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P. A
stie
r E
ucl
id-F
rance
(201
3)
1
Th
e b
rig
hte
r-fa
tter
effe
ctan
d p
ixel
co
rrel
atio
ns
Pie
rre
An
tilo
gu
s, P
ierr
e A
stie
r,
Au
gust
in G
uyo
nn
et, N
icola
s R
egna
ult
LP
NH
E /
IN
2P
3/
CN
RS
, U
niv
ersi
tés
Pa
ris
6&
7.
P. A
stie
r E
ucl
id-F
rance
(201
3)
2
Th
e b
rig
hte
r-fa
tter
eff
ect
(1)
-M
easu
rem
ents
by
P. D
oher
ty(H
arvar
d)
In t
he
lab
ora
tory
.
-”L
ab s
pots
”C
CD
E2V
(L
SS
T)
-In
tensi
ty i
s var
ied
via
inte
gra
tion
tim
e.
Mea
sure
sec
ond m
om
ents
.
P. A
stie
r E
ucl
id-F
rance
(201
3)
3
Th
e b
rig
hte
r-fa
tter
eff
ect
(2)
Bri
ght
spo
ts a
re b
road
erth
anfa
int
ones
, b
y a
sm
all
amo
unt.
-M
easu
rem
ents
by
P. D
oher
ty (
Har
var
d)
Inth
e la
bora
tory
.
-”L
absp
ots
”C
CD
E2V
(L
SS
T)
-In
tensi
ty i
s var
ied
via
inte
gra
tion t
ime.
-ty
pic
ally
a 2
-3%
in
crea
se o
ver
the
full
dynam
ic r
ange.
P. A
stie
r E
ucl
id-F
rance
(201
3)
4
Th
e ef
fect
als
osh
ow
s up
on
Meg
aCam
(@
CF
HT
)...
An
d i
t is
pre
tty
mu
chac
hro
mat
ic(S
NL
S p
hoto
met
ryte
chnic
al p
aper
, A
&A
557, A
.55 2
013 )L
ess
than
0.5
%over
the
wh
ole
ra
ng
e.
Chip
s :
E2V
CC
D42
-90
(thin
ned
chip
s)
(CF
HT
LS
dat
a)
P. A
stie
r E
ucl
id-F
rance
(201
3)
5
…an
d o
n D
EC
am (
@C
TIO
-4m
)
Mea
sure
men
ts f
rom
Sci
ence
Ver
ific
atio
nD
ata
(i.e
. on s
ky)
wit
ha
tiny
colo
r co
rrec
tion
1 t
o 2
%.
LB
L/D
AL
SA
chip
shig
h-r
ho
250 µ
m t
hic
k
r ban
d
P. A
stie
r E
ucl
id-F
rance
(201
3)
6
Hy
per
Su
pri
me
Cam
Fro
mR
. L
upto
n.
P. A
stie
r E
ucl
id-F
rance
(201
3)
7
Th
e b
righ
ter-
fatt
er e
ffec
t
●T
he
sou
rce
of
the
effe
cth
asto
be
no
n-l
inea
r.
–If
it w
her
e li
nea
r, s
hap
e w
ou
ldn
ot
chan
ge
wit
h
flu
x.
–It
hen
ce c
annot
be
due
to d
iffu
sion
.
●N
on
-lin
eari
tyof
ov
eral
l re
spo
nse
?
–O
bvio
usl
y p
oss
ible
–L
inea
r w
ith
flu
x?
P. A
stie
r E
ucl
id-F
rance
(201
3)
8
Oth
er s
tran
ge
effe
cts
on
CC
Ds
(1)
Var
ian
ce o
f fl
atfi
eld
s is
not
exac
tly
pro
port
ion
al t
o t
hei
r av
erag
e
??
No
n-l
inea
rity
of
PT
Cte
nds
to g
od
ow
n
wh
en r
e-b
innin
g
the
imag
e.
Pho
ton T
ransf
er C
urv
e (P
TC
) :
var
iance
=f(
aver
age)
Sim
éon D
enis
Po
isso
n
CC
D E
2V
250
P. A
stie
r E
ucl
id-F
rance
(201
3)
9
Oth
er s
tran
ge
effe
cts
on
CC
Ds
(2)
Fla
t-fi
eld
pix
els
are
no
tst
atis
tica
lly
in
dep
end
ent.
