errors in airglow & auroral emission...
TRANSCRIPT
Erro
rs in
Airg
low
&
Aur
oral
Em
issi
on
Mea
sure
men
ts
D. P
alla
mra
juC
ente
r for
Spa
ce P
hysi
csB
osto
n U
nive
rsity
CE
DA
R T
utor
ial:
June
17,
200
3
Ack
now
ledg
men
ts
•Je
ffre
yB
aum
gard
ner
Bos
ton
Uni
vers
ity
•Ti
mot
hy C
ook
’’
•Su
priy
a C
hakr
abar
ti
’’
•
Out
line
Intro
duct
ion
•Er
rors
rela
ted
to a
irglo
w/a
uroa
lbrig
htne
ss
mea
sure
men
ts:
Syst
emat
ic (D
eter
min
ate)
err
ors
Lim
itatio
nsR
ando
m (I
ndet
erm
inat
e) e
rror
s•
SNR
for d
iffer
ent s
cena
rios
•Su
mm
ary
Scop
e of
the
tuto
rial
•K
now
the
limita
tions
and
err
ors i
n ai
rglo
w/a
uror
al b
right
ness
mea
sure
men
ts.
•W
ith th
is in
form
atio
n, ta
ke p
rope
r ac
coun
t of t
he so
urce
s in
the
data
an
alys
is.
•G
uide
one
to e
stim
ate
the
SNR
to e
xpec
t fo
r a g
iven
syst
em.
Wha
t is a
irgl
ow/a
uror
a ?
Airg
low
/Aur
ora
is th
e lu
min
osity
of a
n at
mos
pher
e.
Air
glow
:Ini
tial e
xcita
tion
sour
ce is
sola
r pho
tons
.A
uror
a:In
itial
exc
itatio
n so
urce
is e
nerg
etic
par
ticle
s.
hν(F
UV
-IR
) (A
IRG
LOW
)X
/XY
/XY
+X
* /X
Y*
/XY
*+
e’-/H
’+X
/XY
/XY
+X
/XY
* /X
Y*+
e’-
H’+ /
hν/
colli
sion
s+ +
+
We
will
use
“E
mis
sion
s” to
ref
er to
bot
h A
irgl
ow &
Aur
ora
Why
mea
sure
Air
glow
/Aur
ora?
Airg
low
/Aur
oral
mea
sure
men
ts a
re e
ffec
tive
and
fairl
y in
expe
nsiv
e m
etho
d of
rem
ote
sens
ing
the
beha
vior
of t
he u
pper
atm
osph
ere.
Red
line
& 7
774
Åem
issi
ons.
Plas
ma
drift
s, TE
C:
Req
uire
men
tsPh
ysic
al P
aram
eter
(s) t
hat
can
be d
eriv
ed
Elec
tron
& p
roto
n in
duce
d au
rora
.En
ergy
inpu
ts in
to e
arth
:
Larg
e fie
ld-o
f-vi
ew; m
easu
rem
ents
from
m
ultip
le si
tes.
Latit
ude
& L
ongi
tude
cou
plin
g:
Emis
sion
rate
s at m
ultip
le w
avel
engt
hs.
Alti
tude
cou
plin
g, (v
ertic
al
prop
agat
ion
of w
aves
):
•H
igh
spec
tral-r
esol
utio
n m
easu
rem
ents
(D
oppl
er &
Rot
atio
nal).
•Tw
iligh
t em
issi
ons.
Neu
tral t
empe
ratu
res a
nd w
inds
:R
eact
ion
rate
s, to
mog
raph
y.C
once
ntra
tions
& C
ompo
sitio
ns:
Diff
eren
t em
issi
ons o
rigi
nate
at d
iffer
ent a
ltitu
des
Emis
sion
alti
tude
s are
a fu
nctio
n of
the
conc
entra
tion
of re
acta
nts,
life
times
of t
he e
xcite
d sp
ecie
s and
col
lisio
n fr
eque
ncie
s.
OI
630
.0nm
(2
50km
)77
7.4n
m(F
-pea
k)55
7.7n
m(1
00km
)N
2+39
1.4n
m
(
150k
m)
427.
8nm
(150
km)
470.
9nm
(150
km)
Hβ
486.
1nm
(100
-20
0km
)
Som
e C
omm
only
mea
sure
d em
issi
ons:
Hα
656.
