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
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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
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
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)