fast computer-free holographic adaptive...

Fast computer-free holographic adaptive optics

Geoff Andersen*, Fassil Ghebremichael, Ravi and Phani Gaddipati HUA Inc., 1532 Shane Circle, Colorado Springs, CO 80907

ABSTRACT

We have constructed an adaptive optics system incorporating a holographic wavefront sensor with the autonomous closed-loop control of a MEMS deformable mirror (DM). HALOS incorporates a multiplexed holographic recording of the response functions of each actuator in a deformable mirror. On reconstruction with an arbitrary input beam, pairs of focal spots are produced. By measuring the relative intensities of these spots a full measurement of the absolute phase can be constructed. Using fast photodiodes, direct feedback correction can be applied to the actuators.

Keywords: Adaptive optics, wavefront sensing, holography, aberration correction

1. INTRODUCTION The standard method for using adaptive optics to correct for aberrations in input wavefronts consists of first detecting and characterizing the wavefront errors, then applying a correction using a phase corrective device. Typically the bottleneck in the process occurs in the sensing process as the conventional methods require a large amount of complex computations to be performed. For example, in a Shack-Hartmann wavefront sensor (SHWFS), the incoming wavefront is deconstructed into a number of focused subapertures using a lenslet array. The focal spots are then analyzed to determine their positions relative to some calibrated ideal using a plane wavefront. The shifts can be converted into local tip/tilt over each subaperture which are then combined to build up a complete wavefront phase. The determination of where the true spot centroid is, how shifted it is from the ideal location, and reconciling all the spots to give a contiguous phase map requires a great deal of processing power and time. While much of this can be reduced into a number of discretized mathematical procedures which in turn can be parsed out to dedicated hardware (such as custom made chipsets) to speed up the process, the size, complexity and cost of the system is significant.

Here we present an alternative approach; a holographic adaptive laser optics system (HALOS) which incorporates a multiplexed hologram that in effect acts as an all-parallel, massively parallel wavefront sensor. The hologram converts local phase information into intensity information in the form of multiple focused beams. By analyzing the relative brightness of a particular pair of focal spots we can obtain a measure of the wavefront phase over a particular location. Beyond this simple ratio measurement there are no complex calculations, and since photodetectors are used rather than CCDs in conventional sensors, the sensing and characterization is extremely fast. HALOS can be configured to determine phase in terms of the modes of the phase correction device, allowing for computer-free feedback control to further increase speeds to hundreds of kilohertz. Most importantly though, the detection and closed-loop correction is all-parallel, so the speed of the system is just as high for one million actuators as it is for one.

2. HOLOGRAPHIC WAVEFRONT SENSOR The operation of the holographic wavefront sensor is best understood in terms of a particular phase correction device for which it is designed to operate in closed-loop correction. In this case we will consider a conventional actuator-driven deformable mirror with a continuous facesheet. The process begins with a plane wave reflected off the deformable mirror which has a single actuator driven to its maximum extent in one direction so that the minimum phase delay is imparted on the wavefront at that location. A hologram is then recorded between this object beam and a diffraction limited reference beam focused to some distant point A (Figure 1a). On reconstruction, if the same object beam conditions are met, the original reference beam will be reconstructed to form a beam focusing to the same point A (Figure 1b).

Adaptive Optics Systems III, edited by Brent L. Ellerbroek, Enrico Marchetti, Jean-Pierre Véran, Proc. of SPIE Vol. 8447,84472L · © 2012 SPIE · CCC code: 0277-786/12/$18 · doi: 10.1117/12.924247

Proc. of SPIE Vol. 8447 84472L-1

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a.

b.

Figure 1: a. Writing. A hologram is constructed with the minimum phase delay imparted by a single actuator, and a reference beam focused to a point A. b. Replay. The same object beam will reconstruct a beam focused to the same point A.

We now create a second hologram multiplexed with the first. Multiplexing of holograms is a straightforward procedure that retains the information of both gratings in a single medium. In this case, the second hologram is written using a reference beam focused to a different spatial location B. Meanwhile, the object beam is generated with the maximum phase delay possible from the same actuator in the deformable mirror (Figure 2). On reconstruction this hologram would take the maximum phase delay wavefront and reconstruct a focused beam to point B in the same manner as the previous hologram demonstrated.

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Figure 2: A second hologram is multiplexed with the first – the one using the maximum phase delay and a reference beam focused to a different spatial location B.

