Method and apparatus for improvement of spectrometer stability, and multivariate calibration transfer
The present invention provides methods and apparatuses that can improve measurement accuracy in interferometers. The invention provides methods for determining digital compensation filters that measure a frequency response or responses to be compensated, and then determining a filter target response from the inverse of the frequency response or responses. A digital compensation filter can be determined from the filter target response using a discrete sum of cosines with a phase argument. The invention also allows other desired filter responses to be integrated into the filter target response before determining the digital compensation filter.
1. A method for determining a digital filter to compensate for a frequency response of one or more sources of error in the measurement of a spectrum with an interferometric spectrometer, comprising:
Step A, measuring the frequency response of one or more sources of error to be compensated;
Step B, determining a target filter response from an inverse of the cumulative response of the responses measured in Step A; and
Step C, determining a digital filter from the target filter response using a discrete sum of cosines with a phase argument.
2. A method as in claim 1 , wherein determining a target filter response further comprises combining the frequency responses of one or more band pass, low pass, or high pass frequency filters with the inverse of the responses measured in Step A.
3. A method as in claim 1 , further comprising apodization, truncation, or both of the digital filter determined in Step C.
4. A method as in claim 1 , wherein the interferometric spectrometer provides for optical path difference by motion of one or more optical components in either of two directions, wherein the method for measuring the frequency response of one or more sources of error comprises:
Step D, measuring double-sided interferograms of a polychromatic light source in both directions of optical component travel;
Step E, determining the frequency response difference substantially related to the difference between interferograms obtained from the two directions of optical travel.
5. A method as in claim 4 , comprising repeating Steps A and B while inducing different velocities on optical component travel, and combining the frequency responses obtained from the different velocities.
6. A method as in claim 1 , further comprising dynamically updating the digital filter for changes in the environment or operating conditions of the interferometric spectrometer, wherein the spectrometer provides for optical path difference by motion of one or more optical components in either of two directions, by
Step D, implementing the digital filter determined in Step C;
Step E, determining a frequency response at a subsequent time by:
Step E-i, measuring double-sided interferograms of the polychromatic light source in both directions of optical component travel;
Step E-ii, determining the frequency response difference substantially related to the difference between interferograms obtained from the two directions of optical component travel;
Step F, updating the frequency response from Step A with the frequency response in Step E;
Step G, determining a target filter response from the inverse of the response in Step F;
Step H, determining an updated digital filter from the updated target filter response of Step G using a discrete sum of cosines with a phase argument; and
Step I, implementing the digital filter of Step H.
7. A method as in claim 1 , further comprising dynamically updating the digital filter for changes in the environment or operating conditions of the interferometric spectrometer, wherein the spectrometer provides for optical path difference by motion of one or more optical components in either of two directions, by:
Step D, implementing the digital filter determined in Step C;
Step E, determining a frequency response at a subsequent time by:
Step E-i, measuring double-sided interferograms of the polychromatic light source in both directions of optical component travel; and
Step E-ii, determining the frequency response difference substantially related to the difference between interferograms obtained from the two directions of optical component travel;
Step F, determining an inverse of the frequency response from Step E
Step G, updating the target filter response from Step B of claim 1 with the inverse response from Step F;
Step H, determining an updated digital filter from the updated target filter response of Step G using a discrete sum of cosines with a phase argument; and
Step I, implementing the digital filter of Step H.
8. The method of claim 6 , further comprising repeating steps E through I one or more times.
9. The method of claim 7 , further comprising repeating steps E through I one or more times.