U.S. patent application number 09/166979 was filed with the patent office on 2002-01-03 for high sensitivity deflection sensing device.
Invention is credited to HANSMA, PAUL K., SCHAFFER, TILMAN E..
Application Number | 20020000511 09/166979 |
Document ID | / |
Family ID | 22605448 |
Filed Date | 2002-01-03 |
United States Patent
Application |
20020000511 |
Kind Code |
A1 |
SCHAFFER, TILMAN E. ; et
al. |
January 3, 2002 |
HIGH SENSITIVITY DEFLECTION SENSING DEVICE
Abstract
A high sensitivity beam deflection sensing optical device, such
as an atomic force microscope, including one or more of the
following: specified means in the path of the incident beam for
adjusting the size and/or power of the incident beam spot, means
for moving the incident beam spot with movement of the object
whereby to maintain the position of the spot on the object, and
means for increasing the signal to noise ratio of the optical
detector in which adjusted gains are applied to different segments
of the optical detector.
Inventors: |
SCHAFFER, TILMAN E.; (SANTA
BARBARA, CA) ; HANSMA, PAUL K.; (ISLA VISTA,
CA) |
Correspondence
Address: |
FULBRIGHT AND JAWORSKI L L P
PATENT DOCKETING 29TH FLOOR
865 SOUTH FIGUEROA STREET
LOS ANGELES
CA
900172576
|
Family ID: |
22605448 |
Appl. No.: |
09/166979 |
Filed: |
October 6, 1998 |
Current U.S.
Class: |
250/216 |
Current CPC
Class: |
Y10S 977/869 20130101;
G01Q 70/06 20130101; Y10S 977/863 20130101; B82Y 35/00 20130101;
G01Q 20/02 20130101; Y10S 977/87 20130101 |
Class at
Publication: |
250/216 |
International
Class: |
H01J 003/14 |
Goverment Interests
[0001] This invention was made with Government support under Grant
(or Contract) No. DMR9,622,169, awarded by the National Science
Foundation. The government has certain rights in this invention.
Claims
We claim:
1. In a beam deflection sensing optical device, having a light
source providing an incident beam, a lens for focusing the incident
beam to a spot on an object and an optical detector for receiving
the beam when reflected from the object the improvement whereby the
sensitivity of the optical device is increased, comprising
providing: (a) control means in the path of the incident beam for
adjusting the size of the incident beam spot and including one or
more objects placeable in the path of the incident beam and a
plurality of movable, or interchangeable lenses, whereby to produce
different size focused spots for respective selected objects;
and/or (b) control means in the path of the incident beam for
adjusting the power of the incident beam spot including a mask
inserted in the path of the incident beam having adjacent regions
through which the beam is transmitted, said adjacent regions having
either different optical transmission characteristics or different
shapes; and/or (c) means for viewing the spot and the object, and
spot position control means based on imaging the object and the
spot through the viewing means for moving the incident beam spot
with movement of the object whereby to maintain the position of the
spot on the object; and/or (d) control means for increasing the
control signal to noise ratio of the optical detector, in which the
optical detector has an array of three or more segments generating
signals with gains adjusted based on evaluation of one or more
segment signals, and means for adding the signals from said three
or more segments to detect a change of position or shape of the
spot as the reflected beam traverses said three or more
segments.
2. The improvement of claim 1 in which said beam deflection sensing
optical device is an atomic force microscope.
3. The improvement of claim 1 in which said light source is a
source of collimated light and comprising control means in the path
of the incident beam for adjusting the size of the incident beam
spot including an adjustable beam expander or zoom optics in the
path of the incident beam.
4. The improvement of claim 3 including a viewing system confocal
with the spot on the cantilever, said beam expander or zoom optics
being also in the path of said confocal viewing system.
5. The improvement of claim 4 including a plurality of cantilevers
selectively placeable in the path of said beam, and including a
plurality of cylindrical lenses or prisms, each cylindrical lens or
prism associated with a cantilever.
6. The improvement of claim 1 including said control means for
adjusting the power of the incident beam and including a cantilever
disposed in a predetermined plane and means for forming an image
plane, with respect to the plane of the cantilever, in the path of
the incident beam, said mask being inserted in said image plane
whereby to produce a desired spot shape.
7. The improvement of claim 1 including said control means for
adjusting the power of the incident beam, said mask being patterned
whereby to produce a desired spot irradiance distribution on the
cantilever.
