  Very-high-energy (VHE, E>0.1 TeV) gamma-ray emission regions with angular
extents comparable to the field-of-view of current imaging air-Cherenkov
telescopes (IACT) require additional observations of source-free regions to
estimate the background contribution to the energy spectrum. This reduces the
effective observation time and deteriorates the sensitivity. A new method of
reconstructing spectra from IACT data without the need of additional
observations of source-free regions is developed. Its application is not
restricted to any specific IACT or data format. On the basis of the template
background method, which defines the background in air-shower parameter space,
a new spectral reconstruction method from IACT data is developed and studied,
the Template Background Spectrum (TBS); TBS is tested on published H.E.S.S.
data and H.E.S.S. results. Good agreement is found between VHE gamma-ray
spectra reported by the H.E.S.S. collaboration and those re-analysed with TBS.
This includes analyses of point-like sources, sources in crowded regions, and
of very extended sources down to sources with fluxes of a few percent of the
Crab Nebula flux and excess-to-background ratios around 0.1. However, the TBS
background normalisation introduces new statistical and systematic errors which
are accounted for, but may constitute a limiting case for very faint extended
sources. The TBS method enables the spectral reconstruction of data when other
methods are hampered or even fail. It does not need dedicated observations of
VHE gamma-ray-free regions (e.g. as the On/Off background does) and circumvents
known geometrical limitations to which other methods (e.g. the reflected-region
background) for reconstructing spectral information of VHE gamma-ray emission
regions are prone to; TBS would be, in specific cases, the only feasible way to
reconstruct energy spectra.
