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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 [3].

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 [7] 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 [11] 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).

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