phototrack_tracking_theory
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revision | |||
phototrack_tracking_theory [2016/09/07 18:26] – ↷ Page moved from documentation:phototrack_tracking_theory to phototrack_tracking_theory asiadmin | phototrack_tracking_theory [2021/09/23 17:15] (current) – external edit 127.0.0.1 | ||
---|---|---|---|
Line 1: | Line 1: | ||
+ | ====== Phototrack Tracking Theory ====== | ||
+ | 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. | ||
+ | |||
+ | [{{ track_theory_1.jpg? | ||
+ | |||
+ | 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. | ||
+ | |||
+ | \begin{equation}X_{err}=\frac{(A +C)- (B+D)}{SUM} \tag{1} \end{equation} | ||
+ | |||
+ | \begin{equation}Y_{err}=\frac{(A +B)- (C+D)}{SUM} \tag{2} \end{equation} | ||
+ | |||
+ | \begin{equation}DIAG_{err}=\frac{(A +D)- (B+C)}{SUM} \tag{3} \end{equation} | ||
+ | |||
+ | \begin{equation}SUM=A+B+C+D \tag{4} | ||
+ | |||
+ | |||
+ | For standard XY tracking, the DIAG< | ||
+ | |||
+ | In microscopy applications there is always the need to maintain focus. | ||
+ | |||
+ | Astigmatism generated by a cylindrical lens can be used to generate the optical effect that is required for Z tracking with a four-pixel detector. | ||
+ | |||
+ | \begin{equation} {1 \over F_{Comb}} ={1 \over F_{Tube}} + {1 \over F_{Cyl}} \tag{5} | ||
+ | |||
+ | 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. | ||
+ | |||
+ | [{{ track_theory_2.jpg? | ||
+ | |||
+ | 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. | ||
+ | |||
+ | [{{ track_theory_3.jpg? | ||
+ | |||
+ | For an ideal thin lens, the focal points f< | ||
+ | |||
+ | \begin{equation} fl ={1 \over f_1} + {1 \over f_2} \tag{6} | ||
+ | |||
+ | A small change in focus, d¬1 « f1, on one side causes a focus shift on the other side such that | ||
+ | |||
+ | \begin{equation} \frac{d_2}{d_1} = \frac{f_2^2}{f_1^2}=M^2 | ||
+ | |||
+ | where \begin{equation}M = {f_2 \over f_1}\end{equation} is the magnification of the lens. The axial displacement in focus position just depends on the magnification of the optical system squared. | ||
+ | |||
+ | \begin{equation} d_r=\frac{F_{Comb}- F_{Tube}}{M^2} | ||
+ | |||
+ | The distance d< | ||
+ | |||
+ | In Figure 2 we see that at the desired photo-detector location, the source point has spread into a square blob. Normal tracking targets are not point sources, so there will remain some shape structure of the original source at the position of the detector. | ||
+ | |||
+ | \begin{equation} d_{source}< | ||
+ | |||
+ | where NA< | ||
+ | |||
+ | ^Objective Magnification ^Objective NA ^PMT Tube lens F.L. (mm) ^Cylindrical lens F.L. (mm) ^Focus range(µm) ^Max source size (µm) ^C-mount Extension (mm) ^ | ||
+ | |100 |1.4 |200 |-400 |7.5 |9.2 |67 | | ||
+ | |60 |1.4 |200 |-1000 |10 |10 |22 | | ||
+ | |40 |1.3 |200 |-400 |47 |53 |67 | | ||
+ | |40 |0.95 |100 |-200 |44 |48 |33 | | ||
+ | |20 |0.75 |200 |-1000 |90 |75 |22 | | ||
+ | |||
+ | {{tag> |
Address: 29391 W Enid Rd. Eugene, OR 97402, USA | Phone: +1 (541) 461-8181
phototrack_tracking_theory.txt · Last modified: 2021/09/23 17:15 by 127.0.0.1