Sparse sampling methods and probe systems for analytical instruments
Sparse sampling approaches and probe systems for analytical instruments are disclosed providing for effective sub-sampling of a specimen and inpainting to reconstruct representations of actual information. The sub-sampling involves serial acquisition of contiguous measured values lying at positions along a scan path extending in a line toward a first direction and having random perturbations in a second direction. The perturbations are limited within a predetermined distance from the line. Inpainting techniques are utilized among the measured values to reconstruct a representation of actual information regarding the specimen.
1. A method for sparse sampling with an analytical probe, the method comprising:
a) acquiring in a serial mode a plurality of contiguous measured values lying at positions along a scan path extending in a line toward a first direction and having random perturbations in a second direction, wherein the random perturbations are limited within a predetermined distance from the line; and
b) inpainting among the measured values and reconstructing a representation of actual information.
2. The method of claim 1 , further comprising repeating said acquiring step at different portions of a sample region, thereby acquiring measured values over substantially the entire sample region.
3. The method of claim 2 , wherein a plurality of the lines are adjacent and resemble a serpentine line form or a sawtooth line form.
4. The method of claim 1 , wherein the line has a curved form.
5. The method of claim 1 , wherein said acquiring further comprises moving an analytical probe and a sample from which the measured values are acquired relative to one another.
6. The method of claim 1 , wherein said acquiring further comprises holding an analytical probe at each of the positions from which measured values are acquired for a dwell time, the dwell time being less than a rise time associated with positional uncertainty of the analytical probe.
7. The method of claim 6 , wherein the dwell time is greater than or equal to 50% of the rise time.
8. The method of claim 6 , wherein the dwell time is between 70% and 90% of the rise time.
9. The method of claim 1 , wherein said acquiring further comprises sensing a sample with a physical tip.
10. The method of claim 1 , wherein said acquiring further comprises illuminating a sample with a charged particle beam, a neutral particle beam, an electromagnetic beam, or an optical beam.
11. The method of claim 10 , wherein said illuminating comprises illuminating with a substantially constant illumination intensity.
12. A sparse sampling analytical probe system comprising:
a) a scanner configured to move a sample and an analytical probe relative to one another and to scan the analytical probe over the sample along a scan path extending in a line toward a first direction and having random perturbations in a second direction, wherein the random perturbations are limited within a predetermined distance from the line;
b) a detector configured to acquire in a serial mode a plurality of contiguous measured values lying at positions along the scan path; and
c) a processor configured to apply inpainting techniques based on the measured values and to reconstruct a representation of actual information.
13. The system of claim 12 , wherein the analytical probe comprises a charged particle beam, a neutral particle beam, an electromagnetic beam, or an optical beam.
14. The system of claim 13 , wherein the analytical probe has a substantially constant illumination intensity at every position at which a measured value is acquired.
15. The system of claim 13 , wherein the scanner comprises electromagnetic deflectors.
16. The system of claim 15 , wherein the electromagnetic deflectors comprise scan coils.
17. The system of claim 13 , wherein the scanner comprises electrostatic deflectors.
18. The system of claim 12 , wherein the analytical probe comprises a physical tip.
19. The system of claim 18 , wherein the scanner comprises piezoelectric manipulators, optical elements, or a combination thereof.
20. The system of claim 13 , wherein the processor is configured to execute computer readable instructions including an inpainting solver stored in a memory device, the inpainting solver applying Bayesian dictionary learning techniques, beta-process factor analysis techniques, or combinations thereof.
21. The system of claim 13 , wherein the representation of actual information comprises an image having N pixels, and the plurality of measured values is fewer than or equal to 1%, 2%, 3%, 5%, 10%, 15%, 20%, 25%, 30%, 33%, 40%, 50%, 60%, 70%, 80%, or 90% of the N pixels.
22. The system of claim 12 , wherein the line comprises a continuous portion of a serpentine form or a sawtooth form.
23. The system of claim 12 , wherein the line has a curved line form.
24. The system of claim 12 , the scanner further configured to hold the analytical probe at each of the positions from which measured values are acquired for a dwell time, the dwell time being less than a rise time associated with positional uncertainty of the analytical probe.
25. The system of claim 24 , wherein the dwell time is greater than or equal to 50% of the rise time.
26. The system of claim 25 , wherein the dwell time is between 70% and 90% of the rise time.