3nm
(100
-20
0km
)
Na
589
.3nm
(92k
m)
OH
731
.6nm
(85k
m)
Obs
erva
tiona
l Mea
ns
Gro
und
Roc
ket
Spac
e
We
will
onl
y di
scus
s gro
und-
base
d ob
serv
atio
ns o
f vis
ible
em
issi
ons
How
bri
ght a
re n
ight
time
atm
osph
eric
em
issi
ons?
Star
s, Zo
diac
al li
ght,
Diff
use
gala
ctic
ligh
t, A
irglo
w
(Dire
ct +
Sca
ttere
d)
Airg
low
= (O
bser
ved
light
–ca
lcul
ated
due
to a
stro
phys
ical
sour
ces)
(Der
ived
)
RV
BU
Ban
d
645
550
400
365
Ref
eren
ce λ
(590
-700
)(4
95-5
90)
(395
-495
)(3
31-3
95)
λR
ange
(nm
)
Prie
dhor
sky,
199
6 (A
ppl.
Opt
)56
%53
%38
%55
%
Air
glow
as f
ract
ion
of to
tal
(%)
His
toric
al d
evel
opm
ent o
f Det
ecto
rs fo
r em
issi
on
mea
sure
men
ts:
5X ?
CC
D, I
CC
D,IP
D
Phot
ogra
phic
Fi
lms
1980
2-D
Inte
nsifi
ed
TV1-
D19
6010
0XPh
otom
ultip
lier
Tube
(PM
T)
1950
1910
Tayl
or a
nd G
arci
a, 1
995
Are
cibo
OI 5
57.7
nm
Kel
ley
et a
l., 2
000
Are
cibo
OI 6
30.0
nm
* * POLA
R V
IS E
arth
Cam
era.
C
ourte
sy: F
. Sig
war
th &
L. F
rank
OI 1
35.6
nmPO
LA
R
Mar
tinis
et a
l., 2
003
OI 6
30.0
nmT
ucum
an
Saga
wa
et a
l., 2
003
OI 1
35.6
nmIM
AG
E
Lar
ge sc
ale
aspe
cts o
f man
y at
mos
pher
ic p
heno
men
a ha
ve
been
dis
cove
red
by a
ll-sk
y op
tical
mea
sure
men
ts
Smith
et a
l., 2
003
McD
onal
d O
bs.
OI 5
57.7
nm
“And
so w
e se
e th
at th
e po
etry
fade
s out
of
the
prob
lem
, and
by
the
time
the
seri
ous
appl
icat
ions
of e
xact
scie
nce
begi
ns w
e ar
e le
ft w
ith o
nly
poin
ter r
eadi
ngs.”
--Si
r E
ddin
gton
Ther
e is
eno
rmou
s bea
uty
to th
e ph
enom
ena
that
occ
ur
in n
atur
e. O
ptic
al e
mis
sion
mea
sure
men
ts a
re a
ver
y ef
fect
ive
tool
to u
nrav
el so
me
of th
e na
ture
’s b
eaut
y!
But,
befo
re a
ppre
ciat
ing
the
beau
ty w
e ne
ed to
rem
embe
r wha
t Sir
Edd
ingt
onsa
id…
Diff
eren
t typ
es o
f err
ors
•U
ncer
tain
ty =
Sys
tem
atic
+ R
ando
m +
Mis
cella
neou
s err
ors.
•U
ncer
tain
ty g
ives
a m
easu
re o
f ove
rall
conf
iden
ce o
f a
mea
sure
men
t (σ)
.Blu
nder
s, di
ffer
ent u
nits
, com
puta
tiona
l gl
itche
s (ro
undi
ng o
ff, i
nsuf
ficie
nt
algo
rithm
s, do
uble
pre
cisi
on, e
tc.)
Illeg
itim
ate
erro
rs:
(Mis
cella
neou
s)
Erro
rs re
late
d to
dyn
amic
pro
perti
es o
f th
e in
stru
men
tatio
n; e
x., s
ettin
g tim
e, ti
me
cons
tant
s, et
c.
