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CTF and Resolution

Although in common parlance we often refer to spatial “resolution” as though it were an independent parameter, Figure 11.10 makes it clear that the number we choose as resolution really represents a somewhat arbitrary choice. It refers to the highest spatial frequency at which the contrast is above some given value; for instance, the Rayleigh criterion for bright, point objects on a black background (i.e., stars on a clear night) really assumes that the minimum visible contrast is 26%. The problem with this simplistic attitude to resolution is that it can give one the idea that no matter what their original contrast (i.e., the staining specificity) in the object, all spatial frequencies up to the resolution are equally visible as is implied by the upper dashed line in Figure 11.10. In fact, the most important message from Figure 11.10 is that contrast-in-the-image is equal to contrast-in-the-object as degraded by the CTF of the imaging system, and in particular, the contrast of small features is much lower than that of larger features.

Visibility, Resolution, and the Rose Criterion

The reciprocal relationship between contrast and resolution is important because usually what one is actually interested in is not resolution but visibility: the ability of an observer to recognize two closely spaced features as being separate. Visibility is a much more slippery concept because it depends not just on the calculable aspects of optical theory but on the higher functions of the visual system used to determine how a particular intensity pattern should be interpreted.

Visibility has the advantage of requiring us to talk about the other important parameter of the image data: the signal-to-noise ratio (RS/N). The Rose criterion states that to be visible, a black feature that is a single pixel in size on a white ground must have an intensity that differs from that of the background by at least five times the noise level of the background (Rose, 1948). Although the factor 5 is lower for lines and other geometrical features, the main point is that visibility depends on more than geometrical optics and diffraction. Assuming that the contrast is measured in units that are proportional to the statistical precision with which each signal level is known, visibility also depends on the absolute and relative difference between the signal level of the feature and that of the background. In the case of the Rayleigh criterion, the condition states that between the central points of two bright features one must be able to recognize a lower intensity in some intervening pixel that allows them to be seen as separate.

Because of the CTF curve, smaller objects have lower contrast and more photons must be counted in order to reduce the intrinsic noise so that the lower contrast features will become visible above the statistical noise.

This necessity brings together the contrast of the object (as embodied in its staining characteristics), the focusing properties of the optical system as defined by the CTF, and the statistical requirements of the Rose criterion. However, there is still one other process that can limit whether or not a feature is visible in the final image: how the signal is digitized (Stelzer, 1997).

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Digitization and the Nyquist Criterion

To convert any continuous, analog signal into a digital representation, it is sampled by measuring its intensity at regular intervals in time (or space). Nyquist’s crucial insight was that there is a fixed relationship between the highest temporal (or spatial) frequency present in the data of interest and the minimum rate at which samples must be taken if they are to record accurately all the possible significant variations in that signal. Specifically, for nonperiodic data, the sampling frequency should be at least 2.3 times higher than the highest important frequency in the data. Consequently, to preserve all the information that could be recorded using the CTF shown in Figure 10, it will be necessary to have the pixels smaller than 1/2.3Fc, where Fc is the cut-off frequency.

The practical problem that arises in CLSM is that, as mentioned above, for a given optical system and wavelength, only one pixel size and one zoom factor match the Nyquist criterion. At zoom settings that provide smaller pixels, the data will be oversampled, with the result that it will be bleached more than necessary and only a smaller field of view can be scanned in a given period. It is now common for manufacturers to display the pixel size as part of the set-up display, but if this is not done, it is not difficult to calculate it by measuring the length of any feature in the image in both pixels and micrometers.

On the other hand, at lower zoom settings, where the pixels are larger than those prescribed by Nyquist, not only may some smaller features be missed entirely, but also features not present in the object may “appear” in the data because of a phenomenon called aliasing.

