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Morphological Restoration of Atomic Force Microscopy Images David L Wilson,*>?$$ Kenneth S. Kump,? Steven J. Eppell,? and Roger E. Marchant? Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106, and Department of Radiology, University Hospitals of Cleveland & Case Western Reserve University, Cleveland, Ohio 44106 Received July 13, 1994. In Final Form: October 4, 1994@ Atomic force microscopy (AFM) images ofbiomolecules, and other structures similar in size, are enlarged because of the finite size of the probe tip. We present a method based on morphological image processing that allows one to analyze and correct the enlargement. Morphological restoration is ideal in some regions, giving the exact sample surface. In other regions, it gives a surface with improved resolution. The method uses measured, realistic tip shapes, not idealized functions. Tip surfaces are generated by restoring images of known gold spheres having diameters of about 10 nm. We generate tip images of carbon and Si3N4 probes and find good correlation with scanning electron microscopy. Generated tip surfaces are used to restore images of unknown objects to produce images at enhanced resolution. Diameters of contours at constant elevation are changed by as much as 25%. In addition to improving resolution, morphological restoration also corrects distortions due to imaging with asymmetrical tips. The approach uses methods and software readily available to the atomic force microscopist.
Introduction The atomic force microscope (AFM) has become well established as a valuable tool in the three-dimensional topographical analysis of bi~polymersl-~ and is rapidly developing as a novel technique for measurement of intermolecular interactions with high spatial resolution.5p6 The three-dimensional structure of most biopolymers falls within the size range of 4 to 10 nm in lateral dimensions by 1 to 5 nm in height. Unfortunately, in this size range, the finite size of the probe tip leads to relatively large systematic enlargements. For example, we reported recently on AFM images, obtained under ambient conditions, of von Willebrand factor (vWF), a plasma glycoprotein of importance in hemostasis and thrombosis of We measured globular-domainlateral dimensions that were 2-3 times larger than expected based upon published electron microscopy (EM) data.8 Similar observations of lateral enlargement have been made by other groups and attributed to artifacts resulting from ambient humidityvJOand large adhesive forces.11-13 The t Department ofBiomedical Engineering, Case Western Reserve University. t Department of Radiology, University Hospitals of Cleveland. Abstract published in Advance A C S Abstracts, December 1, @
1994. (1) Rees, W. A.; Keller, R. W.; Vesenka, J. P.;Yang,G.; Bustamante, C. Science 1993,260, 1646. (2) Hansma, H. G.; Sinsheimer, R. L.; Groppe, J.;Bruice, T. C.; Elings,
V.; Gurley, G.; Bezanilla, M.; Mastrangelo, I. A.; Hough, P. V.; Hansma, P. K. Scanning 1993,15, 296. (31 Ohnishi., S.:. Hara,. M.:. Furuno, T.: Sasabe. H. Biophrs. - - J. 1993,
65, 573. (4) De-Grooth, B. G.; Putman, C. A. J. Microsc. 1992, 168, 239. (5) Florin, E. L.; Moy, V. T.; Gaub, H. E. Science 1994,264,415. (6) Lee, G. U.; Kidwell, D. A.; Colton, R. J. Langmuir 1994,10,354. (7) Eppell, S. J.;Zypman, F. R.; Marchant, R. E. Langmuir 1993,9, 2281.
(8)Fretto, L. J.; Fowler, W. E.; McCaslin, D. R.; Erickson, H. P.; McKee, P. A. J. Bwl. Chem. 1986,261, 15679. (9) Slayter, H.; Loscalzo, J.; Bockenstedt, P.; Handin, R. I. J. Biol. Chem. 1985,260, 8559. (10) Thundat, T.; Warmack, R. J.; Allison, D. P.; Bottomley, L. A.; Lourenco, A.; Ferrell, T. L. J. Vac. Sci. Technol., A 1992, 10, 630. (11) Yang, J.; Shao, Z. Ultramicroscopy 1993, 50, 157. (12)Lyubchenko, Y. L.; Oden, P. I.; Lampner, D.; Lindsay, S. M.; Dunker, K. A. Nucleic Acids Res. 1993,21, 1117. (13) Thundat, T.; Zheng, X.-Y.; Chen, G. Y.; Sharp, S. L.; Warmack, R. J.; Schowalter, L. J. Appl. Phys. Lett. 1993, 63, 2150.