Dyn
amic
err
ors:
(Mis
cella
neou
s)
Ofte
n ca
lled
prec
isio
n.R
ando
m e
rror
s:(I
ndet
erm
inat
e)
Ofte
n ca
lled
accu
racy
; (m
easu
red
valu
e –
the
“tru
th”)
.Sy
stem
atic
err
ors:
(D
eter
min
ate)
Sche
mat
ic o
f a ty
pica
l opt
ical
syst
em
Ape
rture
Dis
pers
ing
elem
ent
Filte
r
Det
ecto
r
Col
limat
or
Rei
mag
ing
Lens
Ban
d pa
ss, i
nter
fere
nce
filte
r, et
c.
Fabr
y Pe
rot,
Gra
ting,
Gris
m, e
tc.
PMT,
IPD
, CC
D, I
CC
D, e
tc.
Not
all
syst
ems m
ay n
eed
all t
hese
com
pone
nts
Ori
gin
of S
yste
mat
ic/D
eter
min
ate
erro
rs (s
ame
size
and
sign
) for
em
issi
on m
easu
rem
ents
Not
e: In
the
follo
win
g, th
e re
leva
nt is
sues
are
in re
d co
lor a
nd th
eir ‘
solu
tions
’ are
show
n in
blu
e.
Syst
emat
icD
etec
tor Q
uant
um e
ffic
ienc
y
(i)V
aria
tion
of Q
E w
ith ti
me.
(ii)M
oist
ure
cond
ensa
tion
on th
e ch
ip w
hile
coo
ling:
(a)
in p
lace
s of h
igh
hum
idity
, or
(b)
due
to lo
ss in
vac
uum
.
Perio
dic
calib
ratio
ns w
ith k
now
n so
urce
(gro
und
stan
dard
s or
star
s).
Syst
emat
icFi
lter T
rans
mis
sion
(i)Fo
r sm
all b
andw
idth
–re
duct
ion
in
trans
mis
sion
from
low
ang
les.
(ii)
For l
arge
ban
dwid
th–
cont
ribut
ion
from
oth
er
wav
elen
gths
not
avo
idab
le.
AT
0o
INC
IDE
NC
E
AT
20o
INC
IDE
NC
E
61%
10%
(a)B
e ca
refu
l with
all-
sky
mea
sure
men
ts w
ith n
arro
w
band
wid
th fi
lters
.
Syst
emat
icFi
lter T
rans
mis
sion
(Con
td.)
(iii)
Tem
pera
ture
tuni
ng–
disc
repa
ncy
betw
een
actu
al a
nd
disp
laye
d te
mpe
ratu
re. (
Typi
cal v
alue
s: 0
.16
–0.
27 Å
o C-1
)
(iv)
Tilti
ng o
f filt
er fo
r bac
kgro
und.
(v) V
aria
tion
of fi
lter c
hara
cter
istic
s with
tim
e.
(vi)
Spat
ial v
aria
tion
in th
e tra
nsm
issi
on.
(b)
Perio
dic
calib
ratio
n.
(c) F
lat-f
ield
ing
with
mon
ochr
omat
or.
Syst
emat
icA
ngul
ar/G
eom
etric
Cal
ibra
tion
The
rela
tion
betw
een
the
view
ang
les/
sky
posi
tion
and
pixe
ls o
n th
e de
tect
or.
•O
bser
vatio
ns o
f sta
rs w
hen
poss
ible
.•
Labo
rato
ry c
alib
ratio
n.
Sky C
CD
HθH ta
nθ
Syst
emat
icva
n R
hijn
eff
ect:
Col
umn
int.
emis
sion
s var
y w
ith z
enith
ang
le (u
nifo
rm sl
ab).
Can
be
corr
ecte
d w
ith th
e as
sum
ptio
n of
uni
form
em
issi
on la
yer
+
−
=
zh
RR
II zeni
thz
22
)(
)(
sin
1
1
Whe
re, z
is th
e ze
nith
ang
le, R
is R
adiu
s of
ear
th, h
is th
e he
ight
of t
he e
mis
sion
an
d I(
z) is
the
Inte
nsity
at a
zen
ith a
ngle
z.
Roa
ch a
nd G
ordo
n, 1
973.
Syst
emat
icFl
at fi
eld
corr
ectio
n:(i)
Vig
netti
ng: T
he d
ecre
ase
in il
lum
inat
ion
away
from
the
optic
al a
xis i
n an
opt
ical
syst
em.
(ii)S
truct
ures
or d
ust w
ithin
the
inst
rum
ent,
“hot
” pi
xels
on
the
dete
ctor
, etc
.
