astro

Class Aperture

java.lang.Object

astro.Aperture

public class Aperture
extends Object

This class uses an recursive algorithm to determine the area of intersection of a quadratic pixel with an arbitrary aperture. The algorithm can be outlined as follows:

• Start with split level i=0, center is the center of the pixel, side length s=1.
• Check, if the pixel intersects with the aperture.
• If no, return (inside ? 1 : 0)*s_i^2.
• If yes, and the current split level is below the maximum split level n_max, split the parental (sub)pixel into four children with half the side length s_i+1=0.5*s_i and at center x,y_i+1 = x,y_i+/-s_i+1*0.5
• Reenter method until subpixel is either completely inside/outside the aperture or the maximum split level is reached.
• If the maximum split level is reached, return 0.5*s_i

This algorithm is rather efficient, as splitting is done only at the aperture's border, it's only weakness is that there is no way of exactely determining the error made, the maximum error is 0.5 times number of final splites times 1/2^(2nmax). Generally, this would be 1/2^(nmax+1). For a circular aperture at 0,0, radius 1 some test were made

 splitlevel     area                  error
        1        0.5                   0.2853981633974483
        3        0.71875               0.06664816339744828
        5        0.775390625           0.010007538397448279
        7        0.7843017578125       0.001096405584948279
       10        0.7853221893310547    7.59740663935915E-5
       15        0.7853977028280497    4.605693986192705E-7
       20        0.7853981612443022    2.1531461058543755E-9
 

For a circular aperture at 100.123, 100.574, diameter 10.23 adding all pixel areas and comparing it to the total known area of (5.115)^2*PI

 splitlevel     area                  error (dA/A)
        1        82.5                  0.0037067217670689635
        3        82.25                 6.784747207682614E-4
        5        82.1943359375         1.7091601457346031E-6
        7        82.1939697265625      2.7462799894133292E-6
       10        82.19415760040283     4.6054141904468886E-7
       15        82.19419539812952     6.823752873478206E-10
       20        82.19419545471465     6.056810455152413E-12
 

Default split level is 10. Note that Sun's implementation of the PathIterator of an ellipse only uses 4*6 points, making it unfavourable to use code like this:

 annulus = new Area(Ellipse2D(80., 80., 20., 20.);
    annulus.subtract(new Area(Ellipse2D(90., 90., 10., 10.)
 

Better results are acheived with two Apertures made from Ellipses and then manually subtract the results.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Aperture.Circular Test the aperture class on a criculare aperture at center zero, zero and with radius 1.
static class	Aperture.Circular100 Test the aperture class on a circulare aperture at center 100, 100 and with radius 10, for x,y = 0->200
private class	Aperture.Pixel A subpixel of the CCD-pixel.

Field Summary

Fields

Modifier and Type	Field and Description
private Shape	aperture The aperture area.
private int	splitmax The maximum split level, defaults to 10.

Constructor Summary

Constructors

Constructor and Description
Aperture(Shape pinhole) Constructs a new aperture class from a given Area that defines the aperture.
Aperture(Shape pinhole, int split) Constructs a new aperture class from a given Area that defines the aperture.

Method Summary

Modifier and Type	Method and Description
double	getInsideAperture(Point2D center) Returns the fractional part of the 1x1 pixel located at the central point passed to this argument within the aperture.
double	getInsideAperture(Point2D center, double width, double height) Returns the fractional part of the pixel with the given dimensions located at the central point passed to this argument within the aperture.
private double	intersect(Aperture.Pixel parent, Shape with) The recursive method that takes a pixel and returns its aperture weight or splits the pixel further if intersection is signaled and the maximum split level is not reached.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

splitmax

private int splitmax

The maximum split level, defaults to 10.

aperture

private Shape aperture

The aperture area.

Constructor Detail

Aperture

public Aperture(Shape pinhole)

Constructs a new aperture class from a given Area that defines the aperture. Fractional area inside the aperture for a pixel at a given position can now be retrieved with #getInsideApertue.

Aperture

public Aperture(Shape pinhole,
                int split)

Constructs a new aperture class from a given Area that defines the aperture. Fractional area inside the aperture for a pixel at a given position can now be retrieved with #getInsideApertue. If the argument is already an area, no new object is created.

Method Detail

getInsideAperture

public double getInsideAperture(Point2D center)

Returns the fractional part of the 1x1 pixel located at the central point passed to this argument within the aperture.

See Also:

#getInsideApertue(Point2D, double, double).

getInsideAperture

public double getInsideAperture(Point2D center,
                                double width,
                                double height)

Returns the fractional part of the pixel with the given dimensions located at the central point passed to this argument within the aperture.

See Also:

#getInsideApertue(Point2D)

intersect

private double intersect(Aperture.Pixel parent,
                         Shape with)

The recursive method that takes a pixel and returns its aperture weight or splits the pixel further if intersection is signaled and the maximum split level is not reached.