Emerging Tools for Single-Cell Analysis

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A

B	C

F i g . 11.5. (A) In microscope systems that do not employ full integration or operate in the pulse-count- ing mode, two physical processes can add uncertainty to the measurement of the photon signal. Statistical variations in the number of secondary electrons produced during the early stages of electron multiplication in the PMT have the effect that identical photons can produce pulses that vary in height by a factor of 10. In addition, inappropriate design of the digitizing circuitry can have the result that even identical pulses from the PMT will be recorded as numbers that may vary by a factor of 10. (B) Spectrum of single-PE pulse heights for three representative PMTs. The spread in the major peak is due to statistical variations in the gain of the early stages of the dynode multiplier. The peaks of smaller pulses represent PE produced thermally from the later dynodes. In pulse counting, these smaller pulses are eliminated by setting the discriminator threshold near the valley in the distribution. (C) An intensity surface representing the pulse heights actually recorded by such a system when digitizing identical pseudo-Gaussian pulses from a signal generator. The overall result of both these processes is to add considerable uncertainty as to the actual intensity of the signal from the specimen.

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Cooled CCD. The only practical alternative photodetector to the PMT is the silicon detector, of which the cooled CCD is the optimal example. This detector has both different capabilities and different problems. On back-illuminated CCDs, the QE can be as high as 85% and extend well into the infrared (Fig. 11.6). Furthermore, as each photon is recorded as an identical amount of current, there is no multiplicative noise. Unfortunately, to keep the noise level acceptably low ( 3 photons per measurement), this detector must usually be cooled to –40 to –80°C and read out at the relatively low rate of 25,000–250,000 pixels/s (vs. 600,000 pixels/s for a normal CLSM). This noise level is clearly too high if the peak signal level is only 10 photons/pixel, as it can be on many CLSMs. It is less serious when the signal from the darkest pixel is at least 10 photoelectrons because then statistical variations in the signal are similar in size to the measurement noise. These features make the cooled-CCD detector more suitable for slowly scanned images (10–100 s/frame) producing relatively high signal levels. So far single-pixel CCDs optimized for use in the confocal microscope have only just reached the prototype stage (Pawley et al., 1996).

In the disk-scanning and line-scanning confocal microscopes, the image data emerge as a real image rather than as a time sequence of intensity values from a single detector. Although this real image can be detected photographically or by eye, these sensors have fairly low QE. However, such confocal microscopes can surpass the photon efficiency of the CLSM if they incorporate a cooled-CCD sensor having detection performance similar to that described above. This combination is now implemented in some commercial instruments presently marketed by EG&G Wallach.

F i g . 11.6. Quantum Efficiency of frontand back-illuminated CCD sensors. (Courtesy of PixelVision Inc., Beaverton, OR.)

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Of even more interest to live-cell microscopists are the microlens multiphoton excitation systems developed independently by Straub and Hell (1998) and Buist et al. (1998). By utilizing multiple excitation beams, these instruments avoid the data-rate constraints imposed on single-beam confocals by fluorescence saturation and do so in a fashion that confines excitation (and damage?) to the focus plane. In addition, they increase the data rate by coupling the high-speed disk-scanning system to a highQE, wide-field detector such as a CCD.

Silicon photon detectors have potential practical advantages besides high QE. As the sensitive element in such a detector is typically very small (7–30 m on a side), use of small planar arrays (3 3 or 5 5) could permit it to operate in the CLSM as a combination pinhole and detector (Pawley et al., 1996). Optical misalignment could be sensed electronically simply by comparing the signal from sensor elements on one side against those opposite during scan retrace. Likewise, the effective size of the detector could be adjusted on a scale of 10–50 µm, a size compatible with that of a pinhole operating at the intermediate image plane. Such a CCD detector could even acquire data at several effective pinhole sizes simultaneously.

Digitization. In the simplest CLSM system, the output of the PMT head amplifier is passed directly to the analog-to-digital converter (ADC), which samples the voltage for a few nanoseconds during the time of each pixel (Tp) and turns the sensed voltage into a digital number (Fig. 11.5a). As Tp is usually a few microseconds, it is important to ensure that the voltage present during the short sampling time is a good measure of the average signal level during Tp. This is usually accomplished by giving the amplifier immediately preceding the ADC a time constant of Tp /4. This simple approach effectively expands the sampling time from ~Tp /1000 to Tp/4 without excessively blending the signal from each pixel with that of its neighbors. However, it still means that the system is only “counting” about 25% of the time, a circumstance that reduces the “effective” system QE by an additional 75%.

