We present a simple autocollimator with sub-microradian sensitivity. To demonstrate the capabilities of our autocollimator, we study the simple harmonic motion of a cantilever beam and apply an external force to affect the cantilever's resonant frequency in the context of dynamic force microscopy. Our setup is ideal for the advanced undergraduate instructional laboratory and allows a variety of high-precision, tabletop experiments.

1.
R.
Cowsik
,
R.
Srinivasan
,
S.
Kasturirengan
,
A.
Senthil Kumar
, and
K.
Wagoner
, “
Design and performance of a sub-nanoradian resolution autocollimating optical lever
,”
Rev. Sci. Instrum.
78
,
035105
(
2007
).
2.
T. B.
Arp
,
C. A.
Hagedorn
,
S.
Schlamminger
, and
J. H.
Gundlach
, “
A reference-beam autocollimator with nanoradian sensitivity from mHz to kHz and dynamic range of 107
,”
Rev. Sci. Instrum.
84
,
095007
(
2013
).
3.
C. D.
Hoyle
,
U.
Schmidt
,
B. R.
Heckel
,
E. G.
Adelberger
,
J. H.
Gundlach
,
D. J.
Kapner
, and
H. E.
Swanson
, “
Submillimeter test of the gravitational inverse-square law: A search for large extra dimensions
,”
Phys. Rev. Lett.
86
,
1418
1421
(
2001
).
4.
C. D.
Hoyle
,
D. J.
Kapner
,
B. R.
Heckel
,
E. G.
Adelberger
,
J. H.
Gundlach
,
U.
Schmidt
, and
H. E.
Swanson
, “
Submillimeter tests of the gravitational inverse-square law
,”
Phys. Rev. D
70
,
042004
(
2004
).
5.
J. H.
Gundlach
and
S. M.
Merkowitz
, “
Measurement of Newton's constant using a torsion balance with angular acceleration feedback
,”
Phys. Rev. Lett.
85
,
2869
2872
(
2000
).
6.
The spectral range of the PSD used in our experiment (First Sensor, DL100-7-PCBA3) was 500–1000 nm, with the maximum spectral responsivity at around 900 nm. As discussed, the PSD measurements are essentially independent of light intensity, although a high-intensity operation is recommended by the manufacturer to an extent so that it does not damage the PSD. A single-mode laser is not required, but it could help reduce possible intensity fluctuations due to mode hopping. Note that the beam spot (e.g., the centroid location) is averaged and tracked by the PSD, so the beam quality factor would only affect the dc-offset.
7.
S.
de Man
,
K.
Heeck
,
R. J.
Wijngaarden
, and
D.
Iannuzzi
, “
Halving the Casimir force with conductive oxides
,”
Phys. Rev. Lett.
103
,
040402
(
2009
).
8.
S.
de Man
,
K.
Heeck
, and
D.
Iannuzzi
, “
Halving the Casimir force with conductive oxides: Experimental details
,”
Phys. Rev. A
82
,
062512
(
2010
).
9.
J. L.
Garrett
,
D. A. T.
Somers
, and
J. N.
Munday
, “
Measurement of the Casimir force between two spheres
,”
Phys. Rev. Lett.
120
,
040401
(
2018
).
10.
D. T.
Chuss
, “
A software-based lock-in measurement for student laboratories
,”
Am. J. Phys.
86
,
154
158
(
2018
).
11.
J. R.
Taylor
,
Classical Mechanics
, 2nd ed. (
University Science Books
,
Sausalito, CA
,
2005
), p.
187
.
12.
G.
Jesensky
,
D.
Dams
,
O.
Khomenko
, and
W. J.
Kim
, “
An optically-driven macroscopic cantilever
,”
Eur. J. Phys.
39
,
045302
(
2018
).
13.
Throughout our measurements, we have employed two types of cantilevers: one is a brass cantilever and the other is an Au-coated silicon cantilever. Both of them have similar dimensions and work well for DFM. The results reported in Fig. 6 are based on the silicon cantilever.
14.
P. R.
Saulson
, “
Thermal noise in mechanical experiments
,”
Phys. Rev. D
42
,
2437
2445
(
1990
).
15.
See supplementary material at http://dx.doi.org/10.1119/10.0001269 for a video demonstration to trace the 24-h measurements of the mechanical hysteresis.

Supplementary Material

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.