Abstract:
A method of imaging a sample present in a solution by employing an atomic force microscope comprises providing an atomic force microscope having a cantilever that is under the solution, contacting the cantilever with energy to cause the cantilever to bend and vibrate, and detecting the amplitude of vibration of the cantilever from the energy. The cantilever has at least one coating present thereon to absorb energy such that the cantilever bends and vibrates.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The instant application claims priority to U.S. Provisional Application No. 60/120,821 filed Feb. 19, 1999, the disclosure of which is incorporated by reference herein in its entirety. 
    
    
     The present invention was made with Government support under Grant Number HPCC ASC-9527192 from the National Science Foundation. The Government has certain rights to this invention. 
    
    
     FIELD OF THE INVENTION 
     The invention generally relates to methods of solution imaging and systems relating to the same. 
     BACKGROUND OF THE INVENTION 
     Atomic force microscopy (AFM) has proven to be a potentially valuable tool for studying biological systems. AFM imaging under solution allows one to potentially monitor biological processes m real time at a macromolecular level. A possible major problem with solution imaging occurs with samples, such as DNA, that are weakly absorbed to a surface, because they are easily displaced during imaging. This problem can be alleviated by resonance techniques that oscillate the cantilever as the sample is scanned laterally. There is a great need for reliable implementation of resonance mode imaging in solution because the most common techniques typically yield quality images infrequently. 
     SUMMARY OF THE INVENTION 
     In one aspect, the invention provides a method of imaging a sample present in a solution. The method comprises providing a microscope having a cantilever that is under the solution, contacting the cantilever with energy to cause the cantilever to bend and vibrate, and detecting the amplitude of vibration of the cantilever from the energy. The cantilever has at least one coating present thereon to absorb energy wherein the cantilever bends and vibrates. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates a diagram of a conventional Atomic Force Microscopy (AFM) system. 
     FIG. 2 illustrates a model for the mechanical and thermal properties of a cantilever. 
     FIG. 3 illustrates a resonance spectra of a blackened 100 μm long triangular cantilever driven (a) mechanically and (b) photothermally in water. 
     FIG. 4 illustrates an image of a 6000 base pair DNA plasmid on mica in a 50 mM HEPES buffer containing 5 mM MgCl 2 . 
     FIGS. 5 through 7 illustrate various embodiments for carrying out the method of the invention. 
     FIG. 8 illustrates the relationship between voltage and frequency for a sweep of a 200 micron triangular cantilever at 0.5 N/m. 
     FIGS. 9A through 9C are photographs illustrating the nanomanipulation of DNA in solution using photothermal modulation for imaging. FIG. 9A illustrates a photograph of the DNA prior to manipulation. FIG. 9B illustrates a photograph of the DNA after manipulation. FIG. 9C illustrates a photograph of the DNA a few minutes after manipulation. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The invention will now be described in greater detail with respect to the preferred embodiments set forth herein. It should be emphasized however that these embodiments are for the purposes of illustration only, and do not limit the scope of the invention defined by the claims. 
     An application of photothermal-modulation excitation of an AFM cantilever for resonance mode imaging in solution is presented. In one aspect of the invention, this application is demonstrated by producing high-quality images of DNA in solution, and presenting a quantitative analysis of the mechanical and thermal properties of a laser-heated cantilever. 
     In one embodiment, the support that holds the chip to which the cantilever is attached is oscillated by a piezoelectric transducer. While this approach can produce reliable resonance spectra in air, in liquid, the coupling of the support vibration to acoustic modes of the liquid produces spectra that contain many features unrelated to the cantilever vibrational modes. In general, this technique is potentially sensitive to solution conditions as well as to the properties of the individual cantilever being employed. It is clearly of interest to limit the vibrational excitation to the cantilever. 
