Method and apparatus for increasing the efficiency and optical bandwidth of microelectromechanical systems piston-mode spatial light modulators

Abstract

To provide methods and apparatus for increasing efficiency and optical bandwidth of a microelectromechanical system piston-mode spatial light modulator.SOLUTION: In methods and apparatus for increasing efficiency and optical bandwidth of a microelectromechanical system piston-mode spatial light modulator, an example apparatus (100) includes: an electrode (106) with spring legs; a base electrode (110); a mirror displacement determiner to determine a periodic signal corresponding to a displacement distance of the electrode (106) beyond an instability point of the electrode (106); and a voltage source to output a periodic voltage to the base electrode (110) in response to the periodic signal. The periodic voltage causes the spring legs to vary displacement of the electrode (106) with respect to the base electrode (110) according to the periodic voltage. The displacement includes distances beyond the instability point.SELECTED DRAWING: Figure 1A

Description

[Technical field]

[0001] This application relates generally to microelectromechanical systems, and more particularly to methods and apparatus for increasing the efficiency and optical bandwidth of piston-mode spatial light modulators in microelectromechanical systems. [Background technology]

[0002] A spatial light modulator (SLM) spatially varies the modulation of a light beam. The SLM operates pixels, each of which includes a respective mirror that moves to vary the intensity and / or phase of the light beam. In some examples, a microelectromechanical system (MEMS) SLM changes the position (e.g., moves) of the mirror to change the intensity and / or phase of the light beam. Such a MEMS includes a base electrode and a spring electrode that are coupled to the mirror. When a voltage difference is created between the base electrode (coupled to the base of the pixel) and the spring electrode, the spring electrode moves toward the base electrode, thereby moving the mirror to a different position. MEMS SLMs are used in a variety of applications, such as in projectors, high dynamic range cinema, light detection and ranging systems, high capacity optical switching (e.g., in telecommunications or server farms), microscopy / spectroscopy / adaptive optics (e.g., in astronomy, ophthalmology, machine vision), and holographic displays. Summary of the Invention

[0003] In an illustrative example of an apparatus for increasing the efficiency and optical bandwidth of a microelectromechanical systems piston mode spatial light modulator, the apparatus includes an electrode having a spring leg. The apparatus further includes a base electrode. The apparatus further includes a mirror displacement determiner for determining a periodic signal corresponding to a displacement distance of the electrode beyond an instability point of the electrode. The apparatus further includes a voltage source for outputting a periodic voltage to the base electrode in response to the periodic signal, the periodic voltage causing the spring leg to vary the displacement of the electrode relative to the base electrode in response to the periodic voltage, the displacement including a distance beyond the instability point.

[0004] In an illustrative example of a method for increasing the efficiency and optical bandwidth of a microelectromechanical system piston mode spatial light modulator, the method includes determining a periodic signal corresponding to a displacement distance of an electrode of a pixel beyond an instability point of the electrode, the method further includes outputting a periodic voltage to a base electrode in response to the periodic signal, the periodic voltage causing a spring leg of the electrode to vary the displacement of the electrode relative to the base electrode in response to the periodic voltage, the displacement including a distance beyond the instability point.

[0005] In an illustrative example of an apparatus for increasing the efficiency and optical bandwidth of a microelectromechanical systems piston mode spatial light modulator, the apparatus includes a mirror. The apparatus further includes an electrode attached to the mirror. The electrode includes a rigid body and three spring legs coupled to the rigid body for displacing the rigid body in response to an electrostatic force applied to the electrode. [Brief description of the drawings]

[0006] [Figure 1A] 1A-1D are side views of an example MEMS SLM pixel in different positions. [Figure 1B] 1A-1D are side views of an example MEMS SLM pixel in different positions.

[0007] [Diagram 2] FIG. 2 is a plan view of an example spring structure of the pixel of FIGS. 1A and 1B.

[0008] [Figure 3A] 3A-3C are perspective views of three exemplary variations of the spring structure of FIGS. 1A, 1B, and 2. FIG. [Figure 3B] 3A-3C are perspective views of three exemplary variations of the spring structure of FIGS. 1A, 1B, and 2. FIG. [Figure 3C] 3A-3C are perspective views of three exemplary variations of the spring structure of FIGS. 1A, 1B, and 2. FIG.

[0009] [Figure 4A] 1A-1C are side views of three exemplary alternative pixel structures of a MEMS SLM. [Figure 4B] 1A-1C are side views of three exemplary alternative pixel structures of a MEMS SLM. [Figure 4C] 1A-1C are side views of three exemplary alternative pixel structures of a MEMS SLM.

[0010] [Diagram 5] FIG. 1C is a block diagram of an example electrode voltage controller of FIGS. 1A and 1B.

[0011] [Figure 6] 4 is a flowchart representing example machine-readable instructions that may be executed to implement the electrode voltage controller of FIGS. 1A and 1B to move the position of the spring structures of FIGS. 1A-4C.

[0012] [Figure 7] 13 is an exemplary graph of the increased range of motion produced by a harmonic resonant excitation waveform.

[0013] [Figure 8] 1C is an example graph of a sampling of light reflected from the example mirror of FIGS. 1A and 1B.

[0014] [Figure 9A] 6 is an example graph of a periodic signal that may be output by the electrode voltage controllers of FIGS. 1A, 1B, and 5 to cycle the mirror of FIGS. 1A and 1B past an instability point without collapse. [Figure 9B] 6 is an example graph of a periodic signal that may be output by the electrode voltage controllers of FIGS. 1A, 1B, and 5 to cycle the mirror of FIGS. 1A and 1B past an instability point without collapse.

[0015] [Figure 10] 1 illustrates example phase-shifted mirror displacements to generate example pixel array frames corresponding to example lighting conditions.

[0016] [Figure 11] FIG. 7 is a block diagram of a processor platform for executing the machine-readable instructions of FIG. 6 to control the electrode voltage controller of FIGS. 1A and 1B. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] The drawings are not necessarily drawn to scale and in the drawings like parts are referred to by like reference numerals.

[0018] The SLM spatially varies the modulation of a light beam by reflecting the light beam to control the properties (e.g., intensity and / or phase) of the reflected beam. To modulate the light beam, the SLM pixels include adjustable (movable, displaceable) mirrors to change the properties of the reflected beam. In some examples, the SLM includes MEMS to move the mirror in response to a combination of electrostatic and spring forces.

[0019] 1A and 1B are side views showing two locations of an example pixel 100 of a MEMS SLM. Figures 1A and 1B show an example mirror 102, an example mirror attachment 104 (e.g., mirror via), an example spring 106 (e.g., referred to herein as a "spring," "spring structure," or "spring electrode") (e.g., a first electrode), example spring attachments 108a-108c (e.g., spring vias), an example base electrode 110 (e.g., a second electrode), and an example electrode voltage controller 112.

