
3.1.8 Error Analysis of Interferometric Retardance Measurements
Jack C.M. Wang Statistical Engineering Division, ITL
Kent B. Rochford Optoelectronics Division, EEEL A NIST effort to develop an accurate and stable retardance SRM has necessitated the development of measurement methods for optical retardance. Retardance is a property of devices commonly known as waveplates, which are used for polarization control. Three methods have been developed. Two methods rely on polarimetric techniques. The third one is based on an interferometric technique that exhibits different error sources and complements the polarimetric measurements.
The retarder is a doublerhomb design. The largest measurement
uncertainty arises from the reflectance of the rhomb faces.
This is because the laser used in this measurement system has a long
coherence length, multiple reflections from the rhomb faces can interfere
coherently and cause variations in retardance measurements. The error in
retardance due to coherent reflections is given by
where r is the reflectivity, is the retardance of rhomb, and U is a random variable and is uniformly distributed over the interval . The pdf of Y is found to be It can be shown that, for a wild range of , the mean of Yis 0 and the standard deviation of Y is proportional to the reflectivity r.
The doublerhomb retarder has endfaces with reflectance r_{a} and
an internal interface with reflectance r_{b}. The total retardance
error, resulting from multiple reflections between the endfaces and
between the internal interface and endfaces, is given by
where U_{1} and U_{2} are independent uniform random variables over the interval . If is close to , it can be shown that the mean of Z is 0 and the variance of Z is well approximated by 2(r^{2}_{a} + r^{2}_{b}). The results indicate that the noise is zeromean and antireflection coatings should be applied to rhomb faces to reduce the variation. A manuscript, describing the interferometric system and the detailed error analysis, has been submitted to Applied Optics.
Figure 8: The top figure displays the sample (based on 100000 simulated values of U) and population (solid line) pdfs of Y with r=0.01 and . The bottom plots the sample pdf of Z (based on 500000 simulated values of U_{1} and U_{2}) with r_{a}=0.002, r_{b}=0.006 and .
Date created: 7/20/2001 