phases.
Applications of electrostatic vertical microactuators with displacements less than 2 pm are mostly optical. Phase shifting
interferometry is one significant application, and a variety of phase shifting methods exist26. The most common technique is
the use of a piezoelectric transducer (PZT) to move a reference surface27. For example, it is by this method that commercial
interferometer manufacturers Wyko and Zygo provide phase shifting for their Fizeau interferometers and interference micro-
scopes. Other methods that produce a change of phase at fixed optical frequency include tilting a glass plate28, translating a
diffraction grating, using PZT to strain an optical fiber30, and using an electro-optic modulator3 . Methods that achieve phase
shifting by changing the optical frequency include using an acousto-optic modulator32, rotating a half-wave plate33, analyzer34,
or radial grating35, and chirping the laser frequency36 3 The frequency shifting methods are dependent upon the difference in
optical path lengths between the reference and test arms, so the fixed frequency methods are generally preferred.
phase shifter PZT
Figure replacing a PZT corner cube phase shifter with a micromirror vertical actuator and a
In this paper, the levitation force is utilized to actively actuate a suspended mass plate in the vertical direction for control-
lable small vertical motions (<2 pm). Other electrostatic vertical motion sensors and actuators typically utilize the parallel plate
capacitor effect. Applications of this device are mostly in optics such as Fabry-Perot interferometry or phase shifting-based in-
terferometry. Equilibrium between the electrostatic force and the folded beam flexure mechanical spring force provides the first
order static equation. The electrostatic force is a function of the bias voltage applied and the position of the actuator. The me-
chanical spring force is a function of the position of the actuator. Combining the two results in a voltage vs. displacement curve
for different mechanical spring constants. This provides a design guide for vertical comb-driven actuators. Also presented in
this paper is the position sensing utilizing a parallel plate capacitive sensing configuration.
2. PRINCIPLE OF OPERATION
The principle of the levitation force is described in much detail by Tang et al.11. Figure 2a illustrates how the levitation force
is realized. When a voltage is applied to the stationary comb fingers with respect to a grounded moving comb finger, and when
the substrate is also at ground potential, the distribution of electrical field lines are asymmetric around the moving comb finger.
This asymmetric distribution of field lines results in an upward levitation force indicated as the z- direction. If the moving comb
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Lee, A. P., LLNL. Electrostatic comb drive for vertical actuation, article, July 10, 1997; (https://digital.library.unt.edu/ark:/67531/metadc619911/m1/4/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.