Direct Fiber Positioning System
We submitted our Phase I SBIR grant application entitled A Novel Dense Fiber Array for Astronomical Spectroscopy to the National Science Foundation (NSF) on December 4, 2020. We began our Phase I work in October 2021. The NSF notified us of our award on January 1, 2022. The initial grant covered twelve months of work. The NSF granted us a three-month extension in August, 2022. We completed our Phase I work in February, 2022. This document is a final report on our Phase I work. For a detailed chronicle of our Phase I work, see our DFPS Development Log.
Our Direct Fiber Positioning System (DFPS) uses the slight bending of a piezo-electric cylinder to displace the tip of an optical fiber at the end of a tube. Each fiber positioner consists of a cylindrical, piezo-electric actuator, a long tube for a mast, a detector fiber held in a ferrule, and a controller and amplifier to generate the actuator's electrode voltages. The DFPS provides one fiber positioner per 5 mm × 5 mm square area. All electronics and services fit within a 25 mm2 footprint. All positioners can be adjusted independently and simultaneously. Adjustment requires no increase in power consumption. We can construct an array of one hundred thousand positioners using the same fundamental design as we would use to construct an array of eighty fibers. When combined with a spectrometer, the DFPS provides one measurement of red shift per 5 mm × 5 mm square. A fiber view camera (FVC) looks down upon the fiber tips from above. Its function is to measure the locations of the detector fibers during the spectrograph exposure. We can back-illuminate the detector fibers so they appear as point sources in the FVC, or we can back-illuminate separate guide fibers mounted adjacent to the detector fibers. Fiducial fibers distributed throughout the array, and around its perimeter, allow us to determine the location of the fibers with respect to the telescope's field of view. The FVC allows us to keep the detector fibers on their targets during arbitrarily long exposures. Our work on the DFPS since October, 2021 has been supported entirely by a Phase I Small Business Initiative Research (SBIR) grant number 2111936 awarded by the National Science Foundation.
The DFPS is the front end of a multi-object spectrograph. The back end is a system of diffraction gratings, mirrors, lenses, and image sensors that creates and records the spectra of the light from each detector fiber. The design and construction of spectrographs is challenging, but the technology and expertise to build such instruments already exists. In our Phase I work, we concentrated upon the design of the fiber positioners, how to mount them in a compact array, how to deliver their control signals, how to fit their control electronics in the space available beneath each positioner, and how to mitigate the effect of creep, hysteresis, and gravitational bending when trying to maintain the position of a fiber tip. In Phase I, our positioners consisted only of guide fibers. We illuminated these at the far end so that they glow in the view of our FVC.
In our Phase I work, we built several prototype positioners, concluding with a 4×4 array equipped with all necessary control electronics, power supplies, and mechanical services, all fitting within the 20 mm × 20 mm area of the array. In the sections below, we present our Phase I work and compare our progress to the milestones we declared in our original application.
For the convenience of our readers, we present the following glossary of terms.
|Positioner||The combination of an actuator, mast, and controller that together move the tip of a fiber.|
|Actuator||The piezo-electric cylinder that bends when we apply voltage to its electrodes.|
|Mast||The long tube that acts as a lever arm to turn the bending of the actuator into translation of the fiber tip.|
|Ferrule||The cylinder with a precision center hole that presents the polished fiber tip.|
|Controller||The logic, converters, and amplifiers that generate a single actuator's four electrode voltages.|
|Base Board||The printed circuit board that supports all the positioners of a single cell.|
|Service Board||The printed circuit board that holds the fiber controllers for all the positioners of a single cell.|
|Detector Cell||A base board, its fibers, its positioners, its service board, and all its controllers.|
|Detector Fiber||A fiber used to capture and transport the light from a celestial object.|
|Guide Fiber||A fiber used to reveal the location of a detector fiber.|
|Dead Reckoning||Moving a fiber to a desired position and keeping it there with no use of guide fibers.|
|Guide Sensor||An image sensor at the edge of the positioner array that records the position of guide stars.|
|Fiducial Fiber||A fiber used to locate the positioner array with respect to celestial guide sensors.|
|Fiber View Camera||A camera looking down on the fiber tips.|
|Front End||The multi-object detector: fibers, positioners, and the fiber view camera.|
|Back End||The spectrometer itself: we plug the fibers into it and it records spectra.|
The detector and guide fibers may be the same fiber, or separate fibers. The fiducial fibers are stationary fibers whose location we know with respect to the guide sensors.
