PDS_VERSION_ID = PDS3
RECORD_TYPE = STREAM
OBJECT = TEXT
PUBLICATION_DATE = 2001-09-01
NOTE = "MSI Calibration Document."
END_OBJECT = TEXT
END
MSI Calibration
---------------
MSI calibration is done in three principal steps:
1. Radiometric calibration - Results from onground and inflight
tests that were used to develop the conversion of raw DN's into
into physical units of radiance.
2. Geometric calibration - Results from onground and inflight
tests that were used to derive image scale and distortion
and imager alignment, as well as the timing of image frames.
3. Scattered light - Results from inflight tests that were used to
quantify scattered light and signal from sources other than
the measured target.
Details of calibrations performed can be found in:
[MURCHIEETAL1999]
[MURCHIEETAL2000]
[LIETAL2000]
A brief description follows:
1. Radiometric Calibration
For radiometric calibration, the main objective of inflight
calibration is solving for variables in the calibration equation for
converting image data numbers (DNs) to physical units of radiance, W
m-2 micro m-1 sr-1.
The calibration equation has two forms. The first form is applied
when the field-of-view is underfilled, or when the field is filled by
accompanying 0-ms exposures taken close in time and in the same filter
are not available:
Radiance(x,y,f,T,t,c) =
{[DN(x,y,f,T,t,c) - Dark(x,y,t,T,MET)] - Smear(x,y,t)} * 100
-------------------------------------------------------- (1)
Flat(x,y,f,c) * Coef(f) * Resp(f,T) * Atten(f,c) * Exp(t)
where DN(x,y,f,T,t,c) is raw DN measured by the pixel in column x, row
y through filter f at exposure time t and temperature T with the cover
status c open or closed. Dark(x,y,t,T,MET) is the dark closed.
Dark(x,y,t,T,MET) is the dark level modeled for this pixel at exposure
time t, temperature T, and mission-elapsed time MET, time t,
temperature T, and mission-elapsed time MET, derived from a model
based on dedicated dark frames taken throughout the the mission.
Smear(x,y,t) is the scene-dependent readout smear for the pixel at
exposure time t. Flat(x,y,f,c) is the flat field for filter f with
the cover status c open or closed. Coef(f) is the coefficient for
converting dark-removed, flat field and smear-corrected DN from filter
f to radiance, for a baseline exposure time of 100 ms. Resp(f,T) is
the responsivity for this filter at temperature T relative to the
baseline, inflight operating temperature (-29.6 deg C). Atten(f,c), if
appropriate, is the attenuation of incoming signal by the lens cover
in filter f when the cover status c is closed. Exp(t) is exposure
time in milliseconds between 1 and 999 ms.
The second version of the calibration equation is used for monochrome
sequences having as an objective photometric accuracy, or for color
sequences, in either case when the asteroid overfills the FOV:
Radiance(x,y,f,T,t,c) =
{[DN(x,y,f,T,t,c)-Dark(x,y,MET,T,t)] -
[DN(x,y,f,T,0,c)-Dark(x,y,MET,T,0)]}*100
-------------------------------------------------- (2)
Flat(x,y,f,c) * Coef(f) * Resp(f,T) * Atten(f,c) * Exp(t)
where DN(x,y,f,T,t,c) is raw DN of an intended image scene.
DN(x,y,f,T,0,c) is an image acquired a few seconds later at an
exposure time of 0 ms. The 0-ms image contains no real scene
information, but has the same transfer smear and leaked light as the
primary image. It differs only in (a) the exact position of the scene
at the sub-pixel level and (b) a slightly lesser accumulation of dark
current at the shorter exposure time. For a typical Eros image exposed
to a DN of approximately 2000, this approach removes approximately 20
DN of leaked light ignored in equation 1. Application of this version
of the equation requires two raw images to produce one calibrated,
reduced image, and this is much more resource-intensive.
1.1. Dark Images
The signal level measured in space is the sum of three components:
(a) dark current from thermal electrons,
(b) a bias of approximately 80 intentionally added to the output
to prevent occurrence of negative values which would reach ground
as zeroes in the 12-bit DN words, and
(c) low-level periodic noise picked up by spacecraft electronics.
Odd and even columns have slightly different biases
(by approximately 6 DN), an inherent property of this Thomson CCD.
This difference introduces a fixed pattern which,
when subtracted from the data, has no measurable effect
on accuracy or signal-to-noise ratio of the image data.
