## Data detection algorithms for multiplexed quantum dot encoding |

Optics Express, Vol. 20, Issue 5, pp. 5762-5774 (2012)

http://dx.doi.org/10.1364/OE.20.005762

Acrobat PDF (835 KB)

### Abstract

A group of quantum dots can be designed to have a unique spectral emission by varying the size of the quantum dots (wavelength) and number of quantum dots (intensity). This technique has been previously proposed for biological tags and object identification. The potential of this system lies in the ability to have a large number of distinguishable wavelengths and intensity levels. This paper presents a communications system model for MxQDs including the interference between neighbouring QD colours and detector noise. An analytical model of the signal-to-noise ratio of a Charge-Coupled Device (CCD) spectrometer is presented and confirmed with experimental results. We then apply a communications system perspective and propose data detection algorithms that increase the readability of the quantum dots tags. It is demonstrated that multiplexed quantum dot barcodes can be read with 99.7% accuracy using the proposed data detection algorithms in a system with 6 colours and 6 intensity values resulting in 46,655 unique spectral codes.

© 2012 OSA

## 1. Introduction

1. S. V. Gaponenko, *Optical Properties of Semiconductor Nanocrystals* (Cambridge University Press, 1998). [CrossRef]

2. M. Bruchez Jr., M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science **281**, 2013–2016 (1998). [CrossRef] [PubMed]

3. W. R. Algar, M. Massey, and U. J. Krull, “The application of quantum dots, gold nanoparticles and molecular switches to optical nucleic-acid diagnostics,” Trends Anal. Chem. **28**, 292–306 (2009). [CrossRef]

2. M. Bruchez Jr., M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science **281**, 2013–2016 (1998). [CrossRef] [PubMed]

4. W. Chan and S. Nie, “Quantum dot bioconjugates for ultrasensitive nonisotopic detection,” Science **281**, 2016–2018 (1998). [CrossRef] [PubMed]

5. M. Han, X. Ming, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. **19**, 631–635 (2001). [CrossRef] [PubMed]

10. S. Chang, M. Zhou, and C. P. Grover, “Information coding and retrieving using fluorescent semiconductor nanocrystals for object identification,” Opt. Express **12**, 143–148 (2004). [CrossRef] [PubMed]

7. P. S. Eastman, W. Ruan, M. Doctolero, R. Nuttall, G. de Feo, J. S. Park, J. S. F. Chu, P. Cooke, J. W. Gray, S. Li, and F. F. Chen, “Qdot nanobarcodes for multiplexed gene expression analysis,” Nano Lett. **6**, 1059–1064 (2006). [CrossRef] [PubMed]

## 2. System description

### 2.1. Physical system

*λ*.

_{i}*λ*, will have a distribution that is approximately Gaussian as a function of

_{i}*λ*with the distribution centered at

*λ*[5

_{i}5. M. Han, X. Ming, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. **19**, 631–635 (2001). [CrossRef] [PubMed]

5. M. Han, X. Ming, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. **19**, 631–635 (2001). [CrossRef] [PubMed]

12. O. I. Mićić, K. M. Jones, A. Cahill, and A. J. Nozik, “Optical, electronic, and structural properties of uncoupled and close-packed arrays of InP quantum dots,” J. Phys. Chem. B **102**9791–9796, 1998. [CrossRef]

11. S. V. Vaidya, M. L. Gilchrist, C. Maldarelli, and A. Couzis, “Spectral bar coding of polystyrene microbeads usign multicolored quantum dots,” Anal. Chem. **79**8520–8530 (2007). [CrossRef] [PubMed]

12. O. I. Mićić, K. M. Jones, A. Cahill, and A. J. Nozik, “Optical, electronic, and structural properties of uncoupled and close-packed arrays of InP quantum dots,” J. Phys. Chem. B **102**9791–9796, 1998. [CrossRef]

### 2.2. Communications model

*λ*

_{1}...

*λ*. The area of

_{N}*δ*(

*λ*–

*λ*) is given by

_{i}*I*, which is proportional to the desired intensity for that QD group. This is an abstraction since, as noted in Section 2.1, it is not possible to fabricate QDs with this kind of ideal emission spectrum.

_{i}*λ*

_{3dB}),

*A*< 1 is applied to the signal to represent system attenuation and amplifier gain. A zero mean, additive noise source is then applied to represent noise from both optical and electronic sources.

