OPTRA Inc. RPA Technical Background Risley Prism Assembly Beamsteerers OPTRA, Inc., 461 Boston Street, Topsfield, MA 10983 [email protected] www.optra.com System Design and Operating Principle Risley prisms are comprised of a symmetric pair of prisms that are independently rotated about the optic axis. Figure 1 illustrates conceptually how a Risley prism pair is used to steer light. In (a) the prism apex’s are aligned and Figure 1 Risley Prism Beam Steering the pair of prisms steer light the same amount as a single prism with twice the apex angle, in (b) both prisms are rotated in opposite directions and reduce the steered angle, and in (c) the prisms apex’s are opposed and light passes through un‐deflected. Conceptually, light anywhere within the conical system field of view is addressed through the two‐step process of adjusting the phase angle between the prism pair to achieve the desired angle off the optic axis and then rotating the pair to the desired direction. In practice, the prisms move independently to the desired location. The key components of the RPA optical‐
mechanical beamsteering assembly are shown in Figure 2 and include hollow core rotary motors, duplex bearings, rotary angle optical feedback encoders, and a matched prism set. A straightforward package can be designed to hold the elements in a compact arrangement that leads to the following advantages: 



Low moment of inertia leading to low power Insensitivity to vibration Independent rotational axes (no carried axes, no need for slip rings) High‐speed and response time Optical beam pointing along a specified direction is accomplished using digital signal processing and closed‐loop motion control to convert the angular pointing command to prism rotation angles. The main hardware components are shown in Figure 3. A Performance Motion Devices (PMD) motion control chipset is used to Figure 2 RPA Key Components close the loop and provide prism commands. The commands are received from the user via the serial interface through the Texas Instruments (TI) 3
OPTRA, Inc. 140519 OPTRA Inc. RPA Technical Background Digitial Signal Processor (DSP) and converted to prism commands through a series of numerical operations. The FPGA provides communication with the PMD chipset, TI DSP, and the optical rotary angle encoders. This allows the system to provide a high‐speed parallel output of the system pointing direction at rates up to 100 kHz. Figure 3 RPA Control Block Diagram Table 1 shows a summary of typical operating specifications achievable with a standard design based on COTS components. Table 1 RPA Typical Operating Specifications Item Clear aperture Specification 10 – 200 mm Beam quality  /8 System Transmission  98% Operating wavelength UV – LWIR range Resolution  1 – 120 deg full angle cone  100 rad Repeatability  100 rad Accuracy  1 mrad Full field slew time  250 ms Closed loop bandwidth Peak scan speed  50 Hz Field of Regard (FOR) Aperture size to system diameter ratio  4000 RPM  63% Comment OPTRA Inc has designed systems with 10, 25, 50, 120, & 185 mm clear apertures Easily achieved with standard optical finishing and mounting techniques Easily achievable with low absorption materials and standard anti‐reflection coatings. OPTRA, Inc has produced system operating at 355 nm, 532 nm, 980 nm, 1064 nm, 1550 nm, 3‐
5 µm, and 8‐12 µm(achromatic) OPTRA Inc has produced systems at 2, 12, 30, 45, 60, 90, 120 deg FOR. Achievable with standard optical encoder technology for measuring prism rotation angle Achievable using standard digital control closed‐
loop positioning technology Full field pointing accuracy (better than 1 part in 2000 at maximum FOR) Compact design and low inertia result in high speed to power ratio Sufficient bandwidth for rejecting beam jitter due to operating on a moving platform Small moment of inertia of prism allows fast scanning speed with low power Achievable with high aspect hollow core rotary brushless motors and bearings 4
OPTRA, Inc. 140519 OPTRA Inc. RPA Technical Background Item Supply voltage Specification 28 VDC Power  25 W Interface Update rate RS‐232  57.6 kBaud Temperature range 0 to +50 C Comment Small moment of inertia allows high scan speed at low supply voltage Low rotating inertia requires minimal current to move; no holding power required at rest due to no carried axes or loads Simple universal serial interface Supports 1 kHz command update rate ideal for closed loop tracking applications Suitable for fielded operating OPTRA has an extensive set of tools available to support RPA design efforts. These include optical ray trace models that can generate simple designs based on a pair of wedges or more completed achromatic designs using combinations of materials for each wedge. OPTRA has also developed models in MATLAB based on the 3D vector form of Snell’s Law. This model allows simulations based on different optical designs to be created for use in projecting design performance and provides the nonlinear relationship between prism angle difference and field angle (ALT), pointing errors due to beam, prism, and mechanical misalignments, beam compression as a function of field angle (ALT), and required electrical power to achieve desired slew rates and scan speeds. Figure 4 shows an example output from the MATLAB model for an SF10 system operating at 1550 nm (18.5 deg wedge angle) and shows the relationship between the prism angles and the direction of the optical axis in the FOR. Note that the relationship is nonlinear and a direct form solution relating desired pointing direction to prism rotation angles, while possible, is resource demanding in practice. Instead, the RPA system is calibrated after assembly and a Look‐Up‐Table (LUT) is used to generate the prism commands to point the optic axis in the desired direction. Figure 4 Example RPA Optical Beam Steering Response Function 5
