Fourier transform fringe-pattern analysis of an absolute distance Michelson interferometer for space-based laser metrology

Future NASA proposals include the placement of optical interferometer systems in space for a wide variety of astrophysical studies including a vastly improved deflection test of general relativity, a precise and direct calibration of the Cepheid distance scale, and the determination of stellar masses (Reasenberg et al., 1988). There are also plans for placing large array telescopes on the moon with the ultimate objective of being able to measure angular separations of less than 10 $\mu$-arc seconds (Burns, 1990). These and other future projects will require interferometric measurement of the (baseline) distance between the optical elements comprising the systems. Eventually, space qualifiable interferometers capable of picometer $(10\rm\sp{-12}m)$ relative precision and nanometer $(10\rm\sp{-9}m)$ absolute precision will be required. A numerical model was developed to emulate the capabilities of systems performing interferometric noncontact absolute distance measurements. The model incorporates known methods to minimize signal processing and digital sampling errors and evaluates the accuracy limitations imposed by spectral peak isolation using Hanning, Blackman, and Gaussian windows in the Fast Fourier Transform Technique. We applied this model to the specific case of measuring the relative lengths of a compound Michelson interferometer using a frequency scanned laser. By processing computer simulated data through our model, the ultimate precision is projected for ideal data, and data containing AM/FM noise. The precision is shown to be limited by non-linearities in the laser scan. A laboratory system was developed by implementing ultra-stable external cavity diode lasers into existing interferometric measuring techniques. The capabilities of the system were evaluated and increased by using the computer modeling results as guidelines for the data analysis. Experimental results measured 1-3 meter baselines with $<$20 micron precision. Comparison of the laboratory and modeling results showed that the laboratory precisions obtained were of the same order of magnitude as those predicted for computer generated results under similar conditions. We believe that our model can be implemented as a tool in the design for new metrology systems capable of meeting the precisions required by space-based interferometers.