Session 12

Two-Wavelength Tracking

John Degnan, Cinzia Luceri

Zim

mer

wal

dZi

mm

erw

ald

Dua

l-W

avel

engt

h O

pera

tion

Dua

l-W

avel

engt

h O

pera

tion

Wer

ner

Gur

tner

Eug

en P

opJo

hann

es U

tzin

ger

Ast

rono

mic

al I

nstit

ute

Uni

vers

ity o

f B

ern

28-3

1 O

ctob

er 2

003

Köt

ztin

g

Two-

Wav

elen

gths

Des

ign

Two-

Wav

elen

gths

Des

ign

uR

ecei

vers

uB

lue

(423

nm

)u

CSP

AD

:Si

ngle

sho

t rm

s:

50 p

s

uH

amam

atsu

PM

T

uIR

(

846

nm)

uH

amam

atsu

PM

T:

Sing

le s

hot r

ms:

150

ps

uB

eam

atte

nuat

ion

uT

rans

mitt

ing

beam

su

Sepa

rate

rot

atin

g po

lari

zer

for

each

col

or

uR

ecei

ving

pat

hsu

Cir

cula

r ad

just

able

ND

filt

ers

uN

eutr

al d

ensi

ty f

ilter

s in

sert

ed f

or c

alib

ratio

n

Tran

smit

Pat

hTr

ansm

it P

ath

Var

iabl

eA

ttenu

ator

Dou

blin

g C

ryst

al

Shut

ter

Shut

ter

Var

iabl

eA

ttenu

ator

Rec

eivi

ng P

ath

Rec

eivi

ng P

ath

CSP

AD

PMT

Spar

e

PMT

Fabr

y-Pe

rot F

ilter

s

Neu

tral

Den

sity

Filt

ers

(Cal

ibra

tion)

Infr

ared

Pat

h

Blu

e P

ath

5 nm

Filt

ers

Exa

mpl

e:

Exa

mpl

e: L

ageo

sLa

geos

-1 P

ass

-1 P

ass

25 A

ugus

t 200

2, 1

9:40

-20:

30 U

T25

Aug

ust 2

002,

19:

40-2

0:30

UT

Wav

elen

gthS

ingl

e sh

otob

serv

atio

nsSi

ngle

shot

RM

SCal

ibra

tionR

MSN

umbe

r ofN

orm

alpo

ints

Ave

rage

diff

eren

ceB

lue

423

nm13

230.

16 n

s0.1

2 ns

18IR

8

46 n

m13

370.

18 n

s0.2

3 ns

210.

05 n

s

Lage

osLa

geos

-1 B

lue

and

IR R

esid

uals

(ns

)-1

Blu

e an

d IR

Res

idua

ls (

ns)

Exp

erie

nces

Exp

erie

nces

uB

eam

alig

nmen

t is

rath

er c

ritic

al

uL

ess

nois

e in

the

infr

ared

cha

nnel

dur

ing

dayl

ight

trac

king

uC

alib

ratio

n R

MS

on I

R la

rger

by

abou

t 100

perc

ents

(18

0 ps

vs.

90

ps)

uA

vera

ge p

ass

diff

eren

ces

IR-b

lue

(aft

erM

.M.-

corr

ectio

n) <

0.0

8 ns

Con

clus

ions

Con

clus

ions

uR

ange

bia

ses

betw

een

the

two

rece

ptio

nch

anne

ls c

ould

stil

l be

in th

e sy

stem

(a

few

mill

imet

ers?

)u

Dif

fere

nces

of

the

Mar

ini-

Mur

ray

refr

actio

nco

rrec

tions

at 4

23 a

nd 8

46 n

m o

bvio

usly

bette

r th

an a

bout

10

mm

uIs

acc

urac

y of

the

two

wav

elen

gths

goo

den

ough

for

map

ping

fun

ctio

n im

prov

emen

t?