[0020] The mirror 102 reflects the light beam in one or more directions depending on the position of the mirror. For example, the mirror 102 is extended in a first position of FIG. 1A to reflect the light, and the mirror 102 is retracted in a second position of FIG. 1B to reflect the light. The mirror 102 reflects light corresponding to a pure phase contrast device with a continuous phase range. In this way, the array of mirrors can be displaced in different positions to create different interference patterns (e.g., corresponding to different intensities).

[0021] The spring 106 is an electrode that includes spring legs and a rigid body. The spring structure 106 is coupled to the mirror 102 via the mirror attachment 104, thereby providing additional stiffness to the rigid body. The spring legs of the spring structure 106 correspond to a mechanical spring constant that, when extended, applies a mechanical force in a direction opposite to the direction of extension. The spring legs are attached to spring attachments 108a-108c, which may be grounded. In this manner, when an electrostatic force is applied to the spring structure 106 in a downward motion, the spring legs extend toward the base electrode 110, lowering the rigid body of the spring structure 106, thereby moving the mirror 102 from the position of FIG. 1A toward the position of FIG. 1B. Although the spring structure 106 may be of any shape, the hexagonal spring structure increases the area-to-perimeter ratio of the rigid body, allowing the voltage applied to the base electrode 110 to be significantly lower than in conventional pixels without degrading the quality of the pixel (e.g., corresponding to the total distance of mirror displacement).

[0022] In some examples, the length of the spring attachments 108a-108c is greater than the length of the mirror attachment 104. In this way, even if the mirror 102 is fully displaced by electrostatic forces, the spring structure 106 will not directly contact (e.g., create an electrical short) the base electrode 110. In some examples, the mirror 102, the mirror attachment 104, the spring structure 106, and / or the spring attachments 108a-108c are covered by a similar material. In this way, there is zero potential difference between the mirror 102, the mirror attachment 104, the spring structure 106, and / or the spring attachments 108a-108c.

[0023] During operation, the base electrode 110 receives a voltage from the electrode voltage controller 112. When the voltage on the base electrode 110 is stronger than the spring constant of the spring structure 106, it generates an electrostatic force that moves the spring structure 106 towards the base electrode 110. As more voltage is applied to the base electrode 110 and / or as more areas of voltage are applied by the base electrode 110, the displacement of the spring structure 106 increases. In some examples, the base electrode 110 is an analog type electrode where the voltage is spread evenly across the base electrode 110. Thus, the electrode voltage controller 112 outputs an analog voltage to move the spring structure 106 and the mirror 102 to different positions (e.g., each voltage level corresponding to a different position). In some examples, the base electrode 110 is a digital type electrode where voltage is applied to different areas (e.g., bits) of the base electrode 110. For example, base electrode 110 may include three bits (bit_0, bit_1, and bit_2) for linear bit spacing, so that the area increases binary (e.g., bit 0 is 1 / 2 the area of ​​bit 1, which is 1 / 2 the area of ​​bit 2). However, this area ratio may be altered to compensate for nonlinearities in electrostatic forces, curved / tilted electrodes, and / or nonlinear springs, as described further below. Although the example of Figures 1A and 1B corresponds to a three-bit electrode configuration, base electrode 110 may include any number of bits, subject to lithography and routing limitations. Thus, (a) when 5V is applied to bit_0, spring structure 106 is moved to a first position, (b) when 5V is applied to bit_0 and bit_1, spring structure 106 is moved to a second position (lower than the first position), and (c) when 5V is applied to bit_0, bit_1, and bit_2, spring structure 106 is moved to a third position (lower than the second position).

[0024] The electrode voltage controller 112 controls the displacement of the mirror 102 by sending a voltage to the base electrode 110 to generate an electrostatic force between the base electrode 110 and the spring structure 106, thereby moving the spring structure 106 (and therefore the mirror 102) towards the base electrode 110. The electrode voltage controller 112 applies a voltage corresponding to the distance according to a desired output (e.g., received from another computing device or circuitry). In some examples, the electrode voltage controller 112 generates a periodic signal (e.g., a digital pulse signal or a sinusoid) that periodically attracts the spring structure 106 (and therefore the mirror 102) towards and away from the base electrode 110. As described herein, by periodically varying the voltage to periodically change the displacement of the spring structure 106, the electrode voltage controller 112 can move the spring structure 106 toward the base electrode 110 beyond a d / 3 threshold distance (e.g., an instability point) without collapse (e.g., without collapsing the spring structure 106 toward the base electrode 110). The electrode voltage controller 112 can move the spring structure 106 approximately 9 / 10 of the distance to the base electrode 110 using a periodic variation technique. As the electrode voltage controller 112 varies the displacement of the spring structure 106 over time, a receiving device (e.g., receiving light reflected by the mirror 102) needs to obtain information about the periodic variation in order to sample the received signal (e.g., the reflected light of the mirror 102) according to the desired displacement. For example, if the electrode voltage controller 112 is varying the voltage applied by the base electrode 110 to move the spring structure 106 at a particular rate with a particular total distance (e.g., the amplitude of the periodic displacement), the receiving device can sample the received signal for the desired displacement according to the known rate and distance. Although the illustrated electrode voltage controller 112 controls the pixel 100, the electrode voltage controller 112 may control multiple pixels.For example, an electrode voltage controller 112 may be coupled to the base electrodes, each of which operates independently, as a group, or as a subgroup (e.g., a first subgroup controlled with a first voltage and a second subgroup controlled by a second voltage). The electrode voltage controller 112 is further described below in connection with FIG. 5.

[0025] Figure 2 shows an example overhead view of spring structure 106 over base electrode 110 of pixel 100 of Figures 1A and 1B. The overhead view of Figure 2 includes mirror attachment 104, spring structure 106, spring attachments 108a-108c, and base electrode 110 of Figures 1A and 1B. Spring structure 106 of Figure 2 includes an example body 200 and example spring legs 202a-202c.

[0026] 2 is a three-legged hexagonal spring structure that increases the area-to-perimeter ratio of the rigid body, thereby allowing the voltage applied to the base electrode 110 to be significantly lower than in conventional pixels without degrading the quality of the pixel (e.g., corresponding to the total distance of mirror displacement). Alternatively, the spring structure 106 can be a different shape with a different area-to-perimeter ratio that corresponds to the different voltages that may need to be applied by the base electrode 110.

[0027] The body 200 of FIG. 2 is a rigid structure that maintains its structure when the base electrode 110 increases the voltage. When the base electrode 110 increases the voltage, the body 200 moves toward the base electrode 110 while maintaining its shape. In this way, the surface area exposed to the base electrode voltage is increased to increase the overall efficiency of the structure. The mirror attachment 104 is attached to the body 200, thereby causing the mirror 102 of FIG. 2 to move with the movement of the body 200. The mirror attachment 104 also provides additional rigidity to the body 200. The mirror attachment 104 is attached to a central spring structure 106, but the mirror attachment 104 may be attached anywhere along the body 200 and / or may include multiple mirror attachments at various locations on the body 200. These multiple attachment points can be used to increase the stiffness of the main bottom electrode body while weakening the spring legs, or vice versa. The body 200 is attached to the spring legs 202a-202c.

