ok, Im looking at the circuit and i will do my best, please correct me.
As I see it, when the transistor receives light it opens up for current. There will be no voltage going into the inverting port because the non-inverting port is grounded. In the LC circuit we have a alternating current and I guess that why we have a diode.
The capacitor stores the current peak voltage. If the input voltage is larger, the op-amp output goes positive until the capacitor is charged up to the new peak value. If the input voltage is smaller, the diode keeps the capacitor from being discharged.
Thats where im at.