The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation

Gazarik, Michael J.

Johnson, David G.

Reisse, Robert A.

Tian, Jialin

NASA Technical Reports Server

GIFTS SM EDU Data Processing and Algorithms
Jialin Tian∗, David G. Johnson† Robert A. Reisse‡, and Michael J. Gazarik†
∗SSAI, MS 468, NASA Langley Research Center, Hampton, VA 23681-2199
Email: Jialin.Tian-1@nasa.gov
† MS 434, NASA Langley Research Center, Hampton, VA 23681-2199
‡ MS 468, NASA Langley Research Center, Hampton, VA 23681-2199
Abstract—The Geosynchronous Imaging Fourier Transform
Spectrometer (GIFTS) Sensor Module (SM) Engineering Demon-
stration Unit (EDU) is a high resolution spectral imager designed
to measure infrared (IR) radiances using a Fourier transform
spectrometer (FTS). The GIFTS instrument employs three Focal
Plane Arrays (FPAs), which gather measurements across the
long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible
spectral bands. The raw interferogram measurements are radio-
metrically and spectrally calibrated to produce radiance spectra,
which are further processed to obtain atmospheric profiles via re-
trieval algorithms. This paper describes the processing algorithms
involved in the calibration stage. The calibration procedures can
be subdivided into three stages. In the pre-calibration stage,
a phase correction algorithm is applied to the decimated and
filtered complex interferogram. The resulting imaginary part
of the spectrum contains only the noise component of the
uncorrected spectrum. Additional random noise reduction can
be accomplished by applying a spectral smoothing routine to the
phase-corrected blackbody reference spectra. In the radiometric
calibration stage, we first compute the spectral responsivity based
on the previous results, from which, the calibrated ambient
blackbody (ABB), hot blackbody (HBB), and scene spectra can
be obtained. During the post-processing stage, we estimate the
noise equivalent spectral radiance (NESR) from the calibrated
ABB and HBB spectra. We then implement a correction scheme
that compensates for the effect of fore-optics offsets. Finally, for
off-axis pixels, the FPA off-axis effects correction is performed.
To estimate the performance of the entire FPA, we developed an
efficient method of generating pixel performance assessments. In
addition, a random pixel selection scheme is designed based on
the pixel performance evaluation.
I. INTRODUCTION
The Geosynchronous Imaging Fourier Transform Spectrom-
eter (GIFTS) Sensor Module (SM) Engineering Demonstration
Unit (EDU) is a high resolution spectral imager designed to
measure infrared (IR) radiances using a Fourier transform
spectrometer (FTS). The GIFTS instrument employs three
Focal Plane Arrays (FPAs), which gather measurements across
the long-wave (685-1130 cm−1) IR (LWIR), short/mid-wave
(1650-2250 cm−1) IR (SMWIR), and visible spectral bands.
The raw interferogram measurements are radiometrically and
spectrally calibrated to produce radiance spectra, which are
further processed to obtain atmospheric profiles via retrieval
algorithms. In this paper, we emphasize on the algorithmic
components of the calibration process, which are divided
in multiple stages. Prior to the radiometric calibration, the
decimated and filtered complex interferograms must be phase-
corrected so that their imaginary spectra contain only noise.
The phase correction is performed on all three types of
measurements for a series of scans, i.e., the ambient blackbody
(ABB) reference, hot blackbody (HBB) reference, and scene
scans. To reduce the random noise embedded in the reference
measurements, a spectral smoothing method can be applied to
the phase-corrected blackbody reference spectra. In the next
stage, the calibrated ABB, HBB, and scene radiance spectra
are computed based on the previous results. An assessment
of the noise equivalent spectral radiance (NESR) is derived
from the calibrated ABB and HBB references. During the
post-processing stage, we implement two additional correction
algorithms to compensate for the fore-optics offsets and FPA
off-axis effects. In the last section, we introduce an efficient
method of estimating the noise performance of the entire
FPA, as well as a random pixel selection strategy that can
be employed for generating a representative pixel sample set.
II. SINGLE-PIXEL CALIBRATION ALGORITHMS
For a single pixel element on the FPA, the calibration pro-
cedures involve the following steps: phase correction, spectral
smoothing, responsivity calculation, radiometric calibration,
NESR assessments, fore-optics offsets adjustment, and off-axis
effects correction.
A. Pre-calibration Algorithms
1) Phase Correction: The phase correction algorithm is
applied to the decimated and filtered complex interferogram
Im(n). Its complex spectrum Nm(σ) has the form of
Nm(σ) = N(σ)ejφ(σ) + n(σ), (1)
where n(σ) represents the noise vector, and N(σ) is the real
and noise-free spectrum. To estimate the phase function φ(σ),
