A CNN encode o modal phase econs uc ion in
Adap i e Op ics sys ems
P. Ve mo , D. G a adou
No embe 24, 2025
ABSTRACT
Con ex : Py amid wa e on sensing (pWFS) o e s some o he bes sensi i i y o adap i e
op ics, bu su e s om s ong non-linea i y. Modula ion can ex end linea ange a he expense
o sensi i i y. Ope a ing he py amid wi hou modula ion is he e o e a ac i e, bu emains
challenging.
Aims: We de elop a non-linea CNN econs uc o o py amid wa e on sensing ha maps
pWFS images di ec ly o a modal phase ep esen a ion, and we assess simple hyb id me hods
combining i wi h a s anda d linea leas -squa es (LS) econs uc o .
Me hods: Using he end- o-end COMPASS simula o , we gene a e a la ge open-loop da ase
spanning wide anges o RMS and powe spec a o ain a compac CNN encode . We hen compa e
he CNN agains an LS baseline and e alua e hyb id schemes in closed-loop simula ions o e a g id
o guide-s a magni udes and F ied pa ame e s, epo ing long-exposu e S ehl a
λ
= 1
.
6
µ
m wi h
con olle gain e-op imized pe me hod and bin. We also epo p elimina y o line bench es s on
SCExAO.
Resul s: The CNN educes open-loop econs uc ion e o and, in closed loop, ou pe o ms LS
ac oss mos (magni ude,
0
) condi ions, wi h he la ges gains o ain s a s whe e i o en closes
he loop while LS does no . In e y s ong u bulence, LS can exceed he CNN; in hese cases he
hyb id me hods a e necessa y o su pass LS, wi h a second-s age NN pe o ming bes . In e ence
is eal- ime capable and he hyb id o e head is negligible. Bench snapsho s on SCExAO show
success ul co ec ion o small s a ic/slow pe u ba ions, wi h ins abili y o s onge / as e cases.
Conclusions: A compac CNN can be ained o pe o m modal econs uc ion o a non-
modula ed pWFS and imp o es pe o mance o e a classical linea econs uc o in mos egimes.
When he CNN alone is no op imal, simple hyb id me hods achie e he bes pe o mance, sugges ing
a p ac ical way o exploi he py amid’s sensi i i y wi hou modula ion.
1. INTRODUCTION
Adap i e op ics (AO) can es o e di ac ion-limi ed pe o mance on la ge elescopes by es ima ing
and co ec ing a mosphe ic phase in eal ime. Among wa e on senso s (WFS), he py amid
WFS (pWFS) [Ragazzoni, 1996, V´e inaud, 2004] has become a leading choice o cu en and u u e
ins umen s hanks o i s high sensi i i y [Esposi o and Ricca di, 2001]. Howe e , i s esponse is
s ongly non-linea and in many cases equi es modula ion o inc ease he linea ange, which is done
a he expense o sensi i i y [Bu all e al., 2006]. Despi e i s s ong nonlinea i ies, non-modula ed
py amid is hus o high in e es o inc eased sensi i i y [Guyon e al., 2011, Agapi o e al., 2023].
In his wo k we di ec ly a ge he nonlinea i y o he pWFS by aining a Con olu ional Neu al
Ne wo k (CNN) o map WFS images o a modal phase ep esen a ion. We adop he B modal
basis [o hono mal modes de i ed om he DM in luence unc ions wi h pu e ip– il sepa a ion
Fe , Pou]. We ain a compac CNN encode on a la ge syn he ic da ase p oduced wi h he
COMPASS end- o-end simula o , spanning wide magni ude and u bulence egimes. We compa e
i s pe o mances agains a leas -squa es (LS) linea econs uc o , which is he pseudoin e se o he
in e ac ion ma ix [Sou hwell, 1980, Roddie , 1999]. Mo i a ed by egimes whe e a linea es ima o
may s ill excel, we also es simple hyb id schemes ha combine CNN and linea es ima es.
