Stray Light Correction Algorithm for Multi-channel Spectrographs

Steve Brown, Yuqin Zong, Ping Shaw, Keith Lykke, Carol Johnson NIST

Stephanie J. Flora, Michael E. Feinholz, Mark A. Yarbrough

Moss Landing Marine Laboratories

Dennis K. Clark Marine Optical Consulting

1

Multi-channel Spectrographs

Typical Layout

• In a conventional single-channel spectrograph, the entrance slit is imaged on the detector plane

• In a multi-channel spectrograph, the entrance slit is divided into channels for inputs from different targets

– Simplest way to do this is to use optical fibers – often simply epoxied onto the entrance slit

2

Entrance slit

Optical fibers

Detector Array

Spectral

Spat

ial

Motivation for the work arises from survey of fields with applications using Multiple-input (or multi-channel) Spectrographs

— Medical imaging

— High throughput screening

— Machine vision

—Multi-channel process monitoring

— Remote sensing

—Astronomy

3

Intermediate step between 1-d SLC algorithm and full point spread response correction algorithm

Ocean Color Multi-channel Spectrograph built by Resonon for Moss Landing

14-channel spectrograph Image on the CCD from an 14-channel spectrograph

4

Detector

Spectrograph

Fiber Input

Characterization/Performance Issues

Output from a standard fiber shows an extended halo that may cause scattered light within the spectrograph

Grating scatter

Ghost image

Spurious reflection peaks

5

Impacts Along-track (spectral) and Cross-track (spatial) performance

Reflection Peak

Wavelength (nm)

Rel

ativ

e R

esp

on

se (

a.u

.)

Astronomy Example: Baryon Oscillation Spectroscopic Survey (BOSS)

Movie Provided by Claire Cramer, NIST

6

images, tunable laser excitation

• BOSS has 1000 fiber inputs >

“Big Boss” – 5000 inputs

• 2.5 m telescope at Apache

Point Observatory, New Mexico

• Used to study large-scale

structure of the universe Wav

elen

gth

Individual fibers

Algorithm for Single Input System: Review

IB SLmeasS S S

S r L dmeas

S r L d r L dmeas ib oob

555 556 557 558 559 560 561 562 563 564

0.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esponse

Wavelength [nm]Wavelength [nm]

Rel

ativ

e R

esp

on

se (

a.u

.)

Wavelength (nm)

In-Band Out-of-Band

SStray Light: Development of the SDF Matrix

The SDF matrix, Dn×n

Spectrum Line Spread Function (LSF)

Stray-light distribution function (SDF)

1,1 1,2 1, 1,n 1 1,n

2,1 2, 2 2, 2, n-1 2, n

i,1 , 2 , , n-1 , n

n-1,1 n-1, 2 n-1, n-1, n-1 n-1, n

n,1 n, 2 n, n, n-1 n, n

. . . .

. . . .

. . . . . . . . .

. . . . . . . . .

. . . .

. . . . . . . . .

. . . . . . . . .

. . . .

. . . .

J

J

i i J i i

J

J

d d d d d

d d d d d

d d d d d

d d d d d

d d d d d

D

Colum 400

Relative scattering from pixel j into all other pixels in the array

Relative scattering from all other pixels in the array into pixel i

Zero’s along the diagonal

The Stray Light Distribution (SDF) matrix, D

9

1,1 1,2 1, 1,n 1 1,n

2,1 2, 2 2, 2, n-1 2, n

i,1 , 2 , , n-1 , n

n-1,1 n-1, 2 n-1, n-1, n-1 n-1, n

n,1 n, 2 n, n, n-1 n, n

. . . .

. . . .

. . . . . . . . .

. . . . . . . . .

. . . .

. . . . . . . . .

. . . . . . . . .

. . . .

. . . .

J

J

i i J i i

J

J

d d d d d

d d d d d

d d d d d

d d d d d

d d d d d

D

A little Matrix Algebra …

10

Stray-light correction matrix.

IB

1

1

meas IB

meas IB

measIB

measIB

S S D S

S I D S

S I D S

C I D

S C S

SL IBD SS

“Truth”

11

Two Example Results of Stray-light Correction

A Green LED A Green Optical Filter

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

Rela

tive S

ign

al

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

8.0E-04

9.0E-04

200 300 400 500 600 700 800 900

Wavelength (nm)

Rela

tive S

ign

al

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

Rela

tive S

ign

al

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

8.0E-04

9.0E-04

200 300 400 500 600 700 800 900

Wavelength (nm)

Rela

tive S

ign

al

1 count

1 count

log log

linear

linear

Magnitude of Stray Light: Broadband v. Narrowband calibrations

6.5E+08

7.0E+08

7.5E+08

8.0E+08

8.5E+08

9.0E+08

730 735 740 745 750

Wavelength [nm]

Ab

so

lute

Sp

ec

tra

l R

es

po

ns

ivit

y

Lamp-ISS Uncorrected for stray light

Lamp-ISS Stray light corrected

SIRCUS

ib iii drR

555 556 557 558 559 560 561 562 563 564

0.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esponse

Wavelength [nm]Wavelength [nm]

Ab

solu

te R

esp

on

sivi

ty (

a.u

.)

~10 %

Extension of the Algorithm to a Multiple Channel Spectrograph

• Take each of the input channels and create one long nx1 matrix, where n=# of channels multiplied by the number of elements in the array (dispersion direction)

• Example:

– For a system with 4 inputs, 1024 elements in the along track direction, the array is a 4096 x 1 array

13

14

describes the cross-track scattering from track I into track j

Consider a 4-channel system 1

11 12 13 142

21 22 23 24

33431 32 33

41 42 43 44 4

SIB

D D D D

SD D D D IBD SIB

D D D D SIB

D D D DS

IB

,Di i

,Di j

D matrix now comprised of sub-arrays

describes the along-track scattering

SL IBD SS

As with the 1-d case,

Only D and S now have different meanings.

