Spot - version 1.2
Spot is a Cocoa program that produces a scatter plot of up to 30000 random rays incident upon the mirror of a Newtonian telescope. Because it's limited to a single mirror you won't be able to design complicated optics with this program. It's purpose is to aid in understanding the concept of focus in optical systems, a concept that is not as clear cut as one might think.
Spot first generates 30000 parallel rays that randomly intersect the circular cross section of the Newtonian mirror. These rays originate outside the computer screen and point into the screen with up to a 5 degree downward tilt. This tilt is set by the bottom slider of the control window. A value of 0.0 means that the rays are parallel to the principle axis of the mirror. Sense the rays have no "x " component all spot diagrams will have left-right symmetry.
The vertical slider on the left of the control window positions the image plane along the principle axis. A value of 0.0 corresponds to the focal point of rays parallel to the principle axis reflected off a paraboloidal mirror. This is the only case in which parallel rays will focus to a point. The actual distance from the mirror to the focal point in this case is equal to half the radius of curvature of the mirror at it's center. Somewhat arbitrarily this distance is also used as the focal distance for spherical mirrors. In practice the best focus (smallest spot) for spherical mirrors is slightly closer to the mirror.
The Control Window shows the present state of the variables that describe the mirror. There are a number of controls in this window which for the most part are self explanatory. The two large toggle buttons on the top of the window violate the usual way buttons are used because they show their present value rather than what their value will be if they are pressed. The top most toggle button controls the way the spot diagrams are scaled. The default value is "Variable Scale" which produces a spot diagram which is as large as practical in it's window. Toggling this button to "Constant Scale" will lock the scale at whatever value it has at the moment. This can be used to graphically view the changes in size of the spot diagram with changing parameters. The other toggle button shows which of the two mirror shapes (Paraboloidal or Spherical) is presently being displayed.
The color coding pop-up menu assigns different colors to the rays depending on which part of the mirror they hit. This can help in determining how the mirror is mapped to the spot diagram. The large red dot corresponds to a ray striking the center of the mirror. The "y" coordinate of it's intersection with the image plane is displayed in the Control Window as "Off Axis:".
The Icon for Spot was found on the web. Unfortunately I'm no longer sure who the author is but will gladly give credit once I do.
Drawing the spot diagrams is much faster due to techniques given in the book Cocoa Programming by Anguish, Buck and Yacktman. This allows the use of many more rays, up to 30000 if you wish. It also allows the animation of the image and incidence sliders. Depending on the speed of your computer you may wish to use fewer rays to get acceptable slider animations.