Ou con ibu ions a e: (i) a ligh -weigh CNN encode ha pe o ms modal econs uc ion om
PWFS ames; (ii) ex ensi e closed-loop e alua ion ac oss guide s a magni ude and F ied pa ame e
0
, showing ha he CNN domina es in mos egimes o in e es ; and (iii) hyb id me hods ha ake
Table 1: COMPASS con igu a ion.
Pupil Diame e D8 m
Cen al obscu a ion 0.14 D(1.12 m)
A mosphe e Numbe o laye s 3
Laye s eng hs [0.50,0.35,0.15]
Laye al i udes [0,4,10] km
Wind speed [15,15,35] m s−1
Wind di ec ion [0◦,20◦,180◦]
Ou e scale L030 m
Wa e on senso Type Py amid
Modula ion mod = 0
Wa eleng h 0.85 µm
Subape u es 56 ×56
Op ical h oughpu 0.15
DM High-o de (PZT) 40 ×40; Gaussian IF
Tip-Til
Con olle Type LS; delay 1 ame
Timing 1 ms (1 kHz)
Science channel Wa eleng h λ0= 1.67 µm
he bes o each es ima o depending on condi ions. We b ie ly epo p elimina y semi-success ul
bench es s on SCExAO o illus a e p ac ical deploymen aspec s Guyon e al. [2010], Jo ano ic
e al. [2015], Lozi e al. [2018].
2. METHODS
2.1 Simula ion se up and da ase gene a ion
The wo k p esen ed in his pape is done wi h end- o-end simula ions using he COMPASS ool Fe .
We simula e a mode n AO sys em on an 8 m elescope wi h a 14% cen al obscu a ion, a py amid
WFS ope a ed wi hou modula ion (56
×
56 subape u es a
λ
= 0
.
85
µ
m), and a 40
×
40 PZT
de o mable mi o complemen ed by a ip– il s age. The con ol loop uns a 1 kHz wi h one- ame
delay, and he a mosphe e is a 3-laye model wi h
L0
= 30 m. A summa y o key pa ame e s is
gi en in Table 1.
2.2 Open-loop da a gene a ion
We d aw a powe -law slope
α∼ U
(0
,
3) and syn hesize a andom phase in he Fou ie domain wi h
ampli ude
A
(
κ
)
∝ ∥κ∥−α
and andom phase
θ
(
κ
)
∼ U
[0
,
2
π
) (pis on emo ed by se ing
A
(0) = 0):
bφ0(κ) = A(κ)eiθ(κ), φ0(x) = ℜF−1[bφ0].
To be able o expo his me hod o a ha dwa e bench la e on, we hen p ojec φ0on o he DM:
φ1(x) = B BTφ0(x).
We se a a ge RMS
σφ= −ln U
2π, U ∼ U(0,1),
and no malize o e he pupil:
φ(x) = σφ
φ1(x)
s dφ1(x).
We hen use COMPASS o gene a e he co esponding WFS ame wi h he guide-s a magni ude
d awn uni o mly
m∼ U
(3
,
13). The WFS images a e p e- o ma ed in o an a ay Iby ex ac ing
ou 60
×
60 pa ches, s acking hem in o a 3-channel a ay, and no malizing his a ay by i s o e all
s anda d de ia ion.
Table 2: CNN encode (de aul con igu a ion).
S age Op. (ke nel / s ide / ac ) Ou pu size (C,H,W)
Inpu — (4,60,60)
Block 1 Con 3×3 / (2,2) + BN + so plus (32,30,30)
Block 2 Con 3×3 / (2,2) + BN + so plus (128,15,15)
Block 3 Con 3×3 / (2,2) + BN + so plus (512,8,8)
Block 4 Con 3×3 / (2,2) + BN + so plus (2048,4,4)
Block 5 Con 3×3 / (2,2) + BN + so plus (8192,2,2)
Head Con 1×1 / (2,2) + linea (1307,1,1)
Ou pu Fla en 1307
Finally, we compu e he DM modal coe icien s by p ojec ing φ(x) on o he modal basis:
a=BTφ,
We gene a e 10
6
[inpu , ou pu ] aining examples and 1
.
