Optics, image processing, and star identification. More...

Files
file	sc_optics.h
	Optical functions and types.

file	sc_star_catalog.h
	Star catalog class definitions.

file	sc_star_image.h
	Star image processing functions.

Classes
struct	camera_data_s

struct	psf_data_s
	Structure for storing point spread function data. More...

struct	gaussian_psf_s
	Structure for implementing a Gaussian psf. More...

struct	airy_psf_s
	Structure for implementing an Airy psf. More...

struct	airydefocused_psf_s
	Structure for implementing a defocused Airy psf. More...

class	ImagePSF
	Helper class for matching PSFs to images. More...

class	star
	Star object. More...

class	star_catalog
	Star catalog. More...

struct	star_triad
	Star triad structure. More...

class	near_matrix
	Near matrix class. More...

class	star_meas
	Identifies stars from a star catalog assuming a pinhole camera model. More...

Typedefs
typedef struct camera_data_s	camera_data_t

typedef struct psf_data_s	psf_data_t
	Structure for storing point spread function data.

typedef gaussian_psf_s	gaussian_psf_t
	Structure for implementing a Gaussian psf.

typedef airy_psf_s	airy_psf_t
	Structure for implementing an Airy psf.

typedef airydefocused_psf_s	airydefocused_psf_t
	Structure for implementing a defocused Airy psf.

typedef struct star_triad	StarTriad
	Star triad structure. More...

Functions
double	effective_focal_length (ml_matrix distance, ml_matrix focal_length)
	Computes effective focal length. More...

double	diffraction_limit (double lambda, double aperture)
	Diffraction resolution limit. More...

ml_matrix	angle_of_view (double focal_length, ml_matrix d)
	Angle of view from focal length with a 2D input. More...

double	angle_of_view (double focal_length, double d)
	Angle of view from focal length with a 1D input. More...

ml_matrix	angle_of_view (ml_matrix focal_length, double d)
	Angle of view from a matrix of focal lengths with a 1D input. More...

double	focal_length_from_angle_of_view (double alpha, double d)
	Focal length from angle of view. More...

ml_matrix	separation_angles (ml_matrix u)
	Separation angles and pairs.

ml_matrix	pix_to_u (ml_matrix p, double f)
	Converts a pixel map to a unit vector assuming a pinhole camera model. More...

ml_matrix	u_to_pix (const ml_matrix &r, double f, double row=0, double col=0)
	Converts a unit vector to a pixel map assuming a pinhole camera model. More...

double	laser_beam_radius (double d, double lambda, double z)
	Laser beam radius. More...

double	laser_power (double d, double lambda, double z, double power)
	Laser power. More...

camera_data_t	camera_calibration (const ml_matrix &pD, const ml_matrix &pW)
	Camera calibration. More...

ml_matrix	calibration_cube (double w, double r, int n)
	Camera cube. More...

ml_matrix	camera_calibration_model (camera_data_t d, const ml_matrix &pW, double f)
	Camera model. More...

ml_matrix	imager_psf (ml_matrix PSF(const ml_matrix &x, const ml_matrix &y, void context), psf_data_t d)
	Imager with point spread functions. More...

void	imager_psf_uint16 (ml_matrix PSF(const ml_matrix &x, const ml_matrix &y, void context), psf_data_t d, uint16_t *frame)
	Imager with point spread function return a uint16_t array. More...

int	any_less_than (const ml_matrix &x, double d)
	Find if any value of x is less than d. More...

ml_matrix	rhs_gaussian_psf (const ml_matrix &x, const ml_matrix &y, void *context)
	Gaussian point spread function. More...

ml_matrix	rhs_airy_psf (const ml_matrix &x, const ml_matrix &y, void *context)
	Airy point spread function. More...

ml_matrix	rhs_airy_defocused_psf (const ml_matrix &x, const ml_matrix &y, void *context)
	Defocused Airy point spread function. More...

ml_matrix	rand_pn (double f, int n, int m)
	Poisson random matrix. More...

ml_matrix	fit_PSF_to_data (const ml_matrix &r0, const ml_matrix &intensity, const ml_matrix &pixels, int nUse, int mUse)
	Fit PSF to coarse centroid data using numerical optimization. More...

double	cost_psf (const ml_matrix &x, void *context)
	PSF cost function.

Detailed Description

Optics, image processing, and star identification.

Structure for storing camera data.

Typedef Documentation

◆ StarTriad

typedef struct star_triad StarTriad

Star triad structure.

Stores the integer ID of the three stars in the triad.

Function Documentation

◆ effective_focal_length()

double effective_focal_length	(	ml_matrix	distance,
		ml_matrix	focal_length
	)

Computes effective focal length.