Cor
rect
ing
the
imag
e w
ith a
stru
ctur
e-le
ss w
hite
ligh
t im
age.K
yx
Iy
xI
yx
Iy
xI
yx
Ida
rkfla
t
dark
corr
ecte
d)
,(
),
()
,(
),
()
,(
−−=
Bef
ore
Afte
rA
fter
Bef
ore
Imag
ing
tech
niqu
es n
eed
to c
orre
ct e
very
imag
e by
a fl
at-f
ield
Lim
itatio
ns o
f opt
ical
em
issi
on
mea
sure
men
ts:I
ssue
s on
whi
ch w
e do
no
t hav
e an
y co
ntro
l
Lim
itatio
nsSk
y Tr
ansm
issi
on:
(i)Th
in su
b-vi
sual
clo
uds.
(ii)
Haz
e, fo
g, m
ist,
dust
.
(iii)
Var
ies f
or d
iffer
ent a
ngle
s.
(iv)G
roun
d lig
hts m
agni
fy th
e ef
fect
.A
B
C
(a)M
easu
rem
ents
from
hig
h al
titud
es.
(b)M
easu
rem
ents
from
dry
/des
ert l
ocat
ions
.
(c)O
bser
ving
star
s of k
now
n in
tens
ities
.
Lim
itatio
nsEm
issi
on h
eigh
t var
iatio
n:(i)
The
F-la
yer m
ovem
ent (
dow
n or
up)
will
pro
duce
mor
e or
le
ss e
mis
sion
s.(ii
)Thi
s will
aff
ect t
he d
oppl
er w
idth
(= T
n) o
f the
obs
erve
d em
issi
on p
rofil
e.
(a)D
ata
from
oth
er in
stru
men
ts, s
uch
as a
dig
ison
desw
ill
effe
ctiv
ely
com
plem
ent t
he e
mis
sion
mea
sure
men
ts to
de
rive
accu
rate
phy
sica
l par
amet
ers.
Emis
sion
laye
rNe
Ne
W1 W
2
Lim
itatio
nsSt
ruct
ures
in E
mis
sion
hei
ght?
The
obta
ined
em
issi
ons a
re c
olum
n in
tegr
ated
. So
the
info
rmat
ion
on v
ertic
al st
ruct
ures
, if a
ny, i
s int
egra
ted
out.
Ori
gin
of R
ando
m/I
ndet
erm
inat
e er
rors
(diff
eren
t siz
e an
d si
gn) f
or
emis
sion
mea
sure
men
ts
Phot
on n
oise
:R
ando
m
(i)D
epen
dent
on
sign
al st
reng
th.
(ii)N
ot a
dditi
ve.
(a)L
arge
sign
al o
r lar
ge ti
me
inte
grat
ion.
(b)
Det
ecto
rs o
f hig
h se
nsiti
vity
.
Ther
mal
noi
se o
r Dar
k cu
rren
t:R
ando
m
(i)C
anno
t be
dist
ingu
ishe
d fr
om p
hoto
elec
trons
due
to si
gnal
.
(ii)P
rodu
ctio
n ra
te o
f the
rmal
ele
ctro
ns e
xpon
entia
lly
incr
ease
s with
tem
pera
ture
.
(iii)T
herm
al e
lect
rons
redu
ce th
e dy
nam
ic ra
nge
of a
det
ecto
r.
(a)R
educ
es b
y a
fact
or o
f 2 fo
r ev
ery
6 C
redu
ctio
n in
te
mpe
ratu
re fo
r CC
Ds.
(b)T
ake
seve
ral d
ark
imag
es a
nd
subt
ract
with
the
imag
e co
ntai
ning
dat
a.
Rea
d N
oise
:R
ando
m(i)
Rea
dout
noi
se is
add
itive
.(ii
)In
depe
nden
t of s
igna
l.(ii
i)D
epen
dent
on
the
read
out r
ates
.(iv
)It h
as a
Gau
ssia
nde
viat
ion
and
is th
eref
ore
expr
esse
d as
its
stan
dard
dev
iatio
n (r
msv
alue
).U
se sm
all n
umbe
r of c
o-ad
ds d
urin
g da
ta a
cqui
sitio
n.
Qua
ntiz
atio
nN
oise
:R
ound
ing
off c
ause
d by
the
Ana
log-
to-d
igita
l con
verte
r in
conv
ertin
g th
e am
plitu
de o
f ele
ctro
nic
sign
al in
to a
bin
ary
repr
esen
tatio
n.In
sign
ifica
nt a
nd u
sual
ly ig
nore
d.
