Caltech Spice-Based Galaxy Calculator User manual

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;E!K92L9M2NEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEG!
GE!7K>AMOMP+*4F2*7K@2 EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEQ!
A.!ADDITIONAL FLAGS.......................................................... 3!
QE!L=PPMP+*4F2*7K@2 EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEER!
A.!SPECIFYING THE TELESCOPE CONFIGURATION ........................................ 5!
B.!TELESCOPE CONFIGURATION FILE FORMAT .......................................... 7!
C.!SPECIFYING THE OBSERVING STRATEGY AND DETECTOR CHARACTERISTICS..................... 8!
D.!WL-SPECIFIC INPUTS....................................................... 10!
E.!BAO-SPECIFIC INPUTS...................................................... 12!
F.!PZCAL-SPECIFIC INPUTS.................................................... 15!
SE!7K@2*K=4A=4!C*NO*247 EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ;R!
RE!7K@2*K=4A=4!C*'TK*247EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ;U!
VE!7K@2*K=4A=4!C*AW7TO*247EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ;H!
UE!@24TMO2@*>24FK@KOK+X*TP@*T!!=>A4MKP!EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ;Y!
A.!BACKGROUND COSMOLOGY ..................................................... 19!
B.!SKY BRIGHTNESS .......................................................... 19!
C.!GALACTIC EXTINCTION ...................................................... 20!
D.!LINE SENSITIVITY AND EFFECTIVE SOLID ANGLE.................................... 20!
E.!EXPECTED VS.OBSERVED SNR................................................. 22!
F.!NOISE MODEL............................................................. 24!
G.!THERMAL BACKGROUND MODEL .................................................. 27!
H.!GALAXY PROFILES ......................................................... 29!
I.!POINT SPREAD FUNCTIONS.................................................... 29!
J.!ELLIPTICITY UNCERTAINTY ................................................... 32!
HE!@T4T*!4L=74=L2!*TP@*Z=P74MKP! EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE QQ!
A.!DATA STRUCTURES ......................................................... 33!
B.!INTERFACE FUNCTIONS ...................................................... 34!
C.!SPECIAL FUNCTIONS ........................................................ 34!
D.!ROUTINES TO SET UP DETECTOR PARAMETERS ....................................... 35!
E.!ROUTINES TO COMPUTE THE THROUGHPUT .......................................... 35!

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0!
F.!ROUTINES TO COMPUTE THE MODULATION TRANSFER FUNCTION (MTF) ...................... 35!
G.!ROUTINES TO COMPUTE GALAXY IMAGE PROPERTIES ................................... 35!
H.!ROUTINES TO COMPUTE COSMOLOGICAL INFORMATION .................................. 37!
I.!ROUTINES TO COMPUTE PROPERTIES OF THE BAO GALAXY DISTRIBUTION .................... 37!
J.!ROUTINES TO COMPUTE DENSITIES OF OBSERVABLE GALAXIES:BAO ....................... 37!
K.!ROUTINES TO COMPUTE DENSITIES OF OBSERVABLE GALAXIES:WL ........................ 38!
L.!ROUTINES TO COMPUTE THE FOREGROUND RADIATION AND ABSORPTION ...................... 38!
M.!ROUTINES TO COMPUTE NOISE AND RELATED QUANTITIES ............................... 39!
N.!I/O AND ASSOCIATED ROUTINES ............................................... 41!
YE!92L!MKP*FM!4KLXEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE S;!
;<E!T7[PKNO2@+2>2P4! EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE SG!
;;E!T7LKPX>! EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE SQ!
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!
1. Overview
!
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2. Compiling the Code
!
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! 1$-!#7.-!2$7/,.!#78*%,-!@%($!($-!#788'5.2D!!
!
gcc exptimecalc.c -lm -Wall -O3 -o wletc.exe -DWL_MODE
gcc exptimecalc.c -lm -Wall -O3 -o baoetc.exe -DBAO_MODE
gcc exptimecalc.c –lm –Wall –O3 –o pzcaletc.exe -DPZCAL_MODE
!
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baoetc.exe!'5.!pzcaletc.exe+!
A. Additional flags
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-DWL_MODE!7&!-DBAO_MODE!7&!-DPZCAL_MODE!-+:+D!
!
gcc exptimecalc.c -lm -Wall -O3 -o wletc.exe -DWL_MODE -DIN_DLON
!
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./baoetc.exe
Enter telescope configuration [0=generic, 1=from file]: 0
Enter aperture outer diameter (meters): 1.5
Enter central obscuration (fractional -linear): 0.5
Enter pixel scale (arcsec): 0.37
Enter throughput (total, all orders): 0.6
Enter throughput (1st order): 0.6
!
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./baoetc.exe
Enter telescope configuration [0=generic, 1=from file]: 1
Input file name: data/JDEM_Omega_nomask_SpC.dat
Using configuration: JDEM_Omega_no_pupil_mask_110323
!
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%2!&-./#-.!AC!'!6'#(7&!76!F"h?2*G0+!J!#752-Y/-5#-!76!($%2!%2!($'(!67&!'5!%8':-&!@-!$'B-!
?\FgGa?',,FgG!e!"h?2*!%52(-'.!76!"+!

!
k!
•1$-!314!.7-2!57(!#/&&-5(,C!%5#,/.-!($-!*&7./#(%75!76!8/,(%*,-!#$'&:-2!*-&!*$7(75H!
@$%#$!8'C!A-!2%:5%6%#'5(!'(!B-&C!A,/-!@'B-,-5:($2+!1$%2!2$7/,.!57(!A-!2%:5%6%#'5(!%5!
($-!&'5:-!76!@'B-,-5:($2!&-#788-5.-.!67&!($-!;<=>?1!;E!'5.!IJK!*&7:&'82H!g!l!
"!r8+!
!
=6!($-!WFE_INPUT!7*(%75!%2!/2-.!F%(!%2!75!AC!.-6'/,(!%5!($-!#7.-!%5!Bp!'5.!,'(-&!/2%5:!
#define WFE_INPUTH!'5.!#'5!A-!(/&5-.!766!75,C!AC!&-87B%5:!($%2!,%5-GH!($-5!($-!#7.-!
*&78*(2! ($-! /2-&! 67&! ($-! &82! @'B-! 6&75(! -&&7&! %5! r8+! 1$-! -66-#(! 76! '5! 'A-&&'(%75! %2! 57(!
/5%Y/-,C!.-(-&8%5-.!AC!($-!&82!@'B-!6&75(!-&&7&H!27!($-!#7.-!/2-2!'!#752-&B'(%B-!6%((%5:!