*λ*

_{1}...

*λ*are uniformly spaced with separation Δ

_{N}*λ*, the output of matched filter is sampled at intervals Δ

*λ*. The

*i*

^{th}sample at the output of the matched filter is equal to where

*z*[

*i*] is the ISI at sample

*i*and

*n*[

*i*] is the additive noise component. The samples

*y*[

*i*] are then fed into a data detection block that attempts to mitigate the ISI,

*z*[

*i*], and produce a best guess as to the identity of the tag. This data detection scheme is discussed in more detail in Section 3.

## 3. Data detection

**I**= [

*I*

_{1}

*I*

_{2}...

*I*], where

_{N}*I*is defined in Section 2.2 as being proportional to the desired intensity at wavelength

_{i}*λ*. The purpose of the data detection block in Fig. 2 is to generate a best guess as to which vector is being represented by the MxQD emission spectrum and will be denoted by

_{i}**Î**. In this paper, the performance of a data detection algorithm will be evaluated based on the probability of a correct read,

*P*(

**Î**=

**I**).

8. H. Xu, M. Y. Sha, E. Y. Wong, J. Uphoff, Y. Xu, J. A. Treadway, A. Truong, E. O’Brien, S. Asquith, M. Stubbins, N. K. Spurr, E. H. Lai, and W. Mahoney, “Multiplexed SNP genotyping using the Qbead ™system: a quantum dot-encoded microsphere-based assay,” Nucleic Acids Res. **31**, e43 (2003). [CrossRef] [PubMed]

9. BD Biosciences, http://www.bdbiosciences.com.

8. H. Xu, M. Y. Sha, E. Y. Wong, J. Uphoff, Y. Xu, J. A. Treadway, A. Truong, E. O’Brien, S. Asquith, M. Stubbins, N. K. Spurr, E. H. Lai, and W. Mahoney, “Multiplexed SNP genotyping using the Qbead ™system: a quantum dot-encoded microsphere-based assay,” Nucleic Acids Res. **31**, e43 (2003). [CrossRef] [PubMed]

9. BD Biosciences, http://www.bdbiosciences.com.

*y*[

*i*] at the output of the matched filter in Fig. 2. The equalizer is implemented as a discrete time finite impulse response filter. The

*n*

^{th}tap in the equalizer filter is represented by

*g*[

*n*]. The samples at the output of the matched filter,

*y*[

*n*], are convolved with

*g*[

*n*] in order to mitigate the ISI present in

*y*[

*n*]. The output of the equalizer is then applied to a threshold detector where the thresholds are placed at the mid-point between the

*L*possible transmitted intensity levels.

**I**and

**Î**=

*g*[

*n*]⊛

*y*[

*n*], where ⊛ indicates convolution. The equalizer taps that achieve this minimization can be calculated using the Weiner-Hopf equations [14],

**g**=

**R**

^{−}

**, where**

^{1}p**g**= [

*g*[1

1. S. V. Gaponenko, *Optical Properties of Semiconductor Nanocrystals* (Cambridge University Press, 1998). [CrossRef]

*g*[2

2. M. Bruchez Jr., M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science **281**, 2013–2016 (1998). [CrossRef] [PubMed]

**R**is the autocorrelation matrix of the matched filter output

*y*[

*n*] and the vector

**p**, is the cross-correlation vector of the output

**Î**and the desired output

**I**. The cross-correlation vector includes information about the noise in the system and the resulting equalizer relaxes the zero ISI requirement to account for noise.

*N*samples of

*y*[

*n*] that correspond to the desired wavelengths are grouped into a vector

**y**∈

*. For all possible*

^{N}**I**vectors, perfect knowledge of the Gaussian emission spectrum

*w*(

*λ*) and the channel attenuation

*A*are used to create the

*L*– 1 possible points in

^{N}*that could appear at the matched filter output. The MLS algorithm then simply chooses the point that is the minimum Euclidean distance from*

^{N}**y**as the most likely transmitted vector.