8. The improvement of claim 1 comprising said spot position control
means, and means for determining a change in position of the
object, comparing it to the position of the spot, and adjusting the
position of the spot until it corresponds to the position of the
object.
9. The improvement of claim 1 comprising said control means for
increasing the control signal to noise ratio of the optical
detector, the amplification of the signal from each segment being
adjusted to optimize the control signal.
10. The improvement of claim 9 in which said array of segments is a
CCD chip or a photodiode array.
11. The improvement of claim 9 including a plurality of
pre-amplifiers associated with respective segments and summing
means to receive the pre-amplified outputs thereof.
12. The improvement of claim 9 wherein said different gains are
applied to the respective pre-amplifiers.
13. The improvement of claim 9 wherein said different gains are
applied to the summing means.
14. The improvement of claim 1 comprising thermal drift limiting
means for regulating the temperature of the environment of said
optical device.
15. The improvement of claim 14 in which said thermal drift
limiting means comprises a housing enclosing said optical
device.
16. In a beam deflection sensing optical device having a light
source providing an incident beam, a lens for focusing the incident
beam to a spot on an object, and an optical detector for receiving
the beam when reflected from the object, the improvement whereby
the sensitivity of the optical device is increased, comprising
providing: (a) control means in the path of the incident beam for
adjusting the size and power of the incident beam spot; and
including one or more objects placeable in the path of the incident
beam and a plurality of movable, or interchangeable lenses, whereby
to produce different size focused spots for respective selected
objects; and/or (b) means for viewing the spot and the objects and
spot position control means based on imaging the object and the
spot through the viewing means for moving the incident beam spot
with movement of the object whereby to maintain the position of the
spot on the object; and (c) control means for increasing the
control signal to noise ratio of the optical detector, in which the
optical detector has an array of three or more segments generating
signals with gains adjusted based on evaluation of one or more
segment signals, and means for adding the signals from said three
or more segments to detect a change os position or shape of the
spot as the reflected beam traverses said three or more
segments.
17. A method for improving the sensitivity of a beam deflection
sensing optical device having a light source providing an incident
beam, a lens for focusing the incident beam to a spot on an object,
and an optical detector having an array of three or more segments
for receiving the beam when reflected from the object, comprising:
(a) modifying the incident beam to adjust the size of the incident
beam spot, said optical device including one or more objects
placeable in the path of the incident beam, comprising the step of
discretely adjusting the size of the incident beam spot whereby to
produce different size focused spots for respective selected
objects; and/or (b) adjusting the power of the incident beam spot
by inserting a mask in the path of the incident beam said mask
having adjacent regions through which the beam is transmitted, said
adjacent regions having either different optical transmission
characteristics or different shapes; and or (c) moving the incident
beam spot with movement of the object whereby to maintain the
position of the spot on the object; and/or (d) adjusting the gains
of different segments of the optical detector based on an
evaluation of one or more segment signals and adding the signals
from said three or more segments to detect a change of position or
shape of the spot as the reflected beam traverses said three or
more segments whereby to increase the signal to noise ratio of the
optical detector.
18. The method of claim 17 in which said beam deflection sensing
optical device is an atomic force microscope.
19. The method of claim 17 in which said light source is a source
of collimated light, and including the step of adjusting the size
of the incident beam spot by diverging or converging said
collimated light beam and then re-collimating said diverged or
converged light beam to a different size spot.
20. The method of claim 17 in which optical device includes a
cantilever disposed in a predetermined plane and means for forming
an image plane, with respect to the plane of the cantilever, in the
path of the incident beam, comprising the step of inserting said
mask in said image plane whereby to produce a desired spot
shape.
21. The method of claim 20 in which said mask is patterned, and
controlling said incident beam whereby to produce a desired spot
irradiance distribution on the cantilever.
22. The method of claim 17 adjusting the power of the incident beam
by inserting said mark in its path, and determining a change in
position of the object, comparing it to the position of the spot,
and adjusting the position of the spot until it corresponds to the
position of the object.
23. The method of claim 17 in which the optical detector has an
array of segments generating signals, including the step of
applying different gains to different segments to amplify the
signals from respective segments, the signal from each segment
being amplified by adjusting it to optimize the control signal.
24. The method of claim 23 in which said array of segments is a CCD
chip on a photodiode array.
25. The method of claim 23 in which said optical detector includes
a plurality of pre-amplifiers associated with respective segments
and summing means to receive the pre-amplified outputs thereof,
comprising the step of applying said different gains to the
respective pre-amplifiers.