Two-

colo

r A

naly

sis

Tech

niqu

eTw

o-co

lor

Ana

lysi

s Te

chni

que

(( Slid

es b

y Sl

ides

by

Van

V

an H

usso

nH

usso

n ))

uZ

imm

erw

ald:

Rob

ust 2

-col

or d

atas

et in

Jul

y –

Aug

ust 2

003

uZ

imm

erw

ald

2-co

lor

conf

igur

atio

nu

Blu

e (4

23nm

): C

SPA

D, S

R62

0 #0

236,

2.5

sig

ma

uIR

(84

6nm

): P

MT

, SR

620

#228

2, 2

.5 s

igm

a

uIn

sim

ulta

neou

s pa

sses

, dif

fere

nce

rang

e bi

ases

(RB

) fr

om e

ach

colo

r [

i.e. I

R(R

B)

– B

lue(

RB

) ]

uU

ses

RB

res

ults

fro

m D

elft

and

CR

L w

eekl

yre

port

s

Zim

mer

wal

d Zi

mm

erw

ald

2-C

olor

RB

Diff

eren

ces

2-C

olor

RB

Diff

eren

ces

Zim

mer

wal

d 2

Co

lor

An

alys

is

-30

-20

-100102030

02-Jul-03

09-Jul-03

16-Jul-03

23-Jul-03

30-Jul-03

06-Aug-03

13-Aug-03

20-Aug-03

27-Aug-03

RB Difference in mm (IR-blue)

Del

ft LA

GE

OS

CR

L LA

GE

OS

Zim

mer

wal

d 2

-Co

lor

An

alys

is

-40

-30

-20

-10010203040

02-Jul-03

09-Jul-03

16-Jul-03

23-Jul-03

30-Jul-03

06-Aug-03

13-Aug-03

20-Aug-03

27-Aug-03

RB Difference in mm (IR-blue)

CR

L LA

GE

OS

CR

L A

jisai

CR

L S

tarle

tte/S

tella

Zim

mer

wal

d Zi

mm

erw

ald

2-C

olor

RB

Diff

eren

ces

2-C

olor

RB

Diff

eren

ces

Cal

ibra

tio

n V

alu

es (

SP

AD

)

32.4

5

32.5

32.5

5

32.6

32.6

5

32.7

32.7

5

32.8 52

700

5272

052

740

5276

052

780

5280

052

820

5284

052

860

5288

052

900

MJD

(52

700=

2-M

ar-2

003,

529

00=1

8-S

ep-2

003)

ns

4-A

ug-0

3

Cal

ibra

tio

n V

alu

es (

PM

IR

)

55.5

55.5

5

55.6

55.6

5

55.7

55.7

5

55.8

55.8

5 5270

052

720

5274

052

760

5278

052

800

5282

052

840

5286

052

880

5290

0

MJD

(52

700=

2-M

ar-2

003,

529

00=1

8-S

ep-2

003)

ns

4-A

ug-0

3

Zim

mer

wal

dZi

mm

erw

ald

2-C

olor

Ana

lysi

s 2

-Col

or A

naly

sis

Zim

mer

wal

d 2

-Co

lor

An

alys

is (

po

st A

ug

4, 2

003)

Del

ft L

AG

EO

SC

RL

LA

GE

OS

CR

L S

tarl

ett

e

CR

L A

jisai

-20

-15

-10-505101520

IR-Blue(mm)

Pos

sibl

e So

urce

of D

iffer

ence

sP

ossi

ble

Sour

ce o

f Diff

eren

ces

uR

efra

ctio

n A

lgor

ithm

uC

oM D

iffe

renc

esu

Det

ecto

rs (

CSP

AD

vs

PMT

)

uD

ual W

avel

engt

hs

uSi

gnal

Str

engt

h

uPo

lari

zatio

n?

uSy

stem

Cal

ibra

tion

uD

iffe

rent

SR

620

Cou

nter

line

ariti

es

uSi

gnal

Str

engt

h

uO

ptic

al P

ath

Dif

fere

nces

?

