The processing change invokes a generalization of the calibration equation to include the emission and reflection of the scan mirror. The generalized calibration equation is

Equation 6

where R, X, q, m, and b are defined as in Eq. (1). The quantity e is the emissivity of the scan mirror, and it is a function of scan angle q. The procedure for determining e[q] is described in the next section. The parameter R_M is the radiance of the scan mirror. This radiance is computed via Eq. (4) from the temperature of the scan mirror, which is monitored by a thermistor embedded in its structure. The validity of Eq. (6) depends on the relationship⁹ in which r is the reflectance and e the emissivity in a particular direction of an opaque, specularly-reflecting surface.

Equation (6) differs from Eq. (1) on the left hand side, where now the scene radiance R is multiplied by (1 - e) instead of 1; this represents the reduction in the radiation received from the scene as the reflectance of the scan mirror is reduced from 1 to 1 - e. Also, there is a second term, which represents the radiation emitted by the scan mirror.

In orbit, the processing goes as follows: At each blackbody look, m is determined from

Equation 7 where the variables are defined as in Eq. (3). However, r_bb is not simply the radiance of the blackbody R_bb, but is related to it by

Equation 8 where R_M,bb is the radiance of the scan mirror computed from its temperature at the time of the blackbody sequence. The quantity e[45] is the scan mirror's emissivity when it is at the blackbody position, for which the angle of incidence of the incoming radiation is 45^o. Similarly, e [sp] is the emissivity at the space look position, which will have an incidence angle of either 40^o or 50^o, depending upon which side of the Earth the space look occurs. (For the imager, 40^o is on the west, while for the sounder it is on the east.)

From Eqs. (7) and (8), it would appear that m depends on the side of Earth on which the space view occurs. Nevertheless, it is, in fact, a property only of the instrument--it is essentially the reciprocal of the responsivity of the radiometer downstream of the scan mirror--and it does not depend on space-view side.

At each space look, b is determined from the equation, where R_M,sp is the mirror radiance at the time of the space look. The value of b may depend on space-clamp side.

It is convenient to define the quantity b_e , as

Equation 9 Then, for each pixel, the radiances are computed from where m is from Eq. (7), and e(q) is e evaluated at the scan angle (pixel position) q.

For the imager, the interpolation of space-look counts within the blackbody sequences, and the interpolation of the intercepts between space looks, are still carried out, as described previously.

Go to next page or Return to contents page