26. The method of claim 23 in which said optical detector includes
a plurality of pre-amplifiers associated with respective segments
and summing means to receive the pre-amplified outputs thereof,
comprising the step of applying said different gains to the summing
means.
27. The method of claim 17 comprising regulating the temperature of
the environment of the optical device to limit thermal drift.
28. The method of claim 27 in which the regulating step comprises
enclosing said optical device in a housing.
29. A method for improving the sensitivity of a beam detection
sensing optical device having a light source providing an incident
beam, a lens for focusing the incident beam to a spot on an object,
and an optical detector having an array of segments for receiving
the beam when reflected from the object, comprising: (a) modifying
the incident beam to adjust the size of the incident beam spot,
said optical device including one or more objects placeable in the
path of the incident beam, comprising the step of discretely
adjusting the size of the incident beam spot whereby to produce
different size focused spots for respective selected objects; (b)
adjusting the power of the incident beam spot by inserting a mask
in the path of the incident beam, said mask having adjacent regions
through which the beam is transmitted, said adjacent regions having
either different optical transmission characteristics or different
shapes. (c) moving the incident beam spot with movement of the
object whereby to maintain the position of the spot on the object;
and (d) adjusting the gains of different segments of the optical
detector based on an evaluation of one or more segment signals and
adding the signals from said one or more segments to detect a
change of position or shape of the spot as the reflected beam
traverses said three or more segments, whereby to increase the
signal to noise ratio of the optical detector.
Description
BACKGROUND
[0002] An atomic force microscope (AFM) is a deflection detection
optical device in which, in a common implementation, forces are
measured by means of a cantilever that deflects when forces act on
it. The deflection of the cantilever is sensed by a detection
system, commonly by focusing an incident beam as a spot onto a
cantilever and directing the reflected beam onto a segmented
detector. Conventionally, a two-segment detector, such as a split
photodiode, is used. Whereas, only two segments are usually used to
sense either vertical or horizontal cantilever deflections, the
photo diode can have four segments for measuring cantilever
deflections in both directions. Initially the beam spot must be
positioned so as to be approximately equally incident on each of
the segments. The deflection of the cantilever is detected as a
difference between the incident powers on each segment.
[0003] In the approximately twelve years since its invention, the
AFM has become more and more advanced, measuring smaller and
smaller forces and utilizing smaller and smaller cantilevers. This
has introduced problems relating to forming appropriate incident
light beam spots on such very small cantilevers and in detecting
cantilever deflection during scanning as well as when different
cantilevers are brought into position for different uses.
[0004] In addition, a fundamental limit is the source of noise in
the AFM, generally resulting from thermal noise of the cantilever.
With the use of smaller cantilevers, this noise source can be
reduced such that very small forces can be measured in principle.
However, with smaller forces, the deflections of the cantilever
become smaller and the detection noise becomes more and more
significant. Therefore, it is important to have a reliable,
low-noise detection system.
SUMMARY OF THE INVENTION
[0005] The present invention provides a high sensitivity deflection
detection device that uses a light spot, with improvements to
reduce detection noise and thermal drift and allow for higher
signal-to-noise ratios of measurements of the beam deflection. Such
a device is illustrated by an atomic force microscope. The
invention provides improvements involving the incident beam as well
as a detection system. In particular, a high sensitivity atomic
force microscope is provided including one or more of the
following: means in the path of the incident beam for adjusting the
size, shape and/or power of the incident beam spot, means for
moving the incident beam spot with movement of the cantilever
whereby to maintain the position of the spot on the cantilever,
means for reducing the signal to noise ratio of the optical
detector in which different gains are applied to different segments
of the optical detector, and means for regulating the temperature
of the environment of the atomic force microscope to limit thermal
drift. The invention incorporates a variety of strategies that
individually, and in particular in combination, provide higher
sensitivity to the atomic force microscope.
[0006] To adjust the size of the incident beam spot, one can place
zoom optics in the path of the incident beam having a plurality of
lenses chosen and arranged to provide an adjustable focal length.
This can be combined with a viewing system that is confocal with
the beam spot on the cantilever. One can selectively place one of a
plurality of cantilevers in the path of the incident beam and, by
placing a selected cylindrical lens in the light path, one can fit
the spot to the selected cantilever.