     Recently, techniques that drive the cantilever directly, such as magnetic modulation and thermal modulation with remote resistive heating, have been proposed for solution imaging. Thermal modulation techniques typically exploit the temperature-dependent bending of a cantilever due to the difference in the thermal expansion coefficients between a deposited metal film and the cantilever material. In other contexts, the temperature-dependent bending of AFM cantilevers has been proposed to develop a femtojoule calorimeter and to observe heat fluctuations of a gas phase chemical reaction. Previously, photothermal modulation of metal-foil cantilevers has been used to image in air. 
     The invention will now be illustrated in reference to the drawings. One example of an instrumental setup is diagrammed in FIG.  1  and depicted as  200 . The numbered elements set forth in FIG. 1 correspond to the following features: position laser  320 , position detector  310 , heating laser  210 , cantilever  220 , modifying circuit  230 , x-y transition stage  240 , drive frequency  250 , reference  260 , lock-in amplifier  270 , feedback signal in  280 , scope base  290 , and response signal  300 . A description of the system is present in Ratliff et al.,  Applied Physics Letters,  72(15), pp. 1911-1913 (1998). In accordance with the present invention, the photothermal modulation of cantilevers using a modulated semiconductor laser to obtain high-quality images is disclosed. If desired, conventional cantilevers can be employed. The vibration of the cantilever may be generated by focusing a modulated diode laser (heating laser  210 ), such as, for example, a modulated/variable-power visible-laser module onto the cantilever  220  using a single lens that produces a spot. A commercial example of such a cantilever is made commercially available by Coherent, Inc. of Santa Clara, Calif. The spots may be of various sizes. One example of a size is about 20 μm. It should be appreciated that other lasers may also be employed. A standard AFM controller (for example, Digital Instruments, Inc. Nanoscope III of Santa Barbara, Calif. may be used, and an AC drive signal may be applied to the diode laser. As an example, the drive signal typically powers the piezoelectric transducer (FIG.  1 ). The position of the laser spot may be preferably determined by observing the oscillating part of the photodiode top-bottom signal. This position is, typically, at the base of the cantilever where it makes contact with the support. Although not wishing to be bound by a single theory, Applicants propose a time-dependent model for heat flow down a thin rod to model temperature-dependent bending of the cantilever. Applicants do not wish to be bound by this time-dependent model. 
     Although not wishing to be bound by theory, the derivation of the response of the cantilever to the illumination by a heating laser involves two parts: the determination of the temperature profile in the cantilever and the mechanical response of the cantilever to the temperature distribution. The bending of the cantilever due to a temperature profile T(x) measured with respect to the ambient temperature, is governed by the second-order differential equation                         2        z            x   2         =     aT        (   x   )         ,           (   1   )                     α   =                6        (       α   2     -     α   1       )                           t   1     +     t   2         t   2   2       [     4   +     6        (       t   1       t   2       )       +     4          (       t   1       t   2       )     2       +       (       E   1       E   2       )            (       t   1       t   2       )     3       +                                        (       E   2       E   1       )          (       t   2       t   1       )       ]       -   1       ,                 (   2   )                                
     where the subscripts refer to the two layers (1: Au, 2: Si 3 N 4 ), α is the thermal coefficient of expansion (α 1 =14.2×10 −6  K −1 , α 2 =3.2×10 −6  K −1 ), t is the layer thickness (t 1 =0.05 μm, t 2 =0.6 μm), E is the Young&#39;s modulus (E 1 =0.8×10 11  N m −2 , E 2 =1.8×10 11  Nm −2 ), z is the coordinate normal to the beam axis, and x is the coordinate along the beam. In general, for the above equation, subscript 1 refers to the substrate and subscript 2 refers to the coating. In a preferred embodiment, to evaluate the temperature profile, it is most preferable to specify the manner in which the energy from the laser beam is deposited into the cantilever, the heat losses, and the boundary conditions. One set of conditions that is typically sufficient to describe the main features of the problem while providing an analytical solution is the periodic heating of a thin rod at its end. The temperature is considered to be substantially constant through the cross section, while sustaining heat loss along the rod to a surrounding medium at a rate proportional to the temperature difference with that medium. 
     Although not intending to be bound by any one theory, an example of the temperature profile may be illustrated by: 
     
