MADRID Measurement Apparatus to Distinguish Rotational and Irrotational Displacement

1. MADRIDMeasurement Apparatus to Distinguish Rotational and Irrotational Displacement Rafael Ortiz Graduate student Universidad de Valladolid (Spain)

2. MADRID • Problem to solve • Reasons of choosing this option • Description of the device • First result • Conclusion

3. Introduction • High accuracy in microsurgery • Vitreoretinal microsurgery MICRON • Neurosurgery LASER MICRON • Involuntary movement of the hand hinder the desired accuracy. • Tremor • Jerk • Drift

4. Vitreoretinal microsurgery • Five degree of freedom • Two rotation • Three translation • Tip tracking ↓↓↓ ASAP

5. Vitreoretinal microsurgery • Four degree of freedom • Two rotation • Two translation • Laser tracking ↓↓↓ 

6. Options to solve the problem • Gyros. • CCD camera • MADRID

7. Use a par of gyros • Translation information is missing • Device should be useful for laser micron calibration. • Impossible to set a gyros above a laser ray

8. CCD camera • High speed ( 100 fps ) • High accuracy ↔ High resolution • Very expensive system

9. B1 g B2 A1 A2 MADRID • First idea: Only two dots are required to draw a line. • If the laser is tracking in two different positions , the angle may be calculated Point 1 Point 2

10. 3D problem

11. Configuration Power Inverse Bias Position Sensing Detector #1 DATA output Band pass Optical filter Standard Cube Beam splitter Position Sensing Detector #2

12. Bandpass optical filter • Benefit: eliminate most of the ambient light • Type: 10LF20-670 • C. Wavelength: 667.3nm • FWHM: 19.4nm • P. Transmission: 53.1% 10LF20-670, Newport, Irvine, CA

13. Laser Diode • Focusable Laser • Features: • CWWavelengths670nm ±10nm, • DiameterLDM, Circular: 5mm;  • Focus Range LDM, Circular: 150mm to Infinity;  Spot Size (mm) at Distance NT38-920,Edmund optics, Barrington, NJ

14. Standard Cube Beamsplitter • BS CUBE STANDARD 12.5MM TS • Size: 12.5mm x 12.5mm • Reflection : 50 % • Transmission : 50 % NT45-111, Edmund optics, Barrington, NJ

15. Channel Meaning Formula PSD #1 Ch0 V(x) Ch1 Sum(x) Ch2 V(y) Ch3 Sum(y) PSD #2 Ch4 V(x) Ch5 Sum(x) Ch6 V(y) Ch7 Sum(y) Position Sensing Detector • 1 cm2 square PSD & associated amplifier circuit. • Voltage analogd of the X,Y and spot intensity • Reverse Bias is applied DL 100- 7PCBA ,Pacific Silicon Sensor Inc. ,Westlake Village, CA

16. - æ ö x x a = ç ÷ 1 2 Arc tan - a d è ø - æ ö y y b = ç ÷ 1 2 tan Arc - a d è ø Calculation of two angles

17. ( ) ( ) = - + + a g x 1 a b c tan x ( ) ( ) = - + + b g y 1 a b c tan y ( ) ( ) = - + + a g x 2 d b c tan x ( ) ( ) = - + + b g y 2 d b c tan y Calculation of displacement

18. General Scheme Band pass Opt filter PSD#2 Beam splitter AD card Laser Ch7 Laser Ambient light Alpha Beta Gx Gy PSD#1 X1 Transform microns into angles and positions Subtract Offset

19. First Result • Different modes • Only translation • Only angle • Angle and translation

20. Only translation • Redundant data (alpha and beta must be null) • Two studies • Full Range (step 0.04 inch or 1mm) • Small step (step 2 mil or 50 micron)

21. Full Range (only translation) 8.7268 6.4684 -0.0058 -0.0058

22. Small Step 6.7942 4.0104 -8.8044 -2.1234

23. Only angles Wheel to reach different orientation of angle BETA Wheel to reach different orientation of angle ALPHA

24. Angle (Alpha) Range =2.5653° Maximum Error 0.0268 ° Linearity =1.04%

25. Angle (Beta) Range =2.2526° Maximum Error 0.0517° Linearity =2.29%

26. Angle in completed mode Standard derivation of error in alpha Std alpha 0.0022° ≈ 8’’ Standard derivation of error in beta Std alpha 0.0022° ≈ 8’’

27. Translation in completed mode Standard derivation of error in x translation Std Gx error 4.1876 micron Standard derivation of error in alpha Std Gy error 4.0152 micron

28. Real tremor (Rotation)

29. Real tremor (translation)

30. Conclusion