shape of the AFM tip is intimately related to this lateral enlargement phenomenon both because of simple, hardsurface, geometric considerations and because sources of interactive forces are distributed over the tip surface as well as the sample surface. If one wishes to calculate a particular net force component between the tip and surface, one must first obtain the shape of the tip using a method such as the one we present. It is probable that AFM images of biopolymers contain additional, complex distortions due to asymmetrical probe tips.14 In initial efforts to quantify the enlargement error caused by the probe tip, we examined objects with welldefined dimensions that provided an experimental model for the protein globular domains of v W F . ~ We imaged polystyrene spheres that were 14 f 4 nm in diameter, as determined by EM, and obtained 39 f 8 nm in lateral dimensions when measured by the AFM. We analyzed these data with a simple geometric model for the tip. Our results were not entirely satisfactory and remained inconsistent with past EM results. In addition, we assumed a smooth symmetrical shape for the tip, a sphere, although there is good evidence that standard Si3N4 tips contain significant asymmetries. A more accurate method was needed to address the problem of tip-induced artifact and to account for the significant error in the images. Furthermore, as the measurement of biomolecule receptor-ligand interactions develops as a major focus of the AFM, it has become increasingly obvious that accurate informationon probe tip size and shape is needed to equate theory with measured forces.15 When contact mode AFM is used to image structures, a portion of the probe tip proportional in size to the height ofthe imaged object makes contact with the surface. When objects of atomic dimensions are imaged, as on mica and graphite surfaces, optimally a single atom contacts the surface. In this case, the probe tip shape and size can be calculated using the van der Waals radius or molecular orbital theory. Interaction near the scale of a single atom has been modeled as a linear superposition of forces (14) Vesenka, J.; Miller, R.; Henderson, E. Rev. Sci. Instrum. 1994, 65, 2249. (15) Leckband, D. D.; Israelachvili, J. N.; Schmitt, F. J.; Knoll, W. Science 1992,255, 1419.
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distributed over atoms at the very end of the tip, and deconvolution is the method of choice to improve resolution.16 This is described for STM17J8and magnetic force m i c r o s c ~ p y When . ~ ~ ~ larger ~ ~ structures are imaged such as gold spheres or globular proteins, many atoms on the probe may interact with the surface. The contact point (points) between the probe and sample shift as the tip goes up, over, and down a structure, while the probe position is always recorded with reference to a single point near the geometric apex of the tip.21 A consequence is that image resolution depends upon the size and shape of the probe. Assuming noncompressible probes and samples, one obtains a contact-point, hard-surface interaction that is decidedly nonlinear: contact is either all or nothing. This has been modeled using Legendre transforms16J4and the “envelope reconstruction’’ technique.22 Markiewicz and Goh present a method with similar assumption^.^^ As described below, such a n interaction can also be modeled using mathematical morphology. A hard-surface, sliding-contact AFM model is described using mathematical morphology. Using the model, we develop an AFM restoration technique whereby image resolution is greatly improved. While the literature shows that morphologicalimage processing techniques are welle ~ t a b l i s h e d , ~ ~use - ~ ’of these techniques has not been reported for AFM image resolution enhancement. Weisman et al. introduced the use of morphological analysis to reduce noise in AFM images.28 After showing that Keller’s envelope reconstruction can be described in the language of mathematical morphology, we extend his analysis to show regions of varying certainty are obtained in a restored AFM image and to measure two-dimensional tip surfaces. Our initial application is to image known samples (gold beads) and generate restored images of two different types of probe tips. We then use a generated tip to restore an AFM image of an “unknown” gold bead and obtain a n image at higher resolution. An identical approach can be used to restore images of biomolecules, and any AFM user can, with the aid of commercially-availableimage analysis software, perform similar state-of-the-art image restorations of their data.
