Slit function can be simply assumed to be a rectangular one; image of entrance slit is the superposition integral of the entrance slit with the optical system Point Spread Function (PSF); if the optical system satisfies spatially invariant condition, the superposition integral can be replaced by convolution .
Further data processing is conducted as follows: several data points near the nominal peak are parabolic fitted to get the finer resolving peak wavelength and the corresponding maximum response; then a superposition integral of the SRF over the horizontal wavelength coordinate is performed, while the wavelength coordinate may be not linear as it is nonlinearly inverse mapped from the computing grid; finally, the effective FWHM is obtained by dividing the throughput of the SRF by the maximum response.
Then the replacement of (3) and (6) can be rewritten in the form of the superposition integral as follows:
This superposition integral can be considered as a convolution.
For input strains having arbitrary time histories, the generalized stress resulting from the Boltzmann superposition integral
may be given by
Most single-integral nonlinear theories are essentially modifications of the Boltzmann superposition integral
. Findley's modified superposition principle (4), one example of a nonlinear single-integral constitutive equation, has been used extensively to describe the nonlinear behavior of various polymeric materials (4,5).