From January to March of of 2022, we worked with our Test Stand Zero (TS0), which provided three fibers mounted on an optical breadboard. Each positioner consisted of a 40-mm actuator, a 300-mm stainless steel mast, a 2.5-mm diameter zirconia ferrule at the tip of the mast, and an optical fiber running down the inside of the mast to a nearby light injector. A monochrome camera looked down upon the fiber tips from above, allowing us to measure fiber position with a precision of better than 5 μm rms.
We used TS0 to study creep and hysteresis in the response of the piezo-electric actuators. We used a spiral reset procedure to mitigate the effect of hysteresis, and we used a prediction and correction strategy to mitigate the effect of creep. Following a spiral reset, we obtain precision of 10 μm rms for a subsequent movement to the corners of our range of motion, regardless of where the fiber was located before the move. Once the movement is complete, the actuator creeps. By watching this creep for 200 s, we can predict where the fiber will be 1800 s later with precision 10 μm rms.
Our creep compensation procedure consists of watching the movement of the fiber for 100 s after its initial, larger movement, and fitting a straight line to its position versus logarithmic time. The creep adheres well to a logarithmic model, allowing us to predict the position of the fiber following the movement with an accuracy of ±1% of the initial movement, or roughly 10 μm rms for randomly chosen movements across the fiber's range of motion.
By combining our spiral reset and our creep compensation calculation, we can, in principle, move to any fiber to any position and hold it there for an hour with precision 10 μm rms. We call this strategy for positioning fibers, where we make use of no measurement of fiber position during the entire spectrograph exposure, dead reckoning. But we have no intention of operating the DFPS in this manner. One of the advantages of the DFPS over competing fiber positioner designs is our ability to adjust all fibers simultaneously and continuously without any significant increase in the power consumption of the control electronics. We will measure the position of all the fibers every ten minutes, so our concern is compensating for creep over a ten-minute period. Our precision improves to 5 μm rms and we have no limit on exposure time. We will use our dead-reckoning calculation to accelerate the initial re-positioning of the fibers and to assess the health of each positioner during its exposure.
Milestone Three: Construct a non-miniaturized, single-fiber DFPS. Our TS0 provided three fibers, which we claim satisfies our first milestone.
One of the weaknesses of TS0 was its vulnerability to floor vibration and the fact that we could not rotate the positioner array into the horizontal position. From April to July of 2022, we worked with our Test Stand One (TS1), which provided four fiber positioners mounted on a two-axis gimbal sitting on a vibration-absorbing optical table. The actuators were piezo-electric cylinders 40-mm long, 3.6-mm outer diameter, 2.8-mm inner diameter, taken from a new set of sixty actuators we purchased for our Phase I work. These actuators provide four electrodes on their outer surfaces, to which the manufacturer recommends we apply up to ±250 V to cause bending. The masts were 300-mm long, 2.40 mm OD, 2.25 mm ID stainless steel tubes. At the tip and base of each positioner were 1.25-mm diameter zirconia ferrules presenting the two ends of a 125-μm diameter, 62-μm core optical fiber running down the center. To the lower end of each fiber, we connected another fiber that ran to a light injector. We made this connection with a zirconia sleeve, pushing the two fiber ends together so that they are held in contact by the static friction within the sleeve.