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

er

Dua

l Wav

elen

gth

Dat

a A

naly

sis

Dua

l Wav

elen

gth

Dat

a A

naly

sis

423

& 8

46 n

m42

3 &

846

nm

Err

icos

E

rric

os C

. C

. Pav

lisP

avlis

Mag

da K

uzm

icz

Mag

da K

uzm

icz -- C

iesl

akC

iesl

ak

Gly

nn

Gly

nn H

ulle

yH

ulle

y

JCE

T/U

MB

C -

NA

SA

/GS

FC

JCE

T/U

MB

C -

NA

SA

/GS

FC

2003

ILR

S W

orks

hop

on L

aser

Ran

ging

2003

ILR

S W

orks

hop

on L

aser

Ran

ging

Oct

ober

28-

31, 2

003,

O

ctob

er 2

8-31

, 200

3, KKöö t

ztin

gtz

ting

, Ger

man

y, G

erm

any

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

22

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erD

escr

iptio

nD

escr

iptio

n

••A

naly

zed

data

spa

n 20

01 t

o M

arch

200

3A

naly

zed

data

spa

n 20

01 t

o M

arch

200

3

••D

ata

com

e fr

om t

wo

site

s:D

ata

com

e fr

om t

wo

site

s:––

Zim

mer

wal

dZ

imm

erw

ald

(78

10)

(78

10)

[PR

IMA

RIL

Y] ,

and

[P

RIM

AR

ILY

] , a

nd

––C

once

ptio

n (T

IGO

)C

once

ptio

n (T

IGO

)

••D

ata

are

com

pute

d fr

om a

lread

y co

nver

ged

Dat

a ar

e co

mpu

ted

from

alre

ady

conv

erge

dor

bits

and

eac

h w

avel

engt

h is

tre

ated

as

anor

bits

and

eac

h w

avel

engt

h is

tre

ated

as

anin

depe

nden

t m

easu

rem

ent

at t

he s

ame

site

inde

pend

ent

mea

sure

men

t at

the

sam

e si

te

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

33

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erD

escr

iptio

n, (

cont

.)D

escr

iptio

n, (

cont

.)

••A

tmos

pher

ic r

efra

ctio

n co

rrec

tions

wer

eA

tmos

pher

ic r

efra

ctio

n co

rrec

tions

wer

eap

plie

d in

tw

o di

ffere

nt w

ays:

appl

ied

in t

wo

diffe

rent

way

s:

––st

anda

rd

stan

dard

Mar

ini

Mar

ini -

Mur

ray

mod

el

- M

urra

y m

odel

[MM

][M

M]

––a

varia

tion

of

a va

riatio

n of

Cid

dor

Cid

dor ’’ s

s Z

D m

odel

by

Men

des

ZD

mod

el b

y M

ende

san

d th

e ne

w F

CU

L (M

ende

s et

al.)

map

ping

and

the

new

FC

UL

(Men

des

et a

l.) m

appi

ng

func

tion

func

tion [M

C]

[MC

]••

Res

idua

l diff

eren

ces

exam

ined

for

bia

s an

dR

esid

ual d

iffer

ence

s ex

amin

ed f

or b

ias

and

scal

e di

ffere

nces

scal

e di

ffere

nces

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

44

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erD

escr

iptio

n, (

cont

.)D

escr

iptio

n, (

cont

.)

••R

esid

uals

gro

uped

by

Res

idua

ls g

roup

ed b

y ““ sig

nsi

gn””

––P

ositi

ve-r

esid

ual d

iffer

ence

s:P

ositi

ve-r

esid

ual d

iffer

ence

s:

