= Linear canonical transformation
{title2=$\mathcal L_{A,B,C,D}$}
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= Linear canonical transform
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A family of <integral transforms> associated with a two-by-two real <matrix> of determinant one. For $B\ne0$, one optical normalization has kernel proportional to $\exp[ik(Ax^2+Dx'^2-2xx')/(2B)]$. It includes free-space <Fresnel diffraction>, quadratic phase multiplication and the <Fourier transform>. The optical amplitude normalization in one transverse dimension is $1/\sqrt{i\lambda B}$ with a consistent phase branch.
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