Abstract

Confocal fluorescence ratiometric imaging is an optical technique used to measure a variety of important biological parameters. A small amount of chromatic aberration in the microscope system can introduce a variation in the signal ratio dependent on the fluorophore concentration gradient along the optical axis and lead to bias in the measurement. We present a theoretical model of this effect. Experimental results and simulations clearly demonstrate that this error can be significant and should not be ignored.

© 2011 Optical Society of America

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    [PubMed]
  2. D. W. Piston, M. S. Kirby, H. Cheng, W. J. Lederer, and W. W. Webb, “Two-photon-excitation fluorescence imaging of three-dimensional calcium-ion activity,” Appl. Opt. 33, 662–669(1994).
    [CrossRef] [PubMed]
  3. G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
    [CrossRef] [PubMed]
  4. H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
    [CrossRef] [PubMed]
  5. E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
    [CrossRef] [PubMed]
  6. R. C. Scaduto and L. W. Grotyohann, “Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives,” Biophys. J. 76, 469–477 (1999).
    [CrossRef] [PubMed]
  7. T. Takamatsu and S. Fujita, “Microscopic tomography by laser scanning microscopy and its three-dimensional reconstruction,” J. Microsc. 149, 167–174 (1988).
    [CrossRef] [PubMed]
  8. M. J. Nasse and J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A 27, 295–302 (2010).
    [CrossRef]
  9. O. Haeberlé, M. Ammar, H. Furukawa, and K. Tenjimbayashi, “Point spread function of optical microscopes imaging through stratified media,” Opt. Express 11, 2964–2969(2003).
    [CrossRef] [PubMed]

2010

2003

1999

H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
[CrossRef] [PubMed]

R. C. Scaduto and L. W. Grotyohann, “Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives,” Biophys. J. 76, 469–477 (1999).
[CrossRef] [PubMed]

1997

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

1994

D. W. Piston, M. S. Kirby, H. Cheng, W. J. Lederer, and W. W. Webb, “Two-photon-excitation fluorescence imaging of three-dimensional calcium-ion activity,” Appl. Opt. 33, 662–669(1994).
[CrossRef] [PubMed]

E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
[CrossRef] [PubMed]

1988

T. Takamatsu and S. Fujita, “Microscopic tomography by laser scanning microscopy and its three-dimensional reconstruction,” J. Microsc. 149, 167–174 (1988).
[CrossRef] [PubMed]

1985

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, “A new generation of Ca2+ indicators with greatly improved fluorescence properties,” J. Biol. Chem. 260, 3440–3450 (1985).
[PubMed]

Ammar, M.

Bedlack, R. S.

E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
[CrossRef] [PubMed]

Cheng, H.

Dellian, M.

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

Fujita, S.

T. Takamatsu and S. Fujita, “Microscopic tomography by laser scanning microscopy and its three-dimensional reconstruction,” J. Microsc. 149, 167–174 (1988).
[CrossRef] [PubMed]

Furukawa, H.

Gross, E.

E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
[CrossRef] [PubMed]

Grotyohann, L. W.

R. C. Scaduto and L. W. Grotyohann, “Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives,” Biophys. J. 76, 469–477 (1999).
[CrossRef] [PubMed]

Grynkiewicz, G.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, “A new generation of Ca2+ indicators with greatly improved fluorescence properties,” J. Biol. Chem. 260, 3440–3450 (1985).
[PubMed]

Haeberlé, O.

Helmlinger, G.

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

Jain, R. K.

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

Jakobsen, M.

H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
[CrossRef] [PubMed]

Kirby, M. S.

Lederer, W. J.

Loew, L. M.

E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
[CrossRef] [PubMed]

Nasse, M. J.

Piston, D. W.

Poenie, M.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, “A new generation of Ca2+ indicators with greatly improved fluorescence properties,” J. Biol. Chem. 260, 3440–3450 (1985).
[PubMed]

Rechinger, K. B.

H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
[CrossRef] [PubMed]

Scaduto, R. C.

R. C. Scaduto and L. W. Grotyohann, “Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives,” Biophys. J. 76, 469–477 (1999).
[CrossRef] [PubMed]

Siegumfeldt, H.

H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
[CrossRef] [PubMed]

Takamatsu, T.

T. Takamatsu and S. Fujita, “Microscopic tomography by laser scanning microscopy and its three-dimensional reconstruction,” J. Microsc. 149, 167–174 (1988).
[CrossRef] [PubMed]

Tenjimbayashi, K.

Tsien, R. Y.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, “A new generation of Ca2+ indicators with greatly improved fluorescence properties,” J. Biol. Chem. 260, 3440–3450 (1985).
[PubMed]

Webb, W. W.

Woehl, J. C.

Yuan, F.

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

Appl. Opt.

Biophys. J.

E. Gross, R. S. Bedlack, Jr., and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67, 208–216 (1994).
[CrossRef] [PubMed]

R. C. Scaduto and L. W. Grotyohann, “Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives,” Biophys. J. 76, 469–477 (1999).
[CrossRef] [PubMed]

J. Biol. Chem.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, “A new generation of Ca2+ indicators with greatly improved fluorescence properties,” J. Biol. Chem. 260, 3440–3450 (1985).
[PubMed]

J. Microsc.

T. Takamatsu and S. Fujita, “Microscopic tomography by laser scanning microscopy and its three-dimensional reconstruction,” J. Microsc. 149, 167–174 (1988).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Microbiology

H. Siegumfeldt, K. B. Rechinger, and M. Jakobsen, “Use of fluorescence ratio imaging for intracellular pH determination of individual bacterial cells in mixed cultures,” Microbiology 145, 1703–1709 (1999).
[CrossRef] [PubMed]

Nature Med.