Theory Gray-ScaleMorphological Image Processing. In this section, we present morphological operations in a graphical form. More formal definitions are given e l ~ e w h e r e . ~Later, ~ - ~ ~we give formulas for performing the necessary operations. Several preliminary definitions are Morphological image processingis most often done with binary (16) Keller, D. Surf. Sci. 1991,253, 353. (17)Tersoff, J.; Hamann, D. Phys. Rev. Lett. 1983,50, 1998. (18)Tersoff, J.; Hamann, D. Phys. Reu. B 1985,31, 805. (19)Xiaodong, C.; Lederman, M.; Gibson, G. A.; Bertram, H. N.; Schultz, S. J. Appl. Phys. 1993, 10, 5805. Judy, J. H.; Fischer, P. (20) Chang, T.; Lagerquist, M.; Zhu, J.-G.; B.; Chou, S. Y. IEEE Trans. Magn. 1992,28, 3138. (21) Experimentally,it is not particularly important where this apex is located on the tip. However, for convenience i t is usually assumed to be the point on the tip which is closest to the plane defined by the z axis of the image collected. (22) Keller, D. J.; Franke, F. S. Surf. Sci. 1993,294,409. (23) Markiewicz, P.; Goh, M. C. Langmuir 1994,10,5. (24) Sternberg,S. R. Computer Vision,Graphics,Image Process. 1986, 35, 333. (25) Haralick, R. M.; Sternberg,S. R.; Zhuang,X. ZEEE Trans.Patten Anal. Mach. Intell. 1987, PAMI-9, 532. (26) Haralick, R. M.; Shapiro, L. G. In Computer and Robot Vision; Adison-Wesley: New York, 1992; Vol. 1. (27) Maragos, P.; Schafer, R. W. Pmc. ZEEE 1990, 78,690. (28) Weisman, A. D.; Dougherty, E. R.; Mizes, H. A.; Dwayne-Miller, R. J. J. Appl. Phys. 1990, 71, 1586.
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x-y distance Figure 1. Erosion and dilation of a gray-scale image are illustrated. In A, the imageM and structuring elementL (inset) are shown. Shaded regions are umbrae of the respective surfaces. In B, a dilationoperationis performed upon the umbra of M. The dilation is obtained by placing the umbra L a t all positions in M such that the origin is contained within M.One marks all points overlapped by L to create the umbra of the dilation. The top operation gives M @ L as shown in D. In C, an erosionis shown, and one position ofL is illustrated. In this case, we use the originofL as a marker and sweepL everywhere that it is contained within M. The erosion lowers the surface whereas the dilation raises the surface (D). The dimensions of both the horizontaland vertical axes are typically nanometers in AFM. images; however, the elevation values in AFM give image gray-scale values, and we consider the more general case of gray-scale morphological image processing. A grayscale image is considered as a two-dimensional surface. We also consider the umbra which consists of all gray values “under” the surface extending to Similarly, there is a top operation, which gives the top surface of an umbra. The structuring element (SE) incorporates the shape of interest, and it is also a two-dimensional grayscale surface. Often, the SE surface is flat, hemispheric, or parabolic. Later, we will use an SE shaped like an AFM probe tip. There are two elementary operations, erosion (0) and dilation (e). These are combined to perform an opening (0)or a closing ( 0 ) . In Figure 1,we illustrate erosion and dilation operations on a one-dimensional signal similar to a row of pixels. The image is M and the structuring element is L (Figure 1A). The umbrae of both M and L are the shaded regions extending to The origins are marked on the axes, and the important origin of L is additionally marked by a dot. In the dilation operation (Figure lB), the origin of the umbraL is placed at all points within umbra M.29One position of L is illustrated. To create the output umbra, we use all points in L as markers and mark all positions occupied byL on the output. This creates an umbra which is the union of the shaded regions in Figure 1B. A top operation creates the final output image surface, M @ L (Figure 1D). A dilation raises the gray-scale surface (Figure 1D). In the case of erosion, we start with the same M and L umbrae. We move L about such that it is totally contained within M. One position of L is illustrated in Figure 1C. Using the origin of L as a marker, we mark all positions where L is contained within M. This creates a new umbra, and the top operation gives the output grayscale image. An erosion lowers the surface (Figure 1D). -00.