[0028] The spring legs 202a-c of FIG. 2 are attached to the spring attachments 108a-c and the spring body 200. In the illustrated example, the spring attachments 108a-c are grounded, and thus the spring legs 202a-c and the spring body 200 are also grounded. The spring legs 202a-c include a spring constant corresponding to a spring force to keep the body 200 in the first position. As the electrostatic force on the base electrode 110 increases (e.g., according to a voltage difference between the grounded spring structure 106 and the biased base electrode 110 of FIGS. 1A and 1B), the spring legs 202a-c are extended toward the base electrode 110, thereby lowering the body 200. The spring constant may be based on the material of the spring structure 106 and / or based on the dimensions of the spring legs 202a-c. For example, the spring legs 202a-202c are long and wrapped around a hexagonal structure before being integrated with the body 200. Such a structure provides a resilience corresponding to the spring constant while preserving the area-to-perimeter ratio of the body 200. In the illustrated example, the spring structure 106 is one integrated piece of integrated material (e.g., the body 200 and the spring legs 202a-202c are made of the same material and integrated into the same structure). However, the body 200 and the spring legs 202a-202c can be different materials attached together (e.g., a first material corresponds to the spring constant of the spring legs 202a-202c, a second material corresponds to the stiffness of the body 200, etc.). The tripod hexagonal structure of FIG. 2 reduces the stiffness (e.g., spring constant) of the spring legs 202a-202c while providing sufficient support to the body 200. do.

[0029] 3A-3C show three example displacements of the spring structure of FIGS. 1A, 1B, and 2. FIGS. 3A-3C include the body 200 and spring legs 202a-202c of the spring structure 106 of FIG. 2. FIG. 3A shows an example first spring displacement 300 corresponding to a first voltage applied to the base electrode 110 of FIGS. 1A and 1B. FIG. 3B shows an example second spring displacement 302 corresponding to a second voltage applied to the base electrode 110 of FIGS. 1A and 1B. FIG. 3C shows an example third spring displacement 304 corresponding to a third voltage applied to the base electrode 110 of FIGS. 1A and 1B.

[0030] In Figure 3A, the electrode voltage controller 112 is not applying a voltage to the base electrode 110. Because there is no voltage difference between the spring structure 106 and the base electrode 110, there is no electrostatic force to attract the body 200 towards the base electrode 110. Thus, Figure 3A shows the spring structure 106 with no displacement. For example, the spring legs 202a-202c are at the same level as the spring body 200, and no downward force is applied.

[0031] In FIG. 3B, the electrode voltage controller 112 applies a first voltage to the base electrode 110 (e.g., a first analog voltage across the base electrode 110, or a voltage corresponding to a first area of ​​the total area of ​​the base electrode 110). The first voltage applied to the base electrode 110 creates a first voltage difference between the base electrode 110 and the spring structure 106, thereby creating an electrostatic force that drives the body 200 downward toward the base electrode 110. The first voltage corresponds to a first electrostatic force that causes the spring legs 202a-202c to extend and lower the body 200 to a first position (e.g., corresponding to a displacement of 10 millimeters (mm) from the position of FIG. 3A).

[0032] In FIG. 3C, the electrode voltage controller 112 applies a second voltage to the base electrode 110 (e.g., a second analog voltage higher than the first analog voltage of FIG. 3B, or a voltage of FIG. 3B corresponding to a second area larger than the first area of ​​the base electrode 110). The second voltage applied to the base electrode 110 (e.g., a higher or over a larger area) creates a second, higher voltage difference between the base electrode 110 and the spring structure 106, thereby creating an electrostatic force that drives the body 200 further downward toward the base electrode 110. The second voltage corresponds to a second electrostatic force that causes the spring legs 202a-202c to further extend and lower the body 200 to a second position (e.g., corresponding to a displacement of 30 millimeters (mm) from the position of FIG. 3A).

[0033] 3A-3C, the stronger the voltage applied to base electrode 110 (e.g., higher voltage, or over a larger area), the further body 200 is displaced toward base electrode 110. As described herein, at each position of body 200, body 200 remains rigid while spring legs 202a-202c extend in response to electrostatic forces.

[0034] Figures 4A-4C illustrate three alternative exemplary pixel structures of a MEMS SLM. The examples of Figures 4A-4C include the mirror 102, mirror attachment 104, spring structure 106, spring attachments 108a-108c, and base electrode 110 of Figures 1A and 1B. The examples of Figures 4A-4C further include an exemplary non-uniform base electrode 402 and an exemplary non-uniform spring structure 404 in a first exemplary pixel structure 400, a second exemplary pixel structure 410, and / or a third exemplary pixel structure 420.

[0035] The first example pixel structure 400 of FIG. 4A includes a non-uniform base electrode 402. The non-uniform base electrode 402 has a grayscale gradient structure rather than flat. The non-uniform base electrode 402 can be curved, bowed, tilted, graded, and / or any other structure other than a flat structure. For example, the non-uniform base electrodes 402 can be curved away from each other (e.g., to gradually increase the distance d above the position). For example, in such a curved structure, the distance d between the base electrode 402 and the spring electrode 106 increases as the position along the actuation structure from the support structure increases. By adjusting (e.g., curving) the base electrode 402, the electrostatic force is changed from a uniform linear force to a non-uniform non-linear force. In this manner, as the spring structure 106 approaches the non-uniform base electrode 402, there will be a greater force near the spring attachments 108a-108c, and there will be a greater restoring force from the spring structure 106 (e.g., the greater the displacement, the greater the resistance of the spring structure 106). By progressively moving the non-uniform base electrode 402 away from the weakest portion of the spring structure 106, the overall pixel movement is increased (e.g., twice as far as a conventional MEMS pixel would travel), from the d / 3 threshold of instability to, for example, the 2d / 3 threshold of instability, without collapse (e.g., without any risk of collapse).