[0007] With collimated light, one can place an adjustable beam
expander in the path of the incident beam, the expander having at
least one lens that diverges or converges the collimated light, and
at least one lens that re-collimates the diverged or converged
light beam to a different size beam. Alternatively, when using a
plurality of cantilevers, a removable and interchangeable lens can
be placed at a distance from each particular cantilever to produce
different size focus spots for respective selected cantilevers.
[0008] To adjust the power of the incident beam spot, a mask of
variable optical transmittance can be inserted in the path of the
incident beam, preferably in an image plane with respect to the
plane of the cantilever. The mask may be patterned to produce a
desired irradiance distribution of the incident beam spot on the
cantilever.
[0009] Other aspects of the invention provide control means for
moving the incident beam spot with movement of the cantilever to
maintain the position of the spot on the cantilever. In particular,
a change in position of the cantilever is determined which is
compared to the position of the spot and the position of the spot
is then adjusted until it corresponds to the position of the
cantilever.
[0010] Detection noise is reduced by providing the segments of the
optical detector with different gains optimized to maximize the
signal to noise ratio of the particular measurement. The segments
are arranged in an array, in a particular embodiment as the
component of a CCD chip. A plurality of pre-amplifiers are
associated with respective segments, and summing means are provided
to receive the pre-amplified outputs of the segments. In one
embodiment, the different gains are applied to the respective
pre-amplifiers. In another embodiment, the different gains are
applied to the summing means.
[0011] Thermal drift of the instrument is limited by regulating the
temperature of the environment, specifically by closing the atomic
force microscope in a housing.
DESCRIPTION OF THE DRAWINGS
[0012] The following briefly describes each of the drawings, in
which components are generally schematic and in some cases greatly
exaggerated for clarity of illustration.
[0013] FIG. 1 is a simplified schematic drawing of a prior art
AFM;
[0014] FIG. 2 displays the signal to noise ratio of a set
cantilever deflection as a function of the width of the aperture in
a prior art AFM with a 10 micrometer cantilever and a 40 micrometer
cantilever;
[0015] FIG. 3 schematically illustrates the insertion of various
optics in the incident beam path: (A) a converging beam expander
and recollimater, (B) a diverging beam expander and recollimater,
and (C) zoom optics.
[0016] FIGS. 4(A) through (D) depict various configurations for
zoom optics usable in the invention;
[0017] FIG. 5 depicts the use of cylindrical lenses with
cantilevers of different length/width aspect ratios;
[0018] FIG. 6 depicts various configurations for a removable and
interchangeable lower moving lens system and the focused spots
associated therewith including: in (a) a depiction of a system not
including the lower lens system of this invention and in (a') the
spot therefore; and in (C) (E) and (G), a lower lens moving systems
of this invention and in (b) (F) and (H) associated spots;
[0019] FIG. 7 schematically depicts a feed-back system for keeping
the incident spot optimized in a scanning cantilever
microscope;
[0020] FIG. 8 schematically depicts a variable density mask in (A)
the incident beam and in (B) in the image plane of the incident
beam; FIG. 9 schematically depicts a multi-element detector
utilizing assigned gains;
[0021] FIG. 10 depicts the (A) power distribution, (B) change in
power of a nineteen element array detector, (C) simulation of a
two-segment detector, and (D) gains for the optimized signal to
noise ratio of the detector; and
[0022] FIG. 11 is a schematic depiction of a housing enclosing the
AFM to limit thermal drift.
DETAILED DESCRIPTION
[0023] Referring to FIG. 1, an AFM as known to the prior art is
schematically illustrated, wherein an incident light beam 10, which
may be collimated, from a source not shown, is projected through an
aperture 12, a polarizing beamsplitter 14, a quarterwave plate 16,
and a focusing lens system 18 to form a spot 20 on a cantilever 22
of the AFM. Light is reflected back from the cantilever 22 through
the focusing lens system 18 and quarterwave plate 16 to reflect
from the polarizing beamsplitter 14 onto a segmented photodetector
24. Prior to the measurement, the reflected beam is centered on the
segmented photodiode so that substantially equal amounts of light
power falls on one segment as on the other. Thereafter, as the
cantilever moves up and down, more or less of the light beam will
fall on one or the other of the segments providing a signal
tracking the height of the cantilever.
