The DIFFERENTIAL integral is not a true integral. It evaluates the reflectance per solid angle in a specified direction, namely, the quantity $f_{\rm r}(\theta_{\rm i},\theta_{\rm s},\phi_{\rm s})\cos\theta_{\rm s}$. When a user specifies a DIFFERENTIAL integral, the following dialog box opens:
Notice that, by default, the variable incidentpol is used as the incident polarization. Any Stokes vector may be substituted for incidentpol. The polarization sensitivity should be set to a four-element Stokes vector.
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Latest MIST Version: 4.10 (October 2017)