[0036] The first example pixel structure 410 of FIG. 4B includes a non-uniform spring structure 404. The non-uniform spring structure 404 has a structure that is not flat but is a grayscale gradient. The non-uniform spring structure 404 can be curved, bowed, tilted, graded, and / or any other structure other than a flat structure. For example, the non-uniform base electrodes 404 can be curved away from each other (e.g., to progressively increase the distance d above the position). For example, in such a curved structure, the distance d between the base electrode 110 and the spring electrode 404 increases as the position along the actuation structure from the support structure increases. By adjusting (e.g., curving) the spring structure 404, the electrostatic force is changed from a uniform linear force to a non-uniform non-linear force. In this manner, as the spring structure 404 approaches the base electrode 110, there will be a greater force near the spring attachments 108a-108c, and there will be a greater restoring force from the spring structure 404 (e.g., the greater the displacement, the greater the resistance of the spring structure 404). By progressively moving the weakest portion of the non-uniform spring structure 404 away from the base electrode 110, the overall pixel movement is increased (e.g., twice as much as a conventional MEMS pixel moves) without collapse, such as from the d / 3 threshold of instability to the 2d / 3 threshold of instability. A third exemplary pixel structure 420 of FIG. 4C includes the non-uniform base electrode 402 and non-uniform spring structure 404 of FIGS. 4A and 4B. Similar to pixel structures 400 and 410, pixel structure 420 accommodates an overall pixel movement increase (e.g., twice as much as a conventional MEMS pixel moves) without collapse, such as from the d / 3 threshold of instability to the 2d / 3 threshold of instability.

[0037] Thus, the MEMS can apply an electrostatic force to move the mirror 102 of the SLM pixel 100, 400, 410, 420. For example, the MEMS pixel 100, 400, 410, 420 includes a first electrode 106, 404 coupled to the mirror 102. The first electrode 106, 404 is also fixed to the attachment 104 and is spaced a distance d from the second electrode 110, 402 (e.g., above the second electrode 110, 402 in a vertical configuration). The first electrode 106, 404 includes one or more springs to maintain the position of the first electrode 106, 404 (e.g., distance d away from the second electrode 110, 402), but allow the first electrode 106, 404 to move inward and outward when a second force overcomes the spring force. The first electrode 106, 404 is grounded and the second electrode 110, 402 is coupled to a voltage regulator 504. The voltage regulator 504 applies a bias voltage to the second electrode 110, 402. As the bias voltage applied to the second electrode 110, 402 increases, the voltage difference between the first electrode 106, 404 and the second electrode 110, 402 generates an electrostatic force that drives the first electrode 106, 404 towards the second electrode 110, 402, thereby moving the mirror 102 towards the second electrode 110, 402. Additionally or alternatively, the size of the area of ​​the second (e.g., base) electrode 110, 402 to which the bias voltage is applied can be increased, thereby increasing the electrostatic force and attracting the first electrode 106, 404 closer to the second electrode 110, 402, as in a digital style electrode. As the voltage decreases (and / or the size of the area over which the voltage is applied on the second electrode 110, 402 decreases), the electrostatic force decreases, thereby allowing the restoring force of the spring to move the first electrode 106, 404 away from the second electrode 110, 402. In this manner, the controller 112 can control the voltage and / or the size of the area over which the voltage is applied to the second electrode 110, 402 to control the position of the first electrode 106, 404, and thereby the position of the mirror 102. The amount of movement of the mirror 102 corresponds to the achievable phase modulation of the device.Thus, the examples described herein increase the travel distance of the mirror 102 in the MEMS pixels 100, 400, 410, 420 without the drawbacks of conventional MEMS pixels.

[0038] The MEMS pixel includes a pull-in point, also referred to as an instability point, that corresponds to the maximum distance the first electrode 106, 404 can move before collapse occurs (before the first electrode 106, 404 collapses towards the second electrode 110, 402, thereby destroying the functionality of the pixel). The instability point is an equilibrium point beyond which the system becomes potentially unstable. The stability of the system depends on the derivative of the net force (e.g., JPEG0007633479000001.jpg47<0 stable equilibrium, and JPEG0007633479000002.jpg47>0It is an unstable equilibrium, and in the above equation, x e is the equilibrium displacement. The net force is expressed as a combination of the electrostatic force and the spring force (e.g., F = F 静電 +F 機械 = JPEG0007633479000003.jpg411, where ∈ is the permittivity of the dielectric between the two electrodes, A is the area of ​​the base electrode, x is the displacement of the spring electrode 106, 404, and -kx is the restoring force in the linear spring). Thus, in this example, the first electrode 106, 404 cannot maintain a position beyond d / 3 threshold distance to the second electrode 110, 402. For example, if the spring electrode 106, 404 is 900 micrometers from the base electrode (without any electrostatic force applied), the spring electrode 106, 404 can only move 300 micrometers toward the base electrode before retraction occurs. However, the examples described herein include techniques for operating the pixel 100, 400, 410, 420 beyond the instability point without collapse.

[0039] Conventional MEMS pixels include four attachments for anchoring a first electrode (e.g., a spring electrode) to a surface. The first electrode of some conventional MEMS pixels includes four legs (having a spring constant) that are attached to a rigid body. In this way, when the electrostatic force increases, the legs can extend to move the rigid body toward the base electrode. However, such a design increases the vertical stiffness of the spring, thereby requiring either (a) an increase in the voltage applied to the base electrode (e.g., energy dissipation) or (b) an increase in the size of the base and / or spring electrodes (e.g., an increase in footprint and a decrease in fill factor). For example, conventional MEMS pixels require a bias voltage of 20-200 V to provide sufficient electrostatic force to move a conventional spring electrode 106, 404 / mirror 102 to a desired position. Increasing the size of the electrodes also limits the beam steering angle, limits the optical bandwidth, and limits the mechanical bandwidth. Examples described herein reduce the power and size of such conventional MEMS pixels by implementing the pixels 100, 400, 410, 420 using only three attachments 108a-108c to secure the spring electrodes 106, 404, thereby reducing the vertical stiffness by 25%. In this manner, the size of the pixel and the bias voltage for controlling the position of the mirror 102 can be reduced. Some examples described herein also include spring electrode designs (e.g., hexagonal base designs) that increase the perimeter-to-area ratio to further increase the efficiency of the MEMS pixels 100, 400, 410, 420. In examples described herein, MEMS pixels with sizes less than 10 micrometers can operate with bias voltages of 10V or less.

[0040] Some conventional pixels further reduce the number of anchors to only two support points. However, such conventional pixels may tilt or rotate the MEMS design due to process non-uniformities and / or deformations caused by thermal stress or thin film deposition stress. In the examples described herein, these stresses are fully compensated for by the anchor designs described. Thus, the examples described herein include very low tilt / displacement / rotation across process non-uniformities and environmental changes.

[0041] Additionally, some examples described herein include techniques for actuating (e.g., moving) the spring electrodes 106, 404 and mirror 102 past the instability point without collapse. In some examples described herein, the voltage applied to the base electrode is periodic (e.g., using a digital pulse or sinusoid) corresponding to a distance beyond the d / 3 threshold distance of the instability point. Because the voltage corresponds to a distance beyond the d / 3 threshold distance for a short period of time, the first electrode 106, 404 can move up to a 9d / 10 distance to the second electrode 110, 402 without collapse, thereby achieving pixel progression nearly three times the distance of conventional MEMS techniques that rely on parallel plate electrostatic actuation. Because the sinusoid or pulse will cause the spring electrodes 106, 404 and mirror 102 to vary in distance in a pulse or sinusoidal pattern, the examples described herein include sending data about the pulse or sinusoid (e.g., phase, amplitude) to a sampler in a receiving device so that the sampler can sample the light beam corresponding to the desired distance of the mirror. For example, if the pixels 100, 400, 410, 420 are periodic, and the mirror 102 corresponds to a distance of 600 micrometers every 5 nanoseconds, the sampler can sample the light beam every 5 nanoseconds, and the sampled light beam will correspond to the 600 micrometer distance of the mirror.