Multiple Input Spectrograph System • ISA (Jobin Yvon) f/2 spectrograph with reflective concave holographic

grating; 25 mm slit

• Andor 1024x256 cooled CCD array, 25 mm pixels

• Breadboard system had 4 1 mm fibers separated by ~500 mm

Lens, aperture, & shutter

CCD &

spectrograph

Fiber bundle

Input fibers

Shutter drive circuit

Lens, aperture, & shutter

CCD &

spectrograph

Fiber bundle

Input fibers

Shutter drive circuit

Spectralon sphere

Input fibers

Spectralon sphere

Input fibers

15

4-Channel Input into Spectrograph

All 4 channels illuminated with LED Image expanded to 1 % full scale

Cross-track coupling

16

Xenon source, Only Track 2 Illuminated

17

Pixel

Sign

al(A

DU

/pix

el/s

eco

nd

) Along-track

Cross-track

0

2000

4000

6000A

ndo

r L

ite

(A

DU

/pix

/se

c)

965 901 837 774 711 648 586 524 463 401 340Wavelength (nm)

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

Pixel

An

do

r L

ite

(A

DU

/pix

/se

c) 0.15%

0.15%

0.06%

Track1

Track2

Track3

Track4

Ratio of Track x to Track 2

0 200 400 600 800 10000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05R

atio T

rack X

/ T

rack 2

Pixel

T1 / T2

T3 / T2

T4 / T2

18

Stray light characterization using tunable lasers

Laser characterization data (subset of full data set)

Second order diffraction

19

400 500 600 700 800 900

10-4

10-3

10-2

Wavelength (nm)

An

do

r T

rack

1 L

ase

r D

ata

(n

orm

alize

d t

o m

axi

mu

m)

Stray Light Distribution Function Matrix

Along-track Sub-Matrix D22 Cross-track Sub-Matrix D43

20

(normalized by the in-band area)

Second order diffraction peak Not zero along the diagonal

4-channel D-matrix

21

Smeas: Track 2 only Illuminated

22 Array Element

Sign

al (

AD

U/p

ixel

/sec

) (L

oga

rith

mic

sca

le)

0 4000

D S

23

1

11 12 13 142

21 22 23 24

33431 32 33

41 42 43 44 4

SIB

D D D D

SD D D D IBD SIB

D D D D SIB

D D D DS

IB

Validation: Single track Illuminated

24

Wavelength [nm]

Log

Sign

al [

a. u

.]

Validation (Logarithmic Scale) Full = all tracks illuminated; Single = single track illuminated

25

400 600 800

100

Tra

ck

1

Full

Single

Cor(F)

Cor(S)

400 600 800

100

Tra

ck

2

400 600 800

100

Wavelenght (nm)

Tra

ck

3

400 600 800

100

Wavelenght (nm)

Tra

ck

4

Wavelength [nm] Wavelength [nm]

Xe source Xe source, PER filter

Xe source, BG-39 filter Xe source, BG-28 filter

Validation (Linear Scale)

26

400 600 800

0

10

20

30

40

50

Tra

ck

1

Full

Single

Cor(F)

Cor(S)

400 600 800

0

10

20

30

40

50

Tra

ck

2

400 600 800

0

10

20

30

40

50

Wavelenght (nm)

Tra

ck

3

400 600 800

0

10

20

30

40

50

Wavelenght (nm)

Tra

ck

4

Wavelength [nm] Wavelength [nm]

Xe source Xe source, PER filter

Xe source, BG-39 filter Xe source, BG-28 filter

Residual signal near 800 nm originates from incomplete characterization

27

400 500 600 700 800 900

10-4

10-3

10-2

Wavelength (nm)

An

do

r T

rack

1 L

ase

r D

ata

(n

orm

alize

d t

o m

axi

mu

m)

400 600 800

0

10

20

30

40

50

Tra

ck

1

Full

Single

Cor(F)

Cor(S)

400 600 800

0

10

20

30

40

50

Tra

ck

2

400 600 800

0

10

20

30

40

50

Wavelenght (nm)

Tra

ck

3

400 600 800

0

10

20

30

40

50

Wavelenght (nm)

Tra

ck

4

400 500 600 700 800 900

Wavelength [nm]

Wavelength [nm]

Wavelength [nm]

Magnitude of the correction

28

400 500 600 700 8000.9

0.92

0.94

0.96

0.98

1T

rack

1Ratio of cor/uncor (Full)

450 500 550 600 650 7000.9

0.92

0.94

0.96

0.98

1

Tra

ck

2

450 500 550 600 650 7000.9

0.92

0.94

0.96

0.98

1

Wavelenght (nm)

Tra

ck

3

400 450 500 550 600 6500.9

0.92

0.94

0.96

0.98

1

Wavelenght (nm)

Tra

ck

4

Future Direction: Finite Point Spread Response correction

• Limit as the width of a channel decreases to one pixel and the # of channels increases to # of elements

29

Proposed point spread response correction for MODIS

30

Random granules analyzed

Analysis of a time series of imagery (same site, different cloud cover) 1. Ground truth site (MOBY Site) 2. A site where the radiometric properties of the ocean are known and constant Southern Ocean?

Y-axis Logarithmic scale For these granules, most measured

elements are close to clouds!

Future Direction

• MODIS

31 Gerhard Meister and Charles R. McClain, Appl. Opt. 49, 6276-6285 (2010)

(Band 11 centered at 531 nm)

Thank you for your attention.

32