Inde
term
inat
e V
s Det
erm
inat
e er
rors
Det
erm
inat
e er
rors
can
be
mor
e se
rious
than
inde
term
inat
e er
rors
. Bec
ause
:
•Th
ere
is n
o m
etho
d of
dis
cove
ring
and
iden
tifyi
ng th
em
just
by
look
ing
at th
e da
ta.
•O
ne c
an n
ot re
duce
its a
dver
se e
ffec
ts b
y re
peat
ing
the
expe
rimen
t as i
t has
the
sam
e si
gn a
nd m
agni
tude
.
Phot
on st
atis
tics i
s gov
erne
d by
Poi
sson
Dis
tribu
tion
Pois
son
stat
istic
s des
crib
es th
e re
sult
of e
xper
imen
ts w
here
on
e co
unts
eve
nts t
hat o
ccur
at r
ando
m, b
ut a
t a d
efin
ite
aver
age
rate
. D
istri
butio
n fo
r diff
eren
t µ
µµ
µ−
=e
xx
Px !
),
(
Mea
n <x
> =
µ;
Stan
dard
dev
iatio
n,
The
final
cou
nt is
= µ
Frac
tiona
l unc
erta
inty
is =µ
σ=
µ±
µµµ
1=
Sign
al to
Noi
se R
atio
(SN
R)
Ass
umin
g th
at sy
stem
atic
err
or is
take
n ca
re o
f, th
e SN
R is
RD
BS
SSN
R+
++
=)
(
Her
e th
e co
ntrib
utio
ns to
noi
se in
ad
ditio
n to
sign
al a
re th
e B
ackg
roun
d B,
da
rk n
oise
or t
herm
al n
oise
of t
he
dete
ctor
, Dan
d th
e re
ad n
oise
of t
he d
etec
tor,
R.
Rel
atio
n be
twee
n U
ncer
tain
ty a
nd S
NR
Mea
sure
men
t unc
erta
inty
= 1
/SN
RSN
R =
10
a 10
% e
rror
in a
sing
le m
easu
rem
ent a
ndSN
R =
20
a 5
% e
rror
in a
sing
le m
easu
rem
ent a
nd so
on.
.
Dar
k no
ise,
e-pi
x-1s-1
d
syst
em e
ffic
ienc
y.sew
here
,
phot
ons s
–1 R
-1in
cide
nt o
n a
pixe
l for
a g
iven
f/#.
knu
mbe
r of c
o-ad
ds,
nonu
mbe
r of p
ixel
s bin
ned
afte
rrea
dout
, af
num
ber o
f pix
els b
inne
d be
fore
read
out,
bere
ad o
ut n
oise
, e–
(RM
S)ro
filte
r are
a (o
r ban
dwid
th w
here
bac
kgro
und
is c
onsi
dere
d), Å
faba
ckgr
ound
con
tinuu
m, R
Å-1bg
expo
sure
tim
e, se
ct
filte
r tra
nsm
issi
on,
ftsi
gnal
stre
ngth
, Rs
dete
ctor
qua
ntum
eff
icie
ncy,
qe
])
()
([
2ro
afno
noaf
bet
dse
kno
afbe
tfa
bgft
sqe
sek
noaf
bet
fts
qeSN
R⋅
+⋅
⋅⋅
⋅+
⋅⋅
⋅⋅
⋅⋅
+⋅
⋅⋅
⋅⋅
⋅⋅
⋅⋅
=
RD
BS
SSN
R+
++
=)
(
Ada
pted
from
:R
oesl
er, 1
987.
Bau
mga
rdne
r et a
l., 1
993.
Atm
osph
eric
em
issi
ons c
an b
e:(i)
Phot
on st
atis
tics l
imite
d or
(ii
)Rea
d no
ise
limite
d.
Let u
s con
side
r diff
eren
t sce
nario
s:
1.Sm
all s
igna
l on
smal
l bac
kgro
und
(ex.
Geo
coro
na o
r pr
oton
aur
ora)
2.
Larg
e si
gnal
on
smal
l bac
kgro
und
(ex.
Airg
low
/ aur
ora
durin
g ni
ght t
ime)
3.
Larg
e si
gnal
on
larg
e ba
ckgr
ound
(ex.