6/5#(%75!'22/8%5:!($-!-&&7&!%2!%5!,7@O7&.-&!Fi]G!N-&5%P-!87.-2!F2--!^k+=!67&!.-('%,2G+!
B. Telescope configuration file format
!
1$-!(-,-2#7*-!#756%:/&'(%75!6%,-!#75('%52!A'2%#!*&7*-&(%-2!2/#$!'2!($-!'*-&(/&-!'5.!
*%L-,!2#',-H!'2!@-,,!'2!'!('A,-!76!($&7/:$*/(!'2!'!6/5#(%75!76!@'B-,-5:($+!=(!%2!',27!*722%A,-!(7!
%5#7&*7&'(-!($-&8',!*&7*-&(%-2!76!($-!(-,-2#7*-!%5!($-!#756%:/&'(%75!6%,-!($'(!7B-&&%.-!($-!
.-6'/,(!2-((%5:2!76!($-!314+!4756%:/&'(%75!6%,-2!'&-!',@'C2!,%8%(-.!(7!,%5-2!76!57!87&-!($'5!
0jb!#$'&'#(-&2+!
J5! -L*,%#%(! -L'8*,-! 76! '!#756%:/&'(%75!6%,-!%2!
data/JDEM_Omega_nomask_SpC.datH!@$%#$!$'2!($-!67&8"D!
!
# JDEM Omega, no pupil mask
# based on 'Throughput table JDEM Omega 110322_cj.xlsx'
# Received: 2011/03/23
#
# This has no pupil mask, so we have 1.5 m outer diameter and 50%
# linear obscuration. The spider is included in the throughput (all
# orders) numbers. For the '1st order' throughput I simply squared
# these (i.e. the spider blocks 2.45% of the radiation and scatters
# an additional 2.45% into the far diffraction wings where it is
# useless but still contributes to background).
#
JDEM_Omega_no_pupil_mask_110323
1.5 0.5 0.37 30
1.1000 0.3947 0.3850
1.1310 0.3973 0.3876
1.1621 0.4371 0.4263
s!
2.0000 0.5618 0.5481
!
1$-!6%,-!A-:%52!@%($!'!2-(!76!#788-5(!,%5-2!($'(!2('&(!@%($!#!F57(-!($'(!/5.-&!($-!#/&&-5(!
#7.-! 2(&/#(/&-H! ',,! #788-5(! ,%5-2! 8/2(! A-! '(! ($-! A-:%55%5:! 76! ($-! 6%,-D! ($-C! 8'C! 57(! A-!
%5(-&2*-&2-.!@%($!($-!%5*/(!.'('G+!1$-!6%&2(!575O#788-5(!,%5-!%2!'!#756%:/&'(%75!,'A-,!F%5!
($%2!#'2-!WJDEM_Omega_no_pupil_mask_110323XG!($'(!8/2(!A-:%5!@%($!'!575O2*-#%',!
#$'&'#(-&!F',*$'5/8-&%#!7&!/5.-&2#7&-G+!1$-!5-L(!,%5-!$'2!67/&!5/8A-&2D!%5!7&.-&!($-2-!'&-!
($-!7/(-&!.%'8-(-&!>!F%5!8-(-&2GV!($-!#-5(&',!7A2#/&'(%75!qV!($-!*%L-,!2#',-!2!F%5!'-#GV!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"!1$-!.'('!67&!($%2!%5*/(!6%,-!@'2!*&7B%.-.!AC!t'B-!475(-5(!'5.!4,%66!u'#P275+!

!
_!
'5.!($-!5/8A-&!76!:&%.!*7%5(2!@!'(!@$%#$!($-!($&7/:$*/(!#/&B-!%2!.-6%5-.+!<7,,7@%5:!($%2!%2!
'!('A,-!@%($!@!,%5-2!-'#$!@%($!($&--!5/8A-&2D!($-!@'B-,-5:($!g!%5!r8V!($-!(7(',!($&7/:$*/(!
?',,FgGV! '5.! ($-! .-2%&-.O7&.-&! ($&7/:$*/(! ?\FgG! 7&! ?"FgG! F67&! %8':-&2! 7&! 2*-#(&78-(-&2H!
&-2*-#(%B-,CG+
! 1$-! ($&7/:$*/(! ('A,-! %2! %5(-&*7,'(-.! ,%5-'&,C! A-(@--5! :&%.! *7%5(2+! =(! %2! '22/8-.!
#752('5(!7/(2%.-!($-!&'5:-!76!($-!('A,-!%6!($-!/2-&!&-Y/-2(2!2/#$!'!@'B-,-5:($H!A/(!76!#7/&2-!
%(!%2!57(!&-#788-5.-.!(7!/2-!($-!314!7/(2%.-!($-!&'5:-!76!($-!($&7/:$*/(!('A,-!/5,-22!($%2!
&-*&-2-5(2!($-!-L*-#(-.!A-$'B%7&!76!($-!2C2(-8v!
!S75O.-6'/,(!($-&8',!-8%22%75!*'&'8-(-&2!#'5!A-!2*-#%6%-.!%5!($-!#756%:/&'(%75!6%,-!
@%($!'!!THERMAL!,%5-+!1$%2!,%5-!8/2(!'**-'&!'6(-&!($-!-5.!76!($-!#788-5(2!'5.!A-67&-!($-!
#756%:/&'(%75!,'A-,+!J5!-L'8*,-!@7/,.!A-D!
!
# JDEM Omega, no pupil mask
# This configuration has thermal parameters.
#
!THERMAL 219. 0.02 1.10 0 219. 0.08 5e-3
JDEM_Omega_no_pupil_mask_110323 (ImC)
1.5 0.5 0.18 30
0.4000 0.4362 0.4255
0.4552 0.5203 0.5076
0.5103 0.5562 0.5426
…
2.0000 0.7109 0.6934
!
1$-!!THERMAL!,%5-H!,%P-!',,!,%5-2!%5!($-!#756%:/&'(%75!6%,-H!%2!,%8%(-.!(7!57!87&-!($'5!0jb!
#$'&'#(-&2+!1$-!k!*'&'8-(-&2!2*-#%6%-.!'&-H!%5!7&.-&D!
!
•1$-!(-,-2#7*-!(-8*-&'(/&-H!A(-,!F%5!w-,B%5GV!
•1$-!-8%22%B%(%-2!*-&!2/&6'#-!d!76!($-!*&%8'&C!'5.!2-#75.'&C!8%&&7&2V!
