## Graded-field autoconfocal microscopy

Optics Express, Vol. 15, Issue 5, pp. 2476-2489 (2007)

http://dx.doi.org/10.1364/OE.15.002476

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### Abstract

Autoconfocal microscopy (ACM) is a simple implementation of a transmitted-light confocal microscopy where a nonlinear detector plays the role of a virtual self-aligned pinhole. We report here a significant improvement of ACM based on the use of graded-field (GF) imaging. The technique of GF imaging involves introducing partial beam blocks in the illumination and detection apertures of an imaging system. These partial beam blocks confer phase-gradient sensitivity to the imaging system and allow control over its background level. We present the theory of the GF contrast in the context of ACM, comparing it to GF contrast in a non-scanning widefield microscope, and discuss various performance characteristics of GF-ACM in terms of resolution, sectioning strength, and an “under-detection” light collection geometry. An advantage of ACM is that it can be readily combined with two-photon excited fluorescence (TPEF) microscopy. We present images of rat brain hippocampus using simultaneous GF-ACM and TPEF microscopy. These images are inherently co-registered.

© 2007 Optical Society of America

## 1. Introduction

2. C. Yang and J. Mertz, “Transmission confocal laser scanning microscopy with a virtual pinhole based on nonlinear detection,” Opt. Lett. **28**, 224–227 (2003). [CrossRef] [PubMed]

3. T. Pons and J. Mertz, “Autoconfocal microscopy with nonlinear transmitted light detection,” J. Opt. Soc. Am. B **21**, 1486–1493 (2004). [CrossRef]

4. R. Yi, K.K. Chu, and J. Mertz, “Graded-field microscopy with white light,” Opt. Express **14**, 5191–5200 (2006). [CrossRef] [PubMed]

6. R.D. Allen, G.B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. **69**, 193–221 (1969). [PubMed]

7. W.B. Amos, S. Reichelt, D.M. Cattermole, and J. Laufer, “Re-evaluation of differential phase contrast (DPC) in a scanning laser microscope using a split detector as an alternative to differential interference contrast (DIC) optics,” J. Microsc. **210**, 166–175 (2003). [CrossRef] [PubMed]

8. Z.F. Mainen, M. Maletic-Savatic, S.H. Shi, Y. Hayashi, R. Malinow, and K. Svoboda, “Two-photon imaging in living brain slices,” Methods **18**, 231–239 (1999). [CrossRef] [PubMed]

## 2. Principle

## 3. Effective pinhole size

3. T. Pons and J. Mertz, “Autoconfocal microscopy with nonlinear transmitted light detection,” J. Opt. Soc. Am. B **21**, 1486–1493 (2004). [CrossRef]

_{det}) and to a first approximation is roughly given by

*w*≈ λ/2NA

_{p}_{det}. As with a conventional confocal microscope, the overall sectioning ability of an ACM is governed by both the illumination spot size and the “virtual” pinhole size. Because there are two separate lens systems for illumination and detection, there may be two different numerical apertures associated with these (see discussion of this condition in section 6), and the overall sectioning ability is determined by the wider of the two NA’s (i.e. the more restrictive of the spot sizes). For a typical configuration of our specific system, our detection NA is ≈ 0.9 and the wavelength 1.03 μm, so the effective pinhole size is ≈ 0.6 μm.

## 4. Axial sectioning

*z*

^{2}, where

*z*is the distance of the plane away from the focus [9]. However, in a transmission confocal system, a uniformly absorbing plane affects the sample equally regardless of its vertical position, a result of the well-known “missing cone” problem [10

10. N. Streibl, “Depth transfer by an imaging system,” Opt. Acta **31**, 1233–1241 (1984). [CrossRef]

*B*(

*x*⃗

_{3})) and scattered (

*S*(

*x*⃗

_{3})), where

*x*⃗

_{3}is a two-dimensional vector representing the spatial coordinates at the detector. Both

*B*and

*S*components combine at the detector. A detailed description of the resultant ACM signal was presented in reference [3

3. T. Pons and J. Mertz, “Autoconfocal microscopy with nonlinear transmitted light detection,” J. Opt. Soc. Am. B **21**, 1486–1493 (2004). [CrossRef]

*z*. We therefore write

*S*as a function of both

*x*⃗

_{3}and

*z*, while

*B*(

*x*⃗

_{3}) is independent of

*z*.