-00.
(29) We use the symbols M and L to mean either the surface or the umbra, and the reader must determine the meaning from the context.
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As described previously, these calculations are performed
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x-y distance Figure 2. An opening and a closing are illustrated. In this case, we use a structuring element,L (inset),that more closely resembles an AF’M probe tip. In A, an opening consistsof sliding L along the underside of the image surface. The output, M 0 L, consists of the highest gray-scalevalues reached by any point in L. In B, a closing consists of placingL tip down and reflected left-right and slidingit along the top of the image surface.The output, M L , consists of the lowest gray-scale values reached by any point in L. The horizontal axis is either the x or y scanning directionwhile the vertical axis is the AFMz elevation. A n opened image is obtained by eroding the input image and then dilating the resultant image using the same SE in both operations, M 0L = M 9L @ L . If the input image is first dilated and then eroded, a closing is obtained, M L = M @ L 8 L . An opening can be interpreted physically as taking a n object whose top surface is described by the SE, pressing it up against the underside intensity surface of the image, and moving it about while marking the highest point reached by the object a t each pixel in the image (Figure 2A). In the figure, L is the top half of a parabola and M 0 L traces how it fits under a triangle and a pulse. In the case of a spherical SE, the algorithm is called the “rollingball algorithm”.24 Positive excursions smaller than the SE are eliminated with a n opening. In a closing, the SE is reflected left-right and flipped up-down. The resulting structure is then pressed down from the top onto the gray-scale image surface and moved about. The minimum gray-scale values reached by the reflected, upside down SE are recorded and become M L (Figure 2B). Negative excursions smaller than the SE are removed by a closing. Equations for two-dimensional calculations are now d e s ~ r i b e d . ~Erosion ~ - ~ ~ of a n image, M(xy), by a n SE, Lo‘,k),follows.
M 8 L = min[M(x+jj+k) j,kGL
(x + j , y
- L(j,k)I
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+ k) E M
Each element of the SE is subtracted from the corresponding image pixel gray level; the minimum of these calculations becomes the output pixel at ( x y ) ,and this is repeated for all output pixels. The output image array size is the same as the input. Dilation is calculated in much the same way except that pixel subtraction is replaced by addition, a maximum replaces the minimum function, and the orientation of the SE with respect to the image is reversed.
M
L = m=[M(x-jj-k) J,kEL
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sequentially to give openings and closings. We now have the morphologydefinitions and operations required to model the AFM process. In the next section, we model the process and develop a morphological restoration technique that can be used to improve AFM image resolution. Morphological Restoration of AFM Images. We assume that under the conditions of imaging, there is a hard-surface, sliding-contact interaction between the probe and sample. For such a n interaction, we obtain the situation in Figure 3. From the notation of Keller and Franke,22 the original sample surface is s(x), the AFM image surface is z(x), and the restored surface with improved resolution is r(x). The sample is moved up to the probe until the probe contacts a t least one point but does not penetrate the sample surface. In the figure, this occurs at the tip center indicated by the dot. The sample is now moved such that the AFM probe tip raster-scans the sample and a relative elevation of the probe is recorded a t each position of the probe center. This operation gives the AFM image surface, z(x)from the sample surface, s(x). For morphological operations, we assume that the probe is represented by a tip surface, t(x)(Figure 3, inset). Note that the tip surface is defined to be “point up” and that the origin is at the apex of the tip. Also, we place a spike on the probe in order to identify the left-right orientation of the probe. In Figure 4, we relate this description to a morphological operation. In A, we plot the negative of s ( x ) and various positions of a probe tip which is left-right reflected as compared to the inset