Five motivating problems: constructibility in geometry, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures.
The error resources mainly include material property error, geometrical error, dimension error, load error and measuring error.
This novel method has been verified by experiments both in the laboratory and the forging workshop for hot heavy forging pieces, with a dimension error of less than 2%.
A four-step matrix can be constructed, building upon the three dimensions: systematic error, random error, and design error.
The matrix is constructed from the three dimensions of errors: systematic error ('bias'), random error ('play of chance'), and design error ('wrong design to answer the question posed' or 'wrong context').
Cavities with three kinds of dimension errors are also calculated.
The actual profiles of the reflector and SOE before coating the thin film are compared to the designed profiles to investigate the dimension errors and their influence on optical performance.
Based on the concept of equivalent linkage and the derived correlation between the radial-dimension errors and the normal-direction errors of the cam profile, the sensitivity analysis method for equivalent linkages is introduced for analyzing the tolerances in cam-modulated linkages, whose output error equations can be derived through an analytical means.
While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100).
Using the measured reflectivity spectrum, we then use inverse optimization to estimate the realized thin film dimensions, deposition error and unwanted oxidation volume.
This is where the three dimensions of error are of central importance in providing a tool for reliability assessment.