we adopt the Forman-Vanesse-Steel (FVS) method [1]. In this
technique, a Hamming window w(n), of length W , is applied
to the complex interferogram with respect to the zero path
difference (ZPD), i.e., n = nzpd. The windowed interferogram
is written as Iw(n) = w(n)Im(n), where
w(n) =
{
0.54− 0.46 cos ( 2πnW−1), |n− nzpd| ≤ W−12 ,
0, otherwise.
(2)
The resulting interferogram Iw(n) is circular shifted to obtain
I ′w(n) such that I ′w(0) = Iw(nzpd). The spectral response of
I ′w(n) is computed via the Fourier transform, i.e., N ′w(σ) =
F{I ′w(n)}, from which, the phase function can be estimated
https://ntrs.nasa.gov/search.jsp?R=20070031875 2019-08-30T01:38:31+00:00Z
500 600 700 800 900 1000 1100 1200
−2000
0
2000
4000
6000
8000
10000
12000
Wavenumber [cm−1]
[C
ou
nts
]
LW Real (Smoothed) and Imag. Spectra Pixel (64, 65), 25 scans, ABB00494_HBB00483 ,res.=0.57cm−1
ABB−260K
HBB−286K
Fig. 1. Longwave phase-corrected and smoothed real and imaginary
blackbody spectra at ambient (260K) and hot (286K) temperatures, Pixel (64,
65), 25 scans.
as φˆ(σ) = tan−1 Im(N
′
w(σ))
Re(N ′w(σ))
. By applying the phase estimate,
the phase-corrected spectrum becomes
N̂(σ) = N(σ)ej(φ(σ)−φˆ(σ)) + n(σ)e−jφˆ(σ), (3)
and its resulting real and imaginary components are given as
Re{N̂(σ)} ≈ N(σ) + Re{n(σ)} cos(φˆ(σ)), (4)
Im{N̂(σ)} ≈ Im{n(σ)} sin(φˆ(σ)). (5)
Note that the imaginary part of the spectrum contains only
noise, which can be discarded.
2) Spectral Smoothing: The phase correction is performed
on three types of spectra, i.e., ABB, HBB, and scene. An
optional smoothing algorithm can be applied to the blackbody
references to improve the noise performance of the calibrated
radiances. Two smoothing techniques are being considered
for this purpose: the least-squares smoothing filter and the
moving average (MA) filter. The MA smoothing method
approximates the function within the predefined window as a
constant whereas the least-squares algorithm fits a polynomial
to all points within the window. The MA method does not
preserve higher order moments, however, it is less demanding
computationally. See [2], [3] for detailed reviews of these
two techniques. When the final noise performance of these
two methods are compared, no significant differences were
observed; therefore, the MA smoothing technique is chosen
due to its simplicity. Fig. 1 illustrates the phase corrected
and smoothed longwave spectra for the real and imaginary
blackbody references at ambient and hot temperatures.
B. Radiometric Calibration
To obtain the calibrated radiances, the first step involves the
calculation of the spectral responsivity, which can be computed
from
R(σ) =
N
H
(σ)−NA(σ)
BH(σ)−BA(σ) . (6)
N
H
(σ) = 1S
∑S
i=1 N
H
i (σ) and N
A
(σ) = 1S
∑S
i=1 N
A
i (σ)
represent the mean HBB and ABB spectra averaged over S
scans, respectively. Using the relation of
N
H
(σ) = R(σ)(BH(σ) + O(σ)), (7)
the offset term can be solved from
O(σ) =
N
A
(σ)BH(σ)−NH(σ)BA(σ)
N
H
(σ)−NA(σ)
. (8)
Next, the calibrated HBB, ABB, and scene radiance spectra
can be determined, based on the responsivity and offset results,
from
B̂H,Ai (σ) =
NH,Ai (σ)
R(σ)
−O(σ), (9)
N̂Ci (σ) =
NCi (σ)
R(σ)
−O(σ). (10)
respectively. The variable i denotes the scan number, i.e., i =
1, 2, . . . , S.
C. Post-processing
1) Noise Equivalent Spectral Radiance (NESR): This sec-
tion describes the estimation of the noise equivalent spectral
radiance (NESR) from calibrated blackbody references. The
NESR is generally considered as a measure of the instrument
noise performance, and can be estimated as the standard devi-
ation of calibrated blackbody radiance spectra from multiple
scans. The NESR definition is given by
NESRH,A(σ) =
√√√√ 1
S
S∑
i=1
(
B̂H,Ai (σ)− B̂H,A(σ)
)2
. (11)
Fig. 2 depicts the smoothed HBB and ABB NESR estimates
over their corresponding non-smoothed NESRs computed
from 25 interferogram scans.
650 700 750 800 850 900 950 1000 1050 1100 1150
0
0.5
1
1.5
LW ABB and HBB NESR Estimates Pixel (64, 65), 25 scans, ABB00494_HBB00483
Wavenumber [cm−1]
[m
W
 m
−
2  
sr
−
1 (c
m−
1 )−
1 ]
ABB−NESR
HBB−NESR
Smoothed ABB−NESR
Smoothed HBB−NESR
Fig. 2. Smoothed and non-smoothed longwave HBB and ABB NESR
estimates computed from 25 interferogram scans.
2) Fore-optics Offsets: The previous calibration results are
computed using internal blackbody references. To compensate
for the offsets generated from fore-optics, a correction scheme
is incorporated into the previous model. This can be achieved
by using additional data measurements collected from an
extended source. Given CHe (σ) and C
A
e (σ) as calibrated
extended blackbody sources averaged over all scans, we have
C
H,A
e (σ) = Re(σ)B
H,A
e (σ) + Oe(σ). (12)
By solving for Re(σ) and Oe(σ), the actual scene radiances
can be approximated as
N˜Ci (σ) =
N̂Ci (σ)−Oe(σ)
Re(σ)
. (13)
Fig. 3 shows the calibrated longwave HBB, ABB, and scene
radiance spectra after performing the fore-optics offsets cor-
rection.
700 750 800 850 900 950 1000 1050 1100
20
40
60
80
100
120
140
Wavenumber [cm−1]
R
ad
ia
nc
e 
[m
W
⋅
 