*S*term can therefore be neglected. What remains is the ballistic light as well as light scattered from near the focal plane. Both of these components are well-focused on the crystal. The integrand |

*B*(

*x*⃗

_{3})+

*S*(

*x*⃗

_{3},

*z*)|

^{4}is thus a sharply peaked function, and the integral of such a function is approximately equal to the product of the peak value with the characteristic area of the peak. The characteristic area of the peak therefore corresponds to the area of our virtual pinhole, and is effectively diffraction-limited as was already argued in section 3. If we define our coordinate system such that the focus is located at

*x*⃗

_{3}= 0, then Eq. (1) simplifies to

*B*is generally much larger than

*S*. Sectioning in this case is weak because

*B*is invariant with respect to

*z*. On the other hand, when the partial blocks are introduced for GF imaging (as described in section 2), the ballistic light can be gradually reduced to the point where the

*S*-containing terms in Eq. (3) become increasingly significant. Because progressive terms in Eq. (3) contain higher orders of

*S*, they correspondingly exhibit greater sectioning strength. The degree to which the partial blocks are inserted effectively tunes the relative weights of

*B*and

*S*. There is typically insufficient scattered light to rely solely on

*S*to generate a second-harmonic signal, and some degree of

*B*is usually required to amplify

*S*and produce adequate SHG.

*B*essentially acts then like the local oscillator beam in an Optical Coherence Tomography system. GF imaging is normally accomplished in the regime where

*S*≈

*B*.

*S*(0,

*z*) decays as 1/

*z*[9]. Let us also examine the extreme darkfield case where the GF blocks are adjusted such that

*B*is completely excluded, and SHG ∼

*S*(0,

*z*)

^{4}∼ 1/

*z*

^{4}. At first glance it might appear that the GF-ACM sectioning strength in this scenario is better than that of a fluorescence confocal microscope, whose sectioning strength scales as 1/

*z*

^{2}. This is not the case. An extra power of 2 in the GF-ACM sectioning strength is occasioned simply by the quadratic nature of SHG detection (i.e. this extra power of 2 would arise just as well if we squared the detector output of a standard fluorescence confocal microscope). A proper comparison between a darkfield GF-ACM and a fluorescence confocal microscope would require us to take the square root of the GF-ACM image to recover a linear dependence of the GF-ACM signal on the imaging contrast source (namely, scattering cross-section). Once this square-root is taken, then the sectioning strength of a darkfield GF-ACM is the same as that of a fluorescence microscope.

## 5. GF-ACM theory

4. R. Yi, K.K. Chu, and J. Mertz, “Graded-field microscopy with white light,” Opt. Express **14**, 5191–5200 (2006). [CrossRef] [PubMed]

4. R. Yi, K.K. Chu, and J. Mertz, “Graded-field microscopy with white light,” Opt. Express **14**, 5191–5200 (2006). [CrossRef] [PubMed]

*x*and

*y*axes separately (we confine our analysis to the

*x*axis since GF plays no role along the

*y*axis); these conditions do not detract from the generality of our GF analysis. Our goal will be to derive the final optical power incident on the ACM detector, where we will make the approximation that nonlinear ACM detection acts like an ideal pinhole.

*ξ*

_{0}=

*kx*

_{0}/

*f*, and

_{a}*k*= 2

*π*/

*λ*. The parameter

*x*is the effective scan angle, which is a tilt in the plane wave at the illumination aperture that will be translated to a position of the laser focus in the sample.

_{s}*α*

_{1,2}=

*ka*

_{1,2}/

*f*, and

_{a}*a*

_{1,2}are the limits of the illumination aperture along the

*x*axis. The prefactors associated with Fourier transforms have been omitted for simplicity.

*x*

_{1s}=

*x*

_{1}-

*x*. We can further simplify this equation by introducing the variables

_{s}*α*=

_{d}*α*

_{2}-

*α*

_{1}. The parameter

*α*is the location of the aperture centroid, and

_{c}*α*is the width of the aperture in Fourier coordinates, obtaining

_{d}*in*indicates that the mutual coherence function here is incident on the sample.