The situation can be improved if one uses a digitizer employing full integration. Such a system can be implemented by feeding the current from the PMT into a capacitor during the pixel time, then reading the capacitor voltage out to an ADC, and finally resetting the capacitor voltage back to zero (Fig. 11.7). The Bio-Rad MRC600 and later instruments incorporate three circuits of this type in each digitizing channel. Three circuits are used so that one can accumulate while the second is being read out and the third is being reset.

The second method of implementing full integration is to feed the output of a high-bandwidth (Tp /20) head amplifier into a high-speed ADC running at, say, 10 times the pixel rate and then to utilize fast digital circuitry to average the 10 successive readings needed to produce a stored value characteristic of the whole pixel.

Compared to Tp /4 bandwidth limiting, either method of full integration effectively provides four times more useful signal for a fixed amount of light from the specimen. This matter is important enough for it to be worth determining the method used by any confocal instrument that you are considering purchasing.

Photon Counting. Obtaining a digital representation of optical data is ultimately a question of counting photons. This means not only using a high-QE detector but also

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recording a signal in which the contribution of each photon is equal. In the case of solid-state sensors, the uniformity condition is automatically met by the sensing process (1 photon j1 PE). This condition can be met by the PMT only if it is operated in a pulse-counting mode.

In pulse counting, the object is not to measure the average level of the output current during the Tp, but rather to eliminate the effects of multiplicative noise by discriminating and then counting the individual output pulses resulting from the emission of individual PEs from the PC. To reduce the effect of the small noise pulses generated from the dynodes of the PMT, photon pulses are passed through a discriminator; each time the PMT output goes above some preset threshold, one pulse is counted (Fig. 11.7).

Unfortunately, problems arise when large numbers of photons must be counted in a short time because the PMT output does not immediately return to zero after each pulse. If a second pulse arrives before the first one is over, the second, or piled-up, pulse will be missed.

Suppose a laser-scanning instrument scans a 512 768 raster in 1 s and 35% of this time is used for retrace. That leaves Tp ~1.6 s/pixel. If we assume that each photon pulse occupies 20 ns (Tp), the maximum number of pulses that one could possibly count in each pixel would be 80, but because the photons arrive at random times, even at 1/10 of this rate (eight photons), 10% of the photons will still arrive when the circuit is already busy.

Figure 11.8 shows the performance of the fast photon-counting circuitry in the Bio-Rad MRC-600 and MRC-1000. The response is linear up to about 10 counts/pixel with the former and about 20 counts/pixel with the newer model, which

F i g . 11.7. Two alternative approaches to counting single-photon pulses. In both, the signal from a fast head amplifier is passed to a discriminator. Uniform pulses from the discriminator can be either counted with digital circuitry or integrated in a capacitor and then read out through an analog-to-digital converter (ADC).

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F i g . 11.8. Performance of the fast-photon counting circuitry in the MRC-600 and the MRC-1000 CLSMs. The response is linear up to about 10 counts/pixel with the MRC-600 and up to about 20 counts/pixel with the MRC-1000, which employs a faster PMT and head amplifier.

employs a faster PMT and head amplifier. This later instrument is also unusual for employing the optical techniques for QE enhancement mentioned above and for allowing the user to switch easily between the analog and photon-counting modes.

On first hearing, 20 counts/pixel may sound like a very low level of signal. In fact, however, considerable experience shows that much fluorescence confocal microscopy is performed at even lower signal levels. Owners of instruments capable of fastphoton counting can calibrate their PMT gain controls following instructions in Pawley (1995). Those able to follow this procedure may be surprised to find that when they are using “normal” PMT gain on a “normal” specimen, the “256” that they are storing in the memory in the analog mode corresponds to a signal of 10 photons.

Although the signal saturation that occurs when one exceeds the linear range of the fast-photon counting circuitry is of concern, it is also important to remember that one can correct for piled-up losses to some degree with a simple look-up table. Furthermore, such losses need not be reduced to zero but merely made small compared to the intrinsic statistical noise. Pile-up losses will become less important as manufacturers switch to faster pulse-counting PMTs and circuits; the Bio-Rad MRC-1024 saturates at 58 counts/pixel.

Digital counters are not strictly mandatory. Multiplicative noise can be avoided by clipping all the single-PE pulses to a uniform size and feeding them to a fully integrating ADC (Fig. 11.7). In fact, in some commercial instruments, much of the beneficial effect of photon counting has been incorporated into the analog digitization

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system by the simple expedient of arranging the electronic and PMT gain so that the single-PE pulses saturate a fast, high-gain amplifier installed between the PMT and the low-bandwidth amplifier feeding the ADC. Because this saturable amplifier is fast, to a reasonable extent, each pulse is clipped separately to a uniform height, thereby meeting the criterion that each photon contribute equally to the recorded signal.