in Figure 3. The reflection is required to place the correct side of the probe against the sample surface. From the physical interpretation of gray,scale eTosion, we immediately find that -zv= (-SI 8 t , where t indicates a left-right reflection; i.e. t(x)= t(-x). A morphological property, the duality relationship between grFy-scale dilation and erosion, states”-(M @ L ) = (-M) 8 L.25 Hence, we obtain -z = (-SI 8 t = -(s @ t ) , a n d z = s 03 t . The surface traced out by the probe tip is a low resolution image. That is, a steplike edge on the sample surface is broadened in z(x) (Figure 3). If we know the shape of the tip, then we can improve the image resolution. For example, if the probe is a t a position x‘, we are assured that the sample surface lies everywhere below the probe surface. If we place the probe at all possible positions alongx, and mark the lowest possible value obtained, we get the restored surface, r(x). This operation is exactly the closing operation, and r = s t . Substituting, one obtains, r = s t = s @ t 8 t = z 8 t . There are three important regions associated with the restoration (Figure 3). In region (l), both the raw AFM image and the restored AFM image are equal to the sample surface (r = z = s). In region (2),the restoration recovers the sample surface ( r = s), and the raw AFM image is degraded (z t s). In region (3), the restoration improves image resolution but does not exactly recover the sample surface ( r f s). In region (3), restoration error progressively increases as one approaches the baseline. Note that the restored shape in region (3) reflects the probe shape. Restoration in regions (1)and ( 2 )is ideal;it obtains the sample surface. In region (3), restoration gives a n improved version of the image. For completeness, there are other possibilities not shown. If the probe is so large that no portion of it enters a negative excursion in the sample, then restoration does not improve resolution and r = z but r t s. Likewise, it should be understood that restoration does not allow one to image a region on the undersurface of a sample.
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Region: ir
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Figure 3. Morphological restoration is illustrated. The sample surface is imaged by the probe tip. As compared to the normal AFM image, z, the restored image, r, much more closely follows the sample surface, s, and has improved resolution. For the morphological operations, the probe tip surface is considered to point upward with the tip center placed at the origin (inset). A spike on the probe tip shows the proper orientations of the tip. In region (l), r = z = s; in region (2), r = s ;t z ; in region (3), r f s f z . In regions (1) and (2), ideal restoration is obtained and the restored surface equals the sample surface. In region (3), restoration gives an image surface having improved resolution.
r
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r=zet Dilation is commutative, M @ L = L @ MF5 hence z=s@t=t@s
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Figure 4. In A, - s ( x ) and several positions of the AF’M probe are plotted. The process of obtaining the AFM image gives -z(x) as seen by comparingA and B. From the position of the orientation spike on the probe, it is obvious that the probe tip is left-rightreflected ( t )as compared t o the orientationin Figure 3. In B, we find -z = (-SI 8 t. We use this expression to derive the working equations (see text).
Application to AFM Data. Some potential applications are suggested. First, given tip and model sample surfaces, one can predict the AFM image. z=s@t
(3)
Second, given a measured AFM image and a tip surface, one can obtain a restored image having improved resolution.
(5)
Thus, identical AFM images are obtained by dilating the sample by the tip or the tip by the sample. It follows that we get identical AFM image surfaces simply by interchanging the tip and sample surfaces. The ability to “switch” the notion of sample and tip suggests that we can obtain a n image of the tip using a sample of known shape. We can then improve the resolution of the tip by restoration. Recall that r = z 8 t ; switching s and t gives a restored tip surface,
rtip= z
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Given a measured AF’M image and the true sample surface, one can generate a restored tip image. The generated tip surface can then be used to restore a n image of unknown objects.