       
           T ( x )= Ae   −qx  cos (ω t−q′x ), 
       
     
     
       
           q ={[ν+(ν 2 +ω 2 ) ½ ]/2 K}   ½ , 
       
     
     
       
           q ′={[−ν+(ν 2 +ω 2 ) ½ ]/2 K}   ½ , 
       
     
     
       
         ν= Hp /( Cρw ). 
       
     
     The thermal diffusivity K=κ/Cρ is the ratio of the thermal conductance κ to the product of the heat capacity C and the mass density ρ. H characterizes the heat flow into the medium, P is the perimeter of the cantilever, and w is the cantilever width. ω is the pulse frequency of the laser (i.e., 2Π times the laser modulation frequency). 
     Again not intending to be bound by theory, a model for the heat flow into a surrounding medium is to assume that the heat is conducted across a boundary layer of thickness b and set H=κ w /b. In one embodiment, the medium is water (κ w =0.71 W m −1  K −1 ); a boundary layer of b is equal to 10 μm. As an example, a 100 μm long triangular cantilever with legs of width 20 μm as a 100 μm rectangular cantilever with a 40 μm width may be modeled. In the event that the cantilever employs a relatively thin (preferably between about 10 to about 400 nm) metal layer on a dielectric, the thermal properties, like the mechanical properties, should preferably be modeled as a laminated system; Cρ is replaced with (Cρ) eff =(C 1 ρ 1 t 1 +C 2 ρ 2 t 2 )/(t 1 +t 2 ) and κ with κ eff =κ 1 t 1 +κ 2 t 2 )/(t 1 +t 2 ), where the subscripts refer again to the values for the Si 3 N 4  (C 2 =750 J kg −1  K −1 ,ρ 2 =3.4×10 3  kg m −3 , k 2 =32 W m −1  K −1 ), and gold (C 1 =135 J kg −1  K −1 , ρ 1 =19.3×10 3  kg m −3 , k 1 =346 W m −1  K −1 ) layers. These values give ν=85.5×10 3  s −1  (corresponding to 13.6 kHz), and using a typical laser modulation frequency of 8 kHz (ω/2π=8 KHz), q=6.5×10 4  m −1  and q′=1.76×10 4  m −1 . This solution is a heavily damped sine wave with a 1/e length given by 1/q=15.4 μm, and oscillation wavelength λ=2π/q′=357 μm. Not intending to be bound by theory, the above result may provide insight for the qualitative observation that to get substantial oscillation of the cantilever the heating laser should preferably be located near the base of the cantilever where it joins the support chip (x=1). 
     Again not wishing to be bound by theory, in one embodiment, more quantitative insight into the preferred excitation geometry can be provided by evaluating the displacement of the cantilever free end when the temperature profile of the cantilever is given by T(x)=A exp (−q|x−d|) (see FIG.  2 ). This temperature profile is for the embodiment where the heat is absorbed as a delta function at location x=d, assuming the oscillating part of the spatial dependence can be ignored (1/q &lt;&lt;l). It is believed that by setting P=−[κ eff (t 1 =t 2 )w] ∂T/∂x, where P is the amplitude of the modulated laser power that is absorbed, one can solve for A=P/[2qw (κ 1 t 1 +κ 2 t 2 )]. An evaluation of the displacement of the cantilever, obtained by solving the second-order differential equation with the boundary conditions of z(l)=∂z(l)/∂x=0 and enforcing the continuity of z and ∂z/∂x at x=d, is given by z(0)=(aA/q 2 )[l+L)e(Δ−L)−e−Δ−2Δ], wherein the dimensionless quantities L=ql and Δ=qd are introduced A preferred position for the heating laser can be found by determining the value of Δ that maximizes z(0). In one example, Δ=5.15 for L=ql=100 μm/15.4 μm=6.5. For a preferred of values of L of interest (i.e., L=5-20), a preferred position of the heating laser from the cantilever base is about 1-2.5 times the decay length 1/q. For the purposes of the invention, the term “decay length” has its conventional meaning in the art and refers to the length of the cantilever that possesses a temperature different from the bulk environment surrounding the cantilever. The “cantilever base” is defined as the position at which the cantilever is attached to a supporting structure. Although not intending to be bound by theory, it is believed that a potential physical explanation for this result is that the temperature modulation and (and hence, cantilever bending) are confined to a region on the order of 1/q. It is preferable to place this region at the base because any bending there will produce a magnified deflection of the cantilever end. Finally, in an embodiment wherein Δ=5.15 and L=6.5, one observes that a 1 mW modulation amplitude of the absorbed laser power will produce a 40 nm deflection of the free end. In another embodiment, an amplitude modulation of laser illumination of approximately 2 mW with an estimated absorption in the AuPd overlayer of approximately 30% produces an oscillation amplitude of 10 nm. 
     As an example, high-resolution solution images may be obtained using both 100 and 200 μm long Si 3 N 4  cantilevers having preferred spring constants of 0.58 and 0.12 N/m, respectively. In a preferred embodiment, the cantilever has a spring constant ranging from about 0.02 N/m to about 1 N/m. Due to the presence of potentially sizeable amplitude in the solution, it is preferred to darken (e.g., blacken) the top of the cantilever to increase the absorption of the laser light. The back of the cantilever may be darkened by various methods, e.g., by painting the back of the tip chip with black paint or by sputter coating the tip chip with a gold/palladium alloy. Other darkening techniques can be employed. 
