Optimal control of force microscope cantilevers. I. Controller design
In magnetic resonance force microscopy (MRFM) experiments, magnetic forces couple to the motion of microscale cantilever beams. Extension of MRFM to the detection of single electrons will require both...
In magnetic resonance force microscopy (MRFM) experiments, magnetic forces couple to the motion of microscale cantilever beams. Extension of MRFM to the detection of single electrons will require both...
Intense ultraviolet and blue upconversion fluorescence in Tm3+-doped fluoroindate glasses
Much more intense ultraviolet (UV) and blue upconversion fluorescence of Tm3+ was observed in a new stable fluoroindate glass compared with other fluoride or oxide glasses. The intense upconversion in...
Much more intense ultraviolet (UV) and blue upconversion fluorescence of Tm3+ was observed in a new stable fluoroindate glass compared with other fluoride or oxide glasses. The intense upconversion in...
Optimal control of force microscope cantilevers. II. Magnetic coupling implementation
J. Appl. Phys. 80, 1959 (1996); doi:10.1063/1.363086
Issue Date: 15 August 1996
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We describe the implementation of optimal controllers for damping the motion of cantilevers used in magnetic resonance force microscopy. We demonstrate that optimal control is achievable and that torsional magnetic coupling provides an effective actuation method. Cantilever Brownian vibrational amplitude was reduced from 2 to 0.16 Å and resonant quality was reduced from 2000 to 5. Applied control fields were sufficiently small that they would not affect magnetic resonance phenomena. ©1996 American Institute of Physics.
| History: | Received 21 November 1995; accepted 13 May 1996 |
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http://link.aip.org/link/?JAPIAU/80/1959/1 |
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KEYWORDS and PACS
MAGNETIC FORCE MICROSCOPY,
OPTIMAL CONTROL,
RESONANCE,
COUPLING,
MECHANICAL VIBRATIONS,
SIGNAL–,
TO–,
NOISE RATIO,
FEEDBACK
- 07.79.Pk
Instruments, apparatus, components, and techniques common to several branches of physics and astronomy Scanning probe microscopes, components, and techniques Magnetic force microscopes - YEAR: 1996
PUBLICATION DATA
0021-8979 (print)
1089-7550 (online)
AIP
REFERENCES (20)
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- D. Rugar, C. S. Yannoni, and J. A. Sidles,
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Science 264, 1560 (1994 ). - K. J. Bruland, J. Krzystek, J. L. Garbini, and J. A. Sidles, Rev. Sci. Instrum. 66, 2853 (1995).
- For analytic expressions we adopt the convention of two sided power spectrum S
(
) with a transform pair defined as S) = ![[integral]](http://scitation.aip.org/stockgif3/int.gif)
Rx(
)e–j
d, Rx() = (1/2
))ejd, where Rx() = E[x(t)x(t+)]. Numerical values are presented as one sided spectra S(
) = 2S) that are read from standard laboratory instruments. - J. A. Sidles and D. Rugar, Phys. Rev. Lett. 70, 3506 (1993).
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- J. L. Garbini, K. J. Bruland, W. M. Dougherty, and J. A. Sidles, J. Appl. Phys. 80, 1951 (1996).
- MQP-B powder from Magnequench, Anderson, IN.
- Microlevers from Park Scientific Instruments, Sunnyvale, CA.
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- Here optimal control parameters are computed for one controller from previously given experimental parameters, as well as some additional data. Quoted equation numbers refer to Part I of this article (Ref. 11). The desired response amplitude xmax = 0.2 Å and actuation force amplitude umax = 10–13 N determine that X = 4×10–22 m2 and U = 10–26 N2, therefore
= 4.76×10–2 according to Eq. (16). The measured optical noise floor determines V = S/2 = 2.88×10–26 m2/Hz, and Rcant = 7.95×1014 photons/s according to Eq. (45) where Nfib = 1.4591 and R = 1.65×1015 photons/s from the 420 µW optical power. From these data, R
= 2.30×10–39 N2/Hz and R
= 1.26×10–29 N2/Hz, thus, W = 1.26×10–29 N2/Hz, according to Eqs. (42) and (43). From W, V, and Eq. (25),
= 0.1995. The optimal controller parameters can then be determined according to Eqs. (31), (32), and (33): K![[proportional]](http://scitation.aip.org/stockgif3/prop-script.gif)
= 4.16 N/m; Z = –2.74×10–5 rad/s; = 3.45×104 rad/s; and Q = 4.10. - P. Horowitz and W. Hill, The Art of Electronics (Cambridge University, 1989), p. 276.
- D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
- D. Rugar, H. J. Mamin, and P. Guethner, Appl. Phys. Lett. 55, 2588 (1989).
- The laser (single-mode FC connectorized Mitsubishi ML40116R) and photodiodes (FC connectorized Mitsubishi PD-2101) are available from Seastar Optics, Sidney, B.C. Canada.
- S. Hoen, O. Züger, C. S. Yannoni, H. J. Mamin, K. Wago, and D. Rugar, in Technical Digest of the 1994 Solid State Sensor and Actuator Workshop, Hilton Head, SC, (Transducers Research Foundation, Catalog No. 94TRF-0001, 1994), p. 209.
