## Abstract

A phase screen ribbon extrusion process is presented that allows a phase screen ribbon of any specified width to be extruded, one column at a time, producing a ribbon of any desired length, with Kolmogorov statistics (i.e., having a five-thirds power-law-dependent structure function) for all separations up to some selected upper limit—which upper limit can be as large as desired. The method is an adaptation of the method described by [
Assémat *et al.*Opt. Express **14**, 988 (2006)
].

© 2008 Optical Society of America

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### Equations (7)

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(1)
$${\mathbf{P}}_{\mathbf{xx}}=\u27e8{\mathbf{xx}}^{\mathrm{T}}\u27e9,\phantom{\rule{1em}{0ex}}{\mathbf{P}}_{\mathbf{zz}}=\u27e8{\mathbf{zz}}^{\mathrm{T}}\u27e9,\phantom{\rule{1em}{0ex}}{\mathbf{P}}_{\mathbf{xz}}=\u27e8{\mathbf{xz}}^{\mathrm{T}}\u27e9,\phantom{\rule{1em}{0ex}}{\mathbf{P}}_{\mathbf{zx}}=\u27e8{\mathbf{zx}}^{\mathrm{T}}\u27e9.$$
(2)
$$\mathbf{x}=\mathbf{Az}+\mathbf{Bg},$$
(3)
$$\mathbf{A}={\mathbf{P}}_{\mathbf{xz}}{\mathbf{P}}_{\mathbf{zz}}^{-1},\phantom{\rule{1em}{0ex}}\mathbf{B}=\sqrt{{\mathbf{P}}_{\mathbf{xx}}-{\mathbf{P}}_{\mathbf{xz}}{\mathbf{P}}_{\mathbf{zz}}^{-1}{\mathbf{P}}_{\mathbf{zx}}},$$
(4)
$$\mathbf{x}=[\mathbf{A}(\mathbf{z}-{z}_{\mathrm{Ref}})+\mathbf{Bg}]+{z}_{\mathrm{Ref}},$$
(5)
$$\u27e8(\alpha -\gamma )(\beta -\gamma )\u27e9=-{\scriptstyle \frac{1}{2}}\u27e8{(\alpha -\beta )}^{2}\u27e9+{\scriptstyle \frac{1}{2}}\u27e8{(\alpha -\gamma )}^{2}\u27e9+{\scriptstyle \frac{1}{2}}\u27e8{(\beta -\gamma )}^{2}\u27e9.$$
(6)
$${\sigma}^{2}=\frac{2}{{\mathcal{N}}_{\mathrm{RR}}{\mathcal{N}}_{\mathrm{Pairs}}}+(\frac{1}{2{\mathcal{N}}_{\mathrm{RR}}}-\frac{1}{2{\mathcal{N}}_{\mathrm{RR}}{\mathcal{N}}_{\mathrm{Pairs}}})\stackrel{\u0303}{V}(\frac{p}{P},\frac{q}{Q}),$$
(7)
$$\stackrel{\u0303}{V}(\mu ,\nu )={[{\mu}^{2}+{\nu}^{2}]}^{-5\u22153}{\int}_{-(1-\mid \mu \mid )}^{+(1-\mid \mu \mid )}\mathrm{d}x{\int}_{-(\zeta -\mid \nu \mid )}^{+(\zeta -\mid \nu \mid )}\mathrm{d}y\left[\frac{1-\mid \mu \mid -\mid x\mid}{{(1-\mid \mu \mid )}^{2}}\right]\left[\frac{\zeta -\mid \nu \mid -\mid y\mid}{{(\zeta -\mid \nu \mid )}^{2}}\right]{({[{(x+\mu )}^{2}+{(y+\nu )}^{2}]}^{5\u22156}+{[{(x-\mu )}^{2}+{(y-\nu )}^{2}]}^{5\u22156}-2{[{x}^{2}+{y}^{2}]}^{5\u22156})}^{2}.$$