     FIG. 3 illustrates typical responses of a paint-blackened 100 μm cantilever driven mechanically and photothermally in solution. Similar results were obtained with both 100 and 200 μm Au/Pd-coated cantilevers. The mechanically driven lever generates an excitation spectrum with many resonances, while the spectrum for photothermal modulation shows a single resonance at 8 kHz. This resonance frequency and amplitude are believed to be dampened relative to air where a resonance frequency of 40 kHz with an amplitude of 30 to 40 nm is observed. The spurious resonances observed with the mechanically driven lever might potentially complicate frequency selection for imaging, since they are vibrations of the cantilever where the amplitude is not clipped for the feedback signal. 
     The efficacy of this method is demonstrated by the image of DNA shown in FIG.  4 . It should be appreciated, however, that other materials may be imaged in accordance with the invention. Examples of materials that may be imaged include, but are not limited to, biological materials (e.g., proteins, grids), as well as other materials that are typically imaged under solution. In the embodiment illustrated in FIG. 4, consecutive images of the DNA show minimal if any deformations. The measured width and height of the DNA in this embodiment are 7.0 and 2.5 nm, respectively. 
     The present invention demonstrates the application of photothermal modulation to directly drive the vibration of a commercially available AFM cantilever for resonance imaging in solution. Specific types of microscopes that may be employed include, without limitation, thermomicroscopes, and molecular imaging scopes. Preferably, the method of the invention represents a repulsive mode imaging process. The photothermal modulation technique is capable of cleanly exciting the fundamental cantilever vibrational mode of commercially available cantilevers. 
     The invention will now be described in greater detail with reference to FIGS. 5 through 7. In each of these embodiments, although not pictured, the operation of FIG. 5 depicts a cantilever  100  positioned in a solution. Various types of solutions may be employed such as, for example, aqueous solutions, organic solutions, and combinations thereof. The uncoated cantilever  105  may be one which is conventionally known in the art and is typically made of silicon or silicon nitride (Si 3 N 4 ), although other materials can be used. Examples are set forth in U.S. Pat. Nos. 5,753,814; 5,612,491; and 5,513,518, the disclosures of which are incorporated herein by reference in their entirety. The cantilever has a tip  110  and a top surface  120  opposite to the tip  110  that is present on the bottom side of the cantilever depicted by  130 . A beam of radiant energy b 1  from a detection laser (not shown) contacts the cantilever from its top  120  and reflects from the top to a detector  160 . A beam of radiant energy b 2  from a laser (not shown) designed to heat the cantilever contacts the bottom side  130  of the cantilever at a point b 3 . The cantilever then bends and vibrates and the detector  160  aids in monitoring the amplitude of vibration. Although radiant energy is described above, it should be appreciated that the invention is not limited to employing radiant energy. As depicted in FIG. 5, it is preferable that the heating laser beam contact the bottom side of the cantilever at a position distal from the tip  110  (b 3 ), although other configurations may be used. It is most preferred that the position of the source of radiant energy from the cantilever base be about 1 to about 2.5 times the decay length of the cantilever (1/q) as defined herein. For example, the heating laser may be positioned above the cantilever. In many instances, the light passes through the cantilever and is absorbed by an absorbing coating described below. 
     As shown, the top side has at least one coating positioned thereon. In this embodiment, an absorbing coating  140  is present on the top surface  120  of the cantilever  100  and is generally intended to absorb light from the heating laser and reflect light from the detection laser. The absorbing coating  140  may be formed from various materials that allow for the absorption of light. Preferably, the absorbing coating has a thickness ranging from about 5 nm to about 100 nm. In this embodiment, coating  140  is in the form of a layer of black paint. Metals such as, for example, gold, palladium, silver, aluminum, and alloys thereof may also be used. Positioned on the absorbing coating  140  is a reflective coating  150  that allows for the selective reflection of light. As an example, the reflective coating may be formed from various metals and alloys thereof known in the art such as, for example, gold, aluminum, palladium, and silver. A preferred thickness for the reflective coating ranges from about 10 nm to about 400 mn. It is preferred that the reflective layer have an expansion coefficient that is different than a conventional cantilever made from, for example, silicon or silicon nitride. 
     Moreover, although not depicted, the invention may allow for the use of multiple lasers of the same or different wavelengths. In addition, the coating properties of the layers contained on the cantilever may be fashioned to as to reflect light from one laser and absorb light from another laser. 
     An additional embodiment is illustrated by FIG.  6 . In contrast to FIG. 5, the reflective layer  150  is positioned between the absorbing layer  140  and the uncoated cantilever  105 . Moreover, the beam b 2  intended to heat the cantilever  100  is positioned on the same side as the detection beam b 1  relative to the cantilever  100 . 