•• M

M

MM

+

+ -

MC

-

MC

++

––N

egat

ive-

resi

dual

diff

eren

ces

Neg

ativ

e-re

sidu

al d

iffer

ence

s

•• M

M

MM

- - -

MC

-

MC

--

••R

esid

uals

gro

uped

in 1

0R

esid

uals

gro

uped

in 1

0 °° el

evat

ion

band

s e

leva

tion

band

san

d re

gres

sed

to in

vest

igat

e sc

atte

r va

riatio

nan

d re

gres

sed

to in

vest

igat

e sc

atte

r va

riatio

nco

rrel

ated

with

dep

ende

nce

on e

leva

tion

corr

elat

ed w

ith d

epen

denc

e on

ele

vatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

55

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual

Res

idua

l wrt

wrt

Ele

vatio

n E

leva

tion

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

66

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

esid

ual D

iffer

ence

s wrt

w

rt E

leva

tion

Ele

vatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

77

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erZ

D B

ias

as a

Fun

ctio

n of

Wav

elen

gth

ZD

Bia

s as

a F

unct

ion

of W

avel

engt

h

846

nm42

3 nm

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

88

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

er

ZD

Bia

s as

a F

unct

ion

of W

avel

engt

hZ

D B

ias

as a

Fun

ctio

n of

Wav

elen

gth

SS aa aa ss tt aa mm oo ii nn ee nn

Cid

dor

Cid

dor --

Men

des

Men

des

423

nm42

3 nm

1064

nm

1064

nm

532

nm53

2 nm

423

nm42

3 nm

1064

nm

1064

nm

532

nm53

2 nm

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

99

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual

Res

idua

l wrt

wrt

Ele

vatio

n E

leva

tion

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1010

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

esid

ual D

iffer

ence

s wrt

w

rt E

leva

tion

Ele

vatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1111

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

esid

ual D

iffer

ence

s wrt

w

rt E

leva

tion

Ele

vatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1212

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

esid

ual D

iffer

ence

s wrt

w

rt E

leva

tion

Ele

vatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1313

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

egre

ssio

nR

esid

ual D

iffer

ence

s R

egre

ssio

n42

3 nm

423

nm

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1414

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

egre

ssio

nR

esid

ual D

iffer

ence

s R

egre

ssio

n84

6 nm

846

nm

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1515

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erR

esid

ual D

iffer

ence

s R

egre

ssio

nR

esid

ual D

iffer

ence

s R

egre

ssio

n42

3 an

d 84

6 nm

423

and

846

nm -40

-200

20

40

-40

-20

02

04

0

L12

_846

+84

7_M

M+

NM

F.d

at

y =

0.7

2466

+ 1

.000

2x

R=

0.9

9941

NMF Residual [mm]

MM

Res

idua

l [m

m]

20°

< E

leva

tion

< 90

°

-40

-200

20

40

-40

-20

02

04

0

L12

_423

+42

3.5_

MM

+N

MF.

dat

y =

-1.

0535

+ 0

.999

96x

R

= 1

NMF Residual [mm]

MM

Res

idua

l [m

m]

20°

< E

leva

tion

< 90

°

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1616

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erS

umm

ary

& C

oncl

usio

nsS

umm

ary

& C

oncl

usio

ns

§§T

he r

esid

uals

for

eith

er a

tmos

pher

icT

he r

esid

uals

for

eith

er a

tmos

pher

ic

corr

ectio

n m

odel

exh

ibit

very

sim

ilar

scat

ter

corr

ectio

n m

odel

exh

ibit

very

sim

ilar

scat

ter

for

~18

00 N

Ps

so fa

r ex

amin

ed:

for

~18

00 N

Ps

so fa

r ex

amin

ed:

§§@

423

nm

12.

26 m

m@

423

nm

12.

26 m

m

§§@

846

nm

12.

31 m

m@

846

nm

12.

31 m

m

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1717

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erS

umm

ary

& C

oncl

usio

ns (

cont

.)S

umm

ary

& C

oncl

usio

ns (

cont

.)

••@

423

nm

:@

423

nm

:§§

Sm

all b

ias

(~ -

1 m

m)

and

a sc

ale

diffe

renc

eS

mal

l bia

s (~

-1

mm

) an

d a

scal

e di

ffere

nce

( 0.

