The effect of partial coherence of both the source and the detector in a scanning microscope is investigated. The transfer function for the system is derived and various special cases discussed. If the effective source and effective detector are coherent and incoherent, respectively, the microscope (Type 1) is of the form of the scanning transmission electron microscope (STEM). If the effective source and the effective detector are both coherent, the microscope (Type 2) is of the form of the scanning acoustic microscope. Scanning optical microscopes of both these types may be constructed. The effect of using a Type 2 scanning microscope in dark-field is discussed. This arrangement has the advantage over the Type 1 dark-field microscope that imaging for weak contrast specimens may be made linear.