The NAO Systems Imperative
Adaptive Optical (AO) system technology is incredibly interesting and exciting. AO has enabled a revolution in large ground based telescopes – without AO compensation ground based telescope systems would be limited in useful size for imaging applications to 1–2 m, even at the best locations in the world that only have minimal atmospheric turbulence effects at visible and near-IR wavelengths. In the majority of telescope locations around the world, the useful aperture size would be limited to 10–50 cm – hardly sufficient resolving power to make useful measurements for astronomical research that relies on high resolution imaging. AO system technology using Laser Guide Stars (LGS), pioneered in the US DoD community [1–2], while highly complicated, offers a sound and viable solution for wide field of view imaging with very high sky coverage .
Given the success that AO technology has seen in the astronomy community, one must wonder about the utility of AO technology for applications involving horizontal path propagation and / or low elevation angle propagation. There are many candidate applications, however, none have surfaced as a “killer application”. Nutronics, Inc. believes we understand the fundamental reasons behind this fact well and we tell this story here.
The bottom line is that the high cost of AO systems drives a challenging cost / benefit trade – unless the turbulence is very severe (either due to the operational conditions of the location of interest or due to the need to use a large aperture diameter) it is difficult to justify the cost of implementation and integration of an AO system for many applications. A further more subtle aspect of the story is that just when the turbulence is severe enough to be significant in a horizontal path application – conventional Hartmann sensor-based AO system technology is ineffective due to the onset of branch points in the phase function when the Rytov Number exceeds 0.2 [4–6] [Note: The Rytov Number refers to the log-amplitude variance due to laser propagation through turbulence computed using the Rytov approximation]. While recent work indeed identified the solution to this problem with a cooperative point source beacon  and subsequently the Self-Referencing Interferometer (SRI) solution approach was implemented in practice [8–10] and Nutronics, Inc. includes point diffraction interferometer (PDI) and SRI based systems in its AO system technology portfolio, implementation of a successful solution that is effective when a point source beacon is not available remains one of the most significant challenges in the field of laser beam control for propagation through turbulence.
It is well known that turbulence along the propagation path causes a projected laser beam to break up at a target. This is illustrated in Figure 1. The extent of the beam breakup is well characterized by the ratio D/r0, where D is the aperture diameter of the projected laser beam telescope and r0 is the Fried coherence diameter. The Fried coherence diameter was defined heuristically to correspond to the aperture diameter where image resolution begins to be significantly limited by atmospheric turbulence, i.e. when D/r0 ~ 1. However, what is less known is that up to D/r0 ~ 4, compensation of only the tilt component of the aberrations is quite effective and certainly the cost/benefit trade is not in favor of the addition of an AO system.
Figure 1: Turbulence along the propagation path causes the beam to break up at the target.
When turbulence is severe enough to justify AO compensation (as is the case in the example in Figure 1), AO compensation with a point source beacon (i.e. a laser pointing back at the transmitting aperture) is very effective as illustrated in Figure 2. This example is a Deep Turbulence scenario (Rytov Number greater than 1.0) and an SRI wavefront sensor based AO system is used to provide effective compensation.
Figure 2: AO compensation with a point source target is effective even in Deep Turbulence conditions (Rytov Number > 1.0).
However, when the target is “non-cooperative” the effectiveness of any AO system is poor as shown in Figure 3. The phrase non-cooperative indicates that the signal light used for wavefront sensing must be provided either through active or passive illumination of the target. The system in Figure 3 is denoted by Nutronics, Inc. as a “Compensated Beacon AO” or CBAO system. The beacon laser is pre-compensated by the AO system, presumably leading to a more focused beam at the target and in turn leading to improved compensation. This type of system has been studied in the literature  and Nutronics, Inc. has studied this type of system using vector space projection methods, proving that the only metric optimized by a CBAO system is the ratio of the round trip power collected in the receive aperture to the transmitted power – which has no guaranteed relationship with the distribution of laser power on the target, particularly in the Deep Turbulence regime.
Figure 3: AO compensation, even when the beacon laser is pre-compensated by the AO system to provide better focusing of the beam on the target is not effective when the Rytov Number exceeds 0.2 and in particular is very poor in the Deep Turbulence regime when the Rytov Number exceeds 1.0.
Nutronics has developed a proprietary candidate solution method for this problem as illustrated in Figure 4 using wave optical simulation. Development and verification of such a method is the NAO Systems Imperative.
Figure 4: Example simulation data for candidate NAO Systems solution method.
The NAO Systems Imperative is punctuated by Figure 5 where the Rytov Number is plotted as a function of the ratio D/r0 for horizontal path applications with three sample strengths of turbulence with diamond-tick-marks delineating 1 km range increase increments. We highlight three general regimes of interest: (1) the regime where D/r0 < 4 and where AO compensation is not justified; (2) the regime where D/r0 > 4 and Rytov Number < 0.2 where conventional Hartmann sensor based AO compensation is effective and often justified; and (3) the regime where D/r0 > 4 and Rytov Number > 0.2 where a new solution method is required. Clearly the horizontal path application is one where the regime in which AO compensation using conventional Hartmann sensor based AO technology has limited relevance but the regime for which advanced AO technology is required is significant. In contrast, we note that astronomical AO applications, as illustrated with the same style chart in Figure 6, have a significant need for conventional Hartmann sensor AO based technology but almost no need for advanced AO technology. While conventional AO technology revolutionized astronomical AO, it has failed to impact any other significant applications – Nutronics, Inc. is working toward changing the state of the current reality.
Figure 5: Rytov Number as a function of D/r0 for horizontal path applications with varying levels of turbulence strength and an assumed D = 0.5 m. The diamond markers indicate increasing range increments of 1 km each. Clearly there is a need for technology solutions that can address the regime where Rytov Number exceeds 0.2 and D/r0 > 4.
Figure 6: Rytov Number as a function of D/r0 for astronomical applications with varying levels of turbulence strength and an assumed aperture diameter D = 1.5 (which we note is very small by astronomical AO standards!). The diamond markers indicate increasing zenith angle increments of 10° each. Clearly there is a significant need for conventional Hartmann sensor AO based technology solutions but a very limited need for technology solutions that can address the regime where Rytov Number exceeds 0.2 and D/r0 > 4.
1. C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, ‘‘Compensation of atmospheric optical distortion using a synthetic beacon,’’ Nature 353, 141–143 (1991).
2. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, and L. M. Wopat, ‘‘Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,’’ Nature 353, 144–146 (1991).
3. B. L. Ellerbroek and D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Publications of the Astronomical Society of the Pacific 110:165–185, 1998.
4. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,”Appl. Opt. 31, 2865–2882, 1992.
5. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768, 1998.
6. Barchers, J. D., Fried, D. L. and Link, D., “Evaluation of the performance of Hartmann sensors in strong scintillation”. Feb. 2002, Applied Optics, Vol. 41, pp. 1012–1021.
7. J. D. Barchers and T. A. Rhoadarmer, “Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function,” Applied Optics, 41:7499–7509, Dec. 2002
8. T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112 (2004).
9. T. A. Rhoadarmer and L. M. Klein, “Design of spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
10. T. A. Rhoadarmer and T. A. Brennan, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060K (2006).
11. M.A. Vorontsov, V.V. Kolosov, A. Kohnle, Adaptive Laser Beam Projection on an Extended Target: phase and field-conjugate pre-compensation,” JOSA A, 24, 1975–1973 (2007).