In this paper, we seek to establish reliable methods for extracting energy spectra for TeV gamma-ray sources observed using the atmospheric Cherenkov Imaging Technique. Careful attention has been paid to the calculation of the telescope gain, and we obtain good agreement between direct measurements, with a statistical error of about 10%, and an absolute calibration from the background cosmic-ray trigger rate that has an overall error of 18%. Two independent analyses that are based on different Monte Carlo shower simulations, employ different selection criteria in order to retain a large fraction of gamma-ray events, and use different approaches to spectral estimation are presented here. The first is a fairly traditional method that builds on established image selection techniques and calculates the detector collection area and an energy estimation function. The error in measuring the enrgy of a single event is estimated at 36%, and we try to compensate for this poor energy resolution. The second analysis uses more elegant gamma-ray selection criteria and implicity incorporates the properties of the detector into the simulations that are then compared with the data in order to obtain source spectra. The two simulations are compared to each other and to the data, with the aim of establishing that each method is robust and insensitive to simulation details. Finally, we consider the main sources of systematic errors, the largest of which is in the telescope gain calibration, arising from an incomplete knowledge of the relevant factors, and is estimated to be 16%. The effect of possible errors in the simulations is also considered. Both methods have been applied to a part of the Whipple observatory database on the Crab Nebula for the 1988/89 observing season, while the first method has also been applied to data taken in 1995/96. The statistical error in the flux constant is about 8% and that in the spectral index is about 5%, while the corresponding systematic errors are estimated to be 18% and 2%, respectively. The results presented here show good agreement between the two methods as well as between the two seasons. However, a comprehensive consideration of the implications of the derived spectra and a comparison to other work is addressed in another paper.

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{{Explor lien
   |wiki=    Wicri/Amerique
   |area=    CaltechV1
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     ISTEX:17B1B5B75052F3B686A5BA49D15C4702C83056D2
   |texte=   Measurement of TeV gamma-ray spectra with the Cherenkov imaging technique
}}