[0024] Previous work has shown that the size of the focused spot on
the cantilever in an AFM affects the signal to noise ratio of the
cantilever deflection system and that the signal to noise ratio of
the detection system is maximized when the focused spot
approximately fills the cantilever. An AFM designed for use with
different size cantilevers needs to be capable of producing
different size focused spots in order to use each cantilever at its
maximum detection signal to noise ratio. A previous AFM developed
by the inventors included an adjustable aperture in the incident
beam path to change the focused spot size on the cantilever. The
diameter, w, of the focused spot on the cantilever is related to
the wavelength, .lambda., and to the effective numerical aperture,
NA, of the incident beam by diffraction theory: 1 w NA . ( 1 )
[0025] In the case of a collimated incident beam, 2 w f , ( 2 )
[0026] where a is the diameter of the incident beam and f is the
focal length of the lens/lens system. Therefore, a small aperture
width decreases the incident beam diameter and thus increases the
focused spot diameter on the cantilever.
[0027] The measured signal to noise ratio of a set cantilever
deflection for 10 .mu.m and 40 .mu.m cantilevers is displayed in
FIG. 2 as a function of the aperture width. The signal to noise
ratio with the 40, .mu.m cantilever is about 3 times higher at an
aperture width of a.ident.0.5 mm than it is at full aperture. This
is due to the fact that the focused spot size matches the
cantilever size better at a.ident.0.5 mm than it does at full
aperture width.
[0028] One disadvantage of an adjustable aperture is that light
power is cut out from the incident beam and lost for the detection
of the cantilever deflection. This lowers the sensitivity of the
detection. In accordance with one embodiment of the invention,
shown in FIGS. 3(A) and 3(B), the incident beam size is reduced
without significantly reducing the incident beam power by placing a
beam expander in the incident beam path. A beam expander is a lens
system that first diverges or converges a collimated input beam and
then re-collimates it to a different size output beam.
[0029] In FIG. 3(A) a converging lens 26 is combined with a
diverging lens 28, acting as a re-collimating lens, to reduce the
diameter of the incident beam 30. In FIG. 3(B) a diverging lens 32
is combined with a converging lens 34 acting as a re-collimator to
increase the diameter of the incident beam 36.
[0030] Alternatively, as shown in FIG. 3(C), zoom optics 38 can be
used as part of the focusing lens system. Zoom optics are
constituted by a lens system that has an adjustable focal length.
Using the same input beam 40, different size focused spots can be
produced according to equation (2). Zoom optics do not necessarily
require a collimated input beam.
[0031] In a particular embodiment, the zoom optics would be common
to the laser beam path and to a viewing system that is confocal
with the laser beam. FIGS. 4(A) through (D) illustrate variations
on an AFM with zoom optics in which light from a laser diode 42 is
projected successively through a beamsplitting plate 44, zoom
optics 46, a polarizing beamsplitter 48, a focusing system 50 and
an objective 52 to form an incident beam spot on a cantilever 54.
In one of the embodiments, in FIG. 4(C), a quarterwave plate 56 is
interposed between the focusing system 50 and objective 52. In
other embodiments, it is placed just below the beam splitter 48.
After being reflected from the cantilever 54, the reflected beam
travels back through the objective 52, focusing system 50,
polarizing beamsplitter 48 and quarterwave plate 56 (in the order
of its placement) to impinge on a photodiode detector 58. In FIGS.
4(A) and 4(B), light from the laser diode goes in a straight line
through the polarizing beamsplitter and is reflected on the
beamsplitter on the return path to the photodiode detector 58. In
FIGS. 4(C) and 4(D), light from the laser diode is reflected by the
polarizing beamsplitter 48 onto the cantilever 54 and the return
beam travels directly through the polarizing beamsplitter 48 to the
photodiode detector 58. In each of the embodiments, reflected light
traveling back through the zoom optics 46 is reflected by the
beamsplitting plate 44 onto a CCD 59 for confocal observation of
the cantilever 54. The cantilever is illuminated by means of a
source of illumination 60 and beamsplitting plate 62 located below
the zoom optics 46 in FIGS. 4(A), (B) and (D) and above the zoom
optics in FIG. 4(C).
[0032] The zoom optics can be set up so that adjustments to it
would change the cantilever's magnification in the viewing system
but would not de-focus the cantilever in the viewing system. Since
the zoom optics is common to both laser beam path and viewing
system path, the focused spot changes size, too, but the apparent
size of the focused spot in the viewing system stays constant. Zoom
optics also allows the user to zoom out to have a large field of
view. The user could then zoom in on the cantilever of interest and
bring it to a pre-set size in the viewing system, to automatically
fit the focused spot in size to the cantilever. This size is set by
the size of the focused spot in the viewing system (which is
constant).
