Increasing the measurement precision of optical instrumentation using Kalman-type filters

A system comprising:

• an optical instrument, configured to measure an optical property and comprising:
• an optical path having two reflective surfaces and a transmission medium therebetween, the two reflective surfaces separated by a distance, the transmission medium having an index of refraction, and
• a sensor configured to measure an environmental parameter that influences a magnitude of one or both of the distance and the index of refraction;
• a control system comprising one or more processors and memory storing instructions that are configured to perform operations when executed by the one or more processors, the operations comprising:
• determining, based on optical data and environmental data, a measured value of the optical property, wherein:
• the optical data is generated by the optical instrument in response to an optical signal traversing the optical path, and
• the environmental data is generated by the sensor measuring the environmental parameter;
• determining a predicted value of the optical property based on a model representing time evolution of the optical instrument;
• and
• calculating an effective value of the optical property based on:
• the measured value,
• the predicted value, and
• a Kalman gain based on respective uncertainties in the measured and predicted values, the Kalman gain defining a relative weighting of the measured and predicted values in the effective value.

A non-transitory computer-readable medium comprising instructions that are operable, when executed by one or more processors, to perform operations comprising:

• determining, based on optical data and environmental data, a measured value of an optical property measured by an optical instrument, wherein:
• the optical instrument comprises:
• an optical path having two reflective surfaces and a transmission medium therebetween, and
• a sensor configured to measure an environmental parameter of the transmission medium between the two reflective surfaces,
• the optical data is generated by the optical instrument in response to an optical signal traversing the optical path, and
• the environmental data is generated by the sensor measuring the environmental parameter;
• determining a predicted value of the optical property based on a model representing time evolution of the optical instrument;
• and
• calculating an effective value of the optical property based on:
• the measured value,
• the predicted value, and
• a Kalman gain based on respective uncertainties in the measured and predicted values, the Kalman gain defining a relative weighting of the measured and predicted values in the effective value.