## Analog single-photon counter for high-speed scanning microscopy

Optics Express, Vol. 16, Issue 18, pp. 13990-14003 (2008)

http://dx.doi.org/10.1364/OE.16.013990

Acrobat PDF (642 KB)

### Abstract

We introduce a novel single-photon sensitive photodetection method of analog single-photon counting (SPC) for the application of high-speed scanning microscopy that requires high measurement speed and wide dynamic range for the photodetector. This scheme is based on analog electronic circuits which can perform proper differentiation and integration operations before and after discrimination of the analog signal from the photomultiplier tube (PMT), respectively. In spite of its simpler implementation, our analog SPC scheme exhibits good sensitivity and operation stability. Related with the dynamic range, the maximum count rate of our analog SPC is significantly improved due to the fast operation of the analog circuitry. This characteristic of the higher counting rate makes this scheme very suitable for high-speed scanning microscopy. It has also been demonstrated that the afterpulsing problem of an analog-mode PMT is the major noise source that degrades the image quality in the application of scanning microscopy, and our SPC scheme successfully neutralizes this kind of impulse noises to obtain a nearly shot-noise-limited imaging performance.

© 2008 Optical Society of America

## 1. Introduction

*single-photon sensitivity*, high-gain photodetectors such as photomultiplier tubes (PMTs) [1

1. K.K. Hamamatsu Photonics, *Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

2. B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, I. Tikhomirov, and Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods Res. **A 563**, 368–376 (2006). [CrossRef]

4. S. Tisa, A. Tosi, and F. Zappa, “Fully-integrated CMOS single photon counter,” Opt. Express **15**, 2873–2887 (2007). [CrossRef] [PubMed]

5. A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. **83**, 791–793 (2003). [CrossRef]

1. K.K. Hamamatsu Photonics, *Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

6. K.K. Hamamatsu Photonics, *Photon Counting Using Photomultiplier Tubes*, http://sales.hamamatsu.com/assets/applications/ETD/PhotonCounting_TPHO9001E04.pdf.

^{7}counts per second. In spite of its many attractive features, slow measurement speed has been the major obstacle in some applications.

7. J. B. Pawley ed., *Handbook of Biological Confocal Microscopy*3rd Ed. (Springer, 2006). [CrossRef]

^{6}) for single-photon sensitivity in the Geiger-mode operation [2

2. B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, I. Tikhomirov, and Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods Res. **A 563**, 368–376 (2006). [CrossRef]

*SPC-equivalent*detector by itself. For a single-cell APD in the Geiger mode, the maximum count rate is limited by the

*dead time or recovery time*, typically longer than hundreds of nanoseconds. The maximum count rate of a Si-PM can be improved by increasing the number of the cells. Si-PMs of more than 1,000 cells are commercially available and their maximum count rates are estimated more than 100 Mcps. Although APD’s quantum efficiency can be as high as >80% in principle, the G-APD’s photon detection efficiency is reduced by the geometrical fill factor of the active area and probability of successful avalanche. For a multi-cell Si-PM, the net photon detection efficiency is 10~30%, which is just comparable to that of PMTs. The dark count rate per unit detection area is significantly higher than that of PMTs and limits its capability in some applications.

^{™}of Hamamatsu, Japan) [1

1. K.K. Hamamatsu Photonics, *Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

^{™}of PerkinElmer, USA) [8

8.
Perkin Elmer Optoelectronics, Channel Photomultipliers — *New Technology for More Accurate and Efficient Photon Detection*, http://optoelectronics.perkinelmer.com/content/WhitePapers/WTP_CPMPhotonCounting.pdf.

*et*

*al*. proposed an SPC scheme utilizing multiple discriminators to increase the maximum count rate of a PMT-based SPC [9

9. J. Soukka, A. Virkki, P. Hänninen, and J. Soini, “Optimization of multi-photon event discrimination levels using Poisson statistics,” Opt. Express **12**, 84–89 (2004). [CrossRef] [PubMed]

*multi-photon discrimination*for a few photons detected simultaneously. However, the enhancement in the maximum count rate is practically limited below ~4 in its principle and requires more complicated electronic implementations in addition to careful optimization of the discrimination levels. In spite of the attractive features of those alternative technologies, they are not frequently used in practical microscopy. This is partially because the conventional PMTs in analog operation mode are believed to be sufficiently good in terms of SNR for high-speed scanning microscopes. In those cases, the shot noise overwhelms the other noise sources including thermal noise and random height fluctuation noise of a PMT [1

*Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

## 2. Principle of Analog SPC

*SNR*≈

*N*/√

*N*=√

*N*, where N is the number of detected photons. Notice that the shot noise can not be eliminated by photon counting because it is an optical noise. Therefore, integer precision in photon counting is not thought to be necessary in obtaining a good SNR unless the error in counting is very high. Increasing the count rate can be achieved at the sacrifice of counting precision and does not degrade the overall performance.