Parameters

distance	Array of distances between lenses
focal_length	Array of lens focal lengths

Returns: Effective focal length

◆ diffraction_limit()

double diffraction_limit	(	double	lambda,
		double	aperture
	)

Diffraction resolution limit.

Parameters

lambda	Wavelength
aperture	Width of aperture

Returns: Diffraction limited resolution

◆ angle_of_view() [1/3]

ml_matrix angle_of_view	(	double	focal_length,
		ml_matrix	d
	)

Angle of view from focal length with a 2D input.

Parameters

focal_length	Focal length
d	Width of imaging chip

Returns: Angle of view

◆ angle_of_view() [2/3]

double angle_of_view	(	double	focal_length,
		double	d
	)

Angle of view from focal length with a 1D input.

The width and focal length must have the same units.

Parameters

focal_length	Focal length
d	Width of imaging chip

Returns: Angle of view

◆ angle_of_view() [3/3]

ml_matrix angle_of_view	(	ml_matrix	focal_length,
		double	d
	)

Angle of view from a matrix of focal lengths with a 1D input.

Parameters

focal_length	Focal length
d	Width of imaging chip

Returns: Angle of view

◆ focal_length_from_angle_of_view()

double focal_length_from_angle_of_view	(	double	alpha,
		double	d
	)

Focal length from angle of view.

Parameters

alpha Angle of view

Returns: Width of imaging chip

◆ pix_to_u()

ml_matrix pix_to_u	(	ml_matrix	p,
		double	f
	)

Converts a pixel map to a unit vector assuming a pinhole camera model.

Parameters

p	Pixel coordinates
f	Focal length in pixel units

Returns: Unit vectors

Referenced by star_meas::Pyramid().

◆ u_to_pix()

ml_matrix u_to_pix	(	const ml_matrix &	r,
		double	f,
		double	row,
		double	col
	)

Converts a unit vector to a pixel map assuming a pinhole camera model.

Includes an offset. If row and col are zero then 0,0 is the center of the imager.

Parameters

r	Position vector
f	Focal length in pixels

Returns: [col;row] in pixel frames

Referenced by PinholeCamera::Update().

◆ laser_beam_radius()

double laser_beam_radius	(	double	d,
		double	lambda,
		double	z
	)

Laser beam radius.

Parameters

d	Aperture (m)
lambda	Wavelength (m)
range	(m)

Returns: Beam radius (m)

References PI.

Referenced by laser_power().

◆ laser_power()

double laser_power	(	double	d,
		double	lambda,
		double	z,
		double	power
	)

Laser power.

Parameters

d	Aperture (m)
lambda	Wavelength (m)
range	(m)
power	(m)

Returns: Beam radius (m)

References laser_beam_radius().

◆ camera_calibration()

camera_data_t camera_calibration	(	const ml_matrix &	pD,
		const ml_matrix &	pW
	)

Camera calibration.

Parameters

d	Measured coordinates (m)
pW	World points (m)

Returns: Camera parameters

References camera_data_s::alpha, camera_data_s::f, camera_data_s::k1, camera_data_s::k2, camera_data_s::o, orthogonalize(), pinv(), camera_data_s::R, camera_data_s::s, and camera_data_s::T.

◆ calibration_cube()

ml_matrix calibration_cube	(	double	w,
		double	r,
		int	n
	)

Camera cube.

Parameters

w	Width of square (m)
r	Cube width (m)
n	Number of squares

Returns: Points of square corners

◆ camera_calibration_model()

ml_matrix camera_calibration_model	(	camera_data_t	d,
		const ml_matrix &	pW,
		double	f
	)

Camera model.

Parameters

d	Camera data structure
pW	World points (m)

Returns: Points in pixel frame

References camera_data_s::o, camera_data_s::R, camera_data_s::s, and camera_data_s::T.

◆ imager_psf()

ml_matrix imager_psf	(	ml_matrix	PSFconst ml_matrix &x, const ml_matrix &y, void *context,
		psf_data_t *	d
	)

Imager with point spread functions.

The functions are integrated using two_dimensional_integration().

Parameters

PSF	Point spread function
d	Data to be passed to PSF

Returns: Imager pixel values (n,m)

References any_less_than(), psf_data_s::m, psf_data_s::n, psf_data_s::r, two_dimensional_integration(), psf_data_s::x_pixel, and psf_data_s::y_pixel.

Referenced by cost_psf().

◆ imager_psf_uint16()

void imager_psf_uint16	(	ml_matrix	PSFconst ml_matrix &x, const ml_matrix &y, void *context,
		psf_data_t *	d,
		uint16_t *	frame
	)

Imager with point spread function return a uint16_t array.

The functions are integrated using two_dimensional_integration().