     In another embodiment illustrated in FIG. 7, a single coating may be present on top of the cantilever  170 . The coating  170  may exhibit both reflective and absorptive properties and may be fashioned in a manner to be selective to the various properties set forth herein. This coating may be formed from various materials such as, gold, palladium, aluminum, silver, and alloys thereof. Preferably, the coating  170  which exhibits both reflective and absorptive properties has an expansion coefficient different than the material from which the cantilever is formed, e.g., silicon or silicon nitride. The coating  170  should absorb light in sufficient quantities to induce bending and vibration of the cantilever. 
     Other embodiments of the system may be employed for the purposes of the invention. In one embodiment, other layers may be present in addition to the reflective and absorbing coatings  140  and  150 . As an example, a dielectric coating may be present on top of the reflective coating  150  and can be formed by those materials known in the art such as, for example, polymers, magnesium fluoride, and mixtures thereof. 
     The operation of the coated cantilever contemplated by the invention is typically carried out by illuminating the cantilever with beam b 1  from the detection laser. Energy provided from the heating laser in the form of beam b 2  is then imparted to the cantilever  100  at a location b 3  to commence bending and vibration of the cantilever including tip  110 . The intensity of the heating laser may be selected according to various considerations, and preferably ranges from about 0.1 milliwatts (mW) to about 10 mW. The amplitude of the vibration of the cantilever is then monitored by the detection laser, although it should be appreciated that other detection methods may be used. By virtue of the operation described herein, the molecular structure of materials (e.g., biological) may be deduced. Moreover, the molecular structure of various materials may be manipulated by the invention described herein. 
     Advantageously, the coatings used on the cantilever described herein can be designed to select for the wavelength of light, the polarization of the light, the angle of incidence, or the direction of incidence. In addition, the reflection of the detection beam contacting the cantilever, the absorption of the heating beam contacting the cantilever, and the extent of cantilever bending may all be optimized. Although not wishing to be bound by any theory, it is believed that the above parameters can be achieved by manipulating the chemical composition, thicknesses, and/or physical properties of the various coatings present on the cantilever. As an example, the thicknesses of each of the layers used on the cantilever may range from about 1 nanometer (nm) to about 100 nm. 
     The present invention is highly advantageous. In one respect, the invention employs coated cantilevers having bimetallic properties. Since the expansion coefficients of the two materials present on the cantilevers are different, bending of the cantilever may be achieved by heating the cantilever. This can be contrasted to nickel foil cantilevers employed in air as described by the prior art which display a temperature gradient resulting in the bending of the cantilever. The invention is able to operate in the resonance mode of the cantilever. 
     In another respect, the solution imaging methods and apparatuses encompassed by the invention involve repulsive mode and intermittent contact. This is in clear contrast to air imaging which involves attractive mode, non-contact imaging. It should be noted, however, that the invention may be employed in non-contact imaging applications if so desired. 
     In each of these embodiments, although not pictured, the operation of laser and the imaging of the sample may be controlled by an appropriate automated software system. A commercially preferred system is Thermomicroscopes, Molecular Imaging made commercially available by Digital Instruments, Inc. of Santa Barbara, Cailf. 
     The invention will now be described in further detail with respect to the foregoing examples. It should be emphasized however, that the examples are for the purposes of illustration only, and are not intended to limit the scope of the invention as defined by the claims. 
     EXAMPLE 1 
     A comparison of the theoretical deflection for cantilevers having coatings made from various materials. Cantilevers D, E, and F were investigated and were all silicon cantilevers. The cantilevers were each 1 micron in thickness, 300 microns in length, and 35 microns in width. Cantilever D has a length of 300 microns, cantilever E has a length of 350 microns, and cantilever F has a thickness of 250 microns. The force constant of cantilever D was 0.05 N/m, and E and F were 0.03 N/m and 0.08 N/m respectively. Cantilever D has a resonance frequency of 140 kHz, while E and F have resonance frequencies of 10 kHz and 20 kHz respectively. 
     Various deflections were calculated for these cantilevers using various coating materials and thicknesses, the results of which are set forth in Table 1. Equations (1) and (2) were employed in calculating the deflections. 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 COMPARISON OF DIFFERENT COATING MATERIALS 
               