Thei
rco
rrel
atio
ns
incr
ease
(li
nea
rly
) w
ith
illu
min
atio
n.
-L
inea
rin
crea
se w
ith
flat
-fie
ldav
erag
e-
Dep
ends
on
som
e el
ectr
ost
atic
boun
dar
yco
ndit
ion.
- E
2V
CC
D
-Mea
sure
men
tsby P
.Doher
ty(H
arvar
d)
-An
aly
sis
by
A. G
uyonnet
(Par
is)
Nea
rest
ver
tica
lnei
ghbors
Cov
/Var
Aver
age
P. A
stie
r E
ucl
id-F
rance
(201
3)
10
Th
ese
corr
elat
ion
s in
fla
t fi
elds
seem
to
be
achro
mat
ic
So, th
e ef
fect
does
no
t dep
end o
nh
ow
dee
p p
hoto
ns
conver
t.
P. A
stie
r E
ucl
id-F
rance
(201
3)
11
Th
ese
flat
fiel
d c
orr
elat
ions
dec
ay w
ith
dis
tance
- co
rrel
atio
ns
dec
reas
ero
ughly
exponen
tial
lyw
ith s
epar
atio
n.
- T
hey
are
larg
er a
long
Y t
han
alo
ng X
.
P. A
stie
r E
ucl
id-F
rance
(201
3)
12
No
n-l
inea
r P
TC
an
d c
orr
elat
ion
s
Unsu
rpri
singly
, w
hen
acc
ounti
ng f
or
pix
el c
orr
elat
ions,
the
PT
C b
ecom
esm
ore
lin
ear
PT
C f
or
ccd e
2v 2
50
P. A
stie
r E
ucl
id-F
rance
(201
3)
13
So,
We
det
ect
3 e
ffec
ts :
●bri
ghte
r-fa
tter
for
star
s/sp
ots
●V
aria
nce
of
flat
fiel
ds
is s
mal
ler
than
Pois
son
●F
latf
ield
s ex
hib
it c
orr
elat
ions
Lin
earl
y i
ncr
easi
ng w
ith i
llum
inat
ion.
-T
he
two l
ast
effe
cts
are
triv
iall
y r
elat
ed.
-S
mo
oth
ing o
f fl
atfi
elds
and
star
s m
ight
shar
e th
e sa
me
ori
gin
.
All
3 e
ffec
tsre
qu
ire
som
e n
on
-lin
ear
mec
han
ism
P. A
stie
r E
ucl
id-F
rance
(201
3)
14
Co
ulo
mb
forc
es i
n a
CC
D Em
pty
CC
D
P. A
stie
r E
ucl
id-F
rance
(201
3)
15
Co
ulo
mb
forc
es i
n a
CC
D
50
ke
P. A
stie
r E
ucl
id-F
rance
(201
3)
16
50
ke
Dep
endin
g o
n t
he
store
dch
arge,
ele
ctro
ns
dri
ftin
g
her
eg
ole
ft o
r ri
ght
P. A
stie
r E
ucl
id-F
rance
(201
3)
17
Em
pty
CC
DT
op v
iew
P. A
stie
r E
ucl
id-F
rance
(201
3)
18
Add a
bri
ght
star
Top v
iew
P. A
stie
r E
ucl
id-F
rance
(201
3)
19
Sh
ifte
d p
ixel
boundar
ies
(shif
ts x
5)
Top v
iew
P. A
stie
r E
ucl
id-F
rance
(201
3)
20
So,
Du
e to
Co
ulo
mb f
orc
es,
ov
erfi
lled
pix
els
get
smal
ler
w.r
.tth
eav
erag
ep
ixel
si
ze.
Th
is e
ffec
t:
Char
les-
August
inde
Coulo
mb
●R
edu
ces
spat
ial
var
iance
of
flat
-fie
lds
w.r
.t P
ois
son
●C
ause
spo
siti
ve
corr
elat
ion
s in
fla
t fi
eld
s (s
ou
rced
by
Po
isso
nfl
uct
uat
ions)
●B
road
ens
bri
gh
t sp
ots
w.r
.t f
ainte
r on
es
P. A
stie
r E
ucl
id-F
rance
(201
3)
21
Can
Co
ulo
mb
fo
rces
cau
se t
he
obse
rved
size
of
effe
cts
?