9999

6 )

for

M-M

(

0.99

996

) fo

r M

-M w

rt

wrt

Men

des

- M

ende

s - C

iddo

rC

iddo

r

§§C

urre

nt d

ata

set e

xhib

its h

ighe

r sc

atte

r at

Cur

rent

dat

a se

t exh

ibits

hig

her

scat

ter

atlo

w e

leva

tion

band

slo

w e

leva

tion

band

s

§§O

vera

ll sc

atte

r ab

out t

he m

ean

is ~

0.2

mm

Ove

rall

scat

ter

abou

t the

mea

n is

~ 0

.2 m

m

§§T

he e

xam

ined

dat

a se

t is

smal

l ( ~

150

0 N

Ps)

The

exa

min

ed d

ata

set i

s sm

all (

~ 1

500

NP

s)so

mor

e ro

bust

con

clus

ions

can

be

obta

ined

so m

ore

robu

st c

oncl

usio

ns c

an b

e ob

tain

edaf

ter

the

com

plet

e se

t of d

ata

is e

xam

ined

afte

r th

e co

mpl

ete

set o

f dat

a is

exa

min

ed

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1818

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erS

umm

ary

& C

oncl

usio

ns (

cont

.)S

umm

ary

& C

oncl

usio

ns (

cont

.)

••@

846

nm

:@

846

nm

:§§

Sm

all b

ias

(~ +

.7 m

m)

and

a sc

ale

diffe

renc

eS

mal

l bia

s (~

+.7

mm

) an

d a

scal

e di

ffere

nce

( 1.

0002

) fo

r M

-M(

1.00

02)

for

M-M

wrt

w

rt M

ende

s -

Men

des

- Cid

dor

Cid

dor

§§M

ost d

ata

are

colle

cted

at e

leva

tions

< 6

0M

ost d

ata

are

colle

cted

at e

leva

tions

< 6

0 °°an

d ex

hibi

t low

est s

catte

r at

ele

vatio

ns:

and

exhi

bit l

owes

t sca

tter

at e

leva

tions

: 5050

°° <

<

εεεεεεεε <

60

< 6

0 °°

§§O

vera

ll sc

atte

r ab

out t

he m

ean

is ~

0.5

mm

Ove

rall

scat

ter

abou

t the

mea

n is

~ 0

.5 m

m§§

The

exa

min

ed d

ata

set i

s ve

ry s

mal

l ( ~

230

The

exa

min

ed d

ata

set i

s ve

ry s

mal

l ( ~

230

NP

s) s

o w

e ca

n no

t rea

ch a

ny c

oncl

usio

nsN

Ps)

so

we

can

not r

each

any

con

clus

ions

until

afte

r th

e la

rger

set

of d

ata

is e

xam

ined

until

afte

r th

e la

rger

set

of d

ata

is e

xam

ined

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

1919

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erW

ork

in p

rogr

ess

Wor

k in

pro

gres

s

••A

ll of

the

data

col

lect

ed u

p to

pre

sent

All

of th

e da

ta c

olle

cted

up

to p

rese

nt(p

rimar

ily fr

om

(prim

arily

from

Z

imm

erw

ald

Zim

mer

wal

d)

have

now

) ha

ve n

owbe

en p

roce

ssed

and

a m

ore

robu

st r

epor

tbe

en p

roce

ssed

and

a m

ore

robu

st r

epor

tw

ill b

e co

mpi

led

next

mon

th, w

ith a

will

be

com

pile

d ne

xt m

onth

, with

asi

mul

tane

ous

com

paris

on o

f the

dat

a to

sim

ulta

neou

s co

mpa

rison

of t

he d

ata

toat

mos

pher

ic c

orre

ctio

ns d

eriv

ed fr

om th

eat

mos

pher

ic c

orre

ctio

ns d

eriv

ed fr

om th

ere

vise

d re

vise

d C

iddo

r C

iddo

r -

Men

des

mod

el.

- M

ende

s m

odel

.