According to the manufacturer, the maximum bending of these actuators, provided they are constrained only at their top and bottom surfaces, is ±6.3 mrad. Our masts are 300 mm long, so the maximum movement of the fiber we can hope for is ±1.9 mm. In TS1 we constrained the bottom 3 mm of each actuator with solder joints to vertical pins, and we constrained the top 5 mm of the actuator by gluing a steel tube to its inner diameter. Both these modifications we expect to decrease the maximum movement of the fiber tip. In practice, we observed ±1.7 mm movement of the fiber tip, which is a diagonal range of 4.8 mm.
Milestone Two: Choose an actuator tube. We chose a custom-made piezo-electric tube actuator 40 mm made by Physik Instrumente. We paid $250 each for these in quantity 60. In quantity 1000, the same actuators cost $150. If we solder only to the bottom 1 mm of the actuators, and glue the mast only to the top 1 mm, we expect to see ±1.9 mm range of motion.
We used TS1 to extend our study of actuator hysteresis and creep. We showed that our spiral reset combined with our creep compensation model provided repeatability and stability of 10 μm at the fiber tip for weeks at a time. We presented our results at Snowmass in July, 2022 with our poster Direct Positioning of 50,000 Optical Fibers.
Another thing we learned from TS1 is that our steel masts deflect by ±700 μm when we rotate them to the horizontal. At that point, we ordered custom-made carbon fiber masts, in the hope that the sag would be reduced by a factor of two.
Milestone One: Choose a guide tube material. We chose a custom-made carbon fiber tubes 300 mm long. We paid $75 per tube in quantity 20. In quantity 1000, the same tubes cost $35.
Milestone Four: Demonstrate better than 10-μm precision in the single-fiber DFPS, in vertical and horizontal orientations, at temperatures 25°C and −10°C. Our TS1 met this milestone at 25°C. We abandoned our plan to test the system at −10°C for three reasons. First, our choice of carbon fiber tubes greatly decreases the potential distortion of the mast due to temperature changes. Second, we no longer plan to use dead reckoning to hold the fibers on target, so predicting their movement with temperature is no longer important. Third, purchasing a freezer, running cables into the freezer, and conducting the required experiments would have diverted too much effort from the challenges that emerged when we started designing the electronic and mechanical services for our 4×4 array.
From August 2022 to February 2023, we built and studied Test Stand Two (TS2). The purpose of TS2 was to demonstrate that we can load sixteen positioners onto a 20-mm × 20-mm footprint, with all necessary control electronics, high voltage amplifiers, and mechanical services mounted beneath the same 20-mm × 20-mm footprint. Each 4×4 cell of positioners must be constructed in such a way that another identical cell may be loaded on all sides, so as to continue the array with no gaps between the cells. Another purpose of TS2 was to demonstrate that our fiber controller logic and amplifiers are capable of delivering the electrical stability and precision required to place fibers with 10 μm precision, and do so while dissipating less than a few tens of milliwatts per positioner. Our focus in TS2 was upon the assembly procedure, the mechanical design of the plates and circuit boards, and the design and assembly of the electronic circuits and the miniature connectors.
Loading the sixteen positioners onto their base board turned out to be particularly challenging. Our hope was to solder the actuator electrodes to pads on the base board with the help of solder paste and a surface mount reflow oven. But the joints we made this way were unreliable. We ended up having to hand-solder the positioners onto the base board, which was hindered by the fact that every positioner was fully-assembled with mast, and a polished 1.25-mm diameter ferrule at either end. We succeeded in loading all sixteen, but the alignment of the fiber tips was no better than ±1 mm, which meant that the fibers interfered with one another when we eventually set them to moving across their full dynamic range.
The TS2 masts are carbon fiber. At the base of each positioner is a ferrule to which we connect another optical fiber, which in turn runs to a light injector. We can flash all sixteen fiber tips independently. When we rotate the masts into the horizontal position, we observe them to sag by ±350 μm with a repeatability of 10 μm rms. For pointing angles up to 45° from the zenith, we believe we can predict the deflection of the fiber tips to better than 5 μm rms. Predicting the sage to 5 μm rms is useful as a diagnostic check of each fiber, but is not necessary to maintain the fibers on target. Our concern with the sag is that if one mast sags by 1 mm while another sags by 2 mm at the same orientation, we will be unable to compensate for sag by rotating the telescope. It appears, however, that the sag will be within ±50 μm for all masts.