*M*

_{max}is determined by the duration of the one-shot output,

*Δ*

*t*, so that

*M*

_{max}=1/

*Δ*

*t*. In practice, the effective maximum count rate is limited by the nonlinearity of a SPC system. As the detection of a single photon is a stochastic process, there is always a nonzero probability of

*pile-up*or collision of multiple photons. If more than two photons arrive simultaneously within

*Δ*

*t*, a SPC system would count the first one only, and ignore the others. The amount of this error is increased proportionally with the increase of measured photon number and appears as the nonlinearity problem of a SPC system [1

*Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

*ε*can be represented by

*N*is the actual rate of detected photons, and

*M*is the photon rate measured by the SPC system. In most cases of imaging applications, linearity errors within ±20% are acceptable. Or this level of deterministic errors can be compensated almost exactly by the calibrated information of

*M*

_{max}. In this paper, the effective maximum count rate,

*M*

_{e.m.}is defined by the highest count rate that exhibits a linearity error smaller than 20% for the convenience. According to the best of our knowledge, the highest value of the maximum count rates of commercially available SPCs is 200 Mcps and, hence, the effective maximum count rate is estimated to be 40 Mcps [10

10.
Standford Research Systems, *SR400 - Gated Photon Counter (2-channel)*, http://www.thinksrs.com/downloads/PDFs/Catalog/SR400c.pdf.

*M*>400 for an integration time of 10 µs, required minimally for high-speed scanning microscopes. The dynamic range as the ratio of the maximum signal amplitude to the minimum is only 400 in this case. Considering required margins of the dynamic range for practical microscope operations to be ~10, the dynamic range of an image can be <40, and consequently, the peak signal-to-noise ratio is <40

^{1/2}due to the shot noise. There is a need of further enhancement of the dynamic range for better quality of images even for the best of the digital SPC.

*i*.

*e*. a low-pass filter, as long as the output pulses of the discriminator have a constant amplitude and duration. The response of an analog SPC system with respect to a single photon can be determined by the number of electrons in the output port of the low-pass filter. Neglecting additional noises introduced by using the analog electric devices, the only difference between the digital output and the analog output interface is the way of integration. In the digital SPC scheme, the number of photons is added for a well-defined temporal period of a non-overlapping rectangular slot defined by the clock. In the analog SPC, the number of resulted electrons is integrated by a moving window defined by the filter’s impulse response. So, the outputs can be translated to the number of photons in the digital, and the average photon rate in the analog output interface, respectively. The digital approach is more flexible and provides with some useful operation modes like gated integration. However, the analog output interface seems to be more attractive for the microscopy application owing to the system simplicity and direct compatibility with the analog signal interfaces.

*Δ*

*f*is the bandwidth of the signal fed to the capacitor and

*R*is the load resistance of the comparator, which is 50 Ω in our system. As shown in Fig. 2, the waveform at ⓑ is an approximate derivative of the waveform at ⓐ, and this differentiated signal is discriminated by the comparator. The signal bandwidth at ⓐ was measured to be less than 300 MHz in our analog SPC. The capacitance was chosen to be C=7 pF to satisfy the requirement of Eq. (2).

## 3. Photon counting performance

*Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

*plateau region*can be determined, in which the count rate is the most insensitive to the variation of the pulse height. The stability of operation is maximized at that operation condition so that the SPC output least depends on the extrinsic or intrinsic variations of the PMT gain. For a constant light input, the

*stability gain*,

*G*

_{stab}of an SPC system can be defined as the ratio of fractional PMT output change to the fractional variation of an SPC output as

*V*

^{a}

_{p}is the average pulse height or the average peak output voltage of a PMT for a single-photon input,

*V*

^{spc}is the average output amplitude of the SPC system.

