Sparse sampling using a programmatically randomized signal modulating a carrier signal
A system including a sparse sampling system having a processor and a non-transitory computer-readable medium. The sparse sampling system generates, a first programmable primary carrier signal and a first secondary programmable signal that modulates the first programmable primary carrier signal through a first randomized modulation that defines X-coordinates of a set of scan pattern coordinates of an object scan, a second programmable primary carrier signal and a second secondary programmable signal that modulates the second programmable primary carrier signal through a second randomized modulation that defines Y-coordinates of the set of scan pattern coordinates of the object scan, and a third programmable output signal that defines Z-coordinates of the set of scan pattern coordinates of the object scan based on a predetermined rule. The sparse sampling system also transmits the generated signals to a scanning probe device.
1 . A system comprising:
a sparse sampling system having a processor and a non-transitory computer-readable medium, the sparse sampling system configured to generate:
a first programmable primary carrier signal and a first secondary programmable signal that modulates the first programmable primary carrier signal through a first randomized modulation that defines X-coordinates of a set of scan pattern coordinates of an object scan;
a second programmable primary carrier signal and a second secondary programmable signal that modulates the second programmable primary carrier signal through a second randomized modulation that defines Y-coordinates of the set of scan pattern coordinates of the object scan, wherein each of the first and second programmable primary carrier signals comprises X-Y components of a at least two-dimensional space-filling curve, and wherein a resultant randomized modulation produced by combined action of the first and second secondary programmable signals is independent of the at least two-dimensional space-filling curve;
a third programmable output signal that defines Z-coordinates of the set of scan pattern coordinates of the object scan based on a predetermined rule, and
wherein the sparse sampling system is further configured to transmit the generated first and second programmable primary carrier signals, the first and second secondary programmable signals, and the third programmable output signal to a scanning probe device.
2 . The system of claim 1 and wherein the X-coordinates and the Y-coordinates of the set of scan pattern coordinates of the object scan sample less than 100% of a predetermined set of addressable picture elements of the object scan.
3 . The system of claim 1 and wherein the X-coordinates, Y-coordinates and Z-coordinates of the set of scan pattern coordinates of the object scan sample less than 100% of a predetermined set of addressable picture elements of the object scan.
4 . The system of claim 1 and wherein the third programmable primary carrier signal comprises Z-components of a three-dimensional space-filling curve.
5 . The system of claim 1 and wherein:
the first programmable primary carrier signal is divided into different sub-divisions, and wherein each of the different sub-divisions is modulated by the first secondary programmable signal through the first randomized modulation to provide different subsets of X-coordinates that together define the X-coordinates of the set of scan pattern coordinates of the object scan; and
the second programmable primary carrier signal is divided into different sub-divisions, and wherein each of the different sub-divisions is modulated by the second secondary programmable signal through the second randomized modulation to provide different subsets of Y-coordinates that together define the Y-coordinates of the set of scan pattern coordinates of the object scan.
6 . The system of claim 1 and wherein the predetermined rule comprises defining the Z-coordinates of the set of scan pattern coordinates of the object scan by a third programmable primary carrier signal and a third secondary programmable signal that modulates the third programmable primary carrier signal through a third randomized modulation, wherein the third programmable primary carrier signal and the third secondary programmable signal constitute the third programmable output signal.
7 . The system of claim 6 and wherein:
the first programmable primary carrier signal is divided into different sub-divisions, and wherein each of the different sub-divisions is modulated by the first secondary programmable signal through the first randomized modulation to provide different subsets of X-coordinates that together define the X-coordinates of the set of scan pattern coordinates of the object scan;
the second programmable primary carrier signal is divided into different sub-divisions, and wherein each of the different sub-divisions is modulated by the second secondary programmable signal through the second randomized modulation to provide different subsets of Y-coordinates that together define the Y-coordinates of the set of scan pattern coordinates of the object scan; and
the third programmable primary carrier signal is divided into different sub-divisions, and wherein each of the different sub-divisions is modulated by the third secondary programmable signal through the third randomized modulation to provide different subsets of Z-coordinates that together define the Z-coordinates of the set of scan pattern coordinates of the object scan.
8 . The system of claim 6 and wherein the third programmable primary carrier signal comprises Z-components of a three-dimensional space-filling curve.
9 . The system of claim 8 and wherein the three-dimensional space-filling curve comprises a three-dimensional Hilbert space-filling curve.
10 . The system of claim 1 and wherein the predetermined rule comprises the Z-coordinates of the set of scan pattern coordinates of the object scan defined as discretized on at least two pre-defined Z-planes, such that different non-overlapping subsets of the Z-coordinates lie on different Z-planes of the at least two pre-defined Z-planes.