We now set the actuator of the DM to some arbitrary stroke thus generating an arbitrary phase delay at that particular location on the wavefront. When this beam is made to illuminate the multiplexed hologram there will be two wavefronts reconstructed, one focused to each of the points A and B. The reason for this is that the phase matching condition in this case is not a perfect match for either grating so both gratings reconstruct a beam at a low efficiency (Figure 3).

Figure 3: Multiplexed reconstruction. If an arbitrary phase delay is applied to the reconstructing object beam there will be two focal spots on replay.

We can use imperfect phase-matching to our advantage as the relative intensities of the foci provides us with a precise measure of the actual phase error present in the object beam. If the phase is more towards the minimum phase error, then the focal spot A will be bright as that phase condition is better matched, while a more maximized phase delay will result in spot B being brighter. Thus, with a one-off calibration we can thus determine the absolute phase information from a measurement of the relative intensity of the spots. Furthermore, we can simply record a pair of multiplexed holograms for each actuator position on the deformable mirror in the same manner to obtain a full description of the wavefront

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The reconstructed focal spots were incident on a SensL Array4p9 avalanche photodiode array consisting of 144 elements in a 12x12 array. In order to improve signal to noise we placed a pinhole array in front of the array to better isolate the focused light from background illumination. We constructed a circuit to take the outputs from pairs of elements and calculate the first moment measurement; (VA-VB)/(VA-VB). Figure 7 shows a plot of the first moments of two neighboring actuators when one of those actuators is swept through its entire extent of push/pull motion. There are two issues to note:

1. The response function corresponding to the probed actuator is singly defined over its entire range of motion. This makes it possible to determine a particular set point for closed-loop locking.

2. The signal measured in the non-actuated sensor channel does not show any significant fluctuation. This means that there is little cross-talk and that the motion control of actuators can be made independent of one another – a key demonstration of parallel closed-loop control of actuators.

Once the holographic sensor had been demonstrated to operate as expected, we closed the loop using the same digital circuit. First the set point values for pairs of outputs were calibrated by using a known plane wave input. The microcontroller was then programmed to maintain these values by feedback control over each individual actuator in the deformable mirror. Note that in our system there is circuitry required to communicate with an intermediate driver unit for the MEMS DM. This camera-link interface is necessary only because the commercial deformable mirror unit is designed to work with conventional AO systems which require a computer in the loop. In an optimized design we would simply have direct control from the sensor to the DM. Even so, our system still had an update rate of 125 kHz.

The closed-loop system was initiated with the deformable mirror actuators adjusted under the digital control to maintain the output first moments to the calibrated values. We demonstrated that lock could be held under the introduction of significant wavefront aberration to the input beam. This lock was maintained when room lights were turned on and off and even under direct illumination with a halogen lamp. The reason for this is simple to understand: so long as both pixels in a sensing pair see the same increase in light flux, the first moment will be unchanged since only a difference in focused intensities is measured.

Equally significant is the fact that we were able to disconnect the computer from the loop, at any time, and still maintain lock. This is because, after the one-off calibration step, the sensing and feedback was all under autonomous control by the XMOS microcontroller. The computer could also be re-introduced into the control loop at any time to monitor or record the state of adaptive optics system.

5. CONCLUSION

We have presented a holographic adaptive optics system (HALOS) that uses a multiplexed hologram to deconvolve a wavefront phase in terms of the precise response functions of actuators in the corrective deformable mirror. We have constructed and tested a closed-loop prototypes operating without any computer. Beyond the significant speeds achievable the system offers improvements over conventional AO systems in compactness, simplicity, ruggedness and insensitivity to scintillation. As such HALOS is ideal for applications in next generation, high-power, high speed and high fidelity AO systems including:

1. High energy directed energy systems 2. Free-space optical communications 3. Extreme-AO for next-generation astronomical systems 4. Phased arrays of multi-beam laser systems 5. Ultra-lightweight, ultra-compact AO correction systems for unmanned aerial surveillance

6. ACKNOWLEDGMENTS

We would like to acknowledge the support of the Joint Technology Office and Air Force Office of Scientific Research for their support of this research.



REFERENCES

[1] Geary, J.M., [Introduction to Wavefront Sensors] SPIE Press, (1995). [2] Dyson, R., [Principles of Adaptive Optics 2nd Ed.], Academic Press (1998). [3] Roddier, F., [Adaptive Optics in Astronomy], Cambridge Press (1999). [4] Ghebremichael, F., Andersen, G.P., and Gurley, K., “Holography-based wavefront sensing,” Appl. Opt. 47, A62-

A69 (2007). [5] Andersen, G.P., Dussan, L., Ghebremichael F., and Chen, K., “Holographic Wavefront Sensor,” Opt. Eng. 48,

085801 (2009).



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