Proper Nyquist sampling is sometimes neglected because working images that are somewhat oversampled tend to be more pleasant to view on the display screen, and in the absence of standards, the increased bleaching rate is hard to detect. Alternatively, on weakly stained specimens, the pixel intensities involve so few quanta that statistical variations in the signal pose a greater limitation to spatial resolution than does the quantization. Nevertheless, as applications of confocal technology more closely approach the absolute limits, the costs of spatial (and temporal) quantizing will become more apparent.

It should be pointed out that the Nyquist rule also applies to adequate sampling in the z-direction and that the z-step setting used to image a 3D specimen should also be less than half the z-resolution.

Two other matters about sampling should be considered: temporal aliasing and mismatch of probe and pixel shape.

Temporal Aliasing. The accuracy with which temporal changes can be imaged is limited by the frame-scan rate: the “wagon-wheel effect.” In the CLSM, temporal aliasing limits not only the ability to follow motion but also the precision in the measurement of the location (or motion) of objects. Because the pixel time is much shorter than the frame time, motion of the specimen during data collection produces distortion rather than the directional blurring that would occur if the whole field were imaged for the same period of time.

Mismatch of Probe and Pixel Shape. There is a mismatch in shape between the circularly symmetrical shape of the Airy disk of the actual probe, the Gaussian

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shape of the theoretical probe, and the square shape represented by a pixel in a rectangular raster. This is made worse if the probe moves much faster in one direction than the other.

In the case of a signal recorded by a cooled CCD detector on an optimized diskscanning system, the 2D detector spatially quantizes the signal in a manner entirely determined by the sensor geometry and the total optical magnification. However, because the fast-scanning mirror in the CLSM follows a ballistic rather than stepped trajectory, the output from the PMT of these instruments is effectively continuous in the horizontal direction. As a result, averaged over the pixel time, the effective Airy disk is not round but is slightly blurred in the fast-scan direction.

Practical Considerations Relating Resolution to Distortion

To obtain the theoretical spatial resolution of a confocal microscope, it is necessary, but not sufficient, to have a diffraction-limited optical system. This section discusses the limitations imposed by mechanical stability and the repeatability of the scanning system.

In disk-scanning instruments, the image is real and therefore distortion can originate only from the optics, not from the scanning system. If a CCD sensor is used to detect this image, geometrical distortion in the digitized image can be extremely low, and because of the inherent mechanical stability of both the optics and the sensor, any residual distortion can be corrected by digital image processing. The mechanical problems of this instrument are therefore confined to the effects of vibration and the relative motion of the stage and lens.

In all confocal instruments, the relative motion between the objective and the specimen should be kept to less than 10% of the resolution limit in x, y, and z. In the diskscanning instruments, both the rotating disk and sometimes the cooling system of the illumination source represent potential internal sources of vibration. It is important to recognize that it is not sufficient to isolate the microscope mechanically on a vibra- tion-isolation table if laser-cooling fans, spinning disks, or scanning galvanometers are permitted to introduce vibration into the table.

Less straightforward is the effect of vibration (and possibly stray electrical or magnetic fields either acting directly on the galvanometer mirror suspension or introducing spurious signals into the current amplifiers that control them) on the performance of the scanning mirrors in laser confocal systems. In these instruments, accurate imaging depends on the mirrors causing the beam to scan over the sample in a precise pattern, duplicating the mathematically perfect raster represented by the data locations in the image memory. Failure to duplicate this raster produces image distortion. On a system with a 1000-line raster and a 10 : 1 zooming ratio, keeping beam placement to within 0.1 of a pixel requires a scanning accuracy of 1 part in 105. No present system even preserves this level of performance in the electrical signals used to drive their mirror galvanometers, let alone in their actual motion. The electromechanical properties of the galvanometers (e.g., mass, spring constant, frequency response, resonant frequency, overshoot, bearing tolerance, and rigidity) produce additional errors. Image distortions produced by these errors are

266	Limits of Confocal Imaging

often masked by the paucity of test samples having an accurately defined geometry (Pawley et al., 1993b) and by the fact that current instruments at high zoom greatly oversample the image so the smallest visible structural features are many pixels wide. Careful measurements will show that the features recorded of a periodic specimen will vary in size by a few percent as the specimen moves across the field of view.

