Curve::Zernike class reference
[Core module]

This class is a member of the Curve namespace.

This class enables use of zernikes polynomials to define a surface curve. Zernikes terms can be enabled and disabled individually.

Fitting can be used to get best fit Zernike polynomials coefficients of an other curve.

This implementation uses Zernike polynomials set as described in ISO standard 10110-5.

Based on Zernikes pages by James C Wyant and Michael Koch. http://www.optics.arizona.edu/jcwyant/Zernikes/ZernikePolynomials.htm and http://www.astro-electronic.de/faq2.htm

See also the full member list section for this class.

• 5 members inherited from Base

• Zernike (double radius, double unit_scale = [...])
• Zernike (double radius, double coefs[], unsigned int coefs_count, double unit_scale = [...])
• virtual void derivative (const Math::Vector2 &xy, Math::Vector2 &dxdy) const
• double fit (const Base &c, const Trace::Distribution &d = [...])
• double get_coefficient (unsigned int n) const
• double get_radius () const
• bool get_term_state (unsigned int n)
• virtual double sagitta (const Math::Vector2 &xy) const
• void set_coefficient (unsigned int n, double c)
• void set_coefficients_scale (double s)
• void set_coefficients_threshold (double t)
• void set_radius (double radius)
• void set_term_state (unsigned int n, bool enabled)

• static double zernike_poly (unsigned int n, const Math::Vector2 &xy)
• static void zernike_poly_d (unsigned int n, const Math::Vector2 &xy, Math::Vector2 &dxdy)

• static const unsigned int term_count

Zernike(double radius, double unit_scale = 1.0)

Create a Zernike curve defined over the given circle radius.

• radius: Zernike circle radius
• unit_scale: Sagitta scale factor used to change units globally

Zernike(double radius, double coefs[], unsigned int coefs_count, double unit_scale = 1.0)

Create a Zernike curve defined over the given circle radius and initialize coefficients from table.

• radius: Zernike circle radius
• coefs: Table of Zernike coefficients starting with z0 (piston)
• coefs_count: Number of coefficients available in the table
• unit_scale: Sagitta scale factor used to change units globally

virtual void derivative(const Math::Vector2 &xy, Math::Vector2 &dxdy) const

This virtual function overrides the derivative virtual function defined in the Base base abstract class.

Documentation inherited from base class:

Get curve x and y derivative (gradient) at specified point

double fit(const Base &c, const Trace::Distribution &d = default_dist)

Compute all zernike coefficient to best fit the given curve. RMS difference is returned. The specified distribution is used to choose sampling points on curve. Terms state is adjusted according to current threshold

double get_coefficient(unsigned int n) const

Get coefficient associated with zernike term n

double get_radius() const

Get Zernike circle radius

bool get_term_state(unsigned int n)

Get current term enable state

virtual double sagitta(const Math::Vector2 &xy) const

This virtual function implements the sagitta pure function declared in the Base base abstract class.

Documentation inherited from base class:

Get curve sagitta at specified point

void set_coefficient(unsigned int n, double c)

Set coefficient associated with zernike term n and enable term according to current threshold. See set_coefficients_threshold()

void set_coefficients_scale(double s)

Set coefficients unit scale factor. default is 1 (1 mm).

void set_coefficients_threshold(double t)

Set new coefficient threshold and adjust all term states (enabled/disabled) depending on new threshold. Term with coefficient absolute value below the specified threshold will be disabled. Disabling useless terms improve performance. Default threshold is 10^-10.

void set_radius(double radius)

Set Zernike circle radius

void set_term_state(unsigned int n, bool enabled)

This functions must be used to enable/disable a zernike term without changing its coefficient

static const unsigned int term_count

Number of implemented zernike polynomials

static double zernike_poly(unsigned int n, const Math::Vector2 &xy)

Evaluate zernike polynomial n

static void zernike_poly_d(unsigned int n, const Math::Vector2 &xy, Math::Vector2 &dxdy)

Evaluate x and y derivatives of zernike polynomial n