Markham, B.L., F.M. Wood Jr., and S.P. Ahmad. 1988. Radiometric calibration of
the reflective bands of NS001-thematic mapper simulator (TMS) and modular
multispectral radiometers (MMR). In Recent Advances in Sensors Radiometry and
Data Processing for Remote Sensing Proc., SPIE 24, pp. 96-108.
1989 Calibration coefficients used for data reduction (Markham 1989) for
MMR (SN 114):
| Waveband | Gain (Volts Watts-1m-2sr-1um-1) |
Offset (Volts) |
Temperature Sensitivity coefficient (oC) |
|---|---|---|---|
| 1 | 0.00601 | -0.0039 | 625.00 |
| 2 | 0.00689 | -0.0039 | 1112.00 |
| 3 | 0.00712 | -0.0042 | -1486.00 |
| 4 | 0.01024 | -0.0094 | 286.00 |
| 5 | 0.02048 | 0.0096 | -74.40 |
| 6 | 0.04108 | 0.0322 | -73.12 |
| 7 | 0.12229 | 0.0076 | -70.24 |
WAVEBAND'S 1-7 FORMULAE
Temperature Correction Step| Vc(j) = ((R(j) + Td,0) / (R(j) + Td)) * V(j) |
[1] |
where:
j = MMR waveband 1-7
Vc(j) = waveband response corrected to Td,0 (volts)
V(j) = waveband response (volts)
R(j) = specific waveband linear temperature sensitivity coefficient (oC)
Td,0 = reference temperature (oC)
Td = (ln(V10 - 1.9316)) / (-0.04446) from Barnes Engineering
where:
V10 = response of detector thermistor (volts)
Apply Calibration Gain and Offset for Radiances
| Ls(j) or Lp(j) = [Vc(j) - O(j)] / G(j) |
[2] |
where:
Ls(j) = waveband spectral radiance for surface (Watts-1m-2sr-1um-1)
Lp(j) = waveband spectral radiance for reference panel ( Watts-1m-2sr-1um-1)
O(j) = waveband offset (volts)
G(j) = waveband gain (Volts Watts-1m-2sr-1um-1)
Linear Interpolation for Estimated Reference Panel Values from Surrounding Measured Values
| Lp(t,j) = Lp(t1,j) + {((t - t1)/(t2 - t1)) * (Lp(t2,j) - Lp(t1,j))} |
[3] |
where:
Lp(t1,j) and Lp(t2,j) = waveband reference panel radiance bracketing the
surface radiances at times t1 and t2 (Watts-1m-2sr-1um-1)
Lp(t,j) = waveband radiance of the reference panel at the surface radiance
time t (Watts-1m-2sr-1um-1)
Time correction of Reference Panel Value
| Lp(t,j) = Lp(t1,j) * (sin(sea(t1)) / sin(sea(t))) |
[4] |
where:
sea(t1) = solar elevation angle at time t1
sea(t) = solar elevation angle at time t
Calculate Reflectance Factor
| RF(j) = Ls(j) / (Lp(t,j) / RFp(j)) |
[5] |
where:
Ls(j) = waveband surface radiance (Watts-1m-2sr-1um-1)
RF(j) = waveband surface reflectance factor (%)
RFp(j) = waveband reflectance factor for the reference panel(%)
WAVEBAND 8 (THERMAL) FORMULAE
Thermal waveband 8 coefficients 1989 Calibration coefficients used for data reduction (Markham 1989) for MMR (SN 114):
AC = 0.1296
BC = 14.42
AA = -0.75249E-03
AB = -0.43519E-05
KA = 0.39019E-03
KB = 0.19078E-05
Where AC and BC are calibration coefficients for the equation used to calculate the calibration corrected temperature
(Tc), and AA, AB, KA and KB are the calibration coefficients for the equation used to calculate the surface radiance (Ls). All of
these coefficients are unitless.
| Tc = (V9 - AC) * BC |
[6] |
Tc = chopper temperature (oC)
V9 = response (volts) of the chopper thermistor
AC, BC = calibration coefficients
| Lc = 0.11927 / {exp(1278.88 / (Tc + 273.00)) - 1.0} |
[7] |
where:
Lc = chopper radiance (W m-2)
| Ld = 0.11927 / {exp(1278.88 / (Td + 273.00)) - 1.0} |
[8] |
where:
Ld = detector radiance (W m-2)
| Ls = Lc + (KA + KB * Tc) * V8 + (AA + AB * Tc) |
[9] |
where:
V8 = waveband 8 response voltage
Ls = surface radiance (W m-2)
KA, KB, AA, AB = calibration coefficients
| Ls = Ld + (KA + KB * Td) * V8 + (AA + AB * Td) |
[10] |
where:
V8 = waveband 8 response (volt)
Ls = surface radiance (W m-2)
KA, KB, AA, AB = calibration coefficients
| Tc = 1278.88 / ln((0.11927 / Ls) + 1.0) - 273.0 |
[11] |
where:
Tc = calibration corrected temperature measurement (oC)