This problem merits mention here because it is possible to measure the x, y, z position of the centroid of an object in a digital image to an accuracy that is much smaller than the spatial resolution limit of the image. Indeed, WF light microscopy techniques have been used to measure motion on the order of 1 nm (Gelles et al., 1988). However, due to random imprecision in the systems used to position the mirrors, it is unlikely that measurements of similar reliability could be made on any present CLSM. In this context, then, the accuracy and precision with which the mirrors can be controlled is a fundamental limitation on the ability of CLSMs to determine position or motion.

The presence of scan instability can be detected either by visually comparing sequential single-scan images of a diagonal knife-edge viewed at the highest possible magnification, contrast, and signal level or, alternatively, by computing the apparent motion of the centroids of two fixed objects, each covering >100 pixels, as they are recorded on a number of sequential scans. The variations measured by the second method should decrease rapidly with increasing illumination intensity because of improved statistical accuracy, although they may then begin to measure stage drift.

Another important and insidious source of distortion is stage drift. Usually the cause is temperature variations in the microscope body, and the solution is to shield the system from drafts. Beyond this, drift can be corrected for digitally as long as there are features visible within the field of view that can be relied upon to not move of their own volition (i.e., not cells).

To summarize:

•Although resolution in the confocal microscope is primarily a function of the NA of the optical system and the of the light, it can also be limited if the signal level represents so few quanta that the signal lacks the statistical precision to produce a “visible” feature or if the data are not correctly sampled because the pixels are too large.

•To improve the statistical precision of the signal, every effort should be made to count all photons from the specimen as accurately as possible: reduce optical losses, select your PMT, check alignment, and routinely make, analyze, and compare images of stable, calibrated test objects.

•The effects of image quantization should not be ignored. Only one zoom setting is optimal for each , NA, and objective magnification.

•Care should be taken to keep the pinhole diameter close to that of the Airy disk at the half-power points. This setting will change predictably with , NA, and lens magnification.

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•Special circumstances may occasionally dictate breaking the sampling and pinhole rules, but the limitations inherent in doing so should always be understood and acknowledged.

•It should be possible to operate the system both at its diffraction-limited resolution and at larger spot sizes.

•In laser-scanned instruments, imperfect scanning precision can introduce distortion.

•Fluorescence saturation places unexpected limits on the speed with which images can be formed with laser-scanning microscopes.

CONCLUSION

This chapter attempts to highlight some aspects of confocal instrumentation that must be addressed in order to attain performance limited only by optical and information theory (Table 2). Although the constituent aspects of both photon efficiency and resolution have been addressed separately, it has been evident that the effects of both these factors overlap and interact in a fairly complex manner.

Further complication surrounds the question of single-versus multi-photon fluorescence excitation. At present, because of the substantial cost and the relative complexity of the lasers involved, it seems that the latter will be most useful in applications in which relatively thick ( 100- m) living specimens such as brain slices or embryos must be viewed over an extended period.

T A B L E 2. Limitations of Confocal Microscopy

Parameter	Theoretical		Practical
Resolution	Spatial	Y: 1, 2, 1, 2	Alignment, off-axis aberrations
		X: 1, 2, 1, 2	Alignment, off-axis aberrations,
			bandwidth, ballistic scan
		Z: 1, 2, 1, 2	Alignment, off-axis aberrations,
		pinhole diameter	tube length
	Temporal: scan speed, signal		Quantization of t
		decay times
Position	Objective lens distortion,		Mirror accuracy, vibration
	pixellation limitations;
	sampling time
Quantitative	Poisson statistics		Mirror and digitizing losses,
measurement			detector DQE and noise,
			bleaching/photodamage,
			saturation, source brightness

