A method for calibrating an optical imaging spectrograph having physical properties and an array detector placed at a focal plane of the imaging spectrograph and having a horizontal plane and a predetermined number of horizontal plane pixels located at pixel coordinates (n), 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; and deriving a model of the optical imaging spectrograph, said model having spectrograph model parameters based on the physical properties of the optical imaging spectrograph, to approximate the detected spectrum; characterized in that said model of the optical imaging spectrograph is derived using a function-fitting technique that operates in intensity space where the number of observables is always equal to the number of horizontal plane pixels and the number of pixels being greater than the number of variable model parameters; wherein said method of calibrating an optical imaging spectrograph comprising the further steps of: forming an intensity function including said spectrograph model parameters, wherein said intensity function describes the spectrum to be measured by the optical imaging spectrograph as detected by the array detector, and refining said spectrograph model parameters with a residual function to minimize a residual difference between detected spectral intensities and spectral intensities calculated based on said intensity function, representing a wavelength-to-pixel location correlation. 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; and deriving a model of the optical imaging spectrograph, said model having spectrograph model parameters based on the physical properties of the optical imaging spectrograph, to approximate the detected spectrum; characterized in that said model of the optical imaging spectrograph is derived using a function-fitting technique that operates in intensity space where the number of observables is always equal to the number of horizontal plane pixels and the number of pixels being greater than the number of variable model parameters; wherein said method of calibrating an optical imaging spectrograph comprising the further steps of: forming an intensity function including said spectrograph model parameters, wherein said intensity function describes the spectrum to be measured by the optical imaging spectrograph as detected by the array detector, and refining said spectrograph model parameters with a residual function to minimize a residual difference between detected spectral intensities and spectral intensities calculated based on said intensity function, representing a wavelength-to-pixel location correlation. forming an intensity function including said spectrograph model parameters, wherein said intensity function describes the spectrum to be measured by the optical imaging spectrograph as detected by the array detector, and refining said spectrograph model parameters with a residual function to minimize a residual difference between detected spectral intensities and spectral intensities calculated based on said intensity function, representing a wavelength-to-pixel location correlation.