A s
ket
chy s
imula
tion
roughly
rep
roduce
s th
esi
ze o
f th
e obse
rved
co
rrel
atio
ns
and
of
the
bri
ghte
r-fa
tter
sl
ope.
E2V
CC
D
P. A
stie
r E
ucl
id-F
rance
(201
3)
22An e
mp
iric
al m
od
el
●W
edo
no
t k
no
w t
he
det
ails
of
ho
w C
CD
s ar
em
ade
●M
ost
ven
do
rs w
ould
no
t an
swer
ou
r q
ues
tio
ns.
●T
he
effe
ctis
smal
l an
dh
ence
Tay
lor
exp
ansi
ons
shou
ld h
old
●R
ath
erth
anm
akin
gqu
anti
tati
ve
pre
dic
tio
ns
fro
mel
ectr
ost
atic
s, w
e m
ake
a g
ener
al f
irst
ord
er
mod
el a
nd
(tr
y t
o)
der
ive
its
un
kn
ow
ns
from
dat
a.
P. A
stie
r E
ucl
id-F
rance
(201
3)
23A s
imp
list
ic m
odel
-C
har
ges
sto
red
in
a C
CD
sou
rce
an e
lect
ric
fiel
d-
Dri
ft t
raje
cto
ries
are
per
turb
ed b
y t
his
add
itio
nal
ele
ctri
c fi
eld
-P
ixel
sb
oun
dar
ies
are
affe
cted
by
thes
e per
turb
atio
ns.
→ E
ffec
tive
pix
elb
oun
dar
ies
are
(mar
gin
ally
)d
yn
amic
al
(0,0
)
(0,1
)
Qij
(1,0
)
(0,1
)
(0,-
1)
(-1
,0)
P. A
stie
r E
ucl
id-F
rance
(201
3)
24
(0,0
)
(0,1
)
Qij
(1,0
)
(0,1
)
(0,-
1)
(-1,0
)
Boundar
y s
hif
t, t
o f
irst
ord
er i
nso
urc
e ch
arges
:
Char
ge
“tra
nsf
er”
(induce
d b
y a
ll Q
ij):
Sum
over
the
4 s
ides
P. A
stie
r E
ucl
id-F
rance
(201
3)
25
Th
is i
s a
no
n-l
inea
ref
fect
Sourc
e ch
arge
Tes
t ch
arge.
Ass
um
es t
he
imag
eis
wel
l sa
mple
d.
To b
e det
erm
ined
:●
Inte
gra
tes
all
nu
mer
ical
fact
ors
fro
m t
he
pre
vio
us
slid
e●
Char
acte
rist
ic o
f a
dev
ice
(+ o
per
atin
g c
ondit
ion
s)
Char
ge
shu
ffli
ng
: no
char
ge
get
s lo
st
P. A
stie
r E
ucl
id-F
rance
(201
3)
26Co
rrel
atio
ns
in f
lats
For
a fl
at-f
ield
(av
erag
eµ,
var
ian
ce V
)on
eget
s :
Sum
over
4 s
ides
So :
- co
rrel
atio
ns
(Cov/V
) in
crea
seli
nea
rly w
ith i
llum
inat
ion
- var
iance
of
flat
-fie
lds
: P
ois
son t
erm
min
us
a quad
rati
c co
rrec
tion
P. A
stie
r E
ucl
id-F
rance
(201
3)
27
Do
th
e b
rig
hte
r-fa
tter
eff
ect
and
fla
t-fi
eld
corr
elat
ion
s sh
are
the
sam
e o
rig
in ?
TE
ST
:
Der
ive
coef
fici
ents
from
fla
t-fi
eld
corr
elat
ions
Scr
amb
lefa
int
spots
(or
star
s) a
nd c
om
par
eto
bri
ght
ones
P. A
stie
r E
ucl
id-F
rance
(201
3)
28
Fro
m c
orr
elat
ion
s to
co
effi
cien
ts.
