Method for calibrating imaging spectrographs
Disclosed is a method for calibrating optical spectrographs, and in particular optical spectrographs having focal plane array detectors. The method comprises the steps of detecting a spectrum of a known source, referencing a table of known spectral wavelengths and relative intensities, and deriving a spectrograph model based on the spectrograph's physical properties to approximate the observed spectrum, wherein non-linear optimization techniques refine the theoretical model parameters, thereby minimizing the residual difference between observed and calculated spectral intensities in an iterative process producing a set of physical model parameters that best describe the modeling spectrograph for calibration of subsequent spectral acquisitions.
1. A method for calibrating an optical spectrograph adapted to disperse light in a horizontal plane, having physical properties and a detector having a predetermined number of horizontal plane pixels, comprising the steps of:
detecting a spectrum of a known source;
referencing a table of known emission line wavelengths and known relative intensities, or known Raman vibration frequencies and relative intensities, or known intensity spectrum from a NIST calibrated intensity standard;
deriving a spectrograph model in terms of model parameters based on the physical properties of the modeling spectrograph, using a function-fitting technique that functions in intensity space to approximate the observed spectrum;
forming a single intensity function based on said model spectrograph parameters and
refining said spectrograph model parameters with a residual function to minimize residual difference between observed spectral intensities and spectral intensities calculated based on said intensity function.
2. The method of claim 1 , wherein the optical spectrograph comprises focal plane array detectors.
3. The method of claim 1 , wherein the step of detecting an observed spectrum includes measuring a number of observables that is always equal to the number of horizontal plane pixels.
4. The method of claim 1 , wherein said spectrograph model parameters comprise the focal length of the mirrors (f), included angle between the primary focusing and collimating mirrors (γ), and the tilt to the image plane (δ).
5. The method of claim 1 , wherein said residual function is solved to obtain model parameters that are correlated to the spectrograph that minimize the residual differences across said observed spectrum.
6. The method of claim 1 , wherein said the intensity function represents a wavelength-to-pixel location correlation.
7. The method of claim 1 , wherein in said known source is selected from the group consisting of an emission line source, a previously calibrated Raman or fluorescence spectrum, and a spectrum from a NIST calibrated intensity standard.