The model for dark current depends on CCD temperature T,
exposure time t, mission-elapsed time MET, and row number y:
Dark(y,MET,T,t) =
(a1_offset + a1_coeff*y) + ((a2_offset + a2_coeff*y)*MET) +
((a3_offset + a3_coeff*y)*T) + t*((b1_offset + b1_coeff*y) +
((b2_offset + b2_coeff*y)*T))
(3)
where a1_offset is an offset, a1_coeff is a multiplicative
coefficient, and y is row incrementing from 1 to 244.
These ten constants have separate values for
odd and even columns. All values are given in Table 1.
Table 1. Constants in Dark Current Model
-------
----------------------------------------------------------------
Parameter Explanation Even Odd
--------------- -----------------
offset coeff. offset coeff.
------ ------ ------ ------
a1 Bias at MET=0 80.336 4.939e-3 84.543 5.467e-3
reference CCD temp.
a2 Change in bias with 1.918e-8 1.037e-11 1.736e-8 1.054e-11
MET
a3 Change in bias with -5.272e-2 1.159e-4 -4.406e-2 1.345e-4
CCD temperature
b1 Dark accumulation 8.071e-3 2.549e-6 8.491e-3 8.571e-7
perms, reference
CCD temp.
b2 Change in d.c. 2.355e-4 8.767e-8 2.249e-4 2.942e-8
accumulation rate
with change in
CCD temperature
----------------------------------------------------------------
1.2. Response Uniformity
The pixel-to-pixel variation in CCD response to a uniform
extended source, the "flat field," was measured onground,
and retested during flight. The flat-field correction
effectively removes pixel-to-pixel signal variations, with residuals
at the levels expected for shot noise at measured DN levels
(i.e., approximately one part in 200). Files containing
Flat(x,y,f,c) for each filter with the cover off are listed in the
table below. For the condition of the cover still on, that
flat-field file is multiplied by the ratio of the flat fields
with the cover on and off.
All images acquired at or after mission elapsed time (MET)
6427889 (2 May 1996) have the cover off, and all the images
taken before have the cover on.
Table 2. Flat field Files
--------
---------------------------------------------------------
Filter number Cover-off flat field Cover-on ratio
------------- ------------------- --------------------
0 flat0-31C.FIT coverflatratio0.FIT
1 flat1-31C.FIT coverflatratio1.FIT
2 flat2-31C.FIT coverflatratio2.FIT
3 flat3-31C.FIT coverflatratio3.FIT
4 flat4-31C.FIT coverflatratio4.FIT
5 flat5-31C.FIT coverflatratio5.FIT
6 flat6-31Cn.FIT coverflatratio6.FIT
7 flat7-31Cn.FIT coverflatratio7.FIT
--------------------------------------------------------
1.3. Readout Smear
MSI is shuttered electronically. An image is exposed for a
nominal integration (exposure) time, following which it is
transferred in 0.9 ms to a memory zone on the CCD from which
analog signal is digitized line-by-line. Accumulation of
signal continues during the 0.9 ms of frame transfer.
The finite duration of the frame transfer therefore induces a streak
"frame transfer smear" in the wake of an illuminated object in
the field of view, parallel to the direction of frame
transfer. The magnitude of the smear to be removed from the pixel in
column x and line y in an image integrated for exposure time t is:
Smear(x,y,t) = Summation (1 to y-1) {(t2/t) *
DN(x,y,f,T,t,c) - Dark(x,y,T,t) - Smear(x,y,t)
---------------------------------------------- } (4)
Flat(x,y,f,c)
where t2 is the time for frame transfer (0.9 ms) divided
by the number of lines in the image in the direction of frame
transfer (244 lines).
1.4. Linearity
The underlying assumption of radiometric calibration of MSI is
that response of the CCD is linear with exposure time, to the
digitization limit of 4095. Onground testing summarized
summarized by [HAWKINSETAL97] shows that this condition
is satisfied onground. This assumption was tested again
after launch, placing an upper limit of 1% on the variations
in linearity with signal level.
1.5. Cover Attenuation
The attenuation of light by the lens cover is of significance
mostly because the first of the two scheduled lunar calibration
sequences was acquired with the cover on, while the second
lunar calibration sequence, in January 1998, was acquired with
the cover off. The attenuation in filter 0 is poorly determined.