Where Have All the Photons Gone? All present instruments embody design compromises that prevent them from obtaining the ultimate in photon efficiency throughout the four stages discussed above. Many systems employ more refractive optics than is absolutely necessary. Absorption and reflection losses in these produce optical transmission losses in the range of 50–75% (Table 11.1). Although the metal mirrors that produced losses of 85% in early confocal instruments have now been replaced with broadband, dielectric-multilayer mirrors, mirror losses still can reach 25% if many surfaces are involved.

It is also important to pay attention to the selection and adjustment of the PMT itself. While many recognize that any specific tube will operate best over only a narrow range of accelerating voltages and that PMTs with bialkali photocathodes on endwindow tubes have lower dark current and higher QE in the green, while those with S-20, multialkali photocathodes are better in the red and near infrared, it is usually forgotten that the performance of individual tubes often varies from the mean for their type by a factor of more than 3. Therefore, selection of tubes for high performance and to couple the photocathode material to the wavelength to be detected can pay dividends.

As mentioned above, additional degradation is imposed on the data by multiplicative noise and poor digitizing circuitry, and of course, signal can be lost because of poor alignment. Finally, the improper choice of pinhole diameter may exclude as much as 90% of the useful signal from the detector in a vain attempt to extract an “imaginary” improvement in x–y resolution (imaginary because the resulting low signal levels prevent statistically useful information from being obtained before the specimen is destroyed).

Taken together, all these factors can add up to a factor of 100 times or more in photon efficiency between state-of-the-art and sloppy operation on poor equipment. Every action that results in more efficient use of the photons generated within the specimen should be thought of as being directly responsible for making it possible to collect a proportionally larger number of images (or images with better statistics).

As mentioned above, the use of multiphoton excitation with a non-descanned photodetector allows many of these losses (e.g., dichroic, alignment, and scanning mirrors) to be reduced or eliminated, a condition that greatly improves the photon efficiency of such systems. This advantage must be set against the other cost and performance penalties of the technique that are mentioned above.

Measuring Photon Efficiency. The PMT output signal is the only source of readily available data with which to measure the photon efficiency. Unfortunately, a large number of parameters can have a major effect on this single measurement. An incomplete list includes the following:

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•laser power, which is a function of, for example, temperature, cavity gain, stability of stabilizing circuit, and relative power between lines of multiline lasers;

•the transmission at a particular of the ND and other filters used;

•the NA and transmission of the objective lens and other optics, usually a strong function of position in the field-of-view;

•reflectivity of the mirrors for the particular and polarization of the laser;

•the fraction of the laser beam that is actually accepted by the objective entrance pupil;

•pinhole diameter and alignment;

•the PMT itself: the specific tube in use, its QE as a function of wavelength, and its gain as a function of voltage setting;

•the PMT controls: voltage (gain), gamma, and black-level setting;

•staining density, dye type, and local environment; and

•focus level and refractive index of embedding media.

The number and diversity of these parameters make it difficult to measure the fraction of the photons leaving the focused spot that contribute to the stored image data.

What is needed is a stable point source of light of known intensity that can be mounted conveniently below the objective. One way to make such a source is by allowing a measurable amount of laser light to strike a stable phosphor. First measure the light emerging from the objective (as described above) and then adjust it to some standard level. Specimens that maintain a constant level of fluorescent efficiency (i.e., ones that do not bleach or change with time) include such inorganic phosphors as single crystals of CaF2–Eu or YAG–Ce and uranyl glass. Unfortunately, although these materials are very stable under intense laser illumination, they also have a very high refractive index. Consequently, high-NA objectives are unable to form an aber- ration-free focus within them, and therefore, with a given pinhole setting, the signal that they generate at the PMT decreases rapidly as the focal plane moves into the material. However, such samples can be useful to those who normally use objectives of lower NA where refractive index effects are less serious. An alternative fluorescence standard can be fabricated by dissolving dye in immersion oil or water (depending on the correction of the objective), but the fluorescent efficiency of such specimens is seldom stable over long periods.