5
×
10
5
alida ion examples, each
consis ing o a couple [I,a] wi h shapes [(4, 60, 60), (1307)].
2.3 CNN
2.3.1 A chi ec u e
The ne wo k maps he p e- o ma ed pWFS enso I(4
,
60
,
60) o
Nmodes
= 1307 modal coe icien s.
I is a s ided con olu ional encode wi h Ba ch No maliza ion and
so plus
ac i a ions. We use
L
= 5 blocks o 3
×
3 con olu ions wi h s ide (2
,
2); a each block he channel coun g ows by a
ac o o ou (s a ing om 32), ollowed by a inal 1
×
1 con olu ion wi h s ide equal o he cu en
spa ial size o collapse he ea u e map o 1×1, and a linea ac i a ion on he ou pu .
2.3.2 T aining
We ain on 10
6
examples (wi h addi ional 1
.
5
×
10
5
alida ion examples) using Adam op imize
(
β1=
0
.
9
, β2=
0
.
999), ba ch size 256, o 100 epochs. The lea ning a e decays exponen ially om
10
−4
o 10
−7
o e aining. The loss is mean squa ed e o be ween p edic ed and ue modal
coe icien s. Compu a ions an on he Jean–Zay (IDRIS) supe compu e on a single NVIDIA H100
GPU wi h 24 CPU co es (In el Xeon Pla inum 8468): wi h ba ch size 256 he pe -ba ch compu e
ime is 22
ms
(abou 92 s pe epoch), o aling sligh ly unde 3 hou s o all 100 epochs; a in e ence,
he pe -ba ch compu e ime is 3 ms (ba ch size 256).
2.4 Hyb idiza ion
We combine he CNN and LS es ima es in modal space ia linea combina ion o modes. Le
acnn, alin be he p edic ed modal ec o s and a⋆ he g ound u h. We de ine
ahyb
i=wiacnn
i+(1−wi)alin
i, i = 1, . . . , Nmodes,
wi h weigh s
wi∈
[0
,
1]. We conside h ee weigh s a egies, i ed on a sepa a e calib a ion spli :
1.
Median weigh s. Fo each sample
n
and mode
i
, he o acle weigh minimizing he squa ed
e o is w(n)
i,o c = clip[0,1]a⋆
i,(n)−alin
i,(n)
acnn
i,(n)−alin
i,(n).We se wi= mediannw(n)
i,o c.
2.
MMSE weigh s. Assuming ze o-mean es ima ion e o s
ecnn
i
=
acnn
i−a⋆
i
and
elin
i
=
alin
i−a⋆
i
,
he MSE-op imal s a ic weigh pe mode is
wmmse
i=Va (elin
i)−Co (ecnn
i, elin
i)
Va (ecnn
i) + Va (elin
i)−2 Co (ecnn
i, elin
i),
es ima ed om he calib a ion spli and clipped o [0,1].
3.
Second-s age DNN. A small ully connec ed ne wo k (1 hidden laye s wi h 1307 neu ons
and
ReLU
ac i a ion), aking (
acnn, alin
) as inpu and ou pu ing
w∈
[0
,
1]
Nmodes
ia a sigmoid,
ained wi h MSE loss on he o acle weigh s wi,o c.
0.5 1.0 1.5 2.0 2.5
PL index
0.2
0.4
0.6
0.8
SR
ac us_mse_loss_CNN
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
lossCNN
lossRTC
Figu e 1: Open-loop econs uc ion e o a io in he ac ua o domain: pe -bin (by RMS
σφ
and
powe -law index
α
) median o
losscnn/losslinea
. Values
<
1 indica e lowe MSE o he CNN; alues
>1 a o he linea econs uc o .