•1$-!&'(%7!x!76!7/(-&!.%'8-(-&!76!($-!%,,/8%5'(-.!&-:%75!(7!($'(!76!($-!*&%8'&C!8%&&7&V!
•J5!%5(-:-&!6,':!%5.%#'(%5:!@$-($-&!($-&-!%2!'!#7,.!*/*%,!8'2P!F"!e!C-2H!\!e!57GV!
•1$-!(-8*-&'(/&-!76!($-!'6(!7*(%#2!/*2(&-'8!76!($-!6%,(-&H!A'6(!F%5!w-,B%5GV!
•1$-!2/88-.!-8%22%B%(C!d'6(!76!($-!'6(!7*(%#2V!'5.!
•1$-!#7/5(!&'(-!6&78!($-!6%,(-&!'5.!.7@52(&-'8!#78*75-5(2!B.7@5!F%5!%ha*%La2G+!
!
1$-!!THERMAL!,%5-!7B-&&%.-2!($-!.-6'/,(!2-((%5:2!76!',,!($-2-!*'&'8-(-&2+!?--!^k+R!67&!'!
.-('%,-.!.-2#&%*(%75!76!$7@!($-2-!'&-!/2-.+!
C. Specifying the observing strategy and detector characteristics
!
T'B%5:!.-2#&%A-.!($-! (-,-2#7*-H! 75-! 8/2(! 5-L(!2*-#%6C!($-!*&7*-&(%-2!76!($-!6%,(-&H!
.-(-#(7&H!'5.!7A2-&B'(%75',!#%&#/82('5#-2+!1$-!67,,7@%5:!2-(!76!%5*/(2!'&-!&-Y/-2(-.!F$-&-!
@%($!2'8*,-!%5*/(2GD!
!
Enter detector type [e.g. 0=H2RG]: 0
Enter pointing jitter (arcsec rms per axis): 0.04
Enter minimum wavelength (microns): 1.1
Enter maximum wavelength (microns): 2.0

!
c!
Enter single exposure time (s): 150
Enter read noise floor (effective e-rms per pixel): 5
Enter dark current (e-/pix/sec): 0.05
Enter ecliptic latitude (degrees): 45
Enter Galactic reddening, E(B-V) (magnitudes): 0.05
Enter number of exposures: 6
!
!1$-!#/&&-5(,C!'B'%,'A,-!.-(-#(7&!(C*-2!F'5.!($-!%5.-L!67&!%5*/((%5:!($-8G!'&-D!
!
M:)%-*
4."%*
A5-%,*!$#,%!
yr8z!
7D#0\%*@5BB/(53:!
yr8!&82a'L%2z!
PML*@%8%$830*A#0#6%8%0(*
\!
T0>R!FS=>G!0H]!
]0!#$'55-,2!
"_+\!
0+cb!
$6!e!"+]!2V!
€
σ
read
2
!e!0\\!
"!
-0B!44t!
"0+\!
j+\\!
SaJ!
0!
Tb>R!FS=>Gb!
]0!#$'55-,2!
"\+\!
0+cb!
$6!e!j+0b!2V!
€
σ
read
2
!e!0\\!
]!
Tb>R!FS=>G!
pb!#$'55-,2!
"\+\!
0+cb!
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€
σ
read
2
!e!0\\!
!
!1$-!7B-&',,! M?<! %2!('P-5! (7! A-!($-! #75B7,/(%75! 76! ($-!.%66&'#(%75! *'((-&5! 6&78! ($-!
'55/,/2H!'A-&&'(%752!%6!5759-&7!@'B-!6&75(!-&&7&!%2!2*-#%6%-.H!($-!.-(-#(7&!&-2*752-!F*%L-,!
(7*$'(! *,/2! #$'&:-! .%66/2%75GH! '5.! ($-! *7%5(%5:! Q%((-&+! 1$-! .-(-#(7&! %2! '22/8-.! (7! A-! '5!
T0>R!@%($!"_!r8!*%L-,2!F2--!^k+=!67&!.-('%,2G+!
!1$-! @'B-,-5:($! &'5:-! Fg8%5H! g8'LG! '5.! ($-! (%8-! *-&! 2%5:,-! -L*72/&-! F$"G! '&-! ',27!
2*-#%6%-.+!=5!;E!87.-H!($-!#7.-!@%,,!',27!*&78*(!($-!/2-&!67&!'5!%8':%5:!6%,(-&!($&7/:$*/(!
FC7/!#'5!-5(-&!"!%6!($-!6%,(-&!($&7/:$*/(!%2!',&-'.C!%5#,/.-.!%5!($-!(-,-2#7*-!#756%:/&'(%75!
6%,-V!($%2!@%,,!:%B-!'!@'&5%5:!8-22':-H!@$%#$!C7/!#'5!%:57&-!%6!C7/!%5(-5.!67&!57!'..%(%75',!
6%,(-&!,722-2!(7!A-!#752%.-&-.G+!
!1$-!&-'.!57%2-!6,77&!%2!%5!-66-#(%B-!-,-#(&752!&82!*-&!-L*72/&-+!<7&!44t2!($%2!%2!($-!
-5(%&-!&-'.!57%2-V!67&!S=>!.-(-#(7&2!($%2!%2!'..-.!%5!Y/'.&'(/&-!(7!($-!2('(%2(%#',!-&&7&!6&78!
&'8*!6%((%5:+!=5!*&%5#%*,-!($%2!%2!.-(-&8%5-.!AC!($-!&-'.7/(!87.-!'5.!($-!-L*72/&-!(%8-H!
A/(!'(!*&-2-5(!($%2!'5.!($-!.'&P!#/&&-5(!'&-!',,7@-.!(7!A-!/2-&!%5*/(2+!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
0!1$-!#$'&:-!.%66/2%75!,-5:($!%2!8-'2/&-.!(7!A-!"+_k!r8!AC!S+!I'&&75!%$("#H!W?/A*%L-,!
&-2*752-!8-'2/&-8-5(!76!5-'&O%56&'&-.!.-(-#(7&2HX!M/A+!J2(&75+!?7#+!M'#+!;;YDbpp{bkj!
F0\\kG+!1$-!2('5.'&.!.-B%'(%75!76!($-!2-#$!*&76%,-!%2!|a0!(%8-2!($-!.%66/2%75!,-5:($+!}2%5:!
($-!2-#$!*&76%,-!%52(-'.!76!'!R'/22%'5!@7/,.!%5#&-'2-!($-!`1<!AC!75,C!\+0n!'(!"!
#C#,-a'-#!'5.!0n!'(!0!#C#,-2a'-#!'(!($-!\+"_!'-#!*,'(-!2#',-+!