OPTRA, Inc. 140519 OPTRA Inc. RPA Technical Background Contributions to Pointing Errors A number of errors contribute to pointing accuracy: Nadir, bearing misalignment, encoder centration, datum mechanical errors and calibration fixture errors. Nadir error Nadir error is the inability to point within a small region about the optical axis and is due to errors in prism wedge angles. The Nadir error is a function of wedge angle mismatch, , between the prism pair,  Nadir   n  1 , (1) where n is the material index. For example, a pair of SF10 wedges with standard angle tolerances of 0.5 arc‐min would exhibit about 100 microradians of error per wedge, or an expected (RMS) error of less than 150 microradians. Typically, wedge angle tolerances are set to achieve a Nadir error 5‐10 times below the desired pointing accuracy of 1 milliradian. Bearing misalignment (tilt) error Bearing misalignment generates an angular error between the rotation axis and optical axis and leads to a field dependent pointing error. This error is dependent on the maximum steering angle and is linear as a function of bearing tilt angle. The bearing tilt angle is limited by surface flatness and the system diameter, resulting in the following relationship,  bearing  2 0.057 ALTmax tilt N
 tilt 
. Flatness error
Bearing diamter
(2) where N is the number of surfaces coupled between the bearing axes. Note that this is the maximum contribution at the edge of the FOR; all other errors will be less inside the FOR. Precision machining tolerance is limited to 0.0005 inches flatness. As an example, for a 1.75‐inch diameter bearing the expected maximum tilt error is 0.000286 radians. The numbers of surfaces between the bearings is typically 5, which results in an RMS contribution due to bearing tilt of 25 microradians for 60 deg FOR system (ALTmax=30 deg). Centration error Centration error of the encoder arising from mechanical shaft errors and disk location creates a (cyclical) field dependent error. This cyclical rotational error can cause both a radial (system pointing angle deflection change off the optic axis) and rotational (system pointing angle rotation change about the optic axis), with maximum contributions given by  radial  2 rot ALTmax
’  rot   rot ALTmax
(3) where rot is the prism rotational error due to centration error. The radial error is a maximum when the system is pointing along the optic axis and zero at the edge of the field. Conversely, the rotational error is a maximum at the edge of the field and a minimum when pointing along the optic axis. Residual eccentricity after encoder alignment and assembly is typically limited to 0.0005 inches, which results in a maximum rotation error of 667 microradians per prism axis (1.5 degree encoder diameter). For a 30 deg maximum pointing angle, this results in radial and rotational error components of 347 and 174 microradians respectively. Note also that this error is deterministic once the system is assembled and could be removed by performing a two dimensional field calibration. 6
OPTRA, Inc. 140519 OPTRA Inc. RPA Technical Background Datum errors Datum errors include play in the mounting features used to create and align the system pointing frame of reference. This error is driven by the play in the pin and slot mechanical interface used to align the system to the coordinate frame of reference. The mechanical precision is limited to 0.0005 inches and will create a rotational error that will contribute a rotational pointing error as described above. For a mounting diameter of 2‐inches, the rotational error component is 0.00025 radians and results in a maximum pointing error of 125 microradians. The RSS of the bearing, centration, and datum errors provide an estimate of the expected system accuracy across the field outside of the Nadir region. For the 60 deg FOR example system, the expected accuracy is better than 400 microradians and well within the desired system requirement of 1 milliradian. Application Example: Moving Platform Closed Loop Tracking A number of applications operate from moving platforms and require closed‐loop tracking of the optical beam steering assembly to keep the optical system trained on the object of interest. One such example is free space optical communications. The closed loop bandwidth of the optical beam steering system directly relates to the residual pointing error after compensation. The goal is to operate at a closed‐loop bandwidth large enough such that the residual pointing error is smaller than the desired accuracy of the system. Figure 5 shows a measured angular power spectral density (PSD) curve for a Humvee driven off‐
road. Figure 5 Angular Power Spectral Density (PSD) for a Humvee driven off road. The blue curve represents the measured vibration profile along one direction (pitch). The other two directions show a similar response. The red line is representative of white noise with a standard deviation of 2.9 milliradians and the green line is white noise with a standard deviation of 133 microradians shows the expected residual pointing error as a function of frequency subjected to the angular PSD in Figure 5. The RPA system was modeled as a second‐order system with a 75‐Hz closed loop bandwidth, which was sufficient to keep the residual pointing error less than 10 microradians at all frequencies. 7
OPTRA, Inc. 140519 OPTRA Inc. RPA Technical Background Figure 6 Predicted residual pointing error for an RPA system mounted on a Humvee driven off‐road OPTRA, Inc. Risley Prism Product Portfolio OPTRA currently offers four RPA systems that provide high‐torque or high‐scan speed at 25 or 50 mm clear aperture diameters. The specifications for the four systems have been summarized in Table 2. OPTRA continues to develop and release to production new RPA systems in order to meet new customer applications. Table 2 OPTRA Inc. Risley Prism Laser Beam Steering System Specifications RP‐25F RP‐25S
RP‐50S
RP‐50F Steering/Scanning Steering Scanning
Steering
Scanning Peak response time/speed (ms/RPM) 175/3000 275/6000 250/500 350/4000 Closed loop bandwidth (Hz) 75 40 75 40 Clear Aperture (mm) ≥ 25 ≥ 25
≥ 50
≥ 50 Diameter (mm) 86 86
130
130 Length (mm) 50 76
116
116 Weight (kg) 1.0 1.3
2.8
2.8 Power (V) 28 28
28
28 8
OPTRA, Inc. 140519