*V*

^{a}

_{p}can be considered as the voltage at the position of ⓐ in Fig. 2, while

*V*

^{spc}corresponds to the voltage at ⓒ in our analog SPC system.

*Δ*

*V*

^{a}

_{p}represents the variation of

*V*

^{a}

_{p}, which results in the corresponding variation of the SPC output

*Δ*

*V*

^{spc}

_{p}. Thus, the stability gain of the SPC system measures how much the PMT’s output fluctuation is suppressed by the SPC scheme. The output voltage of a PMT,

*V*

^{a}

_{p}in Eq. (3) can be normalized by the discrimination level. For the normalized average pulse height,

*V*

^{a}

_{norm}and its variation,

*Δ*V

^{a}

_{norm}, the stability gain is represented by

*V*

^{spc}as a function of the normalized average pulse height,

*V*

^{a}

_{norm}. The stability gain was calculated from the data by using Eq. (4). The shapes of these curves are basically similar to those of the digital SPCs. But the slope of the plateau region is significantly higher than those of the typical digital SPCs. The maximum sensitivity gain was found to be 3.6 when

*V*

^{a}

_{norm}was around 8. Considering that the digital SPCs usually have sensitivity gains bigger than 10, our analog SPC exhibits a significantly lower stability. But it exhibits an enhanced stability over the analog-mode PMT and must be more resistant to the variation of the PMT gain induced by changes of the bias voltage, external magnetic fields, mechanical vibrations and hysteresis [1

*Photomultiplier Tubes — Basics and Applications*3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.

*i*.

*e*. the time-integrated voltage of a single-photon response was carefully measured to be 7.1 mV·µs for our system by using an oscilloscope with a low-intensity light. The output voltage was normalized by this time-voltage product. The measured photon counting rate as a function of the input light power is shown in Fig. 7(a), and the corresponding linearity error as a function of the measured photon rate is plotted in Fig. 7(b). The average power of the source was measured by an optical power meter. The dashed line in Fig. 7(a) represents the ideal linear response, and the dashed line in Fig. 7(b) shows a linear fit curve obtained from the data up to 120 Mcps. In calculating linearity error, the actual photon counting rate was estimated under the assumption that the linearity error is negligibly small for the case of count rates below 1 Mcps. As clearly observable in Fig. 7(b), the linearity error grows proportionally as the counting rate increases. This result suggests the collision of multiple photons causes errors for the analog SPC system in the same way as the case of a digital SPC system, which is represented by Eq. (1). The effective maximum count rate of 20% error was evaluated to be 100 Mcps in our case, which corresponds to a maximum count rate of 500 Mcps. This is 2.5 times higher than the fastest of commercially available digital SPC systems. If the absolute linearity is not required, it would be even possible to operate the analog SPC system above 200 Mcps for wider dynamic range. In very high count rates above 100 Mcps, our analog SPC exhibited larger linearity errors than expected by the theory as seen in Fig. 7(b). This can be explained by the baseline deviation caused by the AC coupling to the discriminator. For a high pulse rate, the relative discrimination level must have shifted to a higher voltage level owing to the baseline of the signal being lowered and this caused a decrease in the output signal amplitude.

*M*

_{e.m.}can be represented as

*Δ*

*t*is the pulse-width (FWHM) of the single-photon response, and

*γ*is the pile-up factor. The pulse-width measured after the pre-amplifier was 1.6 ns in the full width at half maxima (FWHM) for our case. Thus,

*γ*was evaluated to be 0.8 for our analog SPC system. For example, it is expected to obtain an effective maximum count rate more than 400 Mcps if we use a high-speed MCP-PMT of which duration of the single-photon response is less than 400 ps.