]!1$-!'..%(%75',!S=>!.-(-#(7&!*'&'8-(-&2!'22/8-!'!&-'.!57%2-!76!0\!%h!*-&!4t?!'5.!'!
&-'.7/(!&'(-!76!"\\!PT9!67&!-'#$!76!]0!#$'55-,2+!
b!1$-!Tb>R!%2!'!5-@!.-(-#(7&!'5.!%2!57(!C-(!'(!1>E!p+!=(!%2!($-&-67&-!57(!A'2-,%5-.!67&!
;<=>?1+!1$-!*'&'8-(-&2!'A7B-!'&-!#752%.-&-.!&-'275'A,-!('&:-(2!67&!2/##-226/,!Tb>R!
.-B-,7*8-5(!*&7:&'8+!1$-C!'22/8-!($'(!($-!#$'&:-!.%66/2%75!&-8'%52!6%L-.!%5!*$C2%#',!
/5%(2!Fr8G!'5.!($'(!($-!&-'.!57%2-!*-&!4t?!&-8'%52!6%L-.!'(!0\!%h!*-&!4t?!F',($7/:$!($%2!%2!
57(!C-(!'#$%-B-.G+!1$-!&-'.7/(!&'(-!%2!P-*(!'(!"\\!PT9H!'5.!-%($-&!]0!7&!pb!#$'55-,2!'&-!
/2-.!F($-!,'((-&!%2!'5!7*-5!(&'.-!67&!($-!Tb>R!7*(%752G+!

!
"\!
!1$-! *72%(%75! 76! ($-! 7A2-&B'(%75! 75! ($-! 2PC! %2! &-Y/%&-.! %5! 7&.-&! (7! #',#/,'(-! ($-!
97.%'#',! 67&-:&7/5.! &'.%'(%75+! 1$%2! %5! *&%5#%*,-! &-Y/%&-2! ($-! -#,%*(%#! ,'(%(/.-! ~!'5.!($-!
.%66-&-5#-!%5!-#,%*(%#!,75:%(/.-2!76!($-!7A2-&B'(%75!'5.!($-!?/5H!ghg+!=5!.-6'/,(!87.-!($-!
,'((-&!%2!2-(!(7!c\fH!A/(!#'5!A-!%5.-*-5.-5(,C!2*-#%6%-.!%6!($-!-DIN_DLON!#78*%,'(%75!6,':!%2!
/2-.+!
!! 1$-! R','#(%#! ./2(! #7,/85! %2! 2*-#%6%-.! AC! ($-! #7,7&! -L#-22! CFDhEG+! J,,! 7/(*/(!
2-52%(%B%(%-2!'&-!Y/7(-.!%5!(-&82!76!-L(%5#(%75O#7&&-#(-.!F&'($-&!($'5!7A2-&B-.G!6,/L-2!'5.!
8':5%(/.-2+!=6!7A2-&B-.!6,/L!,%8%(2!'&-!.-2%&-.!F-+:+!67&!R','#(%#!7AQ-#(2!($'(!8'C!A-!%5!6&75(!
76!278-!7&!',,!76!($-!./2(!#7,/85H!7&!67&!#752%2(-5#C!@%($!7($-&!2/&B-C2!($'(!/2/',,C!Y/7(-!
2-52%(%B%(%-2!%5!7A2-&B-.!6,/L-2G!($-5!75-!2$7/,.!%5*/(!CFDhEG!e!\+!
! 1$-!5/8A-&!76!-L*72/&-2!%2!@-L*!Fp!%5!($-!'A7B-!-L'8*,-GV!($-!(7(',!W,%B-X!(%8-!%2!
@-L*$"+!
D. WL-specific inputs
!
1$-!;E!314!&-Y/%&-2!($&--!%5*/(2!6&78!($-!/2-&D!'!#/(!F8%5!75!($-!&-27,/(%75!6'#(7&!
F!76!($-!:','L%-2V!'!#/(!Z%H8'L!75!($-!-,,%*(%#%(C!-&&7&!Z%!76!:','L%-2!(7!A-!8-'2/&-.V!'5.!($-!
:','LC!#'(',7:!(7!/2-!(7!-2(%8'(-!27/&#-!.-52%(%-2+!3L'8*,-!%5*/(2!'&-D!
!
Enter minimum resolution factor: 0.4
Enter maximum ellipticity error: 0.2
Enter input galaxy catalog file: data/CMC1.dat
!
1$-!&-27,/(%75!6'#(7&!F!%2!.-6%5-.!75!'!2#',-!76!\!F:','LC!28',,!#78*'&-.!(7!($-!M?<G!(7!"!
F:','LC!,'&:-!#78*'&-.!(7!($-!M?<GV!($-!.-6%5%(%75!/2-.!$-&-j!%2!
!
€
R=1+EE50PSF
2
r
eff,gal
2
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#
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−1
.
!
!
R','L%-2!@%($!F![[!"!/2/',,C! $'B-! /5&-,%'A,-! 2$'*-2+! =5! ($-! ?t??! ,-52%5:! '5',C2-2p! ($-!
2('5.'&.! #/(! 75! F!@'2!⅓V! ($-! &-#-5(! ;<=>?1! 67&-#'2(2! $'B-! /2-.! \+b+!1$-!-,,%*(%#%(C!%2!
.-6%5-.!/2%5:!($-!#75B-5(%75!
!
€
(e1,e2)=a2−b2
a2+b2(cos2
χ
,sin2
χ
)
H!
!
@$-&-!"!'5.!G!'&-!($-!2-8%O8'Q7&!'5.!2-8%O8%57&!'L-2!76!($-!:','LC!'5.!•!%2!($-!*72%(%75!
'5:,-!76!($-!8'Q7&!'L%2+!3,,%*(%#%(C!-&&7&2!'&-!.-6%5-.!'2!&82!*-&!#78*75-5(+!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
j!<7&!R'/22%'5!*&76%,-2H!($%2!.-6%5%(%75!':&--2!-L'#(,C!@%($!R+!I-&52(-%5!€!`+!u'&B%2H!W?$'*-2!
'5.!2$-'&2H!2('&2!'5.!28-'&2D!K*(%8',!8-'2/&-8-5(2!67&!@-'P!,-52%5:HX!63$;H5I(JI!
;GQDj_]{p"_!F0\\0G+!
p!?--!-+:+!>+!`'5.-,A'/8!%$("#H!W?C2(-8'(%#!-&&7&2!%5!@-'P!,-52%5:D!'**,%#'(%75!(7!?t??!
