aoConstants.hpp

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/** \file aoConstants.hpp
 * \author Jared R. Males (jaredmales@gmail.com)
 * \brief Calculate and provide constants related to adaptive optics.
 * \ingroup mxAO_files
 *
 */
 
#ifndef mx_AO_analysis_aoConstants_hpp
#define mx_AO_analysis_aoConstants_hpp
 
#include <cmath>
 
#include "../../math/constants.hpp"
#include "../../math/func/gamma.hpp"
 
namespace mx
{
namespace AO
{
namespace constants
{
 
/// Calculate the AO constants
template <typename floatT>
void calcConstants( floatT &a_sf, floatT &a_psd )
{
    floatT pi = math::pi<floatT>();
 
    floatT gam1 = math::func::tgamma<floatT>( static_cast<floatT>( 6 ) / static_cast<floatT>( 5 ) );
 
    floatT gam2 = math::func::tgamma<floatT>( static_cast<floatT>( 11 ) / static_cast<floatT>( 6 ) );
 
    a_sf = pow( static_cast<floatT>( 24 ) / static_cast<floatT>( 5 ) * gam1,
                static_cast<floatT>( 5 ) / static_cast<floatT>( 6 ) );
 
    a_psd = a_sf * gam1 * gam1 * sin( static_cast<floatT>( 5 ) * pi / static_cast<floatT>( 6 ) ) /
            pow( pi, static_cast<floatT>( 11 ) / static_cast<floatT>( 3 ) );
 
    a_sf = a_sf * static_cast<floatT>( 2 );
}
 
/// The scaling constant for the Kolmorogov optical phase structure function
/** The optical phase structure function for Kolmogorov turbulence is
 * \f[
 * \mathcal{D}_\phi(r) = a_{SF} \left(\frac{r}{r_0}\right)^{5/3}
 * \f]
 *
 * This constant, given to 50 digits, was caculated using calcConstants with boost::multiprecision::cpp_dec_float_100
 * (100 digits of precision)
 *
 * \returns 6.883877.... cast to type floatT
 *
 * \tparam floatT is the type to cast the value to.
 * \ingroup aoConstants
 *
 */
template <typename floatT>
constexpr floatT a_SF()
{
    return static_cast<floatT>( 6.8838771822938116152935575630969803178936813057678 );
}
 
/// The scaling constant for the Kolmorogov optical phase power spectral density
/** The optical phase PSD for Kolmogorov turbulence is
 * \f[
 * \mathcal{P}_\phi(k) = a_{PSD} \left(\frac{1}{r_0^{5/3} k^{11/3}}\right)
 * \f]
 *
 * This constant, given to 50 digits, was caculated using calcConstants with boost::multiprecision::cpp_dec_float_100
 * (100 digits of precision)
 *
 * \returns 0.02181... cast to type floatT
 *
 * \tparam floatT is the type to cast the value to
 *
 * \ingroup aoConstants
 */
template <typename floatT>
constexpr floatT a_PSD()
{
    return static_cast<floatT>( 0.0218139977034218241674821945866523430205216037234 );
}
 
} // namespace constants
} // namespace AO
} // namespace mx
 
#endif // mx_AO_analysis_aoConstants_hpp