Packing sixteen fiber controllers beneath our array of sixteen positioners requires a connector capable of maintaining isolation between ±250 V signals, and holding each fiber controller in place with its own insertion force, all within a 25-mm2 area. Only one company makes connectors that meet these requirements: Omnetics Connector Corporation in Minnesota. In the photograph below we can see pairs of these connectors mating at the top of each fiber controller circuit.
In the photograph we see a three-cell backplane board equipped with one service board. The fiber controllers are plugged into the service board. A flex cable runs from the service board up to the base board. The actuators are soldered to the base board. The flex cable can be bent at a sharp 90° angle where it emerges from both the base and service boards, thus allowing us to the 19-mm square circuit boards on a 20-mm grid.
The flex cable carries all sixty four high-voltage signals required by the sixteen actuators. The fiber controllers receive high-voltage power from the service board, as well as serial logic control, both of which they share with every other fiber controller on the same backplane. Each fiber controller is addressed with its own four-digit hexadecimal identifier. The base and service board layouts were challenging. We were able to make all the required connections using 125-μm track spacing and a rigid-flex circuit, but we do not believe we could route the traces for a 5×5 cell, and certainly not a 10×10 cell. The number of traces required increases as the number of positioners on the cell, but the width of the flex cable increases only as the square root of the number of positioners. We believe that 4×4 cell to be ideal for the construction of a large array.
Milestone Five: Construct a miniaturized fiber-control circuit. This we did, with complete success. Power consumption per fiber controller is 30 mW. If we reduce the time constant of the controller's response from 100 ms to 1 s we can reduce the current consumption further to 20 mW. But the faster response made our tests much easier.
We made several mistakes during the construction of TS2. We tore off one of the connectors on the service board. After epoxying the remaining fifteen in place, we discovered that five had been deprived of their ground connection. We aligned the fiber tips poorly by hand. We broke half the electrode connections within the base board when we applied pressure to the masts. Nevertheless, TS2 demonstrates that we can pack all necessary electronics in the footprint available, and control all actuators individually.
Milestone Six: Construct a 4×4 fiber-positioning array with monitoring camera. This we did to our satisfaction. All the fibers are loaded on the array, but damage to the electrical connections prevent us from delivering drive signals top half of the fibers, an only three of sixteen receive all four of their electrode potentials. The monitoring camera provides better than 5-μm precision in measuring fiber position.
According to our fiber view camera, the range of motion of our TS2 fibers is 3.2 mm × 3.2 mm, which is significantly smaller than the theoretical maximum of ±3.8 mm. In TS2 we ended up soldering the actuators 6 mm above their bases, and we fastened the carbon fiber masts 5-10 mm from the tops. Our original assembly tooling was designed to reduced the amount by which they bend at their top end, but our original assembly plan turned out to be impractical, and we did not want to wait for another set of assembly fixtures before proceeding. The exact size of the dynamic range is not a source of great concern for us. Even ±3.2 mm covers 40% of the area occupied by the positioner. Our intended use of the DFPS is to permit each fiber to observe one object in each exposure, not to observe a particular object. According to our simulation, 40% coverage is perfectly adequate to permit a large-scale survey of the sky.
Milestone Seven: Demonstrate full range of motion, 10-μm precision, and stability of 4×4 array. The three correctly-connected positioners move in 3.2-mm squares, which is less than the theoretical maximum of ±3.9 mm, but is consistent with our constraining the actuator for 10% of its length. Using our new controllers, we are able move and hold stationary each fiber with 5-μm precision.