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

2020

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erP

repa

ring

for

Dua

l Wav

elen

gth

SLR

Pre

parin

g fo

r D

ual W

avel

engt

h S

LR

§§O

nce

the

diffe

rent

ial d

elay

s be

com

eO

nce

the

diffe

rent

ial d

elay

s be

com

e

avai

labl

e ro

utin

ely,

we

wou

ld li

ke to

avai

labl

e ro

utin

ely,

we

wou

ld li

ke to

com

pare

them

to m

odel

-der

ived

del

ays:

com

pare

them

to m

odel

-der

ived

del

ays:

§§T

he fu

ll pr

ecis

ion

form

ula

of [

The

full

prec

isio

n fo

rmul

a of

[D

egna

nD

egna

n , 9

3], 9

3]

§§A

s w

ell a

s th

e [

As

wel

l as

the

[ Abs

hire

Abs

hire

and

Gar

dner

, 85]

and

Gar

dner

, 85]

appr

oxim

atio

nap

prox

imat

ion

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

2121

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erC

ompa

rison

of t

he tw

o ap

proa

ches

Com

paris

on o

f the

two

appr

oach

es

§§W

e ha

ve u

sed

the

late

st M

ende

s-W

e ha

ve u

sed

the

late

st M

ende

s- Cid

dor

Cid

dor

form

ulat

ion

form

ulat

ion

for

the

grou

p re

frac

tivity

indi

ces

for

each

for

the

grou

p re

frac

tivity

indi

ces

for

each

wav

elen

gth

wav

elen

gth

§§T

he

The

““la

ser

freq

uenc

y fa

ctor

sla

ser

freq

uenc

y fa

ctor

s ”” f( f( λλλλλλλλ

) in

the

) in

the

appr

oxim

ate

[ap

prox

imat

e [ A

bshi

reA

bshi

re-G

ardn

er] f

orm

ula

are

-Gar

dner

] for

mul

a ar

eob

tain

ed fr

om th

e sa

me

form

ulat

ion

(i.e.

Men

des-

obta

ined

from

the

sam

e fo

rmul

atio

n (i.

e. M

ende

s-C

iddo

rC

iddo

r ), r

athe

r th

e su

gges

ted

one

used

in),

rat

her

the

sugg

este

d on

e us

ed in M

arin

i M

arin

i --M

urra

y)M

urra

y)§§

We

have

use

d th

e LA

GE

OS

dat

a fr

om th

e re

cent

We

have

use

d th

e LA

GE

OS

dat

a fr

om th

e re

cent

sum

mer

mon

ths

to c

ompa

re th

e tw

o su

mm

er m

onth

s to

com

pare

the

two ““

γγγγγγγγ ””

fact

ors

fac

tors

§§T

he e

xam

ined

dat

a se

t ind

icat

es th

at w

e M

US

T u

seT

he e

xam

ined

dat

a se

t ind

icat

es th

at w

e M

US

T u

seth

e fu

ll pr

ecis

ion

form

ula,

if w

e w

ant t

o m

aint

ain

the

full

prec

isio

n fo

rmul

a, if

we

wan

t to

mai

ntai

nm

m a

ccur

acy

in o

ur g

eode

tic e

stim

atio

n pr

oble

mm

m a

ccur

acy

in o

ur g

eode

tic e

stim

atio

n pr

oble

m

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

2222

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erLA

GE

OS

1

July

10

- A

ug. 2

1, 2

003

LAG

EO

S 1

Ju

ly 1

0 -

Aug

. 21,

200

3

-4-2024

01

00

20

03

00

40

05

00

60

07

00

Du

al W

avel

engt

h A

tmos

ph

eric

Cor

rect

ion

Com

pu

tati

ons

Full

pre

cisi

on v

s. A

pp

roxi

mat

eL

AG

EO

S 1

AC

pre

cisi

on

AC precision [mm]