:','LCO:','LC!@-'P!,-52%5:HX!)H5I(@H$I(FI(63$;H5I(:H&I!QV;D"0_k{"]00!F0\\jG+!

!
""!
!3B-5!%6!'!:','LC!%2!@-,,O&-27,B-.H!%(!@%,,!57(!A-!/2'A,-!67&!;E!%6!%(2!?S>!%2!(77!,7@!(7!
&-#7B-&! '! 2$'*-+! <7&! ($%2! &-'275H! @-! %5#,/.-! '! 8'L%8/8! -,,%*(%#%(C! -&&7&! Z%H8'L+!1$-!
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6/,,!%5(-:&'(%75!7B-&!2#',-2!'2!.-2#&%A-.!%5!($-!8-($7.7,7:C!2-#(%75+!=(!.7-2!57(!C-(!'##7/5(!
67&!/5.-&2'8*,%5:!#752%.-&'(%752+!1$-!2*-#%6%#2!76!@$-($-&!'!:%B-5!7A2-&B%5:!2(&'(-:C!#'5!
&-#7B-&! 6/,,! 2'8*,%5:! @$%,-! *&-2-&B%5:! ($-! 7&%:%5',! M?<! F7&! 2877($%5:! %(! %5! '! #75(&7,,-.!
@'CG! 8/2(! A-! -B',/'(-.! /2%5:! '5! %8':-! &-#752(&/#(%75! 2%8/,'(7&+k! <%5',,CH! @-! %8*72-! '!
8%5%8/8!?S>!67&!($-!:','LCD!%5!($-!#/&&-5(!B-&2%75!76!($-!#7.-!($%2!%2!$'&.O@%&-.!'(!?S>!l!
"_+_!!
!1$-!%5*/(!:','LC!#'(',7:!%2!'!6%,-+!J5!-L'8*,-!%2!($-!6%,-!CMC1.datD!
!
# Cosmos Mock Catalog (Jouvel et al 2009), 435W-606W-775W-850LP-110-160-Ks
7 438972 1.24
0.431177 0.587964 0.768801 0.901067 1.103397 1.601053 2.160917
1 0.96 0.1463 27.50 26.80 26.11 25.80 25.44 25.19 24.89
9 3.48 0.1283 27.72 26.22 25.94 25.94 25.84 25.22 24.33
10 0.48 0.2228 26.82 26.03 25.45 25.20 24.98 24.63 24.43
…
537990 2.20 0.1404 27.58 26.96 26.52 26.07 25.34 24.27 23.39!
!
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_!1$-!#/(!%2!2-(!AC!($-!#define WL_SNR_MIN 18.0!8'#&7+!

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!
13 0.1200 0.2027 0.17099
41 0.1600 0.2399 0.12337
330 0.0800 0.4840 0.10593
576 0.1600 1.4943 0.06834
…
537695 2.8000 0.2092 0.17434
!
1$-!#7,/852!'&-!($-!:','LC!=t!5/8A-&V!($-!&-.2$%6(H!;-66!%5!'-#V!'5.!Z%+!
E. BAO-specific inputs
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!
Enter significance cut (number of sigmas): 7.0
Enter galaxy population model [suggested = 32]: 0
Using luminosity function model: Geach et al (2009), 50% confidence!
!
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Enter completeness: 0.5
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log10
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log10
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arcsec =−0.62 +0.25 19 +log10
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F. PZCAL-specific inputs
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4. Code Outputs: WL ETC
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General properties:
PSF EE50: 2.96232E-01 arcsec
Spatial frequency cutoff: 8.44514E-01 cycles/pix
Sampling case: Weakly undersampled
Min usable galaxy r_eff: 2.41872E-01 arcsec
Sky background flux: 3.03466E-01 e-/pix/s
Thermal background flux: 3.37757E-02 e-/pix/s
telescope: 2.31562E-02 e-/pix/s
upstream: 5.61950E-03 e-/pix/s
downstream: 5.00000E-03 e-/pix/s
Noise variance per unit solid angle in one exposure:
sky only: 1.68592E+03 e-^2/arcsec^2
total: 3.90252E+03 e-^2/arcsec^2
Source counts per exposure:
at AB mag 20: 2.11038E+04 e-
at AB mag 21: 8.40157E+03 e-
at AB mag 22: 3.34473E+03 e-
at AB mag 23: 1.33156E+03 e-
at AB mag 24: 5.30104E+02 e-
at AB mag 25: 2.11038E+02 e-
5 sigma pt src threshold: 25.694 mag AB
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0%("3:(5J5,58.* 83* 5:)%"%:)%:8,.* $D%$e* 8D#8* 8D%50* $D3(%:* )58D%05:\* "#88%0:* b5,,* J%*
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6'#(7&! %2! :%B-5H! '2! '&-! ($-! 2PC! A'#P:&7/5.2! '5.! #75(&%A/(%752! (7! 57%2-! B'&%'5#-+!`'5C!
%8':%5:!#'2-2!($'(!@-!$'B-!,77P-.!'(!'&-!'#(/',,C!,%8%(-.!AC!.-(-#(7&!F.'&P!o!&-'.G!57%2-!
&'($-&! ($'5! 2PCV! ($-! 7/(*/(2! '&-! .-2%:5-.! (7! 8'P-! #,-'&! @$%#$! &-:%8-! 75-! %2! %5+! 1$-!
5/8A-&!76!#7/5(2!6&78!27/&#-2!'(!.%66-&-5(!8':5%(/.-2!%2!2*-#%6%-.H!'2!%2!($-!76(-5OY/7(-.!
jZ!*7%5(!27/&#-!2-52%(%B%(C!,%8%(!F($%2!%2!57(!.%&-#(,C!&-,-B'5(!67&!;EH!@$%#$!&-Y/%&-2!lljZ!
'5.!'5!-L(-5.-.!27/&#-H!A/(!%2!'!/2-6/,!*7%5(!76!#78*'&%275G+!
S-L(!#78-2!'!('A,-!76!:','LC!*&7*-&(%-2!'2!'!6/5#(%75!76!($-!-66-#(%B-!&'.%/2D!