[0042] Also, some examples described herein include mechanical designs of the base electrodes 110, 402 and / or spring electrodes 106, 404 to increase the d / 3 threshold to a larger threshold (e.g., 2d / 3 threshold) without the need to sample the output by adjusting the characteristics of the base electrodes and / or spring electrodes 106, 404. For example, the base electrodes 402 and spring electrodes 404 are curved away from each other (e.g., to progressively increase the distance d above the position). For example, in such a curved configuration, the distance between the base electrodes 402 and the spring electrodes 404 increases as the position along the actuation structure from the support structure increases. By adjusting the spring electrodes and / or base electrodes, the electrostatic and / or spring forces are changed from a uniform, linear force to a non-uniform, non-linear force. In this way, when the spring electrodes 106, 404 approach the curved base electrodes, there is a greater force closer to the anchor and there is a greater restoring force in the spring (e.g., when the displacement is greater, the resistance of the spring is greater). The electrostatic force is inversely proportional to the square of the reduction in the gap when the restoring force of the spring is linear, as shown in Equation 1 below. JPEG0007633479000004.jpg641

[0043] This linearity can be compensated for by progressively moving the bias electrode away from the weakest part of the spring, so that the overall pixel movement increases from the d / 3 threshold of instability to a larger (e.g., 2d / 3) threshold of instability (e.g., twice the movement of conventional MEMS pixels) or even more. This nonlinear attractive force can also be balanced by pre-curving the spring (e.g., either via process-induced stresses in thin films, lithographic techniques, or other manufacturing processes that create curved or tapered structures) so that it exhibits a nonlinear increase in mechanical stiffness (k) with increasing displacement, increasing the movement until it reaches instability.

[0044] 5 is a block diagram of an electrode voltage controller 112 of FIGS. 1A and 1B described herein for periodically varying the voltage applied to the base electrode 110 to periodically displace the spring structure 106 (e.g., and mirror 102) beyond an instability point corresponding to a conventional MEMS pixel. Although the electrode voltage controller 112 is described with respect to the pixel 100, the electrode voltage controller 112 is useful for controlling the base electrode of any type of pixel. The electrode voltage controller 112 includes an example receiver 500, an example mirror displacement determiner 502, an example voltage source 504, and an example transmitter 506.

[0045] 5 receives commands from a computing device or circuitry to move the mirror 102 of the pixel 100 a certain distance, and the receiver 500 determines when a new command is received to trigger additional movement of the mirror 102.

[0046] The mirror displacement determiner 502 of FIG. 5 processes the received command to identify a desired displacement distance of the mirror 102 / spring structure 106. The mirror displacement determiner 502 determines whether the desired displacement distance of the received command is greater than or less than an instability point (e.g., a d / 3 threshold distance corresponding to the instability point of a conventional MEMS pixel). If the desired displacement distance is less than the instability point, the mirror displacement determiner 502 determines which voltage to apply to the base electrode 110 (e.g., for an analog base electrode) and / or how large an area of ​​the base electrode 110 to apply the voltage to (e.g., for a digital base electrode). If the desired displacement distance is greater than the instability point, the mirror displacement determiner 502 determines a periodic (e.g., digital pulse signal or sinusoidal) signal to apply to the base electrode 110. In some examples, the mirror displacement determiner 502 is responsive to the determined periodic signal to determine when the signal needs to be sampled to correspond to the desired displacement distance.

[0047] 5 generates a voltage in response to the voltage determined by the mirror displacement determiner 502. The voltage source 504 may be capable of outputting a stable voltage and / or a periodic voltage. In some examples, the voltage source 504 may include two or more voltage sources (e.g., one for a stable voltage and one for a periodic voltage). In some examples, the voltage source 504 may generate different periodic signals (e.g., corresponding to different frequencies, amplitudes, phases, etc.).

[0048] The transmitter 506 of FIG. 5 transmits data related to the periodic voltage (e.g., voltage change data) and / or sampling data to a receiving device via a wired or wireless signal. The voltage change data includes the phase, frequency, and amplitude related to the voltage applied by the voltage source 504, and / or the phase, frequency, and amplitude (e.g., if they are not identical) related to the movement of the mirror 102. In this manner, the receiving device can determine when to sample the received signal such that the sample corresponds to a desired mirror displacement position. The sampling data may include when to sample the received signal. In this manner, the receiving device can sample in direct response to the voltage change data (e.g., without calculating when to sample the received optical signal).

[0049] 5 shows an example implementation of the electrode voltage controller 112 of FIGURES 1A and 1B. Additionally, the receiver 500, mirror displacement determiner 502, voltage regulator 504, transmitter 506, and / or more generally the electrode voltage controller 112 of FIGURE 5 may be implemented by hardware, software, firmware, and / or any combination of hardware, software, and / or firmware. For example, any of the receiver 500, mirror displacement determiner 502, voltage regulator 504, transmitter 506, and / or more generally the electrode voltage controller 112 of FIGURE 5 may be implemented by one or more analog or digital circuits, logic circuits, programmable processors, application specific integrated circuits (ASICs), programmable logic devices (PLDs), and / or field programmable logic devices (FPLDs). In an example software and / or firmware implementation, at least one of the receiver 500, mirror displacement determiner 502, voltage regulator 504, transmitter 506, and / or more generally the electrode voltage controller 112 of FIG. 5 includes a computer-readable medium (such as a hard drive, memory, digital versatile disc (DVD), compact disc (CD), Blu-ray disc, or other information storage device) that stores the software and / or firmware.

[0050] A flow chart diagram of example machine-readable instructions for implementing the electrode voltage controller 112 of FIG. 5 is shown in FIG. 6. In this example, the machine-readable instructions form a program processable by an instruction execution device (such as, for example, the processor 1112 shown in the processor platform 1100 described below with respect to FIG. 11) to cause the device to perform the methods and processes described herein. The program may be embodied in software stored on a computer-readable medium, but alternatively, the entire program and / or parts thereof may be executed by devices other than the processor 1112 and / or may be embedded in firmware or dedicated hardware. Also, although the program is described with reference to the flow chart of FIG. 6, alternatively, other methods of implementing the electrode voltage controller 112 may be used. For example, the order of execution of the blocks may be changed, and / or some of the blocks described may be changed, deleted, or combined. Additionally or alternatively, any or all of the blocks may be implemented by one or more hardware circuits (such as discrete and / or integrated analog and / or digital circuit elements, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), comparators, operational amplifiers (opamps), logic circuits, etc.) structured to perform the corresponding operations without executing software or firmware.