G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Med. 3, 177–182 (1997).
[CrossRef] [PubMed]

Opt. Express

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Figures (9)

Fig. 1
Fig. 1

Simplified diagram of a confocal microscope. A point light source is imaged into the sample through collimating lens 1 and the objective. Point F is the nominal focus of the objective. The objective and collimating lens 2 image F onto pinhole P.

Fig. 2
Fig. 2

Effect of axial chromatic aberration on the focal position. The conjugate point of the pinhole in the object space for emission light is F . The shift between F and the nominal focus F is Δ f .

Fig. 3
Fig. 3

The signal intensities from both emission channels near the boundary of a uniform sample for a Nikon 10 × / 0.25 NA Plan objective. The shaded area represents the region where the focal plane of the microscope is inside the sample. Because of chromatic aberration, a shift between the two signal intensity curves along the horizontal axis (z axis) is present. The peak signal intensities are normalized.

Fig. 4
Fig. 4

The ratio variation as a function of stage position near the sample boundary. A uniform sample was measured with both a closed pinhole (a) and an open pinhole (b) with Nikon 1 × / 0.04 NA Plan UW, 2 × / 0.06 NA Plan UW, 4 × / 0.13 NA Plan Fluor, 10 × / 0.25 NA Plan, and 20 × / 0.5 NA Plan Fluor objectives. The shaded regions in the diagrams show the locations where the nominal focal plane is inside the sample.

Fig. 5
Fig. 5

Variation in the ratio on different confocal microscopes. The same uniform sample was scanned on a Zeiss LSM 510 confocal microscope with a 10 × / 0.3 NA Plan Neoflurar objective, a Leica SP5 confocal microscope with a 10 × / 0.4 NA PI Apo objective, and a Nikon Eclipse E600-C1 confocal microscope with a 10 × / 0.25 NA Plan objective. The difference in the magnitude of the variations is presumably due to the different amounts of chromatic aberration present in the systems and the different NAs of the objectives.

Fig. 6
Fig. 6

Simulation of the effect of chromatic aberration on the ratio of the signals for a 10 × / 0.25 NA objective. In the simulation, the assumptions are (i) an excitation wavelength of λ ex = 543 nm , (ii) two emission wavelengths of λ 1 = 595 nm and λ 2 = 650 nm , and (iii) a pinhole size of 2 μm in object space. The variations of the ratio versus depth for different amounts of Δ f 1 and Δ f 2 are shown. The horizontal axis in each of the subfigures is the shift z 0 of the sample along the z axis. The nominal focal plane of the excitation is at z = 0 ; z < 0 is in air, and z > 0 is inside the sample.

Fig. 7
Fig. 7

Comparison of experimental and simulation results. Figure 6c is very close to the experimental results for the Nikon microscope with a 10 × / 0.25 NA objective and a closed pinhole.

Fig. 8
Fig. 8

Comparison of the signal ratios before and after correction. The shift of the signals along the z axis can be found by shifting each dataset to minimize the RMS of the signal ratios through a uniform sample. For the signal intensities shown in Fig. 3, the minimum RMS for the ratio is achieved by shifting the λ 1 channel to the right by 11 μm . The ratio is more consistent near the sample boundary after the correction.

Fig. 9
Fig. 9

The axial z shifts between the two signal channels for the Nikon objectives with both a closed and an open pinhole. The “o” symbol is for the open-pinhole case, “*” for the closed-pinhole case, and the solid line is the fitted quadratic curve of Eq. (15).

Equations (17)

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E ( λ ex , λ em ) = A d 2 r d z I s ( r , z , λ ex , n , NA ) I d ( r , z , λ em , n , NA ) η C ( r , z ) ,
I s ( r , z , λ ex , n , NA ) = I ill ( r , z , λ ex , n , NA ) .
I d ( r , z , λ em , n , NA ) = I det ( r , z , λ em , n , NA ) * T ( r ) ,
T ( r ) = { 1 , r r p 0 , otherwise .
E ( λ ex , λ em , z 0 ) = a d 2 r d z I ill ( r , z , λ ex , n , NA ) [ I det ( r , z , λ em , n , NA ) * T ( r ) ] μ C ( r , z z 0 ) ,
R ( z 0 ) = E ( λ ex , λ 1 , z 0 ) E ( λ ex , λ 2 , z 0 ) ,
Δ W = W λ 020 ( y / R 0 ) 2 ,
Δ f = f f ,
u = Δ W y | y = R 0 = 2 W λ 020 R 0 .
u = u y / f ,
y = y + u z ,
u = 2 W λ 020 R 0 R 0 f .
y = 0 = R 0 ( 2 W λ 020 R 0 + R 0 f ) ( f Δ f ) ,
Δ f = 2 W λ 020 f 2 R 0 2 + 2 W λ 020 f .
Δ f = 2 W λ 020 f 2 R 0 2 2 W λ 020 NA 2 .
E 1 ( z 0 ) = E ( λ ex , λ 1 , z 0 ) = 2 π A η d r d z I ill ( r , z , λ ex , n , NA ) [ I det ( r , z Δ f 1 , λ 1 , n , NA ) * T ( r ) ] C ( r , z z 0 ) ,
E 2 ( z 0 ) = E ( λ ex , λ 2 , z 0 ) = 2 π A η d r d z I ill ( r , z , λ ex , n , NA ) [ I det ( r , z Δ f 2 , λ 2 , n , NA ) * T ( r ) ] C ( r , z z 0 ) .

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