## 4. Case study - quantum dot barcodes

### 4.1. Barcode system model

10. S. Chang, M. Zhou, and C. P. Grover, “Information coding and retrieving using fluorescent semiconductor nanocrystals for object identification,” Opt. Express **12**, 143–148 (2004). [CrossRef] [PubMed]

#### 4.1.1. Desired optical signal power model

*i*represent the QDs designed to emit at

*λ*. The proportion of optical power from these QDs measured at wavelength

_{i}*λ*is denoted

*P*(

_{i}*λ*) and is equal to where

*α*

_{G,i}(

*λ*) accounts for the Gaussian emission spectrum of the QDs,

*α*is grating loss,

_{g}*α*accounts for the amount of light coupled onto the CCD input fiber,

_{f}*T*

_{⊥}is the power transmittance of the air/fiber interface and

*P*is the fluorescent power of the quantum dots.

_{f}*α*

_{G,i}(

*λ*) in Eq. (3) is simply the integral of this Gaussian shape over

*λ*±

*δ*, where 2

_{λ}*δ*is the wavelength resolution of the CCD device.

_{λ}*α*in Eq. (3), the light emitted from the QD pile is modeled as isotropic. Since the QDs rest on an opaque surface, the light will be radiating in a half sphere with surface area

_{f}*r*is the radius away from the QD barcode. Assuming the fiber is a sufficient distance from the QDs to be normal to the light, there is no need to account for the angle of incidence. Therefore,

_{d}*α*is just the area of the fiber relative to the area of the half sphere such that where

_{f}*r*is the radius of the fiber core.

_{f}*T*

_{⊥}in Eq. (3) is the proportion of light transmitted through the air-fiber interface of the fiber connected to the spectrometer. Since the light is assumed to be normal to the interface, the transmittance is determined using Fresnel transmission coefficients [15]. Note that

*T*

_{⊥}is squared in Eq. (3) to also account for the second air-fiber interface within the instrument.

*α*factor in Eq. (3) accounts for the optical loss within the instrument. With no access to the optics within the spectrometer, we assume a typical setup consisting of two mirrors, with negligible loss, and an optical grating to physically separate light as a function of wavelength [16

_{g}16. Ocean Optics - Inventors of the World’s First Miniature Spectrometer, http://www.oceanoptics.com.

*α*.

_{g}*P*in Eq. (3), we can start by using

_{f}*α*to denote the fraction of the laser power,

_{B}*P*, incident on the ID card that illuminates the QDs. This is equal to the ratio of the QD pile area to laser beam area. The fraction of the incident power absorbed by the QDs is denoted

_{laser}*α*. The quantum dots will then fluoresce a fraction of the absorbed light which is described by the quantum efficiency,

_{A}*η*. Therefore, the quantum dot fluorescence power is

_{QD}*P*=

_{f}*η*.

_{QD}α_{A}α_{B}P_{laser}*α*, we can use Beer-Lambert’s law that states that the absorbance of light through a solution has a linear relationship with the extinction coefficient,

_{A}*ε*, molar concentration,

*ρ*, and length traveled by the light through the solution,

*l*. The absorbance is the logarithmic ratio of incident light

*P*to transmitted light

_{inc}*P*The amount of absorbed light is

_{T}*P*=

_{abs}*P*–

_{inc}*P*=

_{T}*α*; therefore, Eq. (5) can be rearranged to show that

_{A}P_{inc}*α*= 1 −10

_{A}^{−}

*.*

^{A}*A*used to calculate

*α*, it is assumed that QD absorbance on the ID card and in solution is the same. To determine the absorbance per quantum dot in solution, the absorbance in a 1cm × 1cm cuvette is calculated by setting

_{A}*l*= 1 cm. The number of quantum dots in the cuvette is calculated by multiplying the QD concentration by the volume through which light travels and Avogadro’s number,

*N*. The volume of solution,

_{A}*V*, which the laser path travels through is the cross-section of the cuvette multiplied by the laser beam width of 1cm resulting in a total volume of

_{c}*V*= 1cm

_{c}^{3}= 1mL. The absorbance per quantum dot,

*A*, is then the absorbance from Eq. (5) divided by the number of quantum dots in the cuvette The number of dots deposited on the ID card is approximated as

_{QD}*N*=

_{QD}*ρV*, where

_{D}N_{A}*V*is the volume deposited, so that

_{D}#### 4.1.2. Signal to noise ratio

17. J. R. Janesick, *Scientific Charge-Coupled Devices* (SPIE Press, 2001). [CrossRef]

*T*. At the end of the integration time, the individual charge packets are moved along the array of pixels. At the end of the array, the charges are placed on a charge sensing capacitor to produce an output voltage. This voltage is then amplified and digitized.

