Optically trapped glass microsphere ( ) in air.
Conceptual sketches of the proposed displacement sensor.
Schematic image of probe behavior when reading an interference scale.
Geometrical model of a computer simulation analyzing the axial trapping force for single laser gradient trap. The symbols are as follows: is the radius of the laser beam, is the radial distance of a ray, is the normal vector of the surface where a ray strikes, is the distance between the axially deviated laser focus and the center of the probe, is the maximum focusing angle for the optical axis, is the focusing angle, is the incident angle at the probe surface, is the refractive index of the surrounding media, is the refractive index of the probe, and and are the gradient and scattering forces generated by a ray, respectively.
Numerical analysis results for the axial trapping force when the laser focus deviates along the optical axis. Positive and negative forces are the forces exerted upward and downward, respectively.
Axial deviation of the probe from the laser focus with variation in distance between the laser focus and the target surface. The analytical results were obtained using Eqs. (4) and (8).
(a) Optical system of the probe, which comprises three elements: trapping a probe, measuring an axial motion of the trapped probe, and imaging the trapped probe. The abbreviations are as follows: L, lens; HM, half mirror; OL, objective lens; P, piezoelectric oscillator; M, mirror; CL, collective lens; IF, interference filter; and PD, photo detector. (b) Configuration of the detection system for axial motion of the probe. is the illuminated area of the backscattered light; , the effective area of PD; , the focal length of the objective lens; and , the axial deflection of the probe.
Probe signal, which corresponds to the axial motion of the probe, when the probe approaches a target surface.
Spatial frequency spectrum of the probe signal when the probe approaches a target surface at constant speed.
(Black line) Displacement measured by proposed displacement sensor when the sensor approaches the target surface. (Red line) Measurement error between the stage displacement and the value obtained from the displacement sensor.
Histogram of the detected pitches of the interference scale.
Probe signal when the probe moves away from a target surface.
Measuring resolution of the displacement sensor. The sensor signal is obtained when the target surface moves at interval of 10 nm. Black and red lines indicate raw data and data processed through a low-pass filter, respectively.
SIM image of a small target surface fabricated by means of a focused ion beam. The material is silicon. The beam was originally an AFM cantilever (Nanosensors, NCH-10V).
Probe signal obtained on a narrow beam with a width of .
Measurable range for the target surface tilted from 0° to 15°.
Fundamental performance of the proposed displacement sensor.
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