11 . The system of claim 10 and wherein the X-coordinates and Y-coordinates form pairs of X-Y coordinates, and wherein each different pre-defined Z-plane of the at least two different pre-defined Z-planes comprises a different non-overlapping subset of the pairs of X-Y coordinates.
12 . The system of claim 1 and wherein the predetermined rule comprises defining Z-coordinates as being modulated randomly in positive or negative directions relative to at least two pre-defined Z planes, such that a first non-overlapping subset of the Z-coordinates is modulated randomly in the positive or negative directions relative to a first pre-defined Z-plane of the at least two pre-defined Z-planes, and a second non-overlapping subset of the Z-coordinates is modulated randomly in the positive or negative directions relative to a second pre-defined Z-plane of the at least two pre-defined Z-planes, and wherein a modulation magnitude is equal to or less than half a distance between the first pre-defined Z-pane and the second pre-defined Z-plane.
13 . The system of claim 1 and wherein the predetermined rule comprises defining the Z-coordinates of the set of scan pattern coordinates of the object scan by a third programmable primary carrier signal and a third secondary programmable signal that modulates the third programmable primary carrier signal through a third randomized modulation in a positive or a negative Z-direction.
14 . The system of claim 1 and wherein the sparse sampling system comprises a controller and a signal converter coupled to the controller, and wherein the signal converter comprises at least one digital-to-analog converter (DAC), and wherein the controller is configured to provide the first and second programmable primary carrier signals and the first and second secondary programmable signals to the signal converter.
15 . The system of claim 1 and wherein the sparse sampling system comprises a controller configured to provide the first and second programmable primary carrier signals and the first and second secondary programmable signals to digital signal inputs on the scanning probe device.
16 . The system of claim 1 and wherein the Z-coordinates of the set of scan pattern coordinates of the object scan are defined by a third programmable primary carrier signal and a third secondary programmable signal that modulates the third programmable primary carrier signal through a third randomized modulation, and wherein the sparse sampling system comprises a controller and a signal converter coupled to the controller, and wherein the signal converter comprises at least one digital-to-analog converter (DAC), and wherein the controller is configured to provide the third programmable primary carrier signal and the third secondary programmable signal to the signal converter.
17 . The system of claim 1 and wherein the sparse sampling system comprises a controller configured to provide signals that define Z-coordinates of the scan pattern coordinates of the object scan to digital signal inputs on the scanning probe device.
18 . A method comprising:
generating, by a sparse sampling system having a processor and a non-transitory computer-readable medium, a first programmable primary carrier signal and a first secondary programmable signal that modulates the first programmable primary carrier signal through a first randomized modulation that defines X-coordinates of a set of scan pattern coordinates of an object scan;
generating, by the sparse sampling system, a second programmable primary carrier signal and a second secondary programmable signal that modulates the second programmable primary carrier signal through a second randomized modulation that defines Y-coordinates of the set of scan pattern coordinates of the object scan, wherein each of the first and second programmable primary carrier signals comprises X-Y components of a at least two-dimensional space-filling curve, and wherein a resultant randomized modulation produced by combined action of the first and second secondary programmable signals is independent of the at least two-dimensional space-filling curve;
generating, by the sparse sampling system, a third programmable output signal that defines Z-coordinates of the set of scan pattern coordinates of the object scan based on a predetermined rule, and
transmitting, by the sparse sampling system, the generated first and second programmable primary carrier signals, the first and second secondary programmable signals, and the third programmable output signal to a scanning probe device.
19 . An apparatus comprising:
a sparse sampling pattern generator configured to generate:
a first programmable primary carrier signal and a first secondary programmable signal that modulates the first primary carrier signal through a first randomized modulation that defines X-coordinates of a set of scan pattern coordinates of an object scan; and
a second programmable primary carrier signal and a second secondary programmable signal that modulates the second primary carrier signal through a second randomized modulation that defines Y-coordinates of the set of scan pattern coordinates of the object scan; and
a third programmable output signal that defines Z-coordinates of the set of scan pattern coordinates of the object scan based on a predetermined rule;
a controller coupled to the sparse sampling pattern generator and configured to provide the first and second programmable primary carrier signal, the first and second secondary programmable signal, and the third programmable output signal to scan inputs of a scanning probe device configured to scan an object;
at least one object signal response converter configured to receive analog scan response signals from at least one object response detector that detects a response of the object to scan probe signals directed at the object by the scanning probe device, the at least one object response converter coupled to the controller and configured to convert the analog scan response signals to digital scan response signals; and
a sampling reconstruction system communicatively coupled to the controller, the sampling reconstruction system configured to receive the digital scan response signals from the controller, and responsively reconstruct an amalgamate image of the object scanned by the scanning probe device from the sampled object response signals.
20 . The apparatus of claim 19 , and wherein the sampling reconstruction system is configured to reconstruct the amalgamate image using adaptive real-time inpainting.