Standard OKO mirrors are circular with a diameter of 10 mm, 15 mm, 30 mm , 40 mm, and 50 mm. We can custom develop devices of up to one inch in diameter and with various geometries of reflective membrane - we have experience with square, rectangular, circular and elliptical membranes.
The reflective surface of an MMDM is a membrane, which is fixed at the edges. Thus for correction of an aberration with arbitrary boundary conditions, a central part of the mirror (approximately 2/3 of the total membrane diameter) should be used. This area is called “working aperture” of the mirror. Thus, for a 15 mm MMDM, a working aperture is about 10 mm.
Any membrane or coating defect located outside the working aperture does not affect the mirror performance.
Making a membrane for MMDM is a complex process, and it’s practically impossible to obtain membranes without any defect. These defects are the result of (dust) particles and are visible as small spots of uncoated membrane or as small particles stuck to the surface. Usually they are near the membrane edge. Up to two defects on a deformable mirror is considered to be OK, as they do not impair the mirror functionality.
The displacement of the mirror surface is proportional to the SQUARE of the applied voltage. The mirror response can be linearized using the operation of square root. For 8-bit biased digital control the following expression can be used to convert the control signal CS (in the range -1…1) into the control byte CB applied directly to the digital board controlling the mirror actuator: CB=(int)sqrt(0.5*(CS+1))*255.; This formula provides linear correspondence between the control signal CS and the mirror displacement and sets the mirror into theoretical biased position when CS=0.
The surface quality is good enough to work with very low scattering in the whole visible spectrum. The initial figure of MMDM is flat with RMS deviation from the nearest reference plane better than 250nm. A mirror a diameter of 10mm will have less than 1 fringe of astigmatism (averaged over a number of devices), an average mirror with a diameter of 15mm has about 2 fringes of astigmatism. These aberrations can be easily corrected during the mirror operation by calibrating the bias voltage.
MMDM consists of a thin (500 to 700nm thick) membrane made of silicon nitride. The membrane is coated by a thin layer of aluminum or gold to produce a highly reflective surface. The membrane is fixed to silicon frame and suspended over a number of planar electrodes - electrostatic actuators. When the membrane is electrically grounded and a voltage is applied to one or a number of the actuators, the membrane is deformed locally changing its shape.
In the simplest case biasing can be achieved by applying a constant voltage to all actuators of the MMDM. Theoretically under the constant bias the MMDM should take a parabolic shape. In practice, MMDM biased with a constant voltage has figure error of up to 300nm RMS from the nearest perfect parabola (sphere). The bias voltages should be adjusted to make the biased surface perfect. The theoretical value of the bias voltage equals to 0.
The device can be specially calibrated to correct for tilts, preserving the diffraction-limited quality of the reflected beam in the range of about 25*lambda/D where lambda is the wavelength and D is the mirror diameter. Contact OKO for details. Using the device in scanner mode will reduce its correction performance for higher order aberrations.
The MMDM membrane can be deflected only in the direction of the electrode structure because the electrostatic force can be only attractive. This means the deflected membrane can produce only concave optical shapes with a reference to a flat surface. To achieve bi-directional operation the membrane should be initially deflected towards the actuators and made perfectly spherical by adjusting the actuator voltages. From this state the membrane can be moved to both positive (from the electrode structure) and negative (to the actuator structure) directions by controlling the actuators voltage.
MMDM is “Micromachined membrane deformable mirror”.