A more direct approach to measuring photon efficiency involves using the microscope simply to image a small light source such as a light-emitting diode (LED) or one formed by the microscope’s normal transmission illumination system set up for Köhler illumination (Fig. 11.9). In the latter case, the arc or incandescent source must be provided with a measurable and regulated power supply. Once this has been set up, the only major variables remaining are the amount of metal deposited on the inside of the glass envelope surrounding the source, the bandpass effects of any filters that remain in the light path, the NA of the condenser, the pinhole diameter, and the PMT voltage. In many instruments, it is relatively easy to turn off or obscure the laser, remove all of the dichroic and bandpass filters, and let the light from the image plane pass directly to the PMT. Under these conditions, one should get a standard reading with a given

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F i g . 11.9. Optical set-up for measuring the detection efficiency or the effective size of the pinhole using the internal transmitted illumination system of the microscope as a standard light source.

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objective, pinhole size, and lamp power. Of course, the microscope is now a flying spot detector that collects photons from only one pixel at a time. This has the result that the effective intensity is about 400,000 times less than if the PMT were measuring the entire field, but even so, it will usually be necessary to place ND filters between the source and the condenser lens to permit the PMT to be operated at a voltage high enough to be stable. Line-frequency variations in the filament-heating current may be visible in the data, as will be any instability in the plasma of arc sources. For this reason, it may be more convenient to measure the PMT output with an analog dc voltmeter than with an image storage system of the confocal microscope.

By introducing ND filters below the stage, it is possible to reduce the intensity of the light to the level at which photon counting is appropriate. On those instruments that have this ability, you can easily make measurements to determine a rough ratio between the actual number of photons being detected (using photon counting) and analog intensity values stored in the memory at the same settings of the PMT gain. This is done by recording and then comparing the same blank, bright-field “image” in both analog and photon-counting modes. Such information should be used to reach a rational decision about when one can use photon counting without fear of pulse pileup. As noted above, with a PMT setting of 8.00 on the Bio-Rad MRC-600, an analog-mode, stored intensity of 256 is usually equivalent to the detection of 15 photons/pixel per 1-s frame.

Nothing increases the probability that normal operating procedures are optimal so much as practicing these techniques under test conditions such as these because one knows if one is getting the “right” answer only if one already knows what the answer should be (Pawley et al., 1993a).

OTHER ASPECTS OF RESOLUTION

Limitations Imposed by Spatial and Temporal Quantization

Although the image viewed in a disk-scanning or slit-scanning confocal microscope is, in principle, as continuous as that from a WF microscope, this distinction is lost when the image is finally sensed using a cooled CCD or a digitized photodetector. The fact that all digital confocal images must be recorded and treated in terms of measurements made within discrete pixels can limit the effective spatial resolution of the instrument in ways that may not be familiar to some who approach digital microscopy for the first time (Stelzer, 1997). In a sense, these limits are more practical than fundamental because if the microscope is operated in conformance to the rules of Nyquist sampling theory as discussed below, these limits should present no obstacle to recording good images. However, because the incautious use of the “zoom” magnification control present on all commercial CLSMs makes it relatively easy to operate these instruments outside the Nyquist conditions, a brief discussion of sampling theory is included here. It is mentioned here under the heading “Resolution” because it involves the ability to record “the separation of two closely spaced objects.”

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Spatial Frequencies and the Contrast Transfer Function

Sampling theory, like resolution itself, is easier to think of in the spatial frequency domain, where we consider not the size of objects themselves (millimeters per feature) but the inverse of their size (features per millimeter). In the spatial frequency domain, an image is seen as being composed of the spacings between features rather than the features themselves. The reason for using this seemingly obscure mental construct is that the ability of an optical system to transmit information depends almost entirely on the spatial frequency of this information. More specifically, all optical systems transmit the contrast of the high spatial frequencies (representing smaller spacings) less effectively than they transmit lower spatial frequencies (which represent larger features). This fact is made evident when one plots the contrast transfer function (CTF) of an optical system by measuring the contrast present in an image of a test object made up of regular arrays of black-and-white bars having specific spacings or frequencies (Oldenbourg et al., 1993). Such a CTF is shown by the solid line in Figure 11.10, the dotted line below it representing the image contrast produced by a test target in which the “black” lines are only 70% gray (i.e., 30% contrast).

F i g . 11.10. Contrast transfer function of a microscope optical system showing how the contrast in the image of a high-contrast bar pattern varies with the spatial frequency of the pattern (spacings per micrometer). The dotted line represents the response measured if the dark bars in the test target reflect (or transmit) 70% of the incident light rather than 0%. The dashed line represents the imaginary situation of a CTF in which all spatial frequencies up to the “resolution limit” really have equal contrast. The diagram makes clear why high-frequency features of a test object are more likely to remain visible above any arbitrary noise level (5% of 26.5% shown) if they have 100% contrast rather than 30%.