mkh.h File Reference

Functions
dsp *	mkhb_cubic (const loc_t *locin, const loc_t *locout, real displacex, real displacey, real scale, real iac)
dsp *	mkh_cubic (const loc_t *locin, const loc_t *locout, real displacex, real displacey, real scale, real iac)
dsp *	mkhb (const loc_t *locin, const loc_t *locout, real displacex, real displacey, real scale)
dsp *	mkh (const loc_t *locin, const loc_t *locout, real displacex, real displacey, real scale)
dsp *	mkhbin1d (const dmat *xin, const dmat *xout)

Detailed Description

Contains functions that create ray tracing operator

Function Documentation

mkhb_cubic()

dsp* mkhb_cubic	(	const loc_t *	locin,
		const loc_t *	locout,
		real	displacex,
		real	displacey,
		real	scale,
		real	cubic_iac
	)

Create transpose of ray tracing operator from locin to locout using cubic influence function that can reproduce piston/tip/tilt.

mkh_cubic()

dsp* mkh_cubic	(	const loc_t *	locin,
		const loc_t *	locout,
		real	displacex,
		real	displacey,
		real	scale,
		real	cubic_iac
	)

Transposes the result from mkhb_cubic.

mkhb()

dsp* mkhb	(	const loc_t *	locin,
		const loc_t *	locout,
		real	displacex,
		real	displacey,
		real	scale
	)

Create transpose of mkh() result.

mkh()

dsp* mkh	(	const loc_t *	locin,
		const loc_t *	locout,
		real	displacex,
		real	displacey,
		real	scale
	)

Create ray tracing operator from coordinate locin to locout. Locin is required to be evenly spaced.

If vector Pin is defined on locin, Pout is defined on locout, H=mkh(locin, locout, ...), Pout=H*Pin does the bilinear interpolation.

If locin->iac is non zero, will call mkh_cubic to produce a cubical interpolation.

A cubic influence function that can reproduce piston/tip/tilt is coined by Ellerbroek to model the piezostack DM actuator. The influence has the form

\[ h(x;x_{i};\delta)=h_{0}((x-x_{i})/\delta) \]

where \(\delta\) is the same as the grid spacing, and \(h_{0}\) is the influence function defined in the normalized coordinates

\begin{eqnarray*} h_{0}(x)=\frac{1}{1+2c}\begin{cases} 1+(4c-\frac{5}{2})|x|^{2}+(\frac{3}{2}-3c)|x|^{3} & |x|\leq1\\ (2c-\frac{1}{2})(2-|x|)^{2}+(\frac{1}{2}-c)(2-|x|)^{3} & 1<|x|\leq2\\ 0 & |x|>2\end{cases}\end{eqnarray*}

where c is the nearest neighbor coupling frequency. The leading coefficient is to normalize the influence function so that it sums to 1.

mkhbin1d()

dsp* mkhbin1d	(	const dmat *	xin,
		const dmat *	xout
	)

Create a matrix to bin from coordinate xin to xout using bilinear interpolation. xin and xout should be 1-d arrays of coordinates. We require the coordinates to order incrementally monotonically, but do not require them to be evenly spaced.