[0033] Optionally, one can allow for different magnifications in
the directions along and across the cantilever with the help of
cylindrical lenses or prisms to be able to fit the focused spot
optimally to a range of cantilevers with different length/width
aspect ratios. In effect, the arrangement is a one-dimensional beam
expander, adjustable by moving the lenses. Referring to FIG. 5(A)
and (B),a simple lens 68 is used to focus a circular incident beam
66 onto a cantilever 70. This produces a circularly shaped spot 71,
as shown in FIG. 5(B). To produce an elongated oval spot 73, as
shown in FIG. 5(D), the cylindrical lens (or lenses) 69 are used as
a one dimensional beam expander, to increase the spot, to increase
the spot length along the lengthwise direction of the cantilever
75. This enables greater sensitivity of detection.
[0034] Adjustments of the size of the incident beam and/or of the
focal length of the lens system can be continuous or discrete. To
implement discrete adjustments of the focused spot size, a
removable focusing element and/or removable beam expander is placed
in the incident beam path. Preferably, different lenses are mounted
into different removable cantilever modules providing different
focused spot sizes for use with different size cantilevers.
Removable, interchangeable focusing elements can be used to enable
a scanning cantilever AFM to be used with small cantilevers. The
total track length of the optics is fixed and pre-set such that the
focused spot tracks the cantilever with the help of an upper moving
lens system. To produce different size focused spots for use with
different size cantilevers in the same scanning cantilever AFM, a
lower moving lens system is provided that is removable and
interchangeable. One can use a ray-tracing computer simulation
program to design replaceable lower lens systems that have
different focused spot sizes at a constant distance between the
cantilever and the upper lens system. Referring to FIGS. 6(A) and
(B), with no lower lens system, the focused spot diameter is
diffraction limited to about 15 .mu.m. With various lower lens
systems, focused spot diameters of 3 .mu.m or smaller can be
achieved. In FIG. 6(C) and (D), a cylindrical lens system 72 is
used. In FIGS. 6(E) and (G), different lens systems 74 and 76 are
used, the lens system 78 of FIG. 6(G) including a ball lens 76.
FIGS. 6(F) and (H) are corresponding spots.
[0035] In a further embodiment of the invention, the position of
the cantilever and/or the focused spot in the viewing system is
monitored to provide input to a feedback system that keeps the spot
on the cantilever even when the cantilever moves, as in a scanning
cantilever microscope. Such a feedback system is shown in FIG. 7.
The position of the cantilever is determined at 80 and the position
of the spot on the cantilever is determined at 82. These are
compared at 84 and if they are the same, the position of the
cantilever is again compared. This repeats, as shown at 86, until a
comparison indicates that the position of the cantilever is not the
same as the position of the spot. In that case, the spot is moved
in the direction of movement of the cantilever, as indicated at 88,
whereupon the position of the spot is redetermined, as indicated at
90, and the cycle repeats.
[0036] Using a beam expander or zoom optics as described above is
advantageous when one can use all of the available laser power in
order to maximize the signal with respect to the shot noise. There
is an upper limit, however, to the usable laser power on the
cantilever, since the laser light heats up the cantilever. In the
case of thin (<.apprxeq.100 nm) metal cantilevers, this heating
can cause softening of the metal and subsequent irreversible
curling of the cantilever. Therefore, the total laser power on the
cantilever is limited. In accordance with another embodiment of
this invention, the optical beam deflection sensitivity and the
heat-conducting properties of the cantilever are taken into account
in tailoring an optimum focused spot shape with an irradiance
distribution I.sub.c(p,q), where p and q are coordinates in the
cantilever plane. The required irradiance distribution (power per
unit area) of the incident beam, I.sub.i(p,q), in order to produce
I.sub.c(p,q) on the cantilever, can be calculated by diffraction
theory: 3 I i ( x , y ) = 2 f 2 cantilever p q I c ( p , q ) - 2 if
/ f ( px + qy ) 2 , ( 3 )
[0037] where .lambda. is the wavelength of the light, f is the
focal length of the lens system, .alpha. is a loss factor due to
absorption and stray reflection in the lens system, p and q are
coordinates in the cantilever plane and x and y are coordinates in
the aperture plane. In accordance with this embodiment, and
referring to FIG. 8(A), to produce this optimum irradiance
distribution of the incident beam 94, a mask 92 of variable optical
transmittance T(x, y) is inserted in the path of the incident beam.