3. RESULTS
3.1 CNN Open-loop esul s
To de e mine he pe o mance le el o ou CNN, he i s es is o compa e he quali y o i s
econs uc ion on open-loop da a. Fo his pu pose, we an in e ence on ou en i e alida ion
da ase (1
.
5
×
10
5
examples) wi h ou CNN and he linea econs uc o and, o each sample,
compu ed he mean squa ed e o (MSE) wi h espec o he g ound u h in he ac ua o (zonal)
domain. In Fig. 1, we p esen a compa ison o he wo algo i hms binned by he a ge RMS
σφ
and he powe -law index
α
o he esidual a mosphe ic phase, showing he pe -bin median a io
losscnn/losslinea
. These esul s indica e a ios below 1 in he as majo i y o bins, i.e., he CNN
ou pe o ms he linea econs uc o ac oss mos o he explo ed g id.
3.2 CNN Closed-loop esul s
As a second s ep, we included he CNN econs uc o in closed-loop simula ions spanning a wide
ange o magni ude and u bulence condi ions. Long-exposu e (LE) S ehl a io is e alua ed a
he science wa eleng h (
λ
= 1
.
6
µ
m) and in eg a ed o e he ull sequence o 1500 i e a ions pe
simula ion. Fo ai ness, he loop gain is op imized pe me hod and pe bin by es ing all gains om
0
.
05 o 1
.
0 in s eps o 0
.
05 and e aining he bes esul . The F ied pa ame e
0
is speci ied a
500 nm. We es m∈[3,12] in s eps o 0.5 and 0∈[0.05,0.39] m in s eps o 0.02 m.
In Fig. 2 we compa e he LE S ehl ob ained wi h he CNN and wi h he linea econs uc o
(LS) as a unc ion o guide-s a magni ude and
0
. The plo shows he pe -bin a io
SRCNN/SRLS
;
blue indica es CNN be e ( a io
>
1), ed indica es LS be e ( a io
<
1), and g ey ma ks bins
whe e nei he con igu a ion “closes he loop,” de ined empi ically as
SR ≤
0
.
1. O e all, in he g ea
majo i y o cases he CNN pe o ms as well as o be e han LS, and only in a mino i y o cases
does i unde pe o m:
1.
In he ain guide-s a egime (mag
>
10), he CNN ou pe o ms LS wi h a ios
≳
2 (deep
blue in Fig. 2); abo e mag
≈
11
.
5, LS equen ly does no close he loop while he CNN does.
2.
In he s anda d ope a ing egime (mag
<
10,
0>
0
.
10 m), CNN and LS pe o m e y simila ly,
wi h a sligh ad an age o he CNN ( a ios close o bu abo e 1).
3.
In he e y high u bulence egime (
0
= 5 cm), LS pe o ms be e han he CNN ( a ios
<1).
0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39
0 (m)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
Magni ude
LE a io (masked <0.1 nume a o ): CNN / Linea
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
LE S ehl a io ( ela i e)
Figu e 2: Closed-loop LE S ehl a io a
λ
= 1
.
6
µ
m, shown as he pe -bin a io
SRCNN/SRLS
o e
he g id
m∈
[3
,
12] (s ep 0
.
5) and
0∈
[0
.
05
,
0
.
39] m a 500 nm (s ep 0
.
02 m). Blue (
>
1) indica es
CNN be e ; ed (
<
1) indica es LS be e ; g ey ma ks bins whe e nei he closes he loop (empi ical
h eshold SR ≤0.1).
3.3 Hyb id me hods closed-loop esul s
We now p esen closed-loop esul s o he h ee hyb id econs uc o s (median weigh s, MMSE
weigh s, and second-s age NN), in addi ion o he LS and CNN baselines. Like p e iously, LE
S ehl is e alua ed a
λ
= 1
.
6
µ
m o e he ull 1500-i e a ion sequence,
0
is speci ied a 500 nm,
and o each me hod and bin he loop gain is op imized. Hyb id weigh s and he second-s age NN
a e calib a ed on he alida ion spli .
