P. Popesso on behalf of the PACS ICC

P.
Popesso
on
behalf
of
the
PACS
ICC
PACS
Photometer
Processing
Level
1
Data
Products
Sky+
TBG
+
1/f
High‐Pass
Filter
(removal
of
running
median)
PhotProject
Point
source
observations
Cosmological
surveys
Inversion
algorithm
(MadMap,
Cantalupo
et
al.
2010)
Extended
Objects
PACS
Photometer
Processing
Level
1
Data
Products
Sky+
TBG
+
1/f
High‐Pass
Filter
(removal
of
running
median)
PhotProject
Point
source
observations
Cosmological
surveys
dominating
final
noise
regulating
behavior
of
individual
noise
components:
• 
noise
per
pixel
• 
cross
correlated
noise
Parameters
to
be
considered:
  High‐pass
filter
width
  Projection
parameters:
output
pixel
size
and
drop
size
Output
pixel
size
Drop
size
Error
map
es7mate
within
Hipe
8.0
  Current
state:
error
estimate
based
on
error
propagation
up
to
PhotHighPassFilter
task
(removes
large
part
of
the
1/f
noise
via
median
filter
removal)
  Due
to
1/f
noise
removal,
the
timeline
noise
power
spectrum
changes
drastically,
making
the
standard
error
propagation
no
longer
feasible
  ICC
discussed
and
approved
two
different
solutions
Solu7ons:
  Error
propagation
is
no
longer
supported
in
the
PACS
pipeline:
error
map
of
Level
2
Product
is
set
to
zero
  Two
solutions
depending
on
data
redundancy:
  high
redundancy
(few
AOR
of
the
same
field
or
high
repetition
number
within
the
same
AOR)
error
maps
from
weighted
mean
error
(see
next
slide)
  low
redundancy
(only
scan
and
cross
scan
without
repetitions):
error
map
derived
from
coverage
map
via
calibration
obtained
from
high
redundancy
case
High
redundancy
data:
1)
error
map
  Method
based
on
high
redundancy
observations
of
blank
fields
in
cosmological
surveys.
  Blank
fields
repeated
AORs
are
mapped
into
maps
with
the
same
WCS
  Error
per
pixel
is
given
by
error
of
the
(coverage)
weighted
mean
of
flux
distribution
  Dedicated
ipipe
script
will
be
provided
soon
to
estimate
the
error
map
with
this
method
for
all
applicable
cases
2)
cross‐correlated
noise
  The
values
in
nearby
pixels
are
found
to
be
correlated
due
to
remaining
1/f
noise
and
projection
effects
  Positive
(negative)
correlations
increase
(decrease)
the
error
in
measured
fluxes
  For
each
case
we
estimate
the
Correlation
map
following
the
method
used
by
the
PEP
Consortium
  Correlation
map
describes
correlation
with
the
central
pixel
  Assumes
that
correlation
depends
only
on
relative
positions
  Calculates
2×NOBS
series
of
pairs
of
pixels
and
averaged
over
>
1000
pairs
with
same
[Δx,Δy]
across
the
map
2)
Cross
correla7on
noise
Cross
correlation
term
PSF
Assuming
pixel
constant
error:
Cross
correlation
factor:
Correlation
matrix
Cross
correlated
noise
factor
to
be
applied
to
any
noise
estimate
to
take
into
account
cross‐correlated
noise
The
Cross
correlated
noise
factor
depends
on
PSF
shape
or
aperture
Dedicated
task
and
ipipe
script
will
soon
be
provided
for
applicable
cases
Low
redundancy
case
  error
map
created
via
calibration
of
coverage
map.
  calibration
parameterized
as
a
function
of
hp
width,
output
pixel
size
and
pixfrac
  calibration
performed
on
data
with
very
high
redundancy
in
medium
and
fast
speed
  cross‐correlation
noise
correction
factor
parameterized
as
well
in
the
same
parameter
space
First
component:
error
map‐coverage
map
calibra7on
• 
tight
relation
between
noise
per
pixel
and
pixel
coverage
• 
dispersion
of
0.07‐0.08
dex
(~17‐20%)
• 
error
≈
coverage‐2
• SPG
and
ipipe
cases
included
• 
calibration
of
the
type:
Log(error)=α×log(coverage)+β
• 
no
dependency
on
initial
coverage
of
the
co‐added
maps,
just
on
final
coverage
• 
almost
no
dependency
on
PhotProject
mapping
flavors:
• 
mean
map
• 
weighted
mean
map
(weights
given
by
stdev
of
running
box
along
the
timeline
suggested
by
ipipe
scripts
for
applicable
cases)
Noise
per
pixel
varia7on
Same
output
pixel
and
drop
size
Different
HP
width
Same
HP
width
and
output
pixel
size
Different
drop
size
(pixfrac)
In
summary…
pixfrac
Log(error)=α×log(coverage)+β
0.01
0.001
0.0001
0
1
2
3
4
Second
component:
cross
correlated
noise
6.4
arcsec
output
pixel
size
3.0
arcsec
output
pixel
size
pixfrac
drop
size/output
pixel
size
Library
of
correlation
matrices
and
PSFs
Cross
correla7on
correc7on
factor
Cross
correlation
term
drop
size/output
pixel
size
See
also
Casertano
et
al.
2000
Assuming
pixel
constant
error:
Cross
correlation
factor
Estimate
available
for
PSF
fitting
of
three
different
sizes
and
for
aperture
photometry
for
three
apertures.
0.01
0.001
0.0001
160
μm
0
1
2
3
4
Noise
per
pixel
and
cross
correlation
correction
go
in
opposite
direction
as
a
function
of
the
drop
size‐outpix
size
ratio
Global
noise
es7mate
Noise
of
the
final
map
is
estimated
by
extracting
the
flux
at
fix
aperture
at
random
position
in
the
map.
The
dispersion
of
the
distribution
of
extracted
fluxes
provide
the
global
noise
estimate
HPF
width
Noise
per
pixel
and
cross
correlated
noise
compensate
each
other
leaving
only
small
differences
due
to
HPF
width
• 
the
smaller
the
width,
the
smaller
the
global
noise
(30‐35%
effect
from
15
to
40
readouts)
• 
pixfrac
and
outputpixel
size
affect
only
at
the
2‐4%
level
Table
example
To
guide
the
User
  We
provide
the
best
fitting
function
through
the
data
to
retrieve
error
components
at
defined
hp
width,
output
pixel
and
drop
size:
  3D
Third
order
polynomial
(22
parameters)
  α
=
Σm=1,Na(m)xiyjzk
i+j+k≤
m
with
m=3
  β
=
Σm=1,Nb(m)xiyjzk
i+j+k≤
m
with
m=3
  f
=
Σm=1,Nc(m)xiyjzk
i+j+k≤
m
with
m=3
‐
where
α
and
β
are
slope
and
normalization
of
error
map‐coverage
map
correlation
best
fit
line;
‐
f
is
the
cross
correlation
noise
correction
factor;
‐
and
x,
y,
z
are
hp
width,
output
pixel
and
drop
size,
respectively
Caveats
  Method
working
for
point
source
observation
where
background
noise
is
dominating
  Error
map
calibration
not
applicable
for
very
bright
point
sources
(like
an
extended
emission
for
PACS
Photometer
)
pointing
jitter
is
the
dominating
source
of
noise
  For
bright
sources
and
extended
emission
calibration
possible
if
flux
is
included
as
additional
parameter