In this blog measurement of optics in a harsh environment with a Fizeau interferometer is discussed.
For large systems, typically telescopes, vibration and air turbulence hinder or prevent the measurement phase by temporal phase shifting. Also interferometers placed on machine tools to measure in situ experience a vibrating environment. When vibration and turbulence hinder measurement then only a simultaneous phase measuring system (SPMI) will be able to acquire data. These systems acquire phase data fast enough to freeze fringe motion due to vibration and turbulence.
SPMI Data Acquisition: Multi-Camera and Carrier Fringe
There are two primary SPMI data acquisition architectures: Multi-camera1 and carrier fringe2 . Multi-camera uses polarization to split the intensity data into multiple images with shifted phases which are analyzed for wavefront phase. Carrier fringe uses tilt in the wavefront coupled with several different analytical approaches to extract phase. Both approaches are successfully employed commercially, and are functionally and performance equivalent.
Averaging is Required
The SPMI system enables phase to be acquired, but the phase is changing rapidly and by large amounts and any single measurement is meaningless. To achieve stable data, averaging must be employed. The amount of averaging required is a function of the frequency and amplitude of the vibration and turbulence. A useful method to determine how much averaging is required is to acquire 100 data sets in a series as would be performed in an average. Calculate the RMS or P-V of this data set, divide the RMS or P-V by the measurement repeatability desired to obtain a ratio. Square this ratio and set the average to this squared value. For example, if the single measurement repeatability is 6,000 nm P-V and desired is 60 nm P-V then 1002 averages must be taken, at a minimum, to achieve 60 nm P-V repeatability, assuming a gaussian distribution. It is often practical to stir the air with a fan to improve convergence, which can take many hours for large cavities with slowly moving fringes. SPMI systems can often acquire and calculate phase in seconds so averaging can be rapid.
Repeatability is Not Accuracy
Finally, note that repeatability is not low measurement uncertainty, or accuracy. Measurement uncertainty is primarily driven by the optical design of the interferometer, temperature variations in all the optics, mechanical stresses in mountings and optical misalignments and null lenses errors – a la Hubble. Controlling these is much harder than averaging and is a topic unto itself.
SPMI Interferometers are Non-Common Path – Hence Lower Accuracy
Also note SPMI systems are non-common path systems – the polarization paths are different or tilt exists between the test and reference wavefronts. These differing paths degrade the optical performance compared to PMI which can be common path, i.e. the test and reference beams perfectly overlap when a sphere or flat is measured in a nulled condition. So from an accuracy point of view PMI- nulled can outperform SPMI, but when data cannot be acquired due to turbulence or vibration then SPMI is required and an accuracy compromise is acceptable.
Summary
Acquiring data in harsh, vibrating and turbulent environments requires an SPMI data acquisition interferometer. Achieving high accuracy results requires careful attention to the all measurement parameters and is typically of lower accuracy than a nulled laser Fizeau phase shifting interferometer in a quiet environment.
1 Smythe, R & Moore, R; “Instantaneous Phase Measuring Interferometry”, Opt Eng, Jul/Aug 1984, 25(4):361 – 364
2 Takeda, M. “Spatial-carrier fringe-patter analysis and its applications to precision interferometry and profilometry: an overview, Ind Metrol 1990;1(2):79-99