This mask can be made, for example, from a liquid crystal device or
from an optical filter. The mask can be patterned such that it
produces the desired irradiance distribution I.sub.i(x, y) of an
appropriately intense and large incident beam that in return
produces, through the lens system 96, the desired focused spot
irradiance distribution on the cantilever 98.
[0038] In another embodiment, shown in FIG. 8(B), an alternate
implementation is obtained by creating an image plane 100 with
respect to the cantilever plane. By placing the variable density
mask 92 in this image plane 100, an image of this mask is projected
through the lens system 96, onto the cantilever 98. Therefore, by
utilizing this embodiment of the invention, the design of a mask
that produces a desired focused spot shape on the cantilever
becomes especially easy. To produce an irradiance distribution
I.sub.c(p, q) on the cantilever, the optical transmittance T(x, y)
of the mask must 4 T ( x , y ) = I c ( mx , my ) I 0 ( x , y ) , (
4 )
[0039] where I.sub.o(x, y) is the irradiance distribution of the
light incident on the mask and m is the magnification of the lower
lens system and I.sub.o(x, y) .gtoreq.I.sub.c(mx, my) for all x, y.
In such an arrangement it can be particularly easy to produce
multiple focused spots at different locations on the cantilever or
on different, neighboring cantilevers. Also, a variable density
mask can be used in conjunction with adjustable beam expander or
zoom optics to produce an optimum focused spot on the
cantilever.
[0040] In another embodiment of the invention, shown in FIG. 9, the
signal to noise ratio of the optical detector can be markedly
improved by using an array of n detector segments 102, where n is
three or more and each segment 102 can be assigned an individual
gain factor. For an undeflected cantilever, the power P.sub.i is
incident on the i'th detector segment and measured. All P.sub.i are
weighted by the gain factors g.sub.i and added together: 5 P z = 0
= i = 1 n g i P i . ( 5 )
[0041] When the cantilever tip is deflected vertically by the
distance z, the incident powers P.sub.i change due to motion of the
spot on the detector:
P.sub.i.fwdarw.P.sub.i+.DELTA.P.sub.i,
[0042] where .DELTA.P.sub.i is the change in the power on each
segment. The weighted sum now becomes: 6 P z = 0 = i = 1 n g i ( P
i + P i ) = i = 1 n g i P i + i = 1 n g i P i . ( 7 )
[0043] The first sum in eq.(7) is a constant and can be subtracted
off, Thus we get for the signal of the measurement of the
cantilever's deflection: 7 P z s = i = 1 n g i P i . ( 8 )
[0044] Physically, the limiting noise in the measurement of P.sub.i
is the shot noise due to the quantum nature of light:
P.sub.i.sup.N=.gamma.{square root}{square root over (P.sub.i)},
(9)
[0045] where .gamma. is a factor dependent on the wavelength of the
light and on the bandwidth of the measurement. We will neglect
.gamma. in the following analysis. The P.sub.i.sup.N of each
element is weighted and added together. But since the noise
fluctuations of the different segments are incoherent, they add in
quadrature: 8 P N = i = 1 n g i 2 P i . ( 10 )
[0046] Here we assume that .DELTA.P.sub.i<<P.sub.i and that
it is thus sufficient to neglect the .DELTA.P.sub.i in the noise.
Using (8) and (10), we can write for the signal-to-noise ratio of
the measurement: 9 SNR = P z s P N = i = 1 n g i P i i = 1 n g i 2
P i ( 11 )
[0047] The goal now is to choose the n gains, g.sub.i, that
maximize the signal to noise ratio. There are n simultaneous
conditions: 10 SNR g j = 0 ( 12 )
[0048] that lead to 11 g j = c P j P j , ( 13 )
[0049] where c is an arbitrary positive constant. Therefore, if the
g.sub.i are chosen according to eq. (13), the signal to noise ratio
will be maximized in the case of shot noise. The constant c can be
chosen to restrict the range of the gains to -1<g.sub.i<1 by
setting c equal to the inverse of the largest element of the set of
the absolute values of the gains: c=1/max{.linevert
split.g.sub.j.linevert split.}. These n gains could be assigned to
the n pre-amplifiers 104 remotely, for example by means of analog
switches or digital to analog converters. Once the gains are set,
the optimized deflection signal is present at the output of the
summing stage 106 and can be used for feedback Just like the
deflection signal in a 2-segment detector. By such means, the
signal to noise ratio of the optical detector can be improved. The
addition of the signals from at least three segments detects a
change of position or shape of the spot as the reflected beam
traverses three or more segments. "Traverse" is meant to include
not only completely crossing the segment but also partially
crossing it.