(0,0
)
(0,1
)
Qij
(1,0
)
(0,1
)
(0,-
1)
(-1
,0)
At
“lar
ge”
dis
tance
, co
rrel
atio
ns
var
y m
ost
lyas
the
der
ivat
ive
of
the
boundar
y d
ispla
cem
ent
wit
h p
osi
tio
n.
P. A
stie
r E
ucl
id-F
rance
(201
3)
29
Get
tin
g t
he
“a”
coef
fici
ents
fro
m f
lat-
fiel
ds
(1)
●If
one
wan
ts t
o m
easu
re t
he
“a”
coef
fici
ents
up t
o s
epar
atio
n o
f n p
ixel
s,th
ere
are
~4 n
2
such
coef
fici
ents
.
●W
ith s
ym
met
ries
,it
dro
ps
to ~
2n
2
●T
her
e ar
e only
~n
2 c
orr
elat
ions
to b
e m
easu
red
●W
ehen
ce h
ave
to c
ook-u
p ~
n2 c
onst
rain
ts.
P. A
stie
r E
ucl
id-F
rance
(201
3)
30
Get
tin
g t
he
“a”
coef
fici
ents
fro
m f
lat-
fiel
ds
(2)
●Im
po
se r
atio
s o
f co
effi
cien
ts a
t si
mil
ar d
ista
nce
su
sin
g t
he
ov
eral
l sh
ape
of
the
dec
ay.
●R
esu
lts
are
reas
onab
ly i
ndep
end
ent
of
the
use
dan
aly
tica
l sh
ape.
●A
ny
bet
ter
sug
ges
tio
n ?
P. A
stie
r E
ucl
id-F
rance
(201
3)
31
- P
redic
ted b
righte
r-fa
tter
slo
pes
are
~20%
larg
er t
han
m
easu
rem
ents
.-
consi
sten
tly f
or
both
x a
nd y
and
55
0an
d 9
00 n
m
Ap
ply
ing
the
“a”
coef
fici
ents
(L
SS
T/E
2V
)
MC
pro
pag
atio
no
fco
rrel
atio
n m
easu
rem
ent
unce
rtai
nti
es
900 n
m
550 n
m
Sca
le u
pfa
int
spots
and s
cram
ble
them
.
P. A
stie
r E
ucl
id-F
rance
(201
3)
32
DE
Cam
Pre
dic
tion
Fro
m c
orr
elat
ion
s
Ap
ply
ing
the
“a”
coef
fici
ents
“Sim
ula
tions”
her
e pro
ceed
from
the
(flu
x-i
ndep
enden
t)
PS
F.
Only
CC
D1
7.
The
com
par
ison
is l
imit
ed b
y s
tati
stic
sof
flat
fiel
ds
and s
tars
.
P. A
stie
r E
ucl
id-F
rance
(201
3)
33
DE
Cam
:al
l ch
ips
Ap
ply
ing
th
e “a
” co
effi
cien
ts
Pre
dic
ted
fro
mco
rrel
atio
ns
Pre
dic
ted
fro
m c
orr
elat
ion
s
●T
he
mea
sure
d b
righte
r-fa
tter
slo
pes
see
mm
argin
ally
com
pat
ible
bet
wee
n c
hip
s●
The
corr
elat
ions
seem
com
pat
ible
, but
the
stat
isti
cs i
s lo
w t
hough.
Agre
emen
tat
the
15-2
0%
level
P. A
stie
r E
ucl
id-F
rance
(201
3)
34
DE
Cam
: n
on
-lin
eari
ty o
fre
spo
nse
●D
EC
amis
susp
ecte
d t
o e
xhib
it n
on-l
inea
riti
es o
f re
sponse
(se
e G
ary's
tal
k)
●T
his
contr
ibu
tes
to t
he
bri
ghte
r-fa
tter
eff
ect.