*J*

^{out}_{1}(

*x*

_{1c},

*x*

_{1d};

*x*) as the mutual coherence function emanating from the sample, we use Eqs. (10) and (11) from our previous publication [4

_{s}**14**, 5191–5200 (2006). [CrossRef] [PubMed]

*J*

^{out}_{1}(

*x*

_{1c},

*x*

_{1d};

*x*) to

_{s}*I*

_{3}(

*x*

_{3}), the intensity function at the detector plane. These equations are

*β*is identical to that for

*α*, except that it refers to the detection aperture.

**14**, 5191–5200 (2006). [CrossRef] [PubMed]

**14**, 5191–5200 (2006). [CrossRef] [PubMed]

*T*(

_{r}*x*

_{1c},

*x*

_{1d}) and

*T*(

_{i}*x*

_{1c},

*x*

_{1d}) are respectively the real and imaginary components of

*T*(

*x*

_{1c},

*x*

_{1d}) (respectively even and odd in

*x*

_{1d}), and we have introduced the transfer functions

*x*

_{1d}.

*T*and

_{r}*T*characterize the sample whereas

_{i}*K*and

_{e}*K*characterize the microscope optics. Eq. (18) will serve as the basis for the remainder of our analysis.

_{o}*I*

_{3}is detected as a total power and not as a distribution. That is,

**14**, 5191–5200 (2006). [CrossRef] [PubMed]

*δ*(

*x*

_{3}+

*x*) in Eq. (20) to represent the descanned pinhole. Such a delta function is somewhat unrealistic in that it corresponds to a pinhole size that is infinitesimally small; however, it provides physical insight into the effects of GF on ACM imaging. The final ACM signal is then given by Eq. (17), except that

_{s}*x*

_{3}is replaced with -

*x*in the definitions of

_{s}*K*and

_{e}*K*(Eqs. (19a) and (19b) respectively).

_{o}*K*and

_{e}*K*play the roles of imaging transfer functions for the coordinate

_{o}*x*

_{1c}, similar to a point spread function. The product of the sinc functions is centered around

*x*

_{1c}=

*x*, effectively confining the imaging to the point being scanned in the sample. This fixes the contributing

_{s}*x*

_{1c}values to those near

*x*.

_{s}*K*and

_{e}*K*also play the roles of window functions for the coordinate

_{o}*x*

_{1d}. For samples that are purely absorbing and exhibit no non-uniform phase-shifting properties,

*T*is zero and

_{i}*K*alone is responsible for imaging the sample to the detector. On the other hand, when the sample contains no phase non-uniformities, then

_{e}*T*has a contribution and

_{i}*K*acts like a first-derivative finder, owing to its odd parity in

_{o}*x*

_{1d}.

*K*and

_{e}*K*are diffraction limited by both the illumination and detection aperture widths (

_{o}*α*and

_{d}*β*respectively), both of which govern lateral GF-ACM resolution. 3D plots of

_{d}*K*and

_{e}*K*as a function of

_{o}*x*

_{1c}and

*x*

_{1d}are illustrated in Fig. 2 for the special case where the illumination and detection apertures have the same width and offset:

*α*=

_{c}*β*and

_{c}*α*=

_{d}*β*. In this case,

_{d}*α*=

_{c}*β*= 0, then

_{c}*K*goes to zero. No phase-gradient information can be gained when the apertures are not offset. This is the case of standard ACM without GF. However, once the apertures are offset by inserting a partial block in either the illumination or detection aperture (or both), then

_{o}*K*becomes nonzero and phase-gradient information is revealed.

_{o}## 6. Transmitted light under-detection

*z*-profile of the detected signal from a polystyrene bead as a function of bead defocus for symmetric NA’s in the illumination and detection optics, and with and without the use of a SHG crystal (in the case of no SHG crystal, our detector was a simple linear photodiode). These

*z*-profiles are shown in Fig. 4. The brightness of the bead never exceeds the background in this case of linear detection, confirming that no under-detection occurs when there is no SHG crystal.

*μ*m, the result of which is shown in Fig. 5. Indeed, we do observe a limited angular acceptance profile. Light incident at high angles is rejected, effectively limiting the NA on the detection side.

## 7. Imaging results

*μ*m.