Airg
low
/ aur
oral
em
issi
ons d
urin
g D
aytim
e or
twili
ght t
ime)
.
1.0
se
0.1
e-pi
x-1s-1
d
For f
/3=
4 x
10-2
; f/1
1 =
2.9
x 10
-3ph
oton
s s –1
R-1
pixe
l-1(f
or 2
4µpi
xel)
k
5-50
no10
.af
1.0
be6.
e–(R
MS)
for C
CD
ro
8 Å
for n
ight
time
and
0.18
Åfo
r day
time
emis
sion
sfa
3 RÅ
-1–
5 M
RÅ-1
bg1-
20 s
t0.
75,
ft20
-300
0 R
s0.
8 fo
r CC
D a
nd 0
.2 fo
r IC
CD
qeFor i
nves
tigat
ing
the
SNR
for d
iffer
ent o
bser
vatio
nal
scen
ario
s, fo
llow
ing
valu
es h
ave
been
use
d in
the
SNR
re
latio
n:
Gal
and
et a
l., 2
003
1.Sm
all s
igna
l on
smal
l bac
kgro
und
(ex.
Geo
coro
na o
r pr
oton
aur
ora)
s= 4
-20R
; bg=
3R/Å
•R
ead
out n
oise
& d
ark
sign
al
affe
ct th
e SN
R.
•IC
CD
a b
ette
r opt
ion
than
bar
e C
CD
for d
ynam
ical
ly v
aryi
ng
phen
omen
a.
RD
BS
SSN
R+
++
=)
(
2.La
rge
sign
al o
n sm
all b
ackg
roun
d (e
x. N
ight
time
emis
sion
s) s=
300
R;b
g=3R
/Å
Bot
h re
ad o
ut n
oise
& d
ark
sign
al
affe
ct th
e SN
R.
•B
are
CC
D to
be
used
with
larg
e in
tegr
atio
ns.
•IC
CD
still
use
ful f
or o
bser
ving
dy
nam
ical
ly v
aryi
ng
phen
omen
a.
RD
BS
SSN
R+
++
=)
(
3.La
rge
sign
al o
n la
rge
back
grou
nd (e
x. D
aytim
e or
tw
iligh
ttim
e em
issi
ons)
s= 3
kR
;bg=
1-5
MR
/Å
RD
BS
SSN
R+
++
=)
(
•SN
R is
lim
ited
by p
hoto
n st
atis
tics.
•R
ead
out n
oise
& D
ark
nois
e D
ON
OT
affe
ct th
e SN
R.
Ring
effe
ct:F
illin
g-in
of S
olar
Fra
unho
ferl
ines
due
to sc
atte
ring
by
earth
s atm
osph
eric
gas
es:
Nee
ds to
be
acco
unte
d fo
r.
App
licat
ion
of S
NR
Rel
atio
n
Rin
g ef
fect
: Pa
llam
raju
et a
l., 2
000;
GR
LPa
llam
raju
et a
l., 2
001;
JGR
Exa
mpl
e: H
IRIS
E d
ata
se=0
.16
Futu
re R
equi
rem
ents
•C
CD
s with
:Ze
ro re
ad n
oise
!Sm
all p
ixel
size
s•
Bet
ter f
ilter
s
200?
5X ?
CC
D, I
CC
D,IP
D
Phot
ogra
phic
Fi
lms
1980
2-D
Inte
nsifi
ed
TV1-
D19
6010
0XPh
otom
ultip
lier
Tube
(PM
T)
1950
1910
Sum
mar
y•
Airg
low
& A
uror
al m
easu
rem
ents
pro
vide
uni
que
pers
pect
ive
of th
e at
mos
pher
ic b
ehav
ior.
•A
tmos
pher
ic tr
ansp
aren
cyis
the
maj
or u
nkno
wn
for t
he n
ight
time
emis
sion
s. •
Stat
istic
al fl
uctu
atio
nof
pho
ton
nois
e is
the
maj
or
fact
or fo
r day
time
mea
sure
men
ts.
•Pe
riod
ic c
alib
ratio
nshe
lp c
orre
ct sy
stem
atic
err
ors.
•R
ando
m e
rror
s can
be
redu
ced
by:
•la
rge
time
inte
grat
ions
, bin
ning
mor
e pi
xels
and
m
ore
co-a
dds,
and
•m
ore
sens
itive
det
ecto
rs.