Table 3. Cover Attenuation
-------
-----------------------------------
Filter number Atten(f,c)
------------- --------------
0 (0.2774)
1 0.2357
2 0.2182
3 0.2444
4 0.2322
5 0.2432
6 0.2305
7 0.2330
-----------------------------------
1.6. Radiometric Responsivity
Radiometric responsivity results from the efficiency
in converting photons of light into photoelectrons measured by the
instrument, and is the key variable for converting DN levels into
physical units of radiance.
Table 4. Calibration Coefficients Coeff(f)
--------
-----------------------------
Filter Coef(f)
------ -------
0 4041.1
1 530.0
2 163.4
3 506.4
4 317.4
5 468.0
6 168.0
7 64.0
----------------------------
1.7. Relative responsivity as a function of temperature
The temperature dependence of responsivity in each filter
Resp(f,T) was determined from fitting onground measurements
of the large integrating sphere at different temperatures
[HAWKINSETAL1997]. This is expressed as a second-order
polynomial:
Resp(f,T) = a + bT + cT**2 (5)
using the coefficients:
Table 5. Coefficients to Resp(f,T)
-------
---------------------------------------------
Filter a b c
---------------------------------------------
0 1.0057 0.00019236 --
1 0.94105 -0.0029599 -3.2714e-05
2 0.9022 -0.0045827 -4.3198e-05
3 1.0499 0.0016854 --
4 1.1311 0.0041073 -1.0833e-05
5 1.1049 0.0051262 5.3421e-05
6 1.1965 0.0070161 1.2722e-05
7 1.3238 0.012328 4.6893e-05
---------------------------------------------
where T is temperature in Celsius and the function is
unity at the nominal inflight operating temperature of -29.6C.
2. Geometric Calibration
2.1. Image Scale and Distortion
The best focal length is 166.850 +/- 0.10 mm. This translates
into accurate angular dimensions for a mean pixel of
95.9 microradians x 161.8 microradians, and a field-of-view of
2.95 degrees x 2.26 degrees.
2.2. Imager Alignment
To within about 150 microradians (1 pixel) accuracy,
pointing over the course of the entire mission may be defined
by simple linear functions of instrument deck
temperature T(deck). In an image reference frame, with
the origin at the upper left, the column (sample) number increases
in the +z direction in the spacecraft reference frame. The line (row)
number in an image increases in the -y' direction in the spacecraft
reference frame. The offset position from the spacecraft
x' axis in the column or spacecraft +z direction is approximated by:
column offset (microradians) = -1260 - 45.81*T(deck) (6)
(+/- 113 microradians), r = 0.83
The offset position in the line or spacecraft -y' direction
is approximated by:
line offset (microradians) = -744 (+/-99 microradians) (7)
3. Scattered Light
Scattered light is measured using inflight images of Canopus.
A failed Eros orbit insertion maneuver on 20 December 1998,
in which more than 28 kg of hydrazine was expended by attitude
control jets on NEAR, caused the deposit of burn products
on the outer optic of the MSI. This resulted in a wavelength-
dependent degradation of the system point-spread function.
The scattered light is progressively worse in the shortest
and longest wavelength filters, especially at 450 and 1050 nm.
The degraded PSF is restored using the Fourier
filtering technique described by [LIETAL2000].
4. Processing levels
NEAR images are archived in up to 8 forms which have
undergone differing calibration pathways and levels of
subsequent processing, depending on the target body,
time during the mission, and intent of the observation:
RAW: Image in units of raw DN as received from the spacecraft
after data were uncompressed
RAD: Image calibrated to units of radiance using equation (1)
CRD: Cleaned image calibrated to units of radiance; calibration
performed using equation (2) with removal of background
levels by subtraction of a 0-ms exposure image
CRDDBL: As with CRD; in addition images are deblurred
by application of the Fourier filtering restoration of a
degraded image PSF
IOF: Image calibrated to units of I/F; following calibration
to radiance using equation (1), image is divided by the pi
times the solar irradiance expected at the target body's
distance from the Sun
IOFDBL: As with IOF; in addition images are deblurred
by application of the Fourier filtering restoration of a
degraded image PSF
CIF: Cleaned image calibrated to units of I/F; as with CRD,
calibration performed using equation (2) with removal of
background levels by subtraction of a 0-ms
exposure image; then image is divided by the pi times
the solar irradiance expected at the target body's distance
from the Sun
CIFDBL: As with CIF; in addition images are deblurred by
application of the Fourier filtering restoration of a
a degraded image PSF