[0051] As discussed above, the process of FIG. 6 may be implemented by coded instructions (eg, computer and / or machine readable instructions) stored on a computer-readable medium.

[0052] Figure 6 is an example flowchart 600 representing example machine-readable instructions that may be executed by the electrode voltage controller 112 of Figures 1A and 1B to apply a voltage to the base electrode 110, 402 (of Figures 1A, 1B, and / or 4) to displace the spring structure 106, 404 beyond a d / 3 threshold distance (e.g., an instability point). Although the instructions in Figure 6 are described with respect to the electrode voltage controller 112 of Figures 1A, 1B, and / or 5, the instructions may be used by any type of electrode voltage controller in any type of pixel structure.

[0053] In block 602, the receiver 500 receives a command to displace the mirror 102 a distance X. As discussed above with respect to FIG. 5, the command may be provided by another device to control the pixel 100 according to a desired output. In block 604, the mirror displacement determiner 502 determines whether X is greater than a collapse threshold distance. The collapse threshold distance corresponds to a displacement distance that will collapse the spring structure 106 (e.g., if held for more than a short period of time). As discussed above, the collapse threshold distance is approximately d / 3, where d is the distance of the spring structure 106 to the base electrode 110 when no voltage is applied by the electrode voltage controller 112.

[0054] If the mirror displacement determiner 502 determines that X is not greater than the depression distance threshold (NO at block 604), the voltage source 504 applies a voltage corresponding to the X distance to the base electrode 110 (block 606). In this manner, the spring structure 106 is attracted toward the base electrode 110 at the desired X distance. In some examples, the voltage source 504 may send a preset voltage to a portion of the area of ​​the base electrode 110 corresponding to the X distance (e.g., corresponding to a digital base electrode). In such examples, to increase the displacement, the voltage source 504 may send a preset voltage to a larger portion of the area of ​​the base electrode 110. In other examples, the voltage source 504 may send a voltage to the entire area of ​​the base electrode 110 corresponding to the X distance. In such examples, to increase the displacement, the voltage source 504 may send a higher voltage to the base electrode 110.

[0055] If the mirror displacement determiner 502 determines that X is greater than the depression distance threshold (YES at block 604), the voltage source 504 periodically varies (e.g., with a digital pulse signal or a sinusoid) the voltage applied to the base electrode 110 corresponding to the X distance (block 608). In some examples, the voltage source 504 may generate a periodic voltage where the peak of the periodic voltage corresponds to the X distance. In other examples, the voltage source 504 may generate a preset periodic voltage where the X distance corresponds to some point along the periodic voltage.

[0056] In block 610, the transmitter 506 transmits the voltage change data and / or the sampling to a receiving device (e.g., a device that receives light reflected off of the mirror 102 in FIG. 2). The voltage change data may include a frequency, amplitude, phase, etc., corresponding to the periodic voltage and / or periodic displacement. The sampling data may include instructions corresponding to when to sample the received signal (e.g., the mirror displacement determiner 502 determines when to sample the received signal in response to the periodic signal or the desired X distance). In this way, the receiving device knows when to sample the received signal such that the sample corresponds to the desired X distance.

[0057] In block 612, the receiver 500 determines whether an additional command corresponding to a new displacement distance has been received. If the receiver 500 determines that a new command has been received (YES at block 612), the process returns to block 604 according to the newly received distance. If the receiver 500 determines that a new command has not been received (NO at block 612), the electrode voltage controller 112 continues to operate corresponding to the X distance until the receiver 500 receives a new displacement distance.

[0058] 7 is an example graph 700 illustrating the increased range of motion produced by a harmonically resonant excitation waveform (e.g., a sinusoidal or repetitive pulse signal). The graph illustrates the change in normalized pixel displacement according to the frequency of the waveform for a first example mirror displacement 702 and a second example mirror displacement 704 of the mirror 102 of FIGS. 1A and 1B. The first mirror displacement 702 corresponds to a first modulation wavelength (e.g., 700 nanometers) and the example mirror displacement 704 corresponds to a second modulation wavelength (e.g., 470 nanometers). Alternatively, the first and second mirror displacements can be scaled to any fractional wavelength for any phase modulation by (a) adjusting the frequency of the drive pulse slightly off resonance and / or (b) reducing the amplitude of the bias voltage of the pulse.

[0059] As shown in graph 700 of Figure 7, when the device is operated in a high Q regime (Q>2), such as in a low pressure packaging environment, the device can be resonantly pumped. As the drive frequency approaches the resonant frequency (e.g., F res = JPEG0007633479000005.jpg67, where k corresponds to the stiffness of the spring legs 202a-202c of the spring structure 106, and m corresponds to the mass of the mirror 102), the pixel displacement of the first mirror displacement 702 can reach a maximum displacement that is an order of magnitude larger or larger than when the bias signal has a period significantly below the resonant frequency. Thus, the scaling of the displacement can be an order of magnitude or more higher than the scaling of the nominal displacement for the same voltage at a frequency below the resonant frequency. In this way, the mirror 102 can be pumped at a lower voltage (e.g., at or near the resonant frequency) to produce a larger oscillation. The second mirror displacement 704 illustrates a scenario in which the bias amplitude is reduced to tune the peak amplitude for different wavelengths. A similar scaling effect can be achieved by periodically biasing slightly below the resonant frequency of the device. As shown in the graph 700, the total movement of the mirror 102 is controlled while avoiding snap-in (e.g., collapse). The achievable amplitude is a function of the Q-factor and / or sampling conditions of the pixel 100. Each MEMS device may have a different resonant frequency proportional to its mass and / or stiffness, but the graph 700 is designed considering the entire system function.

[0060] 8 illustrates an example demonstration 800 corresponding to sampling of light reflected from the mirror 102. The demonstration 800 includes an example pixel movement 802 of the mirror 102 that may be caused by the periodic symbols output by the electrode voltage controller 112 of FIGS. 1A and 1B.