*λ*due to the QDs designed to emit at wavelength

*λ*. The expected number of electrons can be written as where

_{i}*η*is the quantum efficiency of the CCD pixel, and

*P*(

_{i}*λ*)

*λT*/

*hc*is the number of photons incident on the CCD pixel. The term

*P*(

_{i}*λ*) is defined in Eq. (3) and

*λ*/

*hc*is the energy of a photon where

*h*is Planck’s constant and

*c*is the speed of light. To determine the variance in the number of electrons,

*C*. The voltage across the capacitor is then amplified by a MOSFET amplifier [17

17. J. R. Janesick, *Scientific Charge-Coupled Devices* (SPIE Press, 2001). [CrossRef]

*Y*(

_{i}*p*) represent the voltage at the amplifier output for the pixel centered at wavelength

*λ*due to the QDs designed to emit at

_{p}*λ*. This voltage will be a function both of both

_{i}*N*(

_{i}*λ*) and the number of electrons added by the amplifier,

_{p}*N*, such that

_{T}*q*is electron charge. Assuming

_{e}*N*is zero mean with variance

_{T}*Y*(

_{i}*p*) is

17. J. R. Janesick, *Scientific Charge-Coupled Devices* (SPIE Press, 2001). [CrossRef]

*k*is Boltzmann’s constant,

*T°*is the temperature of the device,

*B*is the bandwidth,

*R*is the output resistance of the amplifier,

_{out}*G*is the amplifier gain and

*S*is the sensitivity of the amplifier in units of volts per electron [

*V*/

*e*

^{−}].

### 4.2. SNR experiments

10. S. Chang, M. Zhou, and C. P. Grover, “Information coding and retrieving using fluorescent semiconductor nanocrystals for object identification,” Opt. Express **12**, 143–148 (2004). [CrossRef] [PubMed]

*λ*= 565 nm, from Invitrogen [19

_{i}19. Invitrogen by Life Technologies, http://www.invitrogen.com.

*ρ*= 1

*μ*M are deposited onto an ID card. A volume of

*V*= 10

_{D}*μ*L of the water based quantum dots are confined within a 3mm diameter indent on the card and left to dry. The Thorlabs 405nm solid-state laser emitting 20 mW of power is used to illuminate the quantum dots. A multi-mode optical fiber is used to capture the emissions and guide it to a B&W Tek Inc CCD-based spectrometer. The spectrometer outputs 3000 intensity values in arbitrary units distributed between 385 nm and 750 nm with an average wavelength spacing of

*δλ*= 0.1562 nm. To acquire sufficient data for statistical analysis, 500 measurements are taken for each integration time.

*E*{

*Y*(

_{i}*p*)} and that the variance of the measurements is proportional to

*T*.

*P*(

_{i}*λ*), according to Eq. (3), are shown in Table 1. We anticipate the optical power loss to be −102.7 dB resulting in

_{p}*P*(

_{i}*λ*= 568 nm) = 1.08 × 10

^{−12}W.

*η*and

*η*= 0.02 and

*η*= 0.02 and

*η*, we would expect a value closer to 0.1 for the relatively inexpensive spectrometer used. This amounts to an error of 7 dB which is likely due to residual uncertainty in the estimation of over 100dB of optical power loss. Part of this uncertainty is the ‘blinking’ affect observed in quantum dots [20

20. M. Konu, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, “Nonexponential “blinking” kinetics of single CdSe quantum dots: a universal power law behaviour,” J. Chem. Phys. **112**3117–3120, (2000). [CrossRef]

21. K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empedocles, W. K. Woo, and M. G. Bawendi, “Blinking statistics in single semiconductor nanocrystal quantum dots,” Phys. Rev. B **63**205316, (2001). [CrossRef]

*α*, could be added as an additional source of lost optical power in Eq. (3).

_{B}*B*= 1 × 10

^{6}Hz. The temperature of the device is approximated at room temperature,

*T°*= 293

*K*. The output impedance is approximated at 2 kΩ [22]. The remaining two unknowns are more difficult to estimate as there is a large range of possible values. For scientific CCDs, the range of sensitivity values range from 1 to 20

*μV*/

*e*

^{−}. To match the predicted model of

## 5. Data detection simulations

*L*intensity levels at the input to the matched filter, where desired signal energy is defined using the intensity of light emitted over the entire Gaussian pulse, not just at the desired wavelength.

