A Generalized Combinatorial Technique for Linearity Calibrations Applied to Optical Detectors and Spectrographs

For many quantities, indicating instruments are calibrated only at a limited number of values, and the extension of the calibrations to higher or lower values must rely upon the linearity of the instruments. A method for calibrating or determining the linearity of instruments that exploits the combinatorial properties of a set of different-valued, and mostly uncalibrated, artefacts is described. The presentation describes the underlying principles of the method, its limitations, and examples of the application of the method to very different quantities: mass balances, resistance bridges, optical detectors and spectrographs. The resulting uncertainty due to linearity can be assigned from the residuals of the fitted functional form of the linearity function to the measured signals.

The implementation of this combinatorial method with the NIST Beamconjoiner apparatus is described, and calibrations of visible and infrared photodiodes, and spectrographs for internal and external customers are shown. This method is shown to be capable of determining linearities in the visible and infrared wavelength region to uncertainties of 200 ppm or 0.02 % (k=2). Linearities of spectrographs at a set integration time and as a function of integration times can be measured using this approach. Experimental setups to characterize focal plane arrays placed in cryo-vac chambers will be discussed.