In Fig. 3, we show he e olu ion o he long-exposu e S ehl a io o he i e econs uc o s
(linea , CNN, median weigh s, MMSE weigh s, and second-s age NN) in he h ee cha ac e is ic
egimes iden i ied ea lie ( ain s a , egula condi ions, and high u bulence):
1.
In he “ ain guide-s a egime” (mag
>
10), he linea econs uc o p o ides he lowes
pe o mance (SR
∼
0
.
1), and he CNN pe o ms much be e (SR
∼
0
.
5). Mo e gene ally, he
h ee hyb ids imp o e o e he CNN; so ed by inc easing pe o mance: second-s age NN,
median weigh s, MMSE weigh s.
2.
In he “s anda d ope a ing egime” (mag
<
10,
0>
0
.
1 m), all econs uc o s ha e high
pe o mance (SR
>
0
.
9). The linea econs uc o is signi ican ly below he o he s (SR
∼
0
.
92
s. ∼0.95), while he non-linea and hyb id me hods a e s a is ically indis inguishable.
3.
In he “ e y high u bulence egime” (
0
= 5 cm), he CNN is he wo s (SR
∼
0
.
1). Median
and MMSE weigh s imp o e i (SR
∼
0
.
15) ye emain below linea (SR
∼
0
.
18). The
second-s age NN ou pe o ms all o he s in his egime (SR ∼0.22).
Gene alizing o he ull (
m, 0
) g id, Fig. 4 shows a colo -coded map indica ing which o he i e
me hods is bes in each bin:
1.
In he op- igh ( ain s a wi h good a mosphe ic condi ions), he MMSE-weigh hyb id
domina es.
2.
In he bo om-le (b igh s a wi h bad a mosphe ic condi ions), he second-s age NN p o ides
he bes esul s.
3.
In he alley be ween hese egions, he CNN alone is bes ; no e ha he e all non-linea
me hods ha e e y close pe o mance and di e ences a e no signi ican .
0 200 400 600 800 1000 1200 1400
I e a ion
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
LE S ehl a io
Full LE s I e a ion @ mag=5.00, 0=0.05
linea
CNN
median w s
MMSE
2nd s age NN
0 200 400 600 800 1000 1200 1400
I e a ion
0.2
0.4
0.6
0.8
1.0
LE S ehl a io
Full LE s I e a ion @ mag=7.00, 0=0.21
linea
CNN
median w s
MMSE
2nd s age NN
0 200 400 600 800 1000 1200 1400
I e a ion
0.1
0.2
0.3
0.4
0.5
0.6
0.7
LE S ehl a io
Full LE s I e a ion @ mag=11.50, 0=0.29
linea
CNN
median w s
MMSE
2nd s age NN
Figu e 3: Rep esen a i e long-exposu e S ehl a io examples a di e en guide-s a magni udes
and u bulence s eng hs. Each panel shows he i e econs uc o s (LS, CNN, median weigh s,
MMSE weigh s, second-s age NN).
0.05 0.10 0.15 0.20 0.25 0.30 0.35
0
3
4
5
6
7
8
9
10
11
12
magni ude
Bes Me hod by (mag, 0)
linea
CNN
median w s
MMSE
2nd s age NN
None ( 0.1)
Figu e 4: Winne map o e he (
m, 0
) g id (
m∈
[3
,
12] s ep 0
.
5;
0∈
[0
.
05
,
0
.
39] m a 500 nm s ep
0
.
02 m). Colo indica es he me hod wi h he highes LE S ehl a
λ
= 1
.
6
µ
m (no ie h eshold).
G ey ma ks bins whe e no me hod closes he loop (empi ical h eshold
SR ≤
0
.
1). Gains a e
op imized pe me hod and bin (sweep 0.05:0.05:1.0).