m
−
2 s
r−
1 ⋅
 
(cm
−
1 )−
1 ]
LW Calibrated Spectra Pixel (64, 65), 25 scans, ABB00494_HBB00483_CCE00006 ,res.=0.57cm−1
ABB−260K
HBB−286K
CCE
Fig. 3. Calibrated longwave HBB, ABB, and scene radiance spectra after
the fore-optics offsets correction (25 scans).
3) Off-axis Effects: In this section, the correction of the
FPA off-axis effects is presented. Since the GIFTS FPA
contains 128×128 detector elements, the distortion caused by
the off-axis effects is too great to be neglected. The off-axis
pixels are sampled at slightly shorter optical path differences
(OPDs), which cause the spectra of these pixels to expand
to slightly higher wavenumbers [4]. The correction can be
formulated as a fractional sampling rate conversion problem,
which can be solved via sinc interpolations, i.e.,
NCi (σ) =
M−1∑
m=0
N˜Ci (σ
′) sinc (σ − σ′), σ′ = σ
f
, (14)
where σ is the on-axis wavenumber scale, σ′ is the off-axis
scale, and f is the off-axis factor that is computed from the
FPA geometry. However, the sinc interpolation calculation is
computational intensive, furthermore, the truncation window
associated with the sinc kernels may cause overshoots in
the resulting data. It has been shown that the zero-padding
interpolation in the interferogram domain is equivalent to
the sinc interpolation in the spectral domain except that the
zero-padding method cannot evaluate the interpolation output
at an arbitrary point [5]. To overcome this limitation, we
designed the method of “over-padding”, in which, we assign
an over-padding factor g that is closely correlated to the final
resolution of the corrected spectra. For instance, if f = 0.9977,
and the length of the spectrum is N , then the zero-padded
interferogram length is the roundoff value of g ∗ N/f . If
g = 100, the actual off-axis factor of 0.997702 is obtained;
if g = 1, then the actual value of f becomes 0.99758 due
to roundoff errors. The corrected spectrum can be obtained
by downsampling the Fourier transform of the over-padded
interferogram by the factor g. Fig. 4 depicts the corrected
spectra for two pixels, one pixel is located near the center
of the FPA whereas the other is situated near the corner of
the FPA. A better wavenumber alignment was achieved after
performing the off-axis effects correction.
700 750 800 850 900 950 1000 1050 1100
0
50
100
150
Wavenumber [cm−1]
R
ad
ia
nc
e 
[m
W
⋅
 