[0061] Pixel progression 802 in FIG. 8 is a sinusoidal displacement representing the variation of mirror 102 in response to pulses and / or sinusoids generated by voltage controller 112 in FIG. 1A and FIG. 1B. As shown in demonstration 800, the pixel moves over a range of 0 to λ / 2, where λ is the wavelength of the modulated light. In some examples, the total distance can be scaled to achieve a desired fractional component of the wavelength by pulse timing, amplitude, drive voltage, and / or mechanical design of the pixel. Each displacement corresponds to a difference in the reflected light. Thus, the receiving device can sample the reflected output of the mirror at different times to correspond to different mirror positions. For example, fast frame imaging, each representing a different state that can be used for sampling. As described above, details of the period pixel movement 802 can be transmitted to a receiving device, which can sample according to the desired mirror position. In demonstration 800, periods 1, 2, 3, and 4 represent different sampling points corresponding to different mirror positions. Thus, the mirror position can be sampled at the appropriate time to achieve the desired fractional wavelength. In such harmonic drive modes, wavelength resolution is limited by the complementary metal oxide semiconductor (CMOS) imager timing advance. In some examples, mass or stiffness can be added / removed from the pixel design to adjust the timing. All phase patterns can be captured within a single period, according to application timing requirements, integrated circuit performance, frame upload bandwidth, and / or process uniformity. Additionally or alternatively, the frame can span multiple periods. Additionally or alternatively, averaging can be used to compensate for pixel non-uniformity. Driving the device into resonance provides large displacements without the need to exceed the pull-in voltage.

[0062] Figure 9A illustrates an example periodic signal 900 that may be output by the electrode voltage controller 112 to periodically vary the mirror 102 past the d / 3 instability point without collapse. The example of Figure 9A includes a periodic signal 900 and an example mirror displacement 902. The periodic signal 900 is a series of pulses with a particular period and pulse width, although the periodic signal 900 can be any type of periodic signal.

[0063] The periodic signal 900 of FIG. 9A includes equally spaced pulses (e.g., 1 / resonant frequency) that repeat after 5 microseconds, with the pulses having a width of approximately 1 microsecond. Alternatively, the periodic signal 900 may correspond to any pattern. For example, the periodic signal 900 may be a function of the resonant frequency (e.g., F res = JPEG0007633479000006.jpg67, where k and m can both vary as a function of the particular dimensions, film thickness, and material set of the pixel design) and / or the period of the periodic signal 900 can be shorter or longer (e.g., shorter and higher voltage pulses or longer and lower voltage pulses) according to the drive signal slew rate. Outputting the periodic signal 900 results in a mirror displacement 902. For example, when the pulse of the periodic signal 900 is high, the mirror 102 is displaced, for example, (-0.75) (gap) towards the base electrode 110 of FIGS. 1A and 1B, where the gap corresponds to the distance between the base electrode 110 and the spring electrode 106 and / or the mirror 102. At the end of the pulse, the mirror displacement 902 illustrates that the mirror 102 is displaced (e.g., (.75) (gap)) away from the base electrode 110. Thus, the mirror displacement 902 illustrates that the mirror 102 can be driven beyond the d / 3 instability point without catastrophic contact (e.g., without any risk of catastrophic contact). In some examples, the drive voltage can be reduced and the pulse width can be extended to achieve a similar result. In such examples, the pumping period can be compensated by the drive waveform to improve the transition between states via active and passive cancellation via phase-shifted waveforms and / or reset pulses. When the periodic signal 900 is used in an array of pixels, the pixels can be addressed by only a phase-shifted version of the same drive source, as described below with respect to FIG. 10.

[0064] Figure 9B illustrates an example periodic signal 910 that may be output by the electrode voltage controller 112 to periodicate the mirror 102 past the d / 3 instability point without collapse. The example of Figure 9B includes a periodic signal 912 and an example mirror displacement 914. The example of Figure 9B includes an example transition period 916 for transitioning between a first example pixel phase 918 and a second example pixel phase 920.

[0065] As shown in the periodic signal 910 of FIG. 9B, the electrode voltage controller 112 of FIGS. 1A and 1B may transition one or more pixels 100 from a first example phase 918 to a second example phase 920 to change the way light is reflected by the mirror 102. In some examples, such as in an underdamped environment suitable for phase pumping, the transition period 916 may need to be adjusted instantly from the first example phase 918 to the second example phase 920. For example, the voltage controller 112 may apply one or more asynchronous pulses (e.g., a reset pulse to slow the movement of the pixel and / or a transition pulse to prepare the pixel for the second example phase 920) during the transition period 916 to increase the transition speed. In some examples, the voltage controller 112 may apply the transition across the pixel 100 and / or the array of pixels depending on the drive bandwidth. In some instances, it may be necessary to slow down the pixel 100 for several frames before properly transmitting the second phase for the second image to the pixel 100 and / or pixel array.

[0066] 10 illustrates example phase shifting mirror displacements 1000 for generating an example pixel array frame 1002 corresponding to an example illumination state 1004. The phase shifting mirror displacements 1000 include four example mirror displacements 1006, 1008, 1010, 1012 corresponding to four different delays. The pixel array frame 1002 includes four different frames 1012, 1016, 1018, 1020 corresponding to four different pixel array states. The illumination state 1004 includes four different illumination states 1022, 1024, 1026, 1028.

[0067] The shifted mirror displacement 1000 of Figure 10 includes four example mirror displacements 1006, 1008, 1010, 1012, each corresponding to a different delay. For example, the electrode voltage controller 112 may send different periodic signals corresponding to the different mirror displacements 1006, 1008, 1010, 1012. In some examples, additional circuitry may be included to generate delays of varying amounts. In this manner, the electrode voltage controller 112 may output one periodic signal, and a combination of multiplexers and delay circuitry may facilitate movement of the mirrors of different pixels in an array corresponding to the mirror displacements 1006, 1008, 1010, 1012.

[0068] The pixel array frame 1002 of FIG. 10 includes four different frames 1012, 1016, 1018, 1020 corresponding to a 4×4 pixel array (e.g., including four mirrors at various displacement positions). For example, each of the pixels may correspond to any one of the mirror displacements 1006, 1008, 1010, 1012. Adjusting the displacements of the different pixels of the pixel frame 1002 corresponds to different example lighting states 1004. For example, a first lighting state 1022 corresponds to the reflected light of the first example frame 1014, a second lighting state 1024 corresponds to the reflected light of the second example frame 1016, a third lighting state 1026 corresponds to the reflected light of the third example frame 1018, and a fourth lighting state 1028 corresponds to the reflected light of the fourth example frame 1020. 2 includes four pixel array frames 1002 corresponding to four shift mirror displacements 1000, however, any number and / or pattern of array frames can be used on any size pixel array. Additionally or alternatively, the bias waveforms can be scaled to achieve different displacements.

[0069] Figure 11 is a block diagram of an example processor platform 1100 that may execute the instructions of Figures 3-4 to implement the electrode voltage controller 112 of Figure 5. For example, the processor platform 1100 may be a server, a personal computer, a mobile device (e.g., a mobile phone, a smart phone, a tablet such as an iPad™), a personal digital assistant (PDA), an Internet appliance, a DVD player, a CD player, a digital video recorder, a Blu-ray player, a game console, a personal video recorder, a set-top box, or any other type of computing device.

