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phototrack_tracking_theory [2016/05/24 17:06]
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phototrack_tracking_theory [2016/10/04 15:13] (current)
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 Tracking laterally in XY with a quadrant photo-detector is a well established method that allows for rapid course correction without requiring digital image collection and processing. ​ Such a tracking system images a bright emissive target onto a four-pixel quadrant detector. ​ X and Y corrections are determined from the signal difference from X and Y detector pixel pairs. ​ Achieving zero error difference between the adjacent pixel pairs that determine the X and Y tracking errors does not completely determine the relative signal levels on the four detector pixels. ​ The relative levels of diagonal pixels remain undetermined. ​  ​Figure 1 shows the signal contributions for the X and Y tracking error terms and the undetermined diagonal pixel balance. ​ Tracking laterally in XY with a quadrant photo-detector is a well established method that allows for rapid course correction without requiring digital image collection and processing. ​ Such a tracking system images a bright emissive target onto a four-pixel quadrant detector. ​ X and Y corrections are determined from the signal difference from X and Y detector pixel pairs. ​ Achieving zero error difference between the adjacent pixel pairs that determine the X and Y tracking errors does not completely determine the relative signal levels on the four detector pixels. ​ The relative levels of diagonal pixels remain undetermined. ​  ​Figure 1 shows the signal contributions for the X and Y tracking error terms and the undetermined diagonal pixel balance. ​
  
-[{{ :​documentation:​track_theory_1.jpg?​direct&​400 |Figure 1: Four-pixel detector tracking error contributions}}]+[{{ track_theory_1.jpg?​direct&​400 |Figure 1: Four-pixel detector tracking error contributions}}]
  
 The tracking error contributions can be defined by the following four equations which are uniquely determined from the signal values, A, B, C, and D  on the four pixels. The tracking error contributions can be defined by the following four equations which are uniquely determined from the signal values, A, B, C, and D  on the four pixels.
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 The negative focal-length cylindrical lens will place the focus further back from the usual image plane of the tube lens.  Roughly midway between the flat-axis focus and the curved-axis focus of the lens pair system will be a point where both axes are similarly miss-focused. ​ The negative focal-length cylindrical lens will place the focus further back from the usual image plane of the tube lens.  Roughly midway between the flat-axis focus and the curved-axis focus of the lens pair system will be a point where both axes are similarly miss-focused. ​
  
-[{{ :​documentation:​track_theory_2.jpg?​direct&​400 |Figure 2:  Adding a cylindrical lens to an image system will generate astigmatism at the image. ​ Along the flat-axis of the cylindrical lens (lower rays) the imaging lens focuses the source at the imaging lens focal point. ​ On the curved axis of the lens, the imaging lens and negative cylindrical lens form a compound lens that focuses the source at an axial location further away.  An image screen placed at either of the two foci would see a line image, well focused on one axis and spread on the other, with the two line images perpendicular to one another.}}]+[{{ track_theory_2.jpg?​direct&​400 |Figure 2:  Adding a cylindrical lens to an image system will generate astigmatism at the image. ​ Along the flat-axis of the cylindrical lens (lower rays) the imaging lens focuses the source at the imaging lens focal point. ​ On the curved axis of the lens, the imaging lens and negative cylindrical lens form a compound lens that focuses the source at an axial location further away.  An image screen placed at either of the two foci would see a line image, well focused on one axis and spread on the other, with the two line images perpendicular to one another.}}]
  
 This is the design-location for the four-pixel photo detector is fixed at one location and the relative position of the sample moves in and out of focus with respect to the imaging lens.  To complete the picture we need to understand how a change in the axial focus at the sample is transformed to an axial change in focus near the image.  ​ This is the design-location for the four-pixel photo detector is fixed at one location and the relative position of the sample moves in and out of focus with respect to the imaging lens.  To complete the picture we need to understand how a change in the axial focus at the sample is transformed to an axial change in focus near the image.  ​
  
-[{{ :​documentation:​track_theory_3.jpg?​direct&​400 |Figure 3: Simple lens axial focus}}]+[{{ track_theory_3.jpg?​direct&​400 |Figure 3: Simple lens axial focus}}]
    
 For an ideal thin lens, the focal points f<​sub>​1</​sub>​ and f<​sub>​2</​sub>​ are constrained by the lens focal length, fl. For an ideal thin lens, the focal points f<​sub>​1</​sub>​ and f<​sub>​2</​sub>​ are constrained by the lens focal length, fl.
phototrack_tracking_theory.txt · Last modified: 2016/10/04 15:13 (external edit)