m
−
2 s
r−
1 ⋅
 
(cm
−
1 )−
1 ]
LW Calibrated Spectra (Off−Axis Corrected) for Pixels (64,65) and (1,1), Scan 1, CCE00006 ,res.=0.57cm−1
Pixel (64,65)
Pixel (1,1)
Fig. 4. Calibrated spectra for Pixel (1,1) and Pixel (64, 65) after performing
the off-axis effects correction.
III. FOCAL PLANE ARRAY (FPA) PERFORMANCE
ASSESSMENT
We have discussed the algorithmic procedures required for a
single pixel measurement. To evaluate the entire FPA without
completing all of the calculation steps, we designed a pixel
inventory method, which estimates the FPA responsivity and
noise distributions.
A. Pixel Inventory
The responsivity for any detector element can be approxi-
mated from the normalized intensity value at the ZPD, which
is given by
R̂x,y =
Ix,ym (nzpd)
1
XY
∑
x
∑
y
Ix,ym (nzpd)
∀ x, y, (15)
where x, y are pixel numbers. The FPA responsivity estimate
is shown in Fig. 5(a). The FPA responsivity distribution within
a predefined range of 0.8 ≤ R̂x,y ≤ 1.2 is plotted in Fig. 5(b).
To assess the FPA noise, each interferogram is first normalized
by its value at n = nzpd, i.e.,
I˜x,ym (n) =
Ix,ym (n)
Ix,ym (nzpd)
∀ x, y. (16)
Next, the estimated noise is computed from the root-mean-
square value of the last L samples in each interferogram that
is represented by
N̂x,y =
√√√√ 1
L
M−1∑
n=M−L
∣∣I˜x,ym (n)∣∣2 ∀ x, y. (17)
Similarly, the FPA noise and its distribution are shown in
Figs. 6(a) and 6(b), respectively.
Estimated Responsivity (Normalized by Mean) for lwp_ABB00494_scan_01
20 40 60 80 100 120
20
40
60
80
100
120
0.85
0.9
0.95
1
1.05
1.1
1.15
(a)
0.8 0.9 1 1.1 1.2
0
100
200
300
400
500
600
700
Estimated Responsivity (Normalized by Mean) Distribution for lwp_ABB00494_scan_01
Normalized Responsivity
N
um
be
r o
f P
ixe
ls
mean = 1.0491
median = 1.0491
stdev. = 0.054158
number = 15311
num < 0.8 = 1057
num > 1.2 = 16
total outliers = 1073
% in range = 93.4509
(b)
Fig. 5. Longwave pixel inventory: (a) FPA responsivity estimates, and (b)
FPA responsivity distribution plot.
B. Random Pixel Set Generation
Once we have the knowledge of the FPA responsivity and
noise estimates, a set of selection criteria is established by
defining an acceptable range for the responsivity and noise.
Thus, a random sample set of pixels can be chosen such that
it reflects the statistical properties of the entire FPA. We can
then perform the actual calibration procedures on this sample
set. Fig. 7 shows a sample longwave pixel selection scheme,
in which 64 random pixels are selected with 4 pixels per tap.
The selection is uniformly distributed and unique within each
tap.
IV. CONCLUSION
This paper describes the required stages for calibrating
the GIFTS SM EDU data spectrally and radiometrically. The
following procedures were introduced: phase correction, spec-
tral smoothing, radiometric calibration, NESR computation,
correction algorithms for the fore-optics offsets and the off-
axis effects. In the last section, methods for estimating the
FPA’s performance and generating random pixel sample sets
were discussed.
REFERENCES
[1] M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of asymmetric
interferograms obtained in Fourier transform spectroscopy,” J. Opt. Soc.
Amer., vol. 56, pp. 59-63, 1966.
Estimated Noise (Normalized by ZPD) for lwp_ABB00494_scan_01
20 40 60 80 100 120
20
40
60
80
100
120 1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
x 10−4
(a)
0 1 2 3 4 5 6 7 8
x 10−4
0
100
200
300
400
500
600
700
800
Estimated Noise (Normalized by ZPD) Distribution for lwp_ABB00494_scan_01
Normalized Noise
N
um
be
r o
f P
ixe
ls
mean = 0.00036859
median = 0.00034939
stdev. = 7.8007e−005
number = 12237
num < 0.0001 = 8
num > 0.0007 = 4139
total outliers = 4147
% in range = 74.6887
(b)
Fig. 6. Longwave pixel inventory: (a) FPA noise estimates, and (b) FPA
noise distribution plot.
20 40 60 80 100 120
20
40
60
80
100
120
Fig. 7. A sample longwave random pixel set. Blue pixels: out-of-range noise;
green pixels: out-of-range responsivity; black pixels: out-of-range noise and
responsivity; gray pixels: satisfy both noise and responsivity constraints; and
white pixels: random pixel selection.
[2] W. H. Press et al., Numerical Recipes in C: The Art of Scientific
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[3] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal
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[4] J. Kauppinen and J. Partanen, Fourier Transforms in Spectroscopy.
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[5] P. J. La Rivie`re and X. Pan, “Mathematical equivalence of zero-padding
interpolation and circular sampling theorem interpolation with implication
for direct Fourier image reconstruction,” SPIE Conference on Image
Processing, vol. 3338, pp. 1117-1126, 1998.


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