Parameters

PSF	Point spread function
d	Data to be passed to PSF
frame	Frame uint16_t[n*m]

References any_less_than(), psf_data_s::m, psf_data_s::n, psf_data_s::r, two_dimensional_integration(), psf_data_s::x_pixel, and psf_data_s::y_pixel.

◆ any_less_than()

int any_less_than	(	const ml_matrix &	x,
		double	d
	)

Find if any value of x is less than d.

Parameters

x	matrix to be tested
d	value to test again

Returns: 1 if any value is less thand d

Referenced by imager_psf(), and imager_psf_uint16().

◆ rhs_gaussian_psf()

ml_matrix rhs_gaussian_psf	(	const ml_matrix &	x,
		const ml_matrix &	y,
		void *	context
	)

Gaussian point spread function.

This is in a format to be integrated by two_dimensional_integration. The context pointer should be data of type gaussian_psf_t to be passed to the PSF.

Parameters

x	x pixel coordinates
y	y pixel coordinates
context	Data including rPSF, iPSF, and sigma

Returns: psf

References psf_data_s::i, psf_data_s::r, and gaussian_psf_s::sigma.

Referenced by cost_psf().

◆ rhs_airy_psf()

ml_matrix rhs_airy_psf	(	const ml_matrix &	x,
		const ml_matrix &	y,
		void *	context
	)

Airy point spread function.

This function uses the Bessel function of the first kind, j1.

See also: j1, airy_psf_t

Parameters

x	(n,m) X coordinates (um)
y	(n,m) Y coordinates (um)
context	PSF data of type airy_psf_t

Returns: PSF output (n,m)

References airy_psf_s::aperture, airy_psf_s::f_length, psf_data_s::i, PI, psf_data_s::r, and airy_psf_s::wavelength.

◆ rhs_airy_defocused_psf()

ml_matrix rhs_airy_defocused_psf	(	const ml_matrix &	x,
		const ml_matrix &	y,
		void *	context
	)

Defocused Airy point spread function.

A spherical wavefront W yields an aberration-free image in the Gaussian image plane at a distance R. A defocused image is formed when observed in a plane at a distance z.

The defocused irradiance is:

I(r,z) = (2R/z)^2 | int_0^1 {exp(i B_d rho^2) J0( pi*(R/z)rho*r ) rho drho} |^2

where z is the distance to the defocused image plane and R is the distance to the Gaussian image plane. rho is r/a, 0 <= rho <= 1, and a is the (half) aperture. B_d is the peak defocus phase aberration:

B_d(z) = pi a^2/(lambda*R) * (R/z - 1)

where lambda is the wavelength.

The defocused Airy function requires numerical integration. A trapezoid method is used for speed.

Parameters

x	X coordinates (n,m)
y	Y coordinates (n,m)
context	Data required by PSF

Returns: PSF output (n,m)

See also: airydefocused_psf_s

References airy_psf_s::aperture, airydefocused_psf_s::defocus, airy_psf_s::f_length, psf_data_s::i, PI, psf_data_s::r, trapezoidal_integration(), and airy_psf_s::wavelength.

◆ rand_pn()

ml_matrix rand_pn	(	double	lambda,
		int	n,
		int	m
	)

Poisson random matrix.

Parameters

lambda	Parameter
n	Rows
m	Columns

Returns: Poisson random matrix

Referenced by imager_model::update().

◆ fit_PSF_to_data()

ml_matrix fit_PSF_to_data	(	const ml_matrix &	r0,
		const ml_matrix &	intensity,
		const ml_matrix &	pixels,
		int	nUse,
		int	mUse
	)

Fit PSF to coarse centroid data using numerical optimization.

Refine the pixel fit numerically using search via downhill_simplex().

Parameters

r0	Estimated centroids from COM method (2,n)
intensity	Measured intensity (1,n)
pixels	Pixel data (:,:)

Returns: Updated centroid locations

References cost_psf(), downhill_simplex(), psf_data_s::i, psf_data_s::m, psf_data_s::n, ImagePSF::psf_data, psf_data_s::r, gaussian_psf_s::sigma, psf_data_s::x_pixel, and psf_data_s::y_pixel.

Files

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ StarTriad

Function Documentation

◆ effective_focal_length()

◆ diffraction_limit()

◆ angle_of_view() [1/3]

◆ angle_of_view() [2/3]

◆ angle_of_view() [3/3]

◆ focal_length_from_angle_of_view()

◆ pix_to_u()

◆ u_to_pix()

◆ laser_beam_radius()

◆ laser_power()

◆ camera_calibration()

◆ calibration_cube()

◆ camera_calibration_model()

◆ imager_psf()

◆ imager_psf_uint16()

◆ any_less_than()

◆ rhs_gaussian_psf()

◆ rhs_airy_psf()

◆ rhs_airy_defocused_psf()

◆ rand_pn()

◆ fit_PSF_to_data()