24. S. Chang, K. Yu, and J. Liu, “Advanced secure information retrieval technology for multiplayer information extraction,” J. Nanomater. **2008** (2008). [CrossRef]

*P*(

**I**=

**Î**) plotted versus SNR. The number of colours is set to

*N*= 6 and

*L*= 6 intensity levels to match what Han predicted to be possible when MxQD was first proposed in [5

**19**, 631–635 (2001). [CrossRef] [PubMed]

*SNR*= 15 dB,

*N*= 6,

*L*= 6), as a starting point and then independently increase the number of QD colours,

*N*, and the number of intensity values,

*L*, to observe the effects on accurate reads. Figure 6 shows

*P*(

**I**=

**Î**) plotted versus increasing number of QD colours and Fig. 7 for increasing number of intensity levels.

## 6. Conclusion

## Acknowledgments

## References and links

1. | S. V. Gaponenko, |

2. | M. Bruchez Jr., M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science |

3. | W. R. Algar, M. Massey, and U. J. Krull, “The application of quantum dots, gold nanoparticles and molecular switches to optical nucleic-acid diagnostics,” Trends Anal. Chem. |

4. | W. Chan and S. Nie, “Quantum dot bioconjugates for ultrasensitive nonisotopic detection,” Science |

5. | M. Han, X. Ming, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. |

6. | Multiplexed Solutions For Life - Luminex Corporation, http://www.luminexcorp.com. |

7. | P. S. Eastman, W. Ruan, M. Doctolero, R. Nuttall, G. de Feo, J. S. Park, J. S. F. Chu, P. Cooke, J. W. Gray, S. Li, and F. F. Chen, “Qdot nanobarcodes for multiplexed gene expression analysis,” Nano Lett. |

8. | H. Xu, M. Y. Sha, E. Y. Wong, J. Uphoff, Y. Xu, J. A. Treadway, A. Truong, E. O’Brien, S. Asquith, M. Stubbins, N. K. Spurr, E. H. Lai, and W. Mahoney, “Multiplexed SNP genotyping using the Qbead ™system: a quantum dot-encoded microsphere-based assay,” Nucleic Acids Res. |

9. | BD Biosciences, http://www.bdbiosciences.com. |

10. | S. Chang, M. Zhou, and C. P. Grover, “Information coding and retrieving using fluorescent semiconductor nanocrystals for object identification,” Opt. Express |

11. | S. V. Vaidya, M. L. Gilchrist, C. Maldarelli, and A. Couzis, “Spectral bar coding of polystyrene microbeads usign multicolored quantum dots,” Anal. Chem. |

12. | O. I. Mićić, K. M. Jones, A. Cahill, and A. J. Nozik, “Optical, electronic, and structural properties of uncoupled and close-packed arrays of InP quantum dots,” J. Phys. Chem. B |

13. | J. G. Proakis and M. Salehi, |

14. | S. Haykin, |

15. | E. Hecht, |

16. | Ocean Optics - Inventors of the World’s First Miniature Spectrometer, http://www.oceanoptics.com. |

17. | J. R. Janesick, |

18. | E. Kreyszig, |

19. | Invitrogen by Life Technologies, http://www.invitrogen.com. |

20. | M. Konu, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, “Nonexponential “blinking” kinetics of single CdSe quantum dots: a universal power law behaviour,” J. Chem. Phys. |

21. | K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empedocles, W. K. Woo, and M. G. Bawendi, “Blinking statistics in single semiconductor nanocrystal quantum dots,” Phys. Rev. B |

22. | A. S. Sedra and K. C. Smith, |

23. | Evident Technologies, http://www.evidenttech.com. |

24. | S. Chang, K. Yu, and J. Liu, “Advanced secure information retrieval technology for multiplayer information extraction,” J. Nanomater. |