268	Limits of Confocal Imaging

ACKNOWLEDGMENTS

This chapter is a modified and updated version of Chapter 2 in the Handbook of Biological Confocal Microscopy (2nd ed.). Kind permission to reproduce material from the original chapter was granted by Plenum Press. Like the original, it has benefited greatly from conversations with Sam Wells (then at Cornell), Jon Art (University of Illinois-Chicago), Nick Doe (then with Bio-Rad, Hemel Hempstead, UK, who provided the MRC-1000 data shown in Fig. 11.8), and Ernst Stelzer, who has done much work on the resolution limitations imposed on confocal microscopy by the statistical variations in the small number of photons counted. Victoria Centonze at the Integrated Microscopy Resource in Madison helped obtain the data for Figure 11.8. Cheryle Hughes and Bill Feeney, artists in the Zoology Department, University of Wisconsin, Madison, made the other drawings. This work was supported by grant DIR-90-17534 and DIR 97-24515 from the U.S. National Science Foundation.

REFERENCES

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Buist A, Müller M, Squier J, Brakenhoff GJ (1998): Real time two-photon absorption microscopy using multi point excitation. J Microsc 192(pt2):217–226.

Egger MD, Petran, M (1967): New reflected light microscope for viewing sustained brain and ganglion cells. Science 157:305–307.

Carlsson K, Danielsson PE, Lenz R, Liljeborg L, Majlof L, Aslund N (1985): Three dimensional microscopy using a confocal laser scanning microscope. Optic Lett 10:53.

Centonze V, Pawley JB (1995): Tutorial on practical confocal microscopy and use of the confocal test specimen. In Handbook of Biological Confocal Microscopy. Pawley J (ed). New York: Plenum, pp 549–570.

Denk W, Strickler JH, Webb WW (1990): Two-photon laser scanning fluorescence microscopy. Science 248:73–76.

Gelles J, Schnapp BJ, Steur E, Scheetz MP (1988): Nanometer scale motion analysis of microtubule-based motor enzymes. Proc EMSA 46:68–69.

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Minsky M (1988): Memoir on inventing the confocal scanning microscope. Scanning 10:128–138.

Oldenbourg R, Terada H, Tiberio R, Inoué S (1993): Image sharpness and contrast transfer in coherent confocal microscopy. J Microsc 172:31–39.

Pawley JB (1995): Fundamental limits in confocal microscopy. In Pawley J (ed). Handbook of Biological Confocal Microscopy. New York: Plenum, pp 19–38.

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Pawley JB, Centonze V (1994): Practical laser-scanning confocal light microscopy: Obtaining optimal performance from your instrument. In Celis JE (ed). Cell Biology: A Laboratory Handbook, 2nd ed. New York: Academic Press.

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Emerging Tools for Single-Cell Analysis: Advances in Optical Measurement Technologies

Edited by Gary Durack, J. Paul Robinson Copyright © 2000 Wiley-Liss, Inc.

ISBNs: 0-471-31575-3 (Hardback); 0-471-22484-7 (Electronic)

12

Scanning Near-Field Optical Imaging

and Spectroscopy in Cell Biology

Vinod Subramaniam, Achim K. Kirsch, Attila Jenei, and Thomas M. Jovin

Max Planck Institute for Biophysical Chemistry, Goettingen, Germany

INTRODUCTION

Scanning near-field optical microscopy [SNOM; alternatively near-field scanning optical microscopy (NSOM)] combines the enhanced lateral and vertical resolution characteristic of scanning probe microscopies with simultaneous measurements of optical signals, yielding resolutions beyond the limits of conventional diffraction optics (Pohl et al., 1984; Betzig et al., 1991; Betzig and Trautman, 1992). SNOM can simultaneously map topographic and optical properties with extremely high spatial resolution, is noninvasive, and has the potential for operating in an aqueous environment. The fluorescence detection sensitivity extends to the level of single molecules. Consequently, SNOM is developing into an important technique for imaging biological systems. We do not review the relevant literature, but rather present an overview of our applications of SNOM to cellular systems. For a comprehensive review of SNOM, we refer the reader to the monograph by Paesler and Moyer (1996) and the review by Dunn (1999).

