To observe the polarimetric properties of an uncharacterized infrared transmitting material (IRTM) under various mechanical forces, a Mueller matrix (MM) imaging experiment was augmented with a force apparatus. Principal stress fields were computed from both finite element and closed-form models and spatially aligned with images of birefringence. The slope of the linear relationship between birefringence and principal stress difference is the stress optic coefficient. We discussed the advantages of MM polarimetry for stress optic coefficient measurements. First, no assumptions about the sample’s optical properties are necessary. Second, experimental deviations from the intended in-plane stress field can be identified. Third, independent pixels, over a small but appreciable range of stress values, can be selected to quantify experimental variation and improve statistical significance. To validate our experimental procedures, an N-BK7 sample was characterized at room temperature and compared with the industry-accepted value of 2.77 TPa−1±3% at 589.3 nm. To our knowledge, this is the first report on the stress optic coefficient of N-BK7 in the infrared, which was observed as 2.764±0.1526 TPa−1. The IRTM stress optic coefficient was observed to be 1.948±0.1197 TPa−1. Experimental sources of uncertainty are discussed and quantified.
The stress optic coefficient of an infrared transmitting material was measured at room temperature at a wavelength of 1550nm. This work discusses a Mueller matrix imaging experiment to measure the stress optic coefficient, observe the spatial distribution of birefringence, and quantify experimental sources of uncertainty. A one-inch diameter disk of sample material was diametrically loaded with increasing force, and linear retardance was measured in the central region. Finite element and analytical modeling was done to estimate the magnitude of stress in this central region. A Rotating Retarder Mueller Matrix Imaging Polarimeter measured the spatial distribution of linear retardance. The retardance is related to the change in birefringence with stress magnitude. The slope of this linear fit is the stress optic coefficient. The stress optic coefficient of the infrared transmitting material was measured to be 1.89 ± 0.1424 [TPa]−1. To test the precision of our stress optic coefficient measurement procedure, a 1-inch diameter N-BK7 disk was measured at a wavelength of 1550nm and compared with industry-accepted values. The stress optic coefficient of N-BK7 was measured as 2.83 ± 0.1057[TPa]−1. The published N-BK7 value measured at visible wavelengths is 2.77 [TPa]−1 ± 3%.1–3 This agreement validates the experimental Mueller matrix imaging methods and supports the common assumption of minor wavelength dependence of the stress optic coefficient.
Unit moment analysis minimizes the computational overhead associated with mirror mount design. Since mirrors operate in the linear domain with respect to stress/strain, it is possible to use the principle of superposition to determine overall optical surface deflection from a variety of sources. Surface deflection is calculated by FEA (finite element analysis) when applying unit loads at single mounting point. Deflection coefficients relating moments with surface deflection can be derived from the results of this analysis. These deflection coefficients are then applied, using the principle of superposition, to find the maximum tolerable moments associated with the mirror mount. Finally, manufacturing tolerances as well as environmental effects can be included to determine the required mirror mount compliance. This design approach is applicable to a wide range of mounting types, including classical kinematic and flexure mounts.
A method for transfer of Finite Element Analysis (FEA) results to the optical design program CODE V1 has been developed, although the method can be readily adapted to other optical design codes that support Zernike surfaces. This method is an improvement in many ways over the methods used in commercial codes written to perform this data transfer. The method assumes the surface nodal displacements are purely in the direction of the sag (z-axis) at the radial location of the displaced node point. This eliminates the approximations necessary when transferring the deformations as pseudo-interferograms, and eliminates the approximations made in the ray tracing of interferograms. Special techniques have been included to remove the inaccuracies introduced in the FEA program. The method has been validated on a series of test cases.
The detailed displacement data provided by finite element analysis (FEA) tools must be translated into forms acceptable by most optical ray tracing tools (CODE V specifically). A useful medium for transferring FEA data is the Zernike circular polynomials that many optical ray tracing tools will readily accept as input. However, the translation process is nontrivial, and two specific difficulties are explored in this paper. The first issue involves a coordinate space transformation that is required because the optically relevant coordinate system is not the same as the Cartesian coordinate system typically used in the finite element model. Several algorithms are described to perform this transformation and their pros and cons enumerated. Specifically, comparisons are made between sag based and surface normal (wavefront) based coordinate systems, and it is found that by using the sag equation of the original surface, the accuracy of the data translation can be improved. The second issue discussed is the accuracy of the polynomial fitting process. The loss of orthogonality stemming from undersampling, nonuniform mesh density, and annular surfaces are discussed with potential work-arounds.
Conference Committee Involvement (8)
Optomechanical Engineering 2019
14 August 2019 | San Diego, California, United States
Optomechanical Engineering 2017
9 August 2017 | San Diego, California, United States
Optomechanical Engineering 2015
11 August 2015 | San Diego, California, United States
Optomechanical Engineering 2013
27 August 2013 | San Diego, California, United States
Optomechanics 2011: Innovations and Solutions
23 August 2011 | San Diego, California, United States
Advances in Optomechanics
4 August 2009 | San Diego, California, United States
New Developments in Optomechanics
28 August 2007 | San Diego, California, United States
Optomechanics 2005
3 August 2005 | San Diego, California, United States
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