!
| r_eff |Om_eff |penalty|resolution|lim mag |S/N at |
| | |factor | factor |(shapes)|shape |
|arcsec |arcsec2| | | AB |lim mag|
0.25119 1.7427 5.2704 0.41827 23.49161 22.957
0.28184 1.9602 4.6476 0.47512 23.49603 21.558
0.31623 2.2241 4.1279 0.53261 23.49184 20.317
0.35481 2.5453 3.6967 0.58926 23.47848 19.227
0.39811 2.9375 3.3402 0.64363 23.45574 18.276
0.44668 3.4175 3.0460 0.69454 23.39012 18.000
0.50119 4.0062 2.8030 0.74110 23.30384 18.000
0.56234 4.7299 2.6021 0.78278 23.21368 18.000
0.63096 5.6214 2.4354 0.81939 23.11995 18.000
0.70795 6.7216 2.2967 0.85100 23.02291 18.000
0.79433 8.0819 2.1808 0.87790 22.92286 18.000
0.89125 9.7665 2.0836 0.90052 22.82008 18.000
1.00000 11.8559 2.0017 0.91933 22.71483 18.000
!
1$%2! *&7B%.-2H! '2! '! 6/5#(%75! 76! ;-66H! ($-! -66-#(%B-! 27,%.! '5:,-! 76! ($-! :','LC! '6(-&! M?<!
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σ
e=2fpen
SNR
H!
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@$%#$!%2!"!67&!'!@-,,O&-27,B-.!R'/22%'5!:','LC"k!'5.!'**&7'#$-2!‰!67&!/5&-27,B-.!7AQ-#(2V!
($-!&-27,/(%75!6'#(7&!FV!($-!,%8%(%5:!JI!8':5%(/.-!67&!2$'*-!8-'2/&-8-5(2V!'5.!($-!?S>!
67&!7AQ-#(2!'(!($-!,%8%(%5:!8':5%(/.-!67&!2$'*-2+!1$-!*-5',(C!6'#(7&!%2!#78*/(-.!6&78!($-!
<%2$-&!8'(&%L!67&!($-!:','LC!-,,%*(%#%(CH!'2!.-2#&%A-.!%5!($-!8-($7.7,7:C!2-#(%75+!
! <%5',,CH!/2%5:!($-!:','LC!#'(',7:!*&7B%.-.!75-!8'C!.-&%B-!($-!*7*/,'(%75!76!.-(-#(-.!
:','L%-2!'2!'!6/5#(%75!76!&-.2$%6(+!1$-%&!&-.2$%6(!.%2(&%A/(%75!F#/&&-5(,C!%5!A%52"_!76!@%.($!Š<!
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8-'2/&-.! 2$'*-2V! @-66!%2!.-6%5-.!AC!.7@5O@-%:$(%5:! :','L%-2! @%($! 575O5-:,%:%A,-! 2$'*-!
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!
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Neff =0.42
0.42+
σ
e
2
galaxies
∑
H!
!
@$-&-!\+b!%2!($-!'22/8-.!%5(&%52%#!-,,%*(%#%(C!.%2*-&2%75+!
!
| z | dN/dz/dA |dNeff/dz/dA|
| | deg^-2 | deg^-2 |
0.100 1.23105E+04 1.13740E+04
0.300 4.34395E+04 4.05262E+04
0.500 3.51008E+04 3.26792E+04
0.700 5.21573E+04 4.82890E+04
0.900 5.27903E+04 4.88995E+04
1.100 3.64879E+04 3.34505E+04
1.300 2.95040E+04 2.67773E+04
1.500 2.44677E+04 2.21167E+04
1.700 1.28468E+04 1.14838E+04
1.900 7.81855E+03 6.96697E+03
2.100 1.03629E+04 9.09031E+03
2.300 4.06048E+03 3.55085E+03
2.500 4.10887E+03 3.59047E+03
2.700 2.42339E+03 2.10688E+03
2.900 1.87903E+03 1.62101E+03
Weak lensing n: 6.59516E+04 gal/deg^2
= 1.83199E+01 gal/arcmin^2
Weak lensing n_eff: 6.05045E+04 gal/deg^2
= 1.68068E+01 gal/arcmin^2
5. Code Outputs: BAO ETC
!
1$-!IJK!314!&-(/&52!'!('A,-!76!:','LC!C%-,.2!'2!@-,,!'2!278-!2/88'&C!%567&8'(%75+!J5!
-L'8*,-!C%-,.2!('A,-!%2D!
!
z |lambda| EE50 | dV/dz/dA | [email protected]"| n targets | dN/dz/dA |geom mean F| siglnF |skew lnF|kurt lnF|Num ph 1exp|
| um |arcsec| Mpc3/deg2 | W/m2 | Mpc^-3 | deg^-2 | W/m2 | | | | 1e-19 W/m2|
1.000 1.3130 0.3005 8.29240E+06 3.22901E-19 3.79620E-04 3.14796E+03 6.36092E-19 0.5068 0.7603 0.2992 8.26072E+01
1.050 1.3458 0.2966 8.67969E+06 3.05516E-19 3.92039E-04 3.40278E+03 5.96399E-19 0.5105 0.7642 0.2997 8.72193E+01
1.100 1.3787 0.2924 9.04621E+06 2.77963E-19 4.29332E-04 3.88383E+03 5.41519E-19 0.5223 0.7697 0.2919 9.57537E+01
...
2.650 2.3962 0.2917 1.29985E+07 1.46194E-19 9.35757E-05 1.21635E+03 1.74560E-19 0.3438 0.9389 0.7847 1.90322E+02
!
1$-!('A,-!:%B-2!($-!*&7*-&(%-2!76!($-!'B'%,'A,-!:','LC!2'8*,-!'2!'!6/5#(%75!76!&-.2$%6(!<H!7B-&!
($-!-5(%&-!&'5:-!67&!@$%#$!TU!%2!'B'%,'A,-+!1$-!#7,/852!'&-D!
!
%+ 1$-!&-.2$%6(!<+!

!
"_!
%%+ 1$-!@'B-,-5:($!g!F%5!r8G!'(!@$%#$!TU!%2!7A2-&B-.+!
%%%+ 1$-!33j\!&'.%/2!76!($-!M?<!F%5!'-#G+!
%B+ 1$-!#75B-&2%75!6&78!'&-'!(7!#787B%5:!B7,/8-H!4Ea4<a46!F%5!`*#]!.-:h0G+!
B+ 1$-!`tE<!67&!'!27/&#-!@%($!;-66!e!\+]!'-#!F%5!;!8h0G+"c!
B%+ 1$-!#787B%5:!.-52%(C!76!.-(-#('A,-!:','L%-2!5!F%5!`*#h]G+!
B%%+ 1$-!'&-'!.-52%(C!76!.-(-#('A,-!:','L%-2!*-&!/5%(!27,%.!'5:,-!*-&!Š<!F%5!.-:h0G+!