On February 16th, 2023, we visited the Astronomical Instrumentation Laboratory at Texas Agricultural and Mining University (TAMU) to discuss a collaboration between OSI and TAMU on the construction of a dense fiber positioner and its installation on their 2.1-m Otto Struve telescope at the McDonald Observatory in western Texas. We formed a plan to build an eight-fiber positioner, each positioner equipped with a fiducial and measurement fiber, with measurement fibers connected to the slit of a single refurbished spectrograph, and guide fibers connected to light injectors. Both groups would be funded by a Phase II grant and both groups would collaborate on the installation and commissioning of the spectrometer. We plan to submit our Phase II SBIR application together in April 2023.
One of the things we learned while visiting TAMU is that scientific-grade CMOS image sensors are replacing the long-standing CCDs as the highest-performing image sensors for astronomical applications. The new sCMOS sensors have read noise of less than one electron, which means there is little to be gained from exposing them for long periods of time. Our original DFPS plan was to hold every fiber in position to ±10 μm by dead-reckoning after an initial two-minute monitoring period to assess starting position and creep. With sCMOS sensors, we can instead read out the spectrograph image every three minutes, and spend ten seconds measuring the location of all fibers in our array simultaneously, adjusting their positions as needed, and then continue with the spectrograph exposure for another three minutes. Thus our DFPS no longer requires dead reckoning, but can operate as a control loop, taking advantage of the fact that our micropower, continuous-drive system for all fibers permits simultaneous adjustment of an arbitrarily large number of positioners in steps as small as one micron. Instead of needing creep and hysteresis mitigation to place the fibers correctly, we will use our understanding of creep and hysteresis to assess the health of the fibers during commissioning and maintenance periods, and to generate warnings during exposures.
During our Phase I work, we met all our milestones except one. We built a multi-fiber positioner on a 5-mm grid, with all necessary control electronics and mounting structures packed into the same footprint. During the course of our work, and as a result of discussion with our collaborators at the McDonald Observatory, we have simplified the operation of the DFPS by replacing dead reckoning with monitoring and adjustment during exposure. We met all our milestones, with the exception of testing the system at −10°C, which is not nearly as important to the system now that we will no longer be operating by dead reckoning. Our modular DFPS design will allow us to build fiber positioner arrays of any size, from sixteen fibers to one hundred thousand fibers. In Phase II of our work, we will collaborate with the McDonald observatory to construct an eighty-fiber positioner, install the positioner on their 2.1-m telescope, and connect its detector fibers to a refurbished spectrometer so as to obtain spectra of celestial objects. This collaboration, if successful, will show that the DFPS is ready to be deployed for astronomical observation. It will be clear to astronomers that they can purchase from us a positioner of any size and combine it with a traditional spectrograph they design themselves or purchase from a commercial manufacturer, or commission to be made by an astronomical instrumentation group such as the one we will be collaborating with at the McDonald Observatory. If our demonstration is successful, we intend to market 400-fiber positioners to existing four-meter and similar telescopes, and to push for involvement in the construction of an 80,000-fiber positioner for the Stage Five Spectrograph that is one of the main long-term objectives of the NSF and DoE funding agencies.
Development Log: Development of the DFPS at OSI starting January 2022.
Base and Service Board (A3043): Combined base and service board for mounting fibers and controllers.
Backplane (A3044): Backplane for connection of service boards.
Fiber Controller (A3045): Logic and amplifiers that generate control signals for actuators.
A Novel Dense Fiber Array for Astronomical Spectroscopy: Application to National Science Foundation (NSF) Small Business Innovation Research (SBIR) agency by Open Source Instruments Inc. Submitted 04-DEC-20, awarded 01-JAN-22, grant number 2111936.
Properties of Piezoelectric Tube Actuators: Study of the movement due to creep in piezo-electric tubes. Guadalupe Duran, Brandeis University, May 2020.
Fiber Positioner Circuits (A2089): Prototype circuits developed at Brandeis University for the DFPS.
News 25-MAR-22: Waltham company helps scientists study the expansion of the universe, article in local business journal.
Direct Positioning of 50,000 Optical Fibers: Poster presented at Snowmass, 2022.