●W
ith t
he
non-l
inea
r co
rrec
tions,
the
obse
rved
bri
ghte
r-fa
tter
eff
ect
incr
ease
sb
y~
60 %
.P
red
icte
dfr
om
corr
elat
ion
sP
red
icte
d
fro
m c
orr
elat
ion
s
Shif
t due
tono
n-l
inea
rity
co
rrec
tion
Xy
DE
Cam
non-l
inea
rity
: h
ttps:
//cd
cvs.
fnal
.gov/r
edm
ine/
pro
ject
s/des
-sci
-ver
ific
atio
n/w
iki/
AB
_R
atio
_V
aria
tion
P. A
stie
r E
ucl
id-F
rance
(201
3)
35
Ap
ply
ing
the
“a”
coef
fici
ents
: D
EC
am
●A
gre
emen
t b
etw
een
mea
sure
men
tsan
dp
red
icti
on
s fr
om
fla
t-fi
eld
at
the
–~
20
% l
evel
(ign
ori
ng N
L c
orr
ecti
on
s)
–~
30
% l
evel
(w
ith
no
nli
nea
r co
rrec
tions)
●O
ur
mea
sure
men
ts o
f co
rrel
atio
ns
are
stat
isti
csli
mit
ed.
●N
on
-lin
eari
tyof
resp
onse
str
on
gly
aff
ects
th
e o
bse
rved
bri
gh
ter-
fatt
er s
lope.
P. A
stie
r E
ucl
id-F
rance
(201
3)
36
Ap
ply
ing
the
“a”
coef
fici
ents
Meg
acam
(thin
ned
CC
Ds)
Mea
sure
men
t:sl
ope
~ 0
.5
Pre
dic
tion f
rom
fla
t-fi
elds
slope
~ 0
.34 +
/- 0
.15
(mea
sure
d d
ista
nt
corr
elat
ions
are
“in t
he
nois
e”)
P. A
stie
r E
ucl
id-F
rance
(201
3)
37
- T
he
“a”
coef
fici
ents
are
sm
all:
- C
orr
ect
for
the
effe
ct b
yap
ply
ing
flip
ped
-sig
n c
oef
fici
ents
at
the
pix
el l
evel
- R
emea
sure
sta
r si
zes
as a
funct
ion o
f fl
ux
Un
scra
mb
ling
: c
orr
ecti
on
at t
he
pix
el l
evel
Unce
rtai
nti
es o
f co
rrel
atio
ns
P. A
stie
r E
ucl
id-F
rance
(201
3)
38Pra
ctic
al d
iffi
cult
ies
●M
easu
rin
g s
mal
l co
rrel
atio
ns
–S
tati
stic
s nee
ded
(10
0 M
pix
to r
each
10
-4)
–B
ewar
e o
f oth
er c
orr
elat
ion
sourc
es (
nee
d a
ram
p)
●N
on
-lin
eari
tyof
resp
onse
co
ntr
ibu
tes
toth
e B
Fef
fect –
No
n-l
inea
rity
dif
ficu
ltto
mea
sure
●M
ore
co
effi
cien
ts t
han
mea
sure
men
ts
–Im
pro
ve
elec
trost
atic
s?
●C
orr
ecti
on
–P
ixel
s le
vel
?
–O
rP
SF
mo
del
?
P. A
stie
r E
ucl
id-F
rance
(201
3)
39
Dis
tort
ion
s w
ith
ou
t as
sum
ing
go
od
sam
pli
ng
Sourc
e ch
arge
Tes
t ch
arge.
Ass
um
es t
he
imag
eis
wel
l sa
mple
d.
Corr
ecti
on t
o P
SF
mo
del
:
Pix
el l
evel
:
P. A
stie
r E
ucl
id-F
rance
(201
3)
40
Con
clu
sio
ns
●W
e th
ink t
o h
ave
com
pel
ling
evid
ence
th
at t
he
bri
ghte
r-fa
tter
eff
ect
and c
orr
elat
ion
s in
fla
tfi
eld
s sh
are
the
sam
e ori
gin
: th
e C
oulo
mb l
aw.
●C
orr
elat
ions
are
the
key
toco
nst
rain
the
bri
ghte
r-fa
tter
effe
ct.
●N
on-l
inea
rity
of
resp
onse
an
d o
ther
sourc
es o
fco
rrel
atio
ns
mak
e th
e li
nk
tric
ky.
●P
ract
ical
han
dli
ng o
fth
e ef
fect
stil
lto
be
sett
led
.
●H
andli
ng
the
bri
gh
ter-
fatt
er e
ffec
t at
the
~10
%le
vel
is
pro
bab
ly n
ot
too
dif
ficu
lt.
●W
e ar
e not
qu
ite
atu
nder
stan
din
g t
he
slo
pe
atth
e 1%
lev
el.