## 4. Signal-to-Noise Ratio in imaging

*impulse*

*noises*. The histogram of the analog SPC output just obeyed the characteristic Poisson distribution of the optical shot noise. Figure 8(c) also shows that the impulse noises in the analog-mode PMT made the height distribution deviate from the Poisson distribution at high amplitudes, and these must have originated from other noise sources rather than the shot noise. Even though the occurrence frequency of these exceptionally high-amplitude impulse noises is relatively low, their effect on the image quality is significant. This must be a more serious problem in fluorescence microscopy in which the desired signals often appear as a set of small dots, especially in the case of single-molecule imaging techniques [12

12. S. Nie, D. T. Chiu, and R. N. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science **266**, 1018–1021 (1994). [CrossRef] [PubMed]

13. W. E. Moerner and D. P. Fromm, “Methods of sinlge-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. **74**, 3597–3619 (2003). [CrossRef]

*ion*

*feedback*and

*afterpulse*because it produces a secondary pulse that follows the original photo-electronic pulse after a delay. The afterpulse count rate is proportional to the photoelectron count rate and increases by the increase in the signal intensity. All the kinds of PMTs based on the vacuum-tube technologies can suffer this problem. Helium, the major residual gas species can penetrate from the outside into the glass tubes, especially when a PMT is used in a helium-rich environment for a long time. Therefore, it is deduced that the alternative PMTs such as HPDs and CPMs also generate this kind of impulse noises.

*signal-to-noise-peak-ratio (SNPR)*. SNPR

^{m},

*m*-th order SNPR is defined as the ratio of the signal to the noise peak amplitude of 10

^{-m}integrated probability of appearance. For an area-normalized PDF of height distribution for a CW optical signal that can be measured by the vertical histogram,

*P*(

*ν*), the PDF of noise height distribution,

*P*

_{n}(

*ν*

_{n}) is given by

*P*

_{n}(

*ν*

_{n})=

*P*(

*ν*

_{n}+

*S*), where

*S*≡∫

^{∞}

_{0}

*ν*

*P*(

*ν*)

*d*

*ν*is the mean amplitude as the desired signal. The noise peak of

*m*-th order,

*Ω*

^{m}is determined as

^{m}is defined by

*SNPR*

^{m}≡

*S*/

*Ω*

^{m}. For example, SNPR

^{4}can be interpreted as the ratio of the signal amplitude to the maximum amplitude of the noise that can be observed statistically in 100×100 data points at least. On the other hand, SNR is defined as the ratio of the signal amplitude to the standard deviation of the noise:

^{4}curves for the SPC, analog mode and the theoretical Poisson distribution, respectively. The improvement of our analog SPC in SNR value was not considerably high, just ~10% better to the analog-mode PMT. Note that the SNR performance of the analog-mode PMT is already near the theoretical limit. On the contrary, the improvement in SNPR

^{4}was found to be very significant, and was more obvious for low-intensity irradiations. While the analog-mode PMT suffered from impulse noises, our analog SPC exhibited a good SNPR performance similar to that of the theoretical shot-noise limited photodetection. This observation well explains the results of Fig. 8. In terms of SNPR

^{4}, improvement of factor 3 was achieved by the analog SPC for the case of Fig. 8, and it clearly distinguishes the image quality obtained by the analog SPC from that of the analog mode. After all, this result demonstrates that our analog SPC scheme provides a significantly better noise characteristic.

## 5. Conclusion

*m-th order signal-to-noise-peak-ratio*(SNPR

^{m}). Conventional measures of noise property such as SNR only have focused on standard deviations of the noise amplitudes and cannot efficiently show the effects of noises with high amplitudes but low occurrence probabilities. We have observed that the afterpulse problem is a typical problem for a PMT, and this may degrade the image quality significantly for the analog-mode operation. By measuring SNPR

^{m}for our analog SPC scheme and comparing it with that of analog-mode PMT output and, we have demonstrated that this problem can be effectively solved by our analog SPC detection scheme.

*regulated analog-mode operation*, emphasizing its analog features as well as analog single-photon counting, stressed on the SPC-like properties. This method provides a hybrid approach which mixes those two conventional approaches. We believe that various features of our analog SPC method are very attractive in the high-speed scanning microscopy application. Its high-speed operation capability, wider bandwidth (higher measurement repetition frequency) and higher maximum count rate enables faster data collection with sufficiently high signal amplitudes along with its noise suppression capabilities. Furthermore, its analog output interface provides with direct compatibility to the conventional microscopy instruments that usually use analog-mode PMTs. This technique must be very suitable for nonlinear-optic microscopy techniques such as MPE or CARS microscopy in which signals are relatively weak and ultimate performances are required for the photodetectors.