**OCIS Codes**

(040.1520) Detectors : CCD, charge-coupled device

(070.4790) Fourier optics and signal processing : Spectrum analysis

(160.2540) Materials : Fluorescent and luminescent materials

**ToC Category:**

Detectors

**History**

Original Manuscript: September 23, 2011

Revised Manuscript: February 8, 2012

Manuscript Accepted: February 16, 2012

Published: February 24, 2012

**Virtual Issues**

Vol. 7, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Kelly C. Goss, Geoff G. Messier, and Mike E. Potter, "Data detection algorithms for multiplexed quantum dot encoding," Opt. Express **20**, 5762-5774 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5762

Sort: Year | Journal | Reset

### References

- S. V. Gaponenko, Optical Properties of Semiconductor Nanocrystals (Cambridge University Press, 1998). [CrossRef]
- M. Bruchez, M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science281, 2013–2016 (1998). [CrossRef] [PubMed]
- W. R. Algar, M. Massey, and U. J. Krull, “The application of quantum dots, gold nanoparticles and molecular switches to optical nucleic-acid diagnostics,” Trends Anal. Chem.28, 292–306 (2009). [CrossRef]
- W. Chan and S. Nie, “Quantum dot bioconjugates for ultrasensitive nonisotopic detection,” Science281, 2016–2018 (1998). [CrossRef] [PubMed]
- M. Han, X. Ming, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol.19, 631–635 (2001). [CrossRef] [PubMed]
- Multiplexed Solutions For Life - Luminex Corporation, http://www.luminexcorp.com .
- P. S. Eastman, W. Ruan, M. Doctolero, R. Nuttall, G. de Feo, J. S. Park, J. S. F. Chu, P. Cooke, J. W. Gray, S. Li, and F. F. Chen, “Qdot nanobarcodes for multiplexed gene expression analysis,” Nano Lett.6, 1059–1064 (2006). [CrossRef] [PubMed]
- H. Xu, M. Y. Sha, E. Y. Wong, J. Uphoff, Y. Xu, J. A. Treadway, A. Truong, E. O’Brien, S. Asquith, M. Stubbins, N. K. Spurr, E. H. Lai, and W. Mahoney, “Multiplexed SNP genotyping using the Qbead ™system: a quantum dot-encoded microsphere-based assay,” Nucleic Acids Res.31, e43 (2003). [CrossRef] [PubMed]
- BD Biosciences, http://www.bdbiosciences.com .
- S. Chang, M. Zhou, and C. P. Grover, “Information coding and retrieving using fluorescent semiconductor nanocrystals for object identification,” Opt. Express12, 143–148 (2004). [CrossRef] [PubMed]
- S. V. Vaidya, M. L. Gilchrist, C. Maldarelli, and A. Couzis, “Spectral bar coding of polystyrene microbeads usign multicolored quantum dots,” Anal. Chem.798520–8530 (2007). [CrossRef] [PubMed]
- O. I. Mićić, K. M. Jones, A. Cahill, and A. J. Nozik, “Optical, electronic, and structural properties of uncoupled and close-packed arrays of InP quantum dots,” J. Phys. Chem. B1029791–9796, 1998. [CrossRef]
- J. G. Proakis and M. Salehi, Fundamentals of Communication Systems (Pearson Prentice Hall, 2005).
- S. Haykin, Communication Systems 4th edition (John Wiley & Sons, Inc., 2001).
- E. Hecht, Optics 4th edition (Pearson Education, Inc., 2002).
- Ocean Optics - Inventors of the World’s First Miniature Spectrometer, http://www.oceanoptics.com .
- J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, 2001). [CrossRef]
- E. Kreyszig, Advanced Engineering Mathematics 7th edition (John Wiley & Sons, Inc., 1993).
- Invitrogen by Life Technologies, http://www.invitrogen.com .
- M. Konu, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, “Nonexponential “blinking” kinetics of single CdSe quantum dots: a universal power law behaviour,” J. Chem. Phys.1123117–3120, (2000). [CrossRef]
- K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empedocles, W. K. Woo, and M. G. Bawendi, “Blinking statistics in single semiconductor nanocrystal quantum dots,” Phys. Rev. B63205316, (2001). [CrossRef]
- A. S. Sedra and K. C. Smith, Microelectronic Circuits (Oxford University Press, 1998).
- Evident Technologies, http://www.evidenttech.com .
- S. Chang, K. Yu, and J. Liu, “Advanced secure information retrieval technology for multiplayer information extraction,” J. Nanomater.2008 (2008). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.