Functions involving Bessel Functions.

Functions
template<typename T1 , typename T2 >
T2	mx::math::func::bessel_j (T1 v, T2 x)
	Bessel Functions of the First Kind. More...

template<typename T >
T	mx::math::func::jinc (const T &x)
	The Jinc function. More...

template<typename T1 , typename T2 >
T2	mx::math::func::jincN (const T1 &v, const T2 &x)
	The JincN function. More...

Function Documentation

◆ bessel_j()

template<typename T1 , typename T2 >

T2 mx::math::func::bessel_j	(	T1	v,
		T2	x
	)

Bessel Functions of the First Kind.

This is a wrapper for boost.

Parameters

[in]	v
[in]	x

Definition at line 49 of file bessel.hpp.

Referenced by mx::sigproc::zernikeQNorm().

◆ jinc()

template<typename T >

T mx::math::func::jinc ( const T & x )

The Jinc function.

The Jinc function is defined here as

\[ Ji(x) = \frac{J_1(x)}{x} \]

where \( J_1 \) is the cylindrical bessel function of the first kind of order 1.

Follows the technique in boost sinc_pi, using the Taylor series for small arguments. If x is smaller than \( \epsilon \), then it returns 1/2. If x is larger than \( \epsilon \) but smaller than \( \sqrt{\epsilon} \), then this function returns

\[ Ji(x) \approx \frac{1}{2} - \frac{x^2}{16}. \]

Returns: the value of Ji(x)

Template Parameters

T	is an floating point type

Parameters

[in] x the argument

Definition at line 64 of file jinc.hpp.

Referenced by mx::math::func::airyPattern(), mx::AO::analysis::F_basic(), mx::AO::analysis::F_mod(), mx::AO::analysis::Fm_projMod(), mx::AO::analysis::jincFuncs(), mx::math::func::jincN(), mx::AO::analysis::vonKarmanSpectrum< realT >::operator()(), mx::AO::analysis::phiInt_basic(), mx::AO::analysis::phiInt_mod(), and mx::sigproc::zernikePPiston().

◆ jincN()

template<typename T1 , typename T2 >

T2 mx::math::func::jincN	(	const T1 &	v,
		const T2 &	x
	)

The JincN function.

The JincN function is defined here as

\[ Ji_N(x) = \frac{J_N(x)}{x} \]

where \( J_N \) is the cylindrical bessel function of the first kind of order N, \( N \ge 1 \).

If \( N == 1 \) this returns jinc(x).

Otherwise, if x is smaller than \( \sqrt{\epsilon} \), returns 0.

Returns: the value of JiN(x)

Parameters

[in]	v	the Bessel function order
[in]	x	the argument

Definition at line 120 of file jinc.hpp.

References mx::math::func::jinc().

Referenced by mx::AO::analysis::vonKarmanSpectrum< realT >::operator()(), mx::sigproc::zernikePAstig(), mx::sigproc::zernikePComa(), mx::sigproc::zernikePDefocus(), mx::sigproc::zernikePTipTilt(), and mx::sigproc::zernikePTrefoil().