## Acknowledgments

## References and Links

1. | K.K. Hamamatsu Photonics, |

2. | B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, I. Tikhomirov, and Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods Res. |

3. | M. Song, E. Won, and T. H. Yoon, “Large dynamic range photon detector with a temperature-stabilized Si-based multi-pixel photon counter,” Opt. Express |

4. | S. Tisa, A. Tosi, and F. Zappa, “Fully-integrated CMOS single photon counter,” Opt. Express |

5. | A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. |

6. | K.K. Hamamatsu Photonics, |

7. | J. B. Pawley ed., |

8. |
Perkin Elmer Optoelectronics, Channel Photomultipliers — |

9. | J. Soukka, A. Virkki, P. Hänninen, and J. Soini, “Optimization of multi-photon event discrimination levels using Poisson statistics,” Opt. Express |

10. |
Standford Research Systems, |

11. | C. Buehler, K. H. Kim, U. Greuter, N. Schlumpf, and P. T. C. So, “Single-Photon Counting Multicolor Multiphoton Fluorescence Microscope,” J. Fluorescence |

12. | S. Nie, D. T. Chiu, and R. N. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science |

13. | W. E. Moerner and D. P. Fromm, “Methods of sinlge-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(040.3780) Detectors : Low light level

(040.5250) Detectors : Photomultipliers

(110.4280) Imaging systems : Noise in imaging systems

**ToC Category:**

Detectors

**History**

Original Manuscript: July 3, 2008

Revised Manuscript: August 11, 2008

Manuscript Accepted: August 20, 2008

Published: August 25, 2008

**Virtual Issues**

Vol. 3, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Sucbei Moon and Dug Young Kim, "Analog single-photon counter for high-speed scanning microscopy," Opt. Express **16**, 13990-14003 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13990

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### References

- Hamamatsu PhotonicsK.K. , Photomultiplier Tubes - Basics and Applications 3rd Ed., http://sales.hamamatsu.com/assets/pdf/catsandguides/PMT_handbook_v3aE.pdf.
- B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, and I. Tikhomirov, Calice/SiPM Collaboration, "Status report on silicon photomultiplier development and its applications," Nucl. Instrum. Methods Res. A 563, 368-376 (2006). [CrossRef]
- M. Song, E. Won, and T. H. Yoon, "Large dynamic range photon detector with a temperature-stabilized Si-based multi-pixel photon counter," Opt. Express 15, 17099-17105 (2007). [CrossRef] [PubMed]
- S. Tisa, A. Tosi, and F. Zappa, "Fully-integrated CMOS single photon counter," Opt. Express 15, 2873-2887 (2007). [CrossRef] [PubMed]
- A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791-793 (2003). [CrossRef]
- Hamamatsu PhotonicsK.K. , Photon Counting Using Photomultiplier Tubes, http://sales.hamamatsu.com/assets/applications/ETD/PhotonCounting_TPHO9001E04.pdf.
- J. B. Pawley ed., Handbook of Biological Confocal Microscopy 3rd Ed. (Springer, 2006). [CrossRef]
- Perkin Elmer Optoelectronics, Channel Photomultipliers - New Technology for More Accurate and Efficient Photon Detection,http://optoelectronics.perkinelmer.com/content/WhitePapers/WTP_CPMPhotonCounting.pdf.
- J. Soukka, A. Virkki, P. Hänninen, and J. Soini, "Optimization of multi-photon event discrimination levels using Poisson statistics," Opt. Express 12, 84-89 (2004). [CrossRef] [PubMed]
- Standford Research Systems, SR400 - Gated Photon Counter (2-channel),http://www.thinksrs.com/downloads/PDFs/Catalog/SR400c.pdf.
- C. Buehler, K. H. Kim, U. Greuter, N. Schlumpf, and P. T. C. So, "Single-Photon Counting Multicolor Multiphoton Fluorescence Microscope," J. Fluorescence 15, 41-51 (2005). [CrossRef]
- S. Nie, D. T. Chiu, and R. N. Zare, "Probing individual molecules with confocal fluorescence microscopy," Science 266, 1018-1021 (1994). [CrossRef] [PubMed]
- W. E. Moerner and D. P. Fromm, "Methods of sinlge-molecule fluorescence spectroscopy and microscopy," Rev. Sci. Instrum. 74, 3597-3619 (2003). [CrossRef]

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