Method and apparatus for accurately calibrating a spectrometer

A calibration assembly for a spectrometer, the assembly comprising:

• a spectrometer having first through one hundredth detector elements, each of the first through one hundredth detector elements being assigned predetermined respective wavelength values (λ1, λ2, . . . λ100);
• a first source emitting a first radiation for calibrating the spectrometer;
• a device placed in the path of the first radiation to split the first radiation into a first beam and a second beam;
• wherein one of the first and second beams travels a path-difference distance (d) longer than the other of the first and second beams;
• wherein the spectrometer is configured to generate an actual output signal when the first beam and the second beam enter the spectrometer;
• a controller operable for processing the actual output signal;
• wherein the controller is adapted to calculate respective correction factors for the respective wavelength values by comparing the actual output signal with a theoretically-predicted output signal;
• a first blocking device to selectively block the first beam and a second blocking device to selectively block the second beam;
• wherein the spectrometer is configured to generate a reference signal when the first beam is selectively blocked and the second beam enters the spectrometer;
• wherein the spectrometer is configured to generate a dark signal when the first beam and the second beam are selectively blocked from entering the spectrometer;
• an algorithm stored on and executable by the controller to cause the controller to;
• determine a dark-corrected reference signal by subtracting the dark signal from the reference signal;
• determine a dark-corrected output signal by subtracting the dark signal from the output signal;
• determine an actual normalized output by dividing the dark-corrected output signal by the dark-corrected reference signal;
• correlate the actual normalized output with a correlation function to determine a first function, the correlation function and the first function having a variable parameter z;
• determine a first-approximation for the path-difference distance (d) occurring at a maximum value for the first function;
• add an integration correction factor to the first function to obtain a second function;
• and
• determine the path-difference distance between the first beam and the second beam, the path-difference distance occurring at a maximum value for the second function;
• wherein the correlation function is represented by an array [(cos(2πz/λ1))/λ1, (cos (2πz/λ2))/λ2, . . . , cos(2πz/λ100))/λ100,];
• and
• wherein the first function is approximated by an expression {Σi=1 to 100[(1+cos (2πd/λi))] cos(2πz/λi)(Δλi/λi)}, such that Δλi is a spacing between respective wavelengths.