Polynomial Surface Fitting

SigFit’s analysis capability can use polynomial fitting to represent in optical analysis deformations of optical surfaces or integrated OPD of transmissive optics.

Various forms of polynomials such as standard and fringe Zernike polynomials, X-Y polynomials, and aspheric polynomials can be formatted into files readable by market leading optical analysis tools. Tables of best-fit polynomial coefficients and measures of residual error may be written in various forms convenient for use in reports or subsequent processing.

An example polynomial fitting results table using standard Zernike terms is shown below.

Aberration Magnitude (Waves) Phase (Deg) Residual RMS Residual P-V
Input(wrt zero)   0 1638.2014 7383.8467
Bias           63.93217 0 1639.3527 7383.8467
Tilt           0.0009 -114 1639.3527 7383.8461
Power (Defocus) -593.9952 0 1613.9543 7383.8461
Pri Astigmatism 0.40118 -15 1613.9543 7383.315
Pri Coma        0.00031 3 1613.9543 7383.3148
Pri Spherical   327.16237 0 1608.2828 7383.3148
Pri Trefoil     4239.18502 0 272.9094 1504.1028
Sec Astigmatism 0.03627 75 272.9094 1504.0544
Sec Coma        0.00007 -88.1 272.9094 1504.0544
Sec Spherical   -74.16627 0 271.0498 1504.0544
Pri Tetrafoil   0.02494 -37.8 271.0498 1504.0379
Sec Trefoil     782.27234 60 102.8039 560.073
Ter Astigmatism 0.0058 -15.2 102.8039 560.0672
Ter Coma        0.00013 158 102.8039 560.0671
Ter Spherical   -1.49696 0 102.7954 560.0671
Pri Pentafoil   0.01876 30.2 102.7954 560.0493
Sec Tetrafoil   0.00704 7.2 102.7954 560.0496
Ter Trefoil     114.61334 0 95.8964 467.3619
Qua Astigmatism 0.0011 73.2 95.8964 467.362
Qua Coma       0.00016 24 95.8964 467.3624
Qua Spherical  -17.51442 0 96.0237 500.805
Qin Spherical  14.76491 0 95.7229 459.3212

The polynomial fitting tables show the term coefficients and residual surface error metrics after each polynomial term is subtracted.