Emerging Tools for Single-Cell Analysis

Image Digitization

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They have on-chip circuitry for timing, control, noise reduction, and analog-to-digital conversion. On-chip image compression is planned for the future.

Due to the large amount of on-chip circuitry, the pixel fill factor of these devices can be relatively low. This can be remedied by a microarray of lenslets covering the sensor. These tiny lenses collect light from a larger area and focus it onto the pixel well, bringing the fill factor up near 100%.

APS technology promises to reduce the cost of cameras in the future and perhaps improve their performance as well.

IMAGE DIGITIZATION

Conversion of an image into an array of numbers must be done so as to preserve the specimen content of interest without significant degradation. The noise level must be sufficiently low that specimen apearance and subsequent quantitative image analysis are not compromised. Photometric resolution (number of gray levels in the gray scale), optical resolution (psf diameter), spatial resolution (pixel spacing at the specimen plane), and the number of pixels per row and per column must be adequate for the tasks at hand.

Noise Sources

Quantization Noise. The time-varying electrical signal emerging from the image sensor is sampled and quantized by an ADC circuit. If B is the number of bits used in the quantization, the gray scale goes from zero to 2B – 1. Since quantization alters the gray level at each pixel by a small random amount, it can be viewed as a source of noise. The signal-to-noise ratio for quantization (SNRq) is the (full-scale) signal amplitude divided by the quantization noise level. For images with a Gaussian distribution of gray levels, the SNR, measured in decibels, is

2B
SNRq 20 log10 q 6B 11	(15.3)

where B is the number of bits used in the quantization and q is the standard deviation (root-mean-square value) of the resulting quantization noise. Each 20 dB represents a factor of 10 in the SNR.

The actual ratio of full-scale signal to RMS quantization noise amplitude is

	SNR	2B	10SNR/20 10(6B 11)/20 t			2B	(15.4)
		q		q		10(6B 11)/20

The commonly used 8-bit gray scale (B 8, 2B 256 gray levels, SNR 59 dB t SNR 891) is adequate for many image cytometry applications. Normally this quantization noise level ( 0.11% of full scale) is significantly less than the other two noise sources (photon and readout noise) and is thus tolerable. One should verify this,

336	Camera Technologies for Cytometry Applications

however, and use 10, 12, or more bits of gray-scale resolution when required by the application. At low light levels (where the CCD wells are not being filled to capacity) and without sufficient signal amplification between the sensor and the ADC, the full B-bit range of the ADC may not be utilized. Then the SNR of Equation (4) will not be realized, since it is based on full-scale signal amplitude.

In summary, the camera introduces three uncorrelated random-noise components:

(1) photon noise, which results from the statistical nature of light; (2) readout noise, introduced by the circuitry on the sensor chip; and (3) quantization noise, which results from the conversion of a continuous value into an integer. In general, the three independent random-noise sources combine in such a way that the overall noise level is the square root of the sum of the squares of their individual amplitudes.

n2 2r p2 q2

(15.5)

It often occurs that one of these sources is the dominant one. Which source dominates depends upon the imaging conditions in use at the time. For example, if the chip is read out slowly, readout noise is reduced; and if a 10or 12-bit ADC is used, quantization noise is reduced. Then photon noise may be the dominant source.

Spatial Resolution

The well-known Shannon sampling theorem states that one can reconstruct, by proper interpolation, a sinusoidal signal from equally spaced sample points if there are no fewer than two sample points per cycle of the sine wave (Castleman, 1996). If the sampling is done more sparsely, one can encounter the phenomenon of aliasing, which introduces Moiré patterns into the image.

A microscope objective cannot pass image detail at frequencies higher than the optical cutoff frequency of fc 2NA/ , where NA is its numerical aperture and is the wavelength of narrowband illumination (Goodman, 1988; Born and Wolf, 1980; Castleman, 1996). Thus, aliasing can be avoided completely if the pixel spacing at the specimen is no larger than /4NA. This is about 1/8 m for an objective with NA 1.0 operating in green ( 500 nm) light.