Seq

. #

[

mm

]A

C p

reci

sion

-3.4

Min

imum

2.8

Max

imum

62

2P

oint

s0

.00

1M

ean

0.0

10

Med

ian

0.8

5RM

S0

.85

Std

Dev

iatio

n

10/2

6/03

10/2

6/03

Err

icos

C. P

avlis

Err

icos

C. P

avlis

2323

Godd

ard

Godd

ard

Spac

eSp

ace

Flight

Flig

htCe

nter

Cent

erLA

GE

OS

2

July

10

- A

ug. 2

1, 2

003

LAG

EO

S 2

Ju

ly 1

0 -

Aug

. 21,

200

3

-4-2024

01

00

20

03

00

40

05

00

Du

al W

avel

engt

h A

tmos

ph

eric

Cor

rect

ion

Com

pu

tati

ons

Full

pre

cisi

on v

s. A

pp

roxi

mat

eL

AG

EO

S 2

AC

pre

cisi

on [

mm

]

AC precision [mm]

Seq

. #

[m

m]

AC

pre

cisi

on-2

.59

8M

inim

um2

.61

3M

axim

um4

20

Poi

nts

0.0

25

Mea

n0

.01

5M

edia

n0

.72

RMS

0.7

2S

td D

evia

tion

Tw

o-co

lor

Ana

lysi

s T

echn

ique

•Z

imm

erw

ald:

rob

ust 2

-col

or d

atas

et in

Jul

y –

Aug

ust 2

003

•Z

imm

erw

ald

2-co

lor

conf

igur

atio

n–

Blu

e (4

23nm

): C

SPA

D, S

R62

0 #0

236,

2.5

sig

ma

–IR

(84

6nm

): P

MT

, SR

620

#228

2, 2

.0 s

igm

a

•In

Sim

ulta

neou

s pa

sses

, dif

fere

nce

Ran

ge B

iase

s(R

B)

from

eac

h co

lor

[ i.e

. IR

(RB

) –

Blu

e(R

B)

]•

Use

s R

B r

esul

ts f

rom

Del

ft a

nd C

RL

wee

kly

repo

rts

Zim

mer

wal

d 2-

Col

or R

B D

iffe

renc

esZ

imm

erw

ald

2 C

olo

r A

nal

ysis

-30

-20

-100102030

02-Jul-03

09-Jul-03

16-Jul-03

23-Jul-03

30-Jul-03

06-Aug-03

13-Aug-03

20-Aug-03

27-Aug-03

RB Difference in mm (IR-blue)

Del

ft LA

GE

OS

CR

L LA

GE

OS

Zim

mer

wal

d 2

-Co

lor

An

alys

is

-40

-30

-20

-10010203040

02-Jul-03

09-Jul-03

16-Jul-03

23-Jul-03

30-Jul-03

06-Aug-03

13-Aug-03

20-Aug-03

27-Aug-03

RB Difference in mm (IR-blue)

CR

L LA

GE

OS

CR

L A

jisai

CR

L S

tarle

tte/S

tella

Zim

mer

wal

d 2-

Col

or R

B D

iffe

renc

es

Zim

mer

wal

d 2-

Col

or A

naly

sis

Zim

mer

wal

d 2

-Co

lor

An

alys

is (

po

st A

ug

4, 2

003)

Del

ft L

AG

EO

SC

RL

LA

GE

OS

CR

L S

tarl

ett

e

CR

L A

jisai

-20

-15

-10-505101520

IR-Blue(mm)

Poss

ible

Sou

rce

of D

iffe

renc

es

•R

efra

ctio

n A

lgor

ithm

•C

oM D

iffe

renc

es–

Det

ecto

rs (

CSP

AD

vs

PMT

)–

Dua

l Wav

elen

gths

–Si

gnal

Str

engt

h–

Scre

enin

g L

evel

s (2

.5 v

s 2.

0)–

Pola

riza

tion?

•Sy

stem

Cal

ibra

tion

–D

iffe

rent

SR

620

Cou

nter

line

ariti

es–

Sign

al S

tren

gth

–O

ptic

al P

ath

Dif

fere

nces

?