For most physics studies at the LHC a calibration with electrons will be sufficient for both electrons and photons. For the H decay channel there will, however, be a significant gain in the mass resolution for a special energy calibration.
The idea for the H decay is to use the energy collected in a (,) = (0.075,0.125) window for non-converted photons and in a (,) = (0.075,0.175) for converted photons with separate energy calibrations. Converted photons produce wider showers especially in the direction where the magnetic field bend the electron tracks and by collecting the energy in an highly asymmetric window (,) = (0.075,0.175) , a better energy resolution can be achieved. The special calibration of converted and non-converted photons separately will have to rely on the difference to the electron calibration observed in testbeam measurements and Monte Carlo simulations.
As shown in section 6.3.2 it is possible to identify conversions with a high efficiency and a low rate of fake conversions. That converted photons are not identified if the conversion radius is above 80 cm or at |z| > 280 cm is fully acceptable as those conversions will open up very little and in almost all respects look like non-converted photons. There is a potential gain in further sub-dividing the sample of converted photons into separate samples depending on the reconstructed conversion radius with separate energy calibrations for each sub-sample, the limited amount of events simulated did not allow such an analysis.
As will be seen in the following section the separation of the photons in the H events into a converted and non-converted sample actually provides the main improvement in the H signal significance using the information from the Inner Detector.