Methods Experimental Procedures. All AFM images are collected using a Nanoscope I11 AFM (Center for Cardiovascular Biomaterials, Case Western Reserve University, Cleveland, OH) in the contact mode. The microscope is set so that the cantilever deflection maintains a n applied force of (10 nN; the force of adhesion is e30 nN. We carefully adjust feedback gain and scanning speed to minimize errors due to temporal response limitations. Adjustments are made until trace and retrace lines of a n object ofinterest are as similar as possible. At this optimal adjustment, a n additional increase in feedback gain or
Morphological Restoration of AFM Images
decrease in scanning speed does not change the image. The Si3N4 integrated tiplcantilever assemblies are Nanoprobes (Digital Instruments, Santa Barbara, CA) with a manufacturer's reported spring constant of 0.6N/m. For some experiments, ultrasharp carbon spikes are grown on top of the silicon nitride pyramidal tips. Spikes are grown by first soaking the entire cantilever assembly in EM grade acetone and then exposing the apex of the Si3N4 tip to a stationaryfocused beam at 20-25 kV accelerating voltage for 2 min in a Hitachi S-900 field emission probe scanning electron microscope (Integrated Microscope Facility, University of Wisconsin,Madison, WI).We have difficulty reproducibly forming carbon spikes with this procedure, and we suspect that an adventitious contaminant on the inside surface of the beaker of acetone is responsible for the sucessfully grown tips. The sample surface is prepared by depositing a 4-pL drop of solution containing 18-nm gold beads in distilled water (1 x 10l2 beads/mL) onto a freshly-cleaved mica surface ~1cm2 in size. The surface is then dried in a stainless-steel sorption pumped vacuum chamber at 0.1 Torr for '2 h. The drying process is essential for scanning the surface with the AFM without moving the spheres. Image Processing and Analysis. AFM images are transferred in binary format to a workstation for analysis (SPARC 10, Sun Microsystems). Images are inverted so that excursions of increased elevation are positive, darkto-light excursions on our gray-scale display. We cut regions of interest (ROI's) surrounding the images of the gold beads of size greater than the extent of the probe tip (70-90 pixels). Beads which are close together (within 2 widths of the tip) are not considered. Image processing and analysis are done on general-purpose image processing/analysis software systems (Dip-Station, HIPG, Boulder, CO, and Matlab, Mathworks, Natick, MA). Both packages are available for Macintosh computers as well as Sun workstations.
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The gold beads are assumed to be perfectly spherical. We measure the height of each bead as the mean of peak elevation values from two base-line subtracted, crosssectional measurements. This value becomes the diameter when we calculate the hemispherical, gray-scale SE. This process is repeated for each ROI. We apply the morphological restoration technique to get a n enhanced image of the probe tip surface (eq 6 ) . We compare restored images of a single probe tip that are generated from multiple gold spheres. We register pairs of images usingx and y translation to align the apex of the tips. The apex is defined as the position of the peak height after low-pass filtering with a 3 x 3 averaging kernel. To match peak elevation values, an offset is added such that all tips have a maximum value of zero. We can now examine image differences to determine variations in the measurement.
Results We demonstrate the morphological methods on images of gold beads. From a gray-scale AFM image (Figure 5A), a square ROI surrounding an isolated gold particle is extracted (Figure 5B). The height of the gold particle (13 nm)is used to create an idealized sample surface consisting of the top half of a sphere of diameter 13nm (Figure 5C). Following erosion to create the restored tip surface, the result is rendered using a flat-surface shading technique and a single light source (Figure 5D). Due to contact with the background substrate, the restored tip surface flattens at the bottom, and one can see the beginnings of this in the figure. Useful restored information is obtained toward the top of the image where the contact point (points) are between the probe and gold sphere. Restoration affects elevation values at a fixed position. It also affects the position of a given elevation. In Figure 6, we investigate the latter effect. Matching contours at
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nm 25
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Figure 6. Effect of restoration on tip width is examined.