B%%%+ 1$-!:-78-(&%#!8-'5!TU!6,/L!QTU!76!($-!.-(-#('A,-!:','L%-2!F%5!;!8h0G+!
%L+ 1$-!2('5.'&.!.-B%'(%75!76!,5!QTU!76!($-2-!:','L%-2+!
L+ 1$-!2P-@5-22!76!,5!QTU!76!($-2-!:','L%-2+!
L%+ 1$-!P/&(72%2!76!,5!QTU!76!($-2-!:','L%-2+!
L%%+ 1$-!5/8A-&!76!#7,,-#(-.!-,-#(&752!*-&!-L*72/&-!67&!'!"\h"c!;!8h0!-8%22%75!,%5-+!
!
=(!%2!%8*7&('5(!(7!57(-!($'(!:','L%-2!#'5!A-!.-2#&%A-.!'2!W.-(-#('A,-HX!@$%#$!.7-2!57(!
-Y/'(-!(7!W.-(-#(-.X!ˆ!75-!8/2(!2(%,,!8/,(%*,C!AC!($-!#78*,-(-5-22!%H!@$%#$!%2!:-5-&',,C!["!
./-!(7!-+:+!#7,,%2%752!@%($!2('&!(&'#-2!7&!%8':-!.-6-#(2+!J,27!($-!`Et<!%2!*&7B%.-.!2%8*,C!67&!
&-6-&-5#-D!@$%,-!'5!-66-#(%B-!&'.%/2!76!\+]!'-#!%2!(C*%#',!%(!%2!57(!/5%B-&2',H!'5.!($-!#7.-!
%5(-:&'(-2!($-!5/8A-&!76!:','L%-2!@%($%5!($-!FQTUH;-66G!*,'5-+!
1$-!#7.-!',27!&-(/&52!2/88'&C!2('(%2(%#2D!
!
Summary statistics:
Sky background flux: 3.08083E+00 e-/pix/s
Thermal background flux: 1.38794E-01 e-/pix/s
telescope: 8.75479E-02 e-/pix/s
upstream: 2.12459E-02 e-/pix/s
downstream: 3.00000E-02 e-/pix/s
Noise variance per unit solid angle in one exposure:
sky only: 3.37564E+03 e-^2/arcsec^2
total: 4.65012E+03 e-^2/arcsec^2
Available galaxy density: 4.77475E+03 gal/deg^2
!
1$-2-!%5#,/.-!/2-6/,!'5#%,,'&C!*'&'8-(-&2!2/#$!'2!($-!2PC!#7/5(!&'(-H!($-!57%2-!B'&%'5#-!*-&!
2%5:,-! -L*72/&-! F%5#,/.%5:! Q/2(! ($-! 2PCH! '5.! %5#,/.%5:! .'&P!#/&&-5(!o! &-'.! 57%2-V! ($-!
#78*'&%275!%2!/2-6/,!67&!.-(-&8%5%5:!@$-($-&!75-!%2!2PCO,%8%(-.H!@$%#$!%2!75,C!($-!#'2-!67&!
278-! 76! ($-! B%'A,-! &'5:-! 76! S=>! 2*'#-! 8%22%75! *'&'8-(-&2GH! '5.! ($-! (7(',! .-52%(C! 76!
.-(-#('A,-!:','L%-2+!
6. Code Outputs: PZCAL ETC
!
=5!MN4JE!87.-H!($-!314!'22/8-2!($'(!%(!%2!2-'&#$%5:!67&!-8%22%75!,%5-2!'5.!2%8*,C!&-*7&(2!
'!('A,-!76!,%5-!2-52%(%B%(%-2!'#&722!($-!2*-#(&',!A'5.*'22+!1$-!('A,-!%2!*&-2-5(-.!%5!0_!2(-*2!
%5!g0\!'5.!;-66!6&78!\+\!F*7%5(!27/&#-G!(7!"+\!'-#!%5!2(-*2!76!\+"!'-#+!
! J!(C*%#',!.'('!('A,-!'5.!'227#%'(-.!2/88'&C!2('(%2(%#2!%2D!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"c!S7(-!($'(!"!;!8h0!e!"\\\!-&:!#8h0!2h"+!
0\!1$%2!#'5!A-!#$'5:-.!AC!87.%6C%5:!($-!nstep = 28;!2('(-8-5(!%5!($-!8'%5!*&7:&'8+!

!
"c!
Limiting fluxes in W/m2 vs wavelength and galaxy size
lambda| 0.0" | 0.1" | 0.2" |…| 1.0" |
um | | | |…| |
0.6000 1.71123E-19 2.15580E-19 2.97796E-19 …1.08921E-18
0.6500 1.56623E-19 1.97578E-19 2.72938E-19 …9.95079E-19
0.7000 1.34458E-19 1.69790E-19 2.34528E-19 …8.52248E-19
0.7500 1.16880E-19 1.47663E-19 2.03902E-19 …7.38483E-19
0.8000 1.04460E-19 1.32026E-19 1.82229E-19 …6.57739E-19
…
2.0000 4.95831E-20 5.81933E-20 7.53537E-20 …2.43001E-19
Summary statistics:
Sky background flux: 1.11131E+00 e-/pix/s
Thermal background flux: 6.10119E-02 e-/pix/s
telescope: 1.79270E-02 e-/pix/s
upstream: 3.80850E-02 e-/pix/s
downstream: 5.00000E-03 e-/pix/s
Noise variance per unit solid angle in one exposure:
sky only: 1.02899E+04 e-^2/arcsec^2
total: 1.47232E+04 e-^2/arcsec^2
!
1$-!2/88'&C!2('(%2(%#2!('A,-!%2!%.-5(%#',!(7!($'(!76!IJK!87.-!-L#-*(!67&!($-!:','LC!C%-,.2!
F@$%#$!'&-!57(!#78*/(-.!%5!MN4JE!87.-G+!
7. Detailed Methodology and Assumptions
!
A. Background cosmology
!
1$-!A'#P:&7/5.!#7287,7:C!'22/8-.!67&!5/8A-&!.-52%(C!C%-,.2!F%5!($-!IJK!87.-G!
%2! ($-! 2'8-! '2! ($'(! 76! ($-! <7`?;R0"!F#$72-5!67&!#752%2(-5#CGH! %(2-,6! .-&%B-.! 6&78! ($-!
;`JM!jOC-'&!*'&'8-(-&!#752(&'%5(2+00!1$-!*'&'8-(-&2!'&-!P\!e!k"+c\]!P8a2a`*#H!†8!e!
\+0jpb_H!'5.!9-&7!2*'(%',!#/&B'(/&-+!