[0050] It is also possible to have different electronic setups, for
example one could include the gains in the summing stage.
[0051] The following example demonstrates that a multi-segment
detector is of advantage over a two-segment detector.
EXAMPLE
[0052] A home-made, prototype AFM was used to focus an incident
beam onto a cantilever and the reflected beam was directed onto a
detector. The cantilever was periodically deflected by vibrating it
at its resonance frequency. To simulate a 19-element array
detector, a slit-aperture was moved through the spot at the
detector and P.sub.i and .DELTA.P.sub.i were measured at each
position of the aperture that would represent an array element.
.DELTA.P.sub.i was measured at maximum positive deflection of the
cantilever. The result is displayed in FIGS. 10(A) and (B). The
power distribution in FIG. 10(A) represents the shape of the spot
at the detector (the scale of .DELTA.P.sub.i in FIG. 10(B) is much
smaller than that of P.sub.i in FIG. 10(A)). The gains g.sub.i were
then chosen according to equation (13) with c=0.235: (g.sub.1,
g.sub.2, . . . , g.sub.19)=(0, 0, 0, 0.46, 1, 0.35, -0.26, -0.40,
0.55, 0.05, -0.44, -0.72, -0.95, -0.21, -0.13, 0, 0, 0, 0) as shown
in FIG. 10(D), and used in equation (11), to calculate the signal
to noise ratio of the optimized 19-segment detector: 12 SNR 19 =
166.4 707.2 = 6.26 . ( 14 )
[0053] A regular 2-segment detector can be simulated by setting
g.sub.i=1 for i<=m (forming the first segment) and setting
g.sub.i=-1 for i>m (forming the second segment) as shown in FIG.
10(C). One typically chooses m such that the same power is incident
on each of the two "segments". In the example, m=8 and the
g.sub.i's are (g.sub.i, g.sub.2, . . . , g.sub.19)=(1, 1, 1, 1, 1,
1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1). The signal to
noise ratio of the 2-segment detector calculates to 13 SNR 2 = 87
3051 = 1.58 . ( 15 )
[0054] From equations 14 and (15) it follows that the signal to
noise ratio of the optimized 19-segment segment detector is 4.0
times higher than the signal to noise ratio of a regular 2-segment
detector. Also, the usual procedure of centering the spot on a
2-segment detector was eliminated in the case of the multi-element
detector.
[0055] In the described case of shot noise, the optimizing
g.sub.i's have a particularly simple dependence on the P.sub.i and
.DELTA.P.sub.i (equation (13)). In practice, there may be other
noise sources and/or the signal of interest may be defined
differently from equation (8). For example, one might want to
choose the g.sub.i to suppress a spurious signal. Different
definitions of signal, noise and the "merit" function that is to be
optimized can lead to more complex conditions for the g.sub.i than
equation (13). The optimum gains g.sub.i may have to be found
numerically in those cases. Also, one can consider other or
additional measurements with the individual detector segments
before deciding on the values for the g.sub.i's, such as vibrating
the cantilever at different normal modes.
[0056] In another implementation of using a multi-element detector
with individual gains, a 2-dimensional array of detector elements
(a CCD-chip, for example) can be used that further increase the
signal to noise ratio or that allow for the detection of additional
measurement signals. No constraint need be made to size and shape
of the individual elements.
[0057] The above optimizing method does not distinguish between an
optical beam deflection setup and interferometric setup and
therefore can be used interchangeably for both and in particular
with a combined optical beam deflection-interferometric setup.
Additionally, any signal extracted from the multi element detector
can provide input to a feedback system for regulating certain
tasks, such as dynamically optimizing the g.sub.i's(for example to
account for drift of the spot on the detector) or even to
dynamically adjust the position/size/shape of the focus spot on the
cantilever.
[0058] We are aware that a four segment detector has often been
used to enable an AFM to measure lateral cantilever deflections
next to its vertical deflections. Such use of three or more
segments per se is not a part of the invention.
[0059] Referring to FIG. 11, a housing 108 can be provided
thermally isolating the AFM 110 and can be equipped, as is common
with isolating enclosures with expandable manipulation gloves 112
or, in the alternative, can be operated remotely. By so isolating
the AFM, the temperature of the environment of the AFM is
regulated, thereby limiting thermal drift.
* * * * *