Contours are obtained at constant elevation. The solid curves are contours from the input image and the dashed curves are contours following restoration. Numbers on the figure are elevations in nm. The maximum difference between contours is ~4 nm. equal elevation are shown before (solid line type) and after (dashed line type) restoration. The restoration has more effect as one goes from the apex to the base of the tip. Contour diameters change between 3 and 6 nm. Ideally, one desires identical images of a single probe tip obtained from multiple gold beads. Although restored images of a single probe look similar, there are small differences. Moreover, when a single gold bead is repeatedly scanned, generated tip surfaces are somewhat more consistent, but not identical. It is noteworthy that measurement noise as measured on the mica substrate is much smaller than deviations obtained from repeated scanning of a gold bead. At this molecular scale, much uncertainty exists regarding the reproducibility of the AFM technique. We account for this uncertainty by averaging restored images to obtain an average tip.30 We show average generated tip surfaces for a carbon probe (Figure 7A)and an Si3N4 probe (Figure 7B). These images are obtained by registering and averaging multiple restored tips as described in Methods. SEM tip images are also obtained, and we show a carbon probe attached to a Si3N4 pyramid (Figure 7C). The carbon appendage is quite smooth and has a greater aspect ratio and a smaller radius of curvature than the Si3N4 pyramid. These observations agree well with the AFM tip images. We analyze a magnified SEM image of the same carbon probe from the AFM image in Figure 7A. Despite the limitations of a radius of curvature measurement, a radius of curvature measured from the SEM image (%15 nm) agrees well with that from the generated AFM tip image ( ~ 1 7 nm). In Figure 8,we examine the restoration of an “unknown” bead using a generated tip surface. The bead image prior to restoration (Figure 8A) becomes much narrower following restoration (Figure 8B). We examine dimensional changes in a contour plot (Figure 8C). The maximal change in contour diameter is about 10nm or ~ 2 5 %of the diameter. Because one cannot image the underside of the bead and because one has more confidence in the restored image near the top of the bead, we clip the images at 8 nm from the highest point, about l/2 of the bead diameter. At the very top of the image, r = z, and, in this small cluster of pixels, we are ensured that restoration gives the true sample surface (region (1)of Figure 3).From simulations, we expect that restoration slightly down from the top to be ideal (region (2)of Figure 3). As one proceeds (30)We recognize that averaging may not be the best way to combine tip data and anticipate methods that rely on the morphological model.
Figure 7. Restored tip surfaces are “averaged” to obtain a carbon probe tip surface (A) and a SiSN4 probe tip surface (B).
Prior to averaging, restored tips are registered as described in the text. An SEM image of a carbon probe shows the Si3N4 pyramid with a carbon projection grown on the end (C). The carbon end is very smooth and resembles the AFM tip image. further from the top, the restored surface is improved but does not give the true sample surface (region (3)of Figure 3).
Discussion Morphological restoration greatly improves resolution in AFM images limited by tip size and shape. The improvement can be viewed as a correction of faulty elevation values at a given (xy)point or faulty widths at a given elevation as illustrated by contour analysis (Figure 6). The effect of restoration is much greater when one restores with a large tip SE (Figure 8) than when one restores with a small bead SE (Figure 6). Not only does morphological restoration enhance resolution, it should also correct degradations produced by asymmetrical probe tips. We describe a useful method for imaging probe tips. We are greatly encouraged by the comparison to SEM
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Morphological Restoration of AFM Images
O
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-0 0
Figure 8. Restored tip surfaces are obtained from a bead and used to image an “unkown”bead. The bead image prior to restoration (A) becomes much narrower following restoration (B). One way to view dimensional changes is a contour plot (0.Solid curves are contours from the input image, and gray curves are contours following restoration. Numbers on the figure are elevations in nanometers. The “unknown”bead is 216 nm high. We clip the images at 8 nm from the highest point. (Figure 7). Restored AFM images of carbon probes closely resemble SEM images, and quantitative dimensional comparisons between the two measurements on a single probe are reasonable. With the AFM method, tip information is obtained within the critical region a few nanometers from the apex. This region is most critical for imaging structures such as biomolecules having height 510 nm. SEM has insufficient contrast to image the tip in this region. TEM is inappropriate because carbon is transparent to high-energy electrons. The ability to generate high-resolution tip images should allow one to refine tip construction techniques. From our current study, we conclude that carbon probes are better than the Si3N4 probes for imaging globular proteins. The characterization of the tip surface is a necessary step for quantitative imaging of unknown biomolecules. From the commutative property of morphology (eq 5), the AFM image is a function of both the tip and sample surfaces. One must characterize the tip in order to uncover the sample surface. Tip surface characterization will also be critical in the measurement of biomolecule receptorligand interactions. We recognize some limitations to the tip imaging technique. First, we assume perfect gold spheres. It is likely that the gold particles exhibit a polyhedron structure, perhaps the nucleation shape for fcc metals, a truncated octahedron. Vesenka et attribute deviation from a sphere to poly-Llysine buildup around the gold particles. They pretreat the mica with poly-L-lysine to immobilize particles. Our drying treatment is sufficient to immobilize the gold particles without poly-L-lysine. Nevertheless, we also find a deviation from a sphere in