For applications in which the specimen does not contain detail at the resolution limit of the objective lens, larger pixel spacing will suffice. However, even smaller pixel spacing may be required for accurate measurement of objects in the image or for optimal display of the image. In these cases, reduced pixel spacing can be achieved by interpolation (“resampling”) of the image after it has been digitized (Castleman, 1996).

SELECTING CCD CHIPS AND CAMERAS

An impressive array of solid-state cameras, incorporating a variety of different CCD chips, is commercially available. These cover a wide range of cost and performance, and the CCD camera situation is subject to rapid change.

Conclusion

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The performance of a particular CCD camera depends on two major design factors: the choice of the CCD sensor itself and the design of the supporting electronics in the camera. Overall camera performance cannot exceed the limitations of either the chip or the electronics. A poor-quality chip in a well-designed camera and a good chip embedded in poorly matched circuitry will be equally disappointing. The circuitry in a well-designed camera will tend to exploit the best characteristics of the sensor chip and cover for its weaknesses. Thus a particular CCD camera must be evaluated as a complete system.

CCD Chips

Comparing CCD specifications is difficult since each manufacturer chooses to specify chip characteristics differently. Well capacity and RMS readout noise are usually given in electrons and dark current in electrons per second for a single pixel at 0°C. Dark current doubles for each 6°C increase in temperature, and vice versa. Dynamic range, computed as well capacity divided by readout noise, often appears in the data sheets. The SNR is quite dependent on exposure conditions (light level and exposure time) and thus is seldom listed in a readily usable form.

CCD Cameras

The vast majority of CCD cameras produced have been designed with the human eye (i.e., television applications) in mind. Quantitative electronic imaging imposes a significantly different set of constraints. In some applications, a well-designed television camera can be pressed into service for image cytometry to great advantage. In other applications, however, only a specially designed scientific-grade camera can perform satisfactorily.

The scientific cameras from Photometrics, for example, have three gain settings. The 1 setting matches the full-scale range of the ADC to the well capacity of a single pixel. The 4x gain mode, where one-quarter of full-well capacity saturates the ADC, achieves greater sensitivity for use at low light levels. The 0.5x gain mode, when used with binning, increases the effective well size to improve the SNR at high light levels. Photometrics product literature (see http://www.photomet.com) provides useful specifications and other helpful information about CCD camera operation and performance.

CONCLUSION

Each image cytometry application deserves its own analysis of camera and digitizing requirements. When selecting a specific camera, the camera characteristics should be evaluated in light of the requirements of the planned experiments. In any case, the camera should be well matched to the problem and to the other system components as well. Although an inadequate camera can forestall success, camera overkill can waste resources that might be better applied elsewhere.

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Modern cameras are quite good in performance and reasonable in cost compared to the past and will undoubtedly continue to improve. In addition, some of the image detail lost to camera-induced noise, distortion, and lack of resolution can be recovered with digital image processing.

REFERENCES

Born E, Wolf E (1980): Principles of Optics, 6th ed. Oxford: Pergamon Press.

Castleman KR (1996): Digital Image Processing. Englewood Cliffs, NJ: Prentice Hall.

Fink DG, Christiansen D (1989): Electronics Engineers Handbook. New York: McGraw-Hill.

Fossum ER (1993): Active pixel sensors—are CCDs dinosaurs? Proc SPIE 1900:2–14.

Fossum ER (1995): CMOS image sensors: electronic camera on a chip. IEEE International Electron Devices Meeting Technical Digest, Dec. 10–13, 1995, Washington, DC.

Goodman JW (1988): Introduction to Fourier Optics. New York: McGraw-Hill.

Hutson G, Shepherd P, Brice J (1990): Colour Television Theory: System Principles, Engineering Practice & Applied Technology. New York: McGraw-Hill.

Janesick J, Elliot T (1992): History and advancements of large area array scientific CCD imagers. Astronom Soc Pacific Con Series 23:1–67.

Kaplan H (1990): New jobs for charge-transfer devices. Photonics Spectra, November issue.

Williams B, Carta D (1989): CID cameras: More than an alternative to CCDs. Adv Imag, January issue.