0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39
0 (m)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
Magni ude
LE a io (masked <0.1 nume a o ): CNN + Second s age modes / Linea
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
LE S ehl a io ( ela i e)
Figu e 5: Pe o mance a io o e he (
m, 0
) g id:
SRCNN+2nd/SRLS
a
λ
= 1
.
6
µ
m. Blue (
>
1)
indica es CNN+second-s age NN be e ; ed (
<
1) indica es LS be e ; g ey ma ks bins whe e
nei he closes he loop (
SR ≤
0
.
1). Colo ba ange 0
→
2. Gains a e op imized pe me hod and bin.
The e is no a single me hod ou pe o ming all o he s in e e y egime, bu he e is no egime
in which he linea econs uc o is he bes : including he CNN in he phase econs uc ion
sys ema ically imp o es pe o mance.
3.4 SCExAO
A p elimina y e sion o he me hod was es ed on he SCExAO ins umen in an o line labo a o y
con igu a ion (no on-sky) in Ap il 2025 [Jo ano ic e al., 2015, Guyon e al., 2010, Lozi e al.,
2018]. The bench used a non-modula ed pWFS a 800 nm and a de o mable mi o ; pe o mance
was es ima ed in he science channel in H-band (b oad band). Al hough he implemen a ion was
no ye comple e, we summa ize he expe imen he e.
The SCExAO ins umen is equipped wi h a py amid wa e on senso and a de o mable mi o .
In he o line se up, we implemen ed a p elimina y e sion o ou algo i hm as ollows:
1. Gene a ion o andom phase sc eens and p ojec ion on o he DM.
2. Acquisi ion o he associa ed pWFS ames (non-modula ed, 800 nm).
3.
T aining o a CNN o econs uc he ue modes om he pWFS images ob ained on he
bench; 200,000 examples).
4.
Closed-loop es using he CNN econs uc o (no gain uning; de aul con olle se ings),
assessing H-band long-exposu e PSFs.
The CNN could success ully compensa e a small s a ic pe u ba ion in he sys em and a ain ,
e y slowly e ol ing u bulen wa e on (see Fig. 6). Howe e , when s onge o mo e apidly
e ol ing pe u ba ions we e injec ed, he loop became uns able and di e ged. A likely cause is a
misma ch be ween aining and in e ence condi ions (e.g., WFS e e ence slopes). Resol ing his
will equi e imp o ed on-bench calib a ion ( e e ence upda e) and gain uning, which we lea e o
u u e wo k.
(a) Wi h small s a ic pe u ba ion (be o e co ec-
ion). (b) A e CNN co ec ion (closed loop).
Figu e 6: Illus a i e SCExAO bench snapsho s in H-band. These a e sc eensho s aken du ing he
expe imen and a e shown o quali a i e illus a ion only; quan i a i e pa ame e s (e.g., S ehl
a io, exposu e ime) we e no eco ded.
4. DISCUSSION
Ou esul s show ha a CNN econs uc o can close he loop in egions whe e a linea leas -squa es
(LS) econs uc o canno . Ac oss he magni ude–
0
g id he CNN p o ides be e pe o mance
han he linea econs uc o in he as majo i y o cases and mos no ably o ain s a s, whe e
i o en closes he loop when LS does no , and also in mos s anda d ope a ing egimes whe e i
yields a ew addi ional pe cen o S ehl. Due o compu a ional limi s we used a single ealiza ion
pe bin; howe e , he spa ial cohe ence o he winne map ac oss neighbo ing bins suppo s he
s abili y o hese conclusions.
In e y high u bulence egimes he linea econs uc o ou pe o ms ou CNN. Al hough his is
whe e he py amid is mos non-linea , we belie e he p ima y cause is an unde - ep esen a ion o high-
RMS wa e on s in he aining se . Inc easing he ac ion o high-RMS examples is s aigh o wa d
in p inciple, bu a s ong u bulence he pWFS esponse sa u a es and he “g ound- u h” modal
ec o becomes impossible o de e mine, which p e en s s able supe ised aining and hinde s
con e gence. Add essing his will equi e speci ic da a gene a ion and calib a ion s a egies ha
emain alid in he sa u a ed egime, o be de e mined.