*μ*m below the tissue surface, and the accompanying video clip shows structure beyond 100

*μ*m in depth.

## 8. Conclusion

## Acknowledgments

## References and links

1. | A.E. Dixon and C. Cogswell, “Confocal microscopy with transmitted light,” in |

2. | C. Yang and J. Mertz, “Transmission confocal laser scanning microscopy with a virtual pinhole based on nonlinear detection,” Opt. Lett. |

3. | T. Pons and J. Mertz, “Autoconfocal microscopy with nonlinear transmitted light detection,” J. Opt. Soc. Am. B |

4. | R. Yi, K.K. Chu, and J. Mertz, “Graded-field microscopy with white light,” Opt. Express |

5. | G. Nomarski, “Microinterféromètre différentiel à ondes polarisées [in French],” J. Phys. Radium |

6. | R.D. Allen, G.B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. |

7. | W.B. Amos, S. Reichelt, D.M. Cattermole, and J. Laufer, “Re-evaluation of differential phase contrast (DPC) in a scanning laser microscope using a split detector as an alternative to differential interference contrast (DIC) optics,” J. Microsc. |

8. | Z.F. Mainen, M. Maletic-Savatic, S.H. Shi, Y. Hayashi, R. Malinow, and K. Svoboda, “Two-photon imaging in living brain slices,” Methods |

9. | T. Wilson, “The role of the pinhole in confocal imaging system,” in |

10. | N. Streibl, “Depth transfer by an imaging system,” Opt. Acta |

11. | M. Born and E. Wolf, |

**OCIS Codes**

(110.0180) Imaging systems : Microscopy

(180.1790) Microscopy : Confocal microscopy

(180.5810) Microscopy : Scanning microscopy

(190.4160) Nonlinear optics : Multiharmonic generation

**ToC Category:**

Microscopy

**History**

Original Manuscript: October 9, 2006

Revised Manuscript: January 23, 2007

Manuscript Accepted: January 23, 2007

Published: March 5, 2007

**Virtual Issues**

Vol. 2, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Kengyeh K. Chu, Ran Yi, and Jerome Mertz, "Graded-field autoconfocal microscopy," Opt. Express **15**, 2476-2489 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2476

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### References

- A.E. Dixon and C. Cogswell, "Confocal microscopy with transmitted light," in Handbook of Biological Confocal Microscopy, J.B. Pawley, ed. (Plenum Press, 1995), pp. 479-490.
- C. Yang and J. Mertz, "Transmission confocal laser scanning microscopy with a virtual pinhole based on nonlinear detection," Opt. Lett. 28,224-227 (2003). [CrossRef] [PubMed]
- T. Pons and J. Mertz, "Autoconfocal microscopy with nonlinear transmitted light detection," J. Opt. Soc. Am. B 21,1486-1493 (2004). [CrossRef]
- R. Yi, K.K. Chu, and J. Mertz, "Graded-field microscopy with white light," Opt. Express 14,5191-5200 (2006). [CrossRef] [PubMed]
- G. Nomarski, "Microinterferometre differentiel a ondes polarisees [in French]," J. Phys. Radium 16,S9 (1955).
- R.D. Allen, G.B. David, G. Nomarski, "The Zeiss-Nomarski differential interference equipment for transmittedlight microscopy," Z. Wiss. Mikrosk. 69,193-221 (1969). [PubMed]
- W.B. Amos, S. Reichelt, D.M. Cattermole, and J. Laufer, "Re-evaluation of differential phase contrast (DPC) in a scanning laser microscope using a split detector as an alternative to differential interference contrast (DIC) optics," J. Microsc. 210,166-175 (2003). [CrossRef] [PubMed]
- Z.F. Mainen, M. Maletic-Savatic, S.H. Shi, Y. Hayashi, R. Malinow, K. Svoboda, "Two-photon imaging in living brain slices," Methods 18,231-239 (1999). [CrossRef] [PubMed]
- T. Wilson, "The role of the pinhole in confocal imaging system," in Handbook of Biological Confocal Microscopy, J.B. Pawley, ed. (Plenum Press, 1995), pp. 167-182.
- N. Streibl, "Depth transfer by an imaging system," Opt. Acta 31,1233-1241 (1984). [CrossRef]
- M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, UK, 1999).

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