             
          
           
               
                 COATING 
                   
                   
                   
                   
                   
                   
                   
               
               
                 THICKNESS 
                 Al 
                 Al 
                 Ni 
                 Ni 
                 Au 
                 Au 
                 Mo 
               
               
                   
               
               
                   
                   
                   
                 Not include 
                 Include 
                 not include 
                 Include 
                 not include 
               
               
                   
                   
                   
                 Reflectivity) 
                 Reflectivity) 
                 reflectivity) 
                 Reflectivity) 
                 Reflectivity) 
               
               
                   
                 Deflection 
                 Deflection 
                 Deflection 
                 Deflection 
                 Deflection 
                 Deflection 
                 Deflection 
               
               
                   
                 P: 5 mw 
                 P: 7.5 mw 
                 P: 5 mw 
                 P: 5 mw 
                 P: 5 mw 
                 P: 5 mw 
                 P: 5 mw 
               
               
                   
                 Um 
                 um 
                 Um 
                 Um 
                 um 
                 Um 
                 Um 
               
               
                 Contact D 
               
               
                 no coating 
               
               
                  20 nm 
                 10 
                 15 
                 10 
                  41 
                  5 
                  3 
               
               
                  40 nm 
                 19 
                 28 
                 18 
                  76 
                  9 
                  5 
               
               
                 100 nm 
                 41 
                 61 
                 36 
                 149 
                 19 
                 11 
               
               
                 200 nm 
                 64 
                 96 
                 51 
                 210 
                 29 
                 16 
               
               
                 300 nm 
                 76 
                 113  
                 56 
                 230 
                 33 
                 18 
               
               
                 400 nm 
                 79 
                 119  
                 56 
                 230 
                 34 
                 19 
               
               
                 Contact E 
               
               
                 no coating 
               
               
                  20 nm 
                 16 
                 23 
                 16 
                  65 
                  8 
                  4 
                  4 
               
               
                  40 nm 
                 30 
                 45 
                 29 
                 120 
                 14 
                  8 
                  7 
               
               
                 100 nm 
                 64 
                 97 
                 58 
                 237 
                 30 
                 17 
                 12 
               
               
                 200 nm 
                 102  
                 153  
                 81 
                 334 
                 46 
                 25 
                 15 
               
               
                 300 nm 
                 120  
                 180  
                 89 
                 365 
                 52 
                 29 
                 15 
               
               
                 400 nm 
                 126  
                 189  
                 89 
                 366 
                 53 
                 29 
                 14 
               
               
                 Contact F 
               
               
                 no coating 
               
               
                  20 nm 
                  6 
                  8 
                  6 
                  24 
                  3 
                  2 
               
               
                  40 nm 
                 11 
                 16 
                 11 
                  44 
                  5 
                  3 
               
               
                 100 nm 
                 24 
                 35 
                 21 
                  86 
                 11 
                  6 
               
               
                 200 nm 
                 37 
                 56 
                 30 
                 122 
                 17 
                 10 
               
               
                 300 nm 
                 44 
                 66 
                 32 
                 133 
                 19 
                 11 
               
               
                 400 nm 
                 46 
                 69 
                 32 
                 133 
                 20 
                 11 
               
               
                   
               
               
                 P = The thermal energy absorbed by the cantilever  
               
             
          
         
       
     
     These theoretical calculations allow for bending behavior to be predicted. 
     EXAMPLE 2 
     An experimental example of solution imaging is as follows. A heating laser (variable power 5 mW 640 nm) was focused on a cantilever close to where it is attached to the cantilever base. A detection laser was focused on the other end of the cantilever. A frequency sweep was obtained with standard software that operates the Thermomicroscope AFM. FIG. 8 illustrates the results of the frequency sweep. The arrow set forth in the figure depicts the frequency at which the laser was pulsed and which the cantilever was vibrated. This figure demonstrates that the system is capable of generating a resonance frequency. 
     EXAMPLE 3 
     A 6000 base pair DNA plasmid was imaged on mica in a 50 mM HEPES buffer containing 5 mM MgCl 2 . The DNA was deposited onto a clean mica surface, then placed under solution for imaging. A 200 micron long triangular cantilever with a 15 nm layer of Au/Pd was driven at 17.46 kHz with a 20nm amplitude. A scan rate of 2.65 Hz was used for imaging. The image is illustrated in FIG.  4 . 
     The specification describes preferred embodiments of the invention, particularly in reference to the accompanying drawings. It should be appreciated, however, that these embodiments in no way serve to limit the invention.