Hyb id me hods imp o e upon he CNN in se e al pa s o he g id. Al hough no single hyb id
ou pe o ms all o he s e e ywhe e, including he CNN es ima e in he econs uc ion is always
ad an ageous: in many cases he CNN alone is su icien ; in o he s, combining i wi h he linea
econs uc o yields he bes pe o mance. The compu a ional o e head o he hyb ids is negligible
compa ed o he CNN o wa d pass. Wi h no ully op imized wo k lows (bu Tenso Flow g aph
compila ion) we measu ed sub-millisecond in e ence pe ba ch on he SCExAO bench wi h an
NVIDIA A6000, and e en sho e in e ence imes on he H100 o he ull pipeline (CNN + hyb id),
wi h he hyb id s age being negligible ela i e o he CNN.
P elimina y bench es s on SCExAO we e p omising bu no ye ully success ul. The CNN could
co ec a small s a ic pe u ba ion and a ain , slowly a ying u bulen wa e on , bu des abilized
o s onge o as e pe u ba ions. A likely con ibu o is a misma ch be ween aining and
in e ence condi ions (e.g., WFS e e ence slopes), compounded by he absence o gain uning in
ha un; we plan o e isi he bench wi h imp o ed e e ence upda es and gain op imiza ion.
This wo k has se e al limi a ions and na u al ex ensions. Fi s , only one ealiza ion pe bin
was used; inc easing he numbe o ealiza ions will allow o mal signi icance es ima es. Second, a
sys ema ic obus ness/abla ion s udy (e.g., aining-se composi ion, weigh ing o high-RMS cases,
condi ioning on lux/op ical gain, egis a ion ji e ) emains o be comple ed. Thi d, while his
s udy ocused on an unmodula ed py amid, applying he same CNN and hyb id app oaches o a
modula ed py amid is an in e es ing di ec ion o u u e wo k. Finally, scalabili y o ELT-class
sys ems and b oade ins umen con igu a ions will be in es iga ed in subsequen wo k.
5. CONCLUSIONS
We in oduced a compac CNN econs uc o o he non-modula ed py amid WFS ha es ima es
modal coe icien s di ec ly om pWFS ames, and we e alua ed simple hyb id me hods wi h he
CNN and a linea LS baseline. In open loop, he CNN educes ac ua o -space MSE in he majo i y
o (RMS, powe -law) bins. In closed loop, he CNN ou pe o ms LS ac oss mos o he (
m, 0
) g id,
wi h he la ges gains o ain s a s (e.g.,
m >
10; a ios
≳
2), while LS o en ails abo e
m≈
11
.
5
and he CNN s ill closes. In s anda d condi ions (
m <
10,
0>
0
.
10 m) he gains a e modes bu
consis en .
Unde e y s ong u bulence (
0≈
0
.
05 m), LS exceeds he CNN, likely due o unde -
ep esen a ion o high-RMS in aining and pWFS sa u a ion. Hyb ids u he imp o e pe o mance:
median/MMSE weigh s o a second-s age DNN ma ch o exceed he CNN o LS econs uc o s
alone, wi h no egime whe e LS is o e all bes . The app oach is eal- ime capable (sub-ms in e ence
on A6000; e en as e on H100), and hyb idiza ion o e head is negligible.
P elimina y SCExAO bench es s (o line) showed success ul co ec ion o small s a ic and slow
pe u ba ions, wi h ins abili y o s onge / as e cases (likely om WFS e e ence misma ch and
lack o gain uning). Fu u e wo k will ex end aining o high-RMS and sa u a ed egimes, add
MMSE/Fou ie baselines, es he me hod on a modula ed py amid, and assess scalabili y owa d
ELT-class sys ems and on-sky ope a ion.