1$-! ;E! 87.-!/2-2!'5!%5*/(!:','LC!#'(',7:!'5.!.7-2!57(!#/&&-5(,C!/(%,%9-!($-!
#7287,7:%#',!*'&'8-(-&2+!
B. Sky brightness
!
!1$-!2PC!A&%:$(5-22!%2!('P-5!(7!A-!($'(!76!($-!97.%'#',!,%:$(H!@$%#$!%2!('P-5!(7!A-!'!
6/5#(%75!57(!Q/2(!76!@'B-,-5:($!A/(!',27!-#,%*(%#!,'(%(/.-!~!'5.!,75:%(/.-!&-,'(%B-!(7!($-!?/5!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
0"!J+!J,A&-#$(!%$("#IH!W<%5.%5:2!76!($-!u7%5(!t'&P!35-&:C!`%22%75!<%:/&-!76!`-&%(!?#%-5#-!
;7&P%5:!R&7/*X!F0\\cG+!'&‚%BD\c\"+\k0"!
$((*Daa@6%&2(+:26#+5'2'+:7Ba2#%-5#-a6782@:a6782@:‹(-#$5%#',+*.6!
00!u+!t/5P,-C!%$("#IH!W<%B-OC-'&!;%,P%5275!`%#&7@'B-!J5%27(&7*C!M&7A-!7A2-&B'(%752D!
E%P-,%$77.2!'5.!*'&'8-(-&2!6&78!($-!;`JM!.'('HX!63$;HK'L3I(JI!;H<D]\p{]0c!F0\\cG+!

!
0\!
ghg+!1$-!A&%:$(5-22!Bg!'(!g!e!\+j!r8!@'2!%5(-&*7,'(-.!6&78!1'A,-!"k!76!E-%5-&(!%$("#+0]!1$-!
2PC!A&%:$(5-22!'(!&-..-&!@'B-,-5:($2!@'2!.-(-&8%5-.!/2%5:!($-!27,'&!2*-#(&/80b!'5.!($-!
#7&&-#(%75! 67&! ($-! #7,7&! 76! ($-! 97.%'#',! ,%:$(! F&-,'(%B-! (7! ($-! 27,'&! 2*-#(&/8GH! 3Y+! F00G! 76!
E-%5-&(!%$("#+!J!2%8%,'&!8-($7.!@'2!/2-.!%5!($-!?SJM!87.-,+0j!
!1$-!%5(-&5',!&7/(%5-2!%5!($-!314!$'B-!($-!#'*'A%,%(C!(7!&/5!'(!'5C!-#,%*(%#!,75:%(/.-H!
A/(! AC! .-6'/,(! ($-! .&%B-&! '22/8-2! '5! -,75:'(%75! 76! d! e! c\f! F%8*,C%5:! ghg!e!c\fG+! 1$-!
97.%'#',! ,%:$(! %2! ($/2! '! 6/5#(%75! 76! @'B-,-5:($! '5.! -#,%*(%#! ,'(%(/.-+! K($-&! B'&%'(%752!
.%2#/22-.!%5!E-%5-&(!%$("#!'&-!5-:,-#(-.!F-+:+!'55/',!B'&%'(%75H!.%2#&-(-!2(&/#(/&-2G+!
C. Galactic extinction
!
! R','#(%#!F`%,PC!;'CG!-L(%5#(%75!%2!'22/8-.!(7!67,,7@!($-!FE!e!]+"!,'@!(C*%#',!76!$%:$!
R','#(%#!,'(%(/.-!,%5-2!76!2%:$(+!1$-!&-..-5%5:!CFDhEG!%2!'5!%5*/(!(7!($-!314+!1$-!-L(%5#(%75!
#/&B-!%2!7A('%5-.!6&78!I+!t&'%5-+0p!
<7&! @7&P! %5! ($-! B%2%A,-! '5.! S=>! '5.! '(! $%:$! R','#(%#! ,'(%(/.-H! ($-! =5&%;$"N5$L!
'227#%'(-.!@%($!($-!R','#(%#!-L(%5#(%75!#7&&-#(%75!%2!*&7A'A,C!5-:,%:%A,-+!
D. Line sensitivity and effective solid angle
!
! 1$%2! 2-#(%75! .-2#&%A-2! ($-! #78*/('(%752! 67&! -8%22%75! ,%5-! 2-52%(%B%(C! %5! ($-!
2*-#(&78-(-&+!S7(-!$7@-B-&!($'(!($-!?S>!#78*/('(%752!67&!7AQ-#(2!%5!($-!%8':-&!67,,7@!'5!
'5',7:7/2!*&7#-./&-H!@%($!($-!-L#-*(%752!($'(!F%G!($-! "2(!7&.-&!($&7/:$*/(!?"!%2!&-*,'#-.!
@%($!($-!\($!7&.-&!($&7/:$*/(!?\V!F%%G!75-!/2-2!'!*7,C#$&78'(%#!&'($-&!($'5!8757#$&78'(%#!
M?<V! '5.! F%%%G! ($-&-! %2! 57! W27/&#-! #75(%5//8X! #75(&%A/(%75! F2%5#-! 67&! %8':%5:! ($-! 27/&#-!
#75(%5//8!N3!($-!2%:5',G+!
1$-!,%8%(%5:!2-52%(%B%(C!(7!'!,%5-!-8%((-&!.-*-5.2!75!&-'#$%5:!'!*'&(%#/,'&!?S>+!1$-!
W2%:5',X!%5!($%2!#'2-!%2!($-!5/8A-&!76!*$7(752!&-#-%B-.!6&78!($-!:','LC+!1$%2!%2!:%B-5!AC!
!
€
Signal =Nexp
λ
Af1Ft1
hc ,
!
!
@$-&-!@-L*!%2!($-!5/8A-&!76!-L*72/&-2V!g!%2!($-!7A2-&B-.!@'B-,-5:($!76!($-!,%5-V!6!%2!($-!
:-78-(&%#!#7,,-#(%5:!'&-'!76!($-!(-,-2#7*-V!?"!%2!($-!"2(!7&.-&!($&7/:$*/(H!%+-+!($-!6&'#(%75!76!
($-!*$7(752!-5(-&%5:!($-!:-78-(&%#!'&-'!($'(!*&7./#-!#7,,-#(-.!-,-#(&752!%5!($-!"2(!7&.-&!
2*-#(&/8V!Q!%2!($-!,%5-!6,/L!6&78!($-!:','LCV!$"!%2!($-!./&'(%75!76!-'#$!-L*72/&-V!'5.!'!'5.!&!
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