[0070] The processor platform 1100 of the illustrated example includes a processor 1112. The processor 1112 of the illustrated example is hardware. For example, the processor 1112 can be implemented by one or more integrated circuits, logic circuits, microprocessors, or controllers from any desired family or manufacturer. A hardware processor can be a semiconductor-based (e.g., silicon-based) device. In this example, the processor implements the receiver 500, the mirror displacement determiner 502, the voltage source 504, and the transmitter 506.

[0071] In this example, the processor 1112 includes a local memory 1113 (e.g., a cache). Also in this example, the processor 1112 communicates with a main memory including a volatile memory 1114 and a non-volatile memory 1116 via a bus 1118. The volatile memory 1114 may be implemented by synchronous dynamic random access memory (SDRAM), dynamic random access memory (DRAM), RAMBUS dynamic random access memory (RDRAM), and / or any other type of random access memory device. The non-volatile memory 1116 may be implemented by flash memory and / or any other desired type of memory device. Access to the main memory 1114, 1116 is controlled by a memory controller.

[0072] The processor platform 1100 of the illustrated example also includes an interface circuit 1120. The interface circuit 1120 may be implemented with any type of interface standard, such as an Ethernet interface, a Universal Serial Bus (USB), and / or a PCI Express interface.

[0073] In the illustrated example, one or more input devices 1122 are coupled to the interface circuit 1120. The input devices 1122 enable a user to input data and / or commands to the processor 1112. For example, the input devices may be implemented by audio sensors, a microphone, a camera (still or video), a keyboard, buttons, a mouse, a touch screen, a trackpad, a trackball, an isopoint, and / or a voice recognition system.

[0074] One or more output devices 1124 are also connected to the interface circuitry 1120 of the illustrated example. For example, the output device(s) 1124 can be implemented by a display device (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display, a cathode ray tube display (CRT), a touch screen, a tactile output device, a printer, and / or a speaker). Thus, the interface circuitry 1120 of the illustrated example typically includes a graphics driver card, a graphics driver chip, and / or a graphics driver processor.

[0075] The interface circuitry 1120 of the illustrated example also includes communications devices such as a transmitter, receiver, transceiver, modem, and / or network interface card to facilitate data exchange with an external machine (e.g., any type of computing device) via a network 1126 (such as an Ethernet connection, a Digital Subscriber Line (DSL), a phone line, a coaxial cable, a cellular telephone system, etc.).

[0076] The processor platform 1100 of the illustrated example also includes one or more mass storage devices 1128 for storing software and / or data. Examples of such mass storage devices 1128 include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and digital versatile disk (DVD) drives.

[0077] The coded instructions 1132 of FIG. 6 may be stored in the mass storage device 1128, the volatile memory 1114, the non-volatile memory 1116, and / or another computer-readable medium.

[0078] A computer program product is a product having (a) a computer-readable medium and (b) a computer-readable program stored on such medium. Such a program is processable (e.g., executable) by an instruction-execution device to cause the device to perform the operations described above. For example, in response to processing (e.g., executing) instructions of such a program, the device performs the operations described above such that such operations are at least partially computer-implemented.

[0079] Such programs (e.g., software, firmware, and / or microcode) may be written in one or more programming languages, such as object-oriented programming languages ​​(e.g., C++), procedural programming languages ​​(e.g., C), and / or any suitable combination thereof. In a first example, the computer-readable medium is a computer-readable storage medium. In a second example, the computer-readable medium is a computer-readable signal medium.

[0080] A computer-readable storage medium includes any system, device, and / or other non-transitory tangible apparatus (e.g., electronic, magnetic, optical, electromagnetic, infrared, semiconductor, and / or any suitable combination thereof) suitable for storing a program such that such program is processable by an instruction execution apparatus to cause the instruction execution apparatus to perform the operations described above. Examples of computer-readable storage media include an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory ("RAM"), a read-only memory ("ROM"), an erasable programmable read-only memory ("EPROM" or flash memory), optical fiber, a portable compact disk read-only memory ("CD-ROM"), an optical storage device, a magnetic storage device, and / or any suitable combination thereof.

[0081] A computer-readable signal medium includes any computer-readable medium (other than a computer-readable storage medium) suitable for communicating (e.g., propagating or transmitting) a program such that such a program is processable by an instruction execution device to cause the instruction execution device to perform the operations described above. In one example, a computer-readable signal medium includes a data signal having computer-readable program code embodied therein (e.g., in baseband or as part of a carrier wave) and communicated (e.g., electronically, electromagnetically, and / or optically) via wire, wireless, fiber optic cable, and / or any suitable combination thereof.

[0082] Thus, exemplary methods, apparatus, and products are described herein for increasing the efficiency and optical bandwidth of MEMS piston mode SLMs. Examples described herein include novel spring structures for MEMS pixels that can be sized below 10 micrometers and operate at bias voltages of 10V or less while achieving significant displacement for lightwave modulation beyond visible wavelengths. Examples described herein also include non-uniformly shaped spring structures and / or base electrodes (e.g., grayscale gradient, curvature, etc.) to increase the instability point from a d / 3 displacement distance (e.g., corresponding to a conventional MEMS pixel) to a larger displacement distance (e.g., 2d / 3 displacement distance). A further example described herein applies a periodic voltage (e.g., using a digital pulse or sinusoid) to the base electrode for a voltage corresponding to a distance above (e.g., away from) the d / 3 threshold distance corresponding to the instability point. Because the voltage corresponds to a distance exceeding the d / 3 threshold distance for a short period of time, the first electrode can travel up to a 9d / 10 distance to the second electrode without collapse, thereby achieving approximately three times longer pixel travel compared to conventional MEMS approaches. Thus, the examples described herein provide sub-10 micron pixels capable of modulating large wavelengths of light (e.g., 1550 nm) using low drive voltages (e.g., 10 V).

[0083] Modifications in the described embodiments are possible, and other embodiments are possible, within the scope of the claims.

Claims

1. 1. A microelectromechanical systems piston mode spatial light modulator device, comprising: Miller and a mirror via having a first end attached to the mirror and a second end; A spring structure, a rigid body attached to a second end of the mirror via; three spring legs coupled to the rigid body for displacing the rigid body in response to an electrostatic force applied to the spring structure; the spring structure including: a base electrode configured to apply a voltage to generate the electrostatic force; Including, The apparatus wherein the rigid body curves away from the base electrode.

2. 2. The apparatus of claim 1, The apparatus, wherein the spring structure has a hexagonal shape.

3. 2. The apparatus of claim 1, The apparatus wherein the three spring legs wrap partially around a periphery of the rigid body.

4. 2. The apparatus of claim 1, a spring attachment for attaching the spring leg to a base; The apparatus, wherein the spring structure, the mirror via and the spring attachment are made of the same material.

5. 5. The apparatus of claim 4, The apparatus wherein the spring attachment is coupled to ground.

6. 5. The apparatus of claim 4, The apparatus wherein the mirror via is shorter than the spring attachment.

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