our restored bead images (Figure 8). This may be due to hydrocarbon build up around the particles via a mechanism similar to that proposed by Vesenka e t al.31 It is difficult to verify the actual shape of the gold particles. Potential methods are high-resolution electron microscopy and light scattering. Our experimental setup does not allow one to perform such a technique and AFM on a single identified particle. At best, we can obtain averages of the particle population on a surface. With the advent ofAFMs interfaced with high-resolution SEM’s, corroborative measurements of the same particle with two techniques will be possible. Polystyrene spheres may offer a more uniform object to use as a standard. However, the charging problem inherent in the use of very small polystyrene spheres prevents accurate measurement of their height.’ In addition, polystyrene spheres are not readily available in the interesting 1-10 nm range. Second, we find variations in our gold particle images that are not removed by restoration, and some analysis follows. For the carbon probe, we register four generated tip images and compute the difference of each from the mean. Over a circular region of radius 20 nm, the maximum elevation deviation is 4.4 nm and the standard deviation is 1.3 nm. Similar results are obtained for a SisN4 probe. An interesting observation is that multiple scans of a single particle yield similar but not identical images. The subtle differences between images are not fully explained by cantilever bending or motion of a tethered particle being pushed by lateral forces of the tip on the sample surface. Scanning reproducibility is the subject of current investigation. A third limitation is that we assume that the surface has a negligible coefficient offriction and that the modulus of both the tip and the surface is effectively infinite. By addition of data from lateral force and compliance (dF/dz) modes of the AFM, a more accurate image of the surface might be obtained. Fourth, the restoration process does not perfectly recover the sample surface at all areas in the image (Figure 3). In regions (1) and (2), there is ideal restoration and the sample surface is obtained. In region (3), an improved surface is obtained with enhanced resolution. An interesting issue is the size of the gold beads used to generate a tip image. We use a size similar to that of globular proteins, and this is probably near optimal. Gold particles of various sizes pose the interesting possibility of combining multiple measurements to create a tip image containing the best information from each image. Someof these observations underscore the experimental difficulty in making measurements at the molecular scale. A particular advantage of the morphologicalmodel is that it allows us to analyze these issues in greater detail. For example, the restoration process applied to multiple tip images should account for most differences in gold bead diameters and give almost identical results. Otherwise, there is no straightforward way to compare such data. A distinct advantage over the “envelopereconstruction” method of Keller and Franke22 is that morphological restoration uses standard image processing operat i o n ~ . ~Morphological ~ ~ ~ ~ - ~processing ~ * ~ ~ is included in commerical image processing software packages and is accessible to any AFM user. A wealth of theoretical and technological advances can be applied. Examples are the duality and commutativity theorems used in this report. (31)Vesenka, J.; Manne, S.;Giberson,R. Biophys. J . 1990,65,992. (32) Giardina, C.R.;Dougherty, E. R. In Morphological Methods in Image and Signal Processing; Prentice Hall: Englewood Cliffs, NJ, 1988. (33) Serra, J. In Image Analysis and Mathematical Morphology; Academic Press: New York, 1982.
Wilson et al.
272 Langmuir, Vol. 11, No.1, 1995 Other examples are SE decomposition techniques and special hardware that does fast morphological processingeZ5The latter techniques offer the possibility of realtime restoration of AFM data. Because morphological techniques reduce noise while retaining edges, nonlinear, morphological pseudomean and pseudomedian noise reduction filters were recently found to be superior to a linear Wiener filter.28 This method of noise reduction should not be confused with our method of morphological restoration that improves image resolution. Interestingly, our morphological restoration process should be immune to some image noise sources, particularly positive-excursion scan-line streaks.
This follows from the definition of erosion (Figure 1). Considering that morphology models the interaction between the probe and sample surfaces, combined morphological restoration methods that attack both resolution and noise degradations are anticipated.
Acknowledgment. We thank Scott Simmons for performing all SEM work. Support for Steven J. Eppell and Roger E. Marchant is provided by NIH HL40047, the Whitaker Foundation, and the Center for Cardiovascular Biomaterials. LA940553L