SNOM achieves spatial resolution beyond the diffraction limit by scanning a sub–wavelength-sized aperture confining the excitation light in close proximity to

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272	Scanning Near-Field Optical Imaging and Spectroscopy in Cell Biology

the sample (Pohl et al., 1984; Isaacson et al., 1986; see Fig. 12.1A for a schematic). The resulting resolution is a function only of the aperture size and the probe-to- sample distance, and not of the wavelength. In practice, the most commonly used near-field probe is an aluminum-coated tapered optical fiber with an aperture diameter 100 nm. The light transmitted or emitted from the sample is generally collected with an objective lens and processed according to the different contrast mechanisms. In our laboratory, the SNOM was designed as an optical module for operation with a standard commercial scanning probe microscope (SPM) system. It has been operated to date in a shared-aperture mode, that is, with uncoated tips supplying a near-field mode for excitation as well as for detection of fluorescence signals. The spatial resolution achieved in such a system has been estimated to be200 nm, that is, considerably better than the diffraction limit of the conventional optical microscope. In addition, the microscope has the unique capability, not

F i g . 12.1. (A) Schematic of the principle behind SNOM. A sub–wavelength-sized aperture (hole in the opaque screen) confines the excitation light and is scanned in close proximity (typically 10nm) to the sample. (B) Three-dimensional representation (fluorescence overlaid on topography) of a SNOM image of a 3T3 Balb/c cell labeled with fluorescently conjugated concanavalin A bound to cell surface lectin receptors. The fiber tip is raster scanned across the sample to generate the simultaneously acquired topographic and fluorescence images.

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achievable in the confocal laser scanning microscope (CLSM), of providing a correlation between high-resolution surface topography and the fluorescence signal(s) (Fig. 12.1B).

BIOLOGICAL APPLICATIONS OF SNOM

The correlation between topography and optical signals is of particular relevance in biological applications. Thus, for example, one can ask questions regarding the distribution of cell surface receptors for external signaling molecules such as growth factors and hormones (see Fig. 12.3 below). While the resolution of SNOM is not sufficient to directly image individual complexes of small proteins or ligands and receptors, in combination with fluorescence resonance energy transfer (FRET) methods, SNOM can be operated with contrast modes dependent on intermolecular separations on the order of 2–10 nm (see below).

Our SNOM was intended primarily for investigations of cellular processes and biological macromolecules engaged in dynamic biochemical processes. The philosophy has been to implement all the available photophysical processes associated with fluorescence, thereby exploiting the specificity and sensitivity of fluorescence probes. The latter can be intrinsic (cellular autofluorescence) or extrinsic (covalent adducts to proteins, nucleic acids, or small molecules) or introduced by cellular transfection and transformation with green fluorescent protein (GFP). The latter protein is unique in its manifestation of a visible fluorophore formed spontaneously by chemical transformation of amino acid residues. The GFP can be targeted to intracellular compartments by genetic fusion to proteins of interest and can thus be expressed in living cells, tissues, and whole organisms.

Some of the biologically relevant applications of our SNOM carried out to date include the study of the following:

•the domain structure of Langmuir–Blodgett films with electron transfer systems (Kirsch et al., 1998a, 1998b);

•GFP expression in bacteria, in fruitfly embryo cells, and in mammalian cells as a fusion protein with the epidermal growth factor (EGF) receptor (Subramaniam et al., 1997, 1998);

•distributions of transmembrane receptors for EGF and platelet-derived growth factors (PDGFs; Vereb et al., 1997);

•distribution and clustering on cell surfaces of the erbB growth factor family of transmembrane receptor tyrosine kinases (particularly erbB2) as a function of activation (Nagy et al., 1998);

•interactions of cell surface proteins via FRET (Subramaniam et al., 1998; Kirsch et al., 1999); and

•multiphoton (two-, three-photon) simultaneous excitation of probes for different intracellular compartments (mitochondrial, nuclear; Kirsch et al., 1998c; Jenei et al., 1999).