Abstract

We describe a simple and robust technique for transmission confocal laser scanning microscopy wherein the detection pinhole is replaced by a thin second-harmonic generation crystal. The advantage of this technique is that self-aligned confocality is achieved without the need for signal descanning. We derive the point-spread function of our instrument and quantify both signal degradation and background rejection when imaging deep within a turbid slab. As an example, we consider a slab whose index of refraction fluctuations exhibit Gaussian statistics. Our model is corroborated by experiment.

© 2004 Optical Society of America

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References

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  1. 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]
  2. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).
  3. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Heidelberg, 1987).
  4. J. W. Goodman, Statistical Optics (Wiley, New York, 1984).
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1978).
  6. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  7. C. J. R. Sheppard and X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill New York, 1968).
  9. N. Streibl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1241 (1984).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics (Academic, New York, 1970).
  11. V. Tuchin, Tissue Optics (SPIE Press, Bellingham, Wash. 2000).
  12. E. Beaurepaire and J. Mertz, “Epifluorescence collection in two-photon microscopy,” Appl. Opt. 41, 5376–5382 (2002).
    [CrossRef] [PubMed]

2003 (1)

2002 (1)

1989 (1)

1984 (1)

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

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

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

Opt. Lett. (1)

Other (8)

M. Born and E. Wolf, Principles of Optics (Academic, New York, 1970).

V. Tuchin, Tissue Optics (SPIE Press, Bellingham, Wash. 2000).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Heidelberg, 1987).

J. W. Goodman, Statistical Optics (Wiley, New York, 1984).

A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE/OUP Series on Electromagnetic Wave Theory (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1978).

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill New York, 1968).

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Figures (6)

Fig. 1
Fig. 1

Parfocal unit magnification configuration of a quadratic detection ACM. A scanning laser beam is focused onto a sample and refocused onto a thin SHG crystal. The resulting SHG is isolated (filter) and detected by a photomultiplier tube (PMT).

Fig. 2
Fig. 2

Quadratic detection ACM PSFs. First-order signal responses produced by a point object that is purely absorbing, (a) axial and (b) radial, or purely phase shifting, (c) axial with null radial response; o.u., optical units.

Fig. 3
Fig. 3

(a) Configuration in which a point object is embedded at a depth LA within a turbid slab of thickness L. (b) Equivalent configuration in which phase variations provoked by the slab are projected into appropriate lens pupils.

Fig. 4
Fig. 4

Filter function HL as a function of normalized spatial frequency ξd. Ballistic light is attenuated by a factor exp[-ΓL(ϕ)(0)] (dotted line). Nonballistic light is transmitted only below the cutoff frequency ξ3dB.

Fig. 5
Fig. 5

Background ACM signal (filled circles) obtained experimentally when translating a scattering slab in the z direction (slab is centered when zslab=0). The slab is composed of 1-µm latex beads in agarose (λ=870 nm, ls=39 µm, ls*=490 µm, L=340 µm). The theoretical trace (solid curve) from Eq. (35) is shown for comparison.

Fig. 6
Fig. 6

(a) Simultaneous TPEF (left) and ACM (right) images of a 500-nm fluorescent latex bead. (b) Corresponding ACM contrast (squares) produced by nonfluorescent beads as a function of penetration depth LA in a scattering medium (λ=870 nm, ls=126 µm, ls*=1800 µm, L=700 µm) consisting of 1-µm-diameter nonfluorescent beads; and sparsely distributed 0.5-µm-diameter fluorescent beads. (c) ACM contrast as a function of depth for a different scattering medium (λ=870 nm, ls=39 µm, ls*=490 µm, L=340 µm). The solid line represents the theoretical traces for ACM contrast decay as a function of depth (no free parameters). For reference we illustrate decays of the TPEF signal (circles).

Equations (38)

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h(v1, u1)=P(ξ)exp(-iv1·ξ)×exp{iu1[1/4 sin2(α/2)-ξ2/2]}dξ,
U(v)= h(v1, u1)t(v1, u1)h(v-v1,-u1)dv1du1,
U0(ν)= h(v1, 0)h(v-v1, 0)dv1=h(ν, 0).
I0(ν)=|U0(ν)|2= P(ξ1)P(ξ2)exp[-iv·(ξ1-ξ2)]dξ1dξ2.
H0(ξd)= P(ξc+ξd/2)P(ξc-ξd/2)dξc.
t(v1, u1; v, u)=δ(u1)-δ(v1-v)δ(u1-u),
I(v; v, u)=|U0(v)-U(v; v, u)|2,
U(v; v, u)=h(v, u)h(v-v,-u),
SHG(v, u)= I2(v;v, u)dv=S0+4 Re[S1(v, u)]+,
S0= |U0(ν)|4dv= I02(ν)dv= H02(ξd)dξd,
S1(v, u)= I0(ν)U0(ν)U*(v; v, u)dv.
t(v1, u1; us)=δ(u1)+n nδ(v1-vn)δ(u1-us),
PA,B(ξ)P(ξ)exp[iδϕA,B(ξ)].
Γϕ(A)(ξd)=δϕA(ξ1)δϕA(ξ2),
U0(v) P(ξ1)exp(-iv·ξ1)exp[iδϕL(ξ1)]dξ1,
S0= P(ξ1)P(ξ2)P(ξ3)P(ξ4)exp[-iv·(ξ1-ξ2+ξ3-ξ4)]KL1,2,3,4dξ1dξ2dξ3dξ4dv,
KL1,2,3,4=exp{i[δϕL(ξ1)-δϕL(ξ2)+δϕL(ξ3)-δϕL(ξ4)]}.
KL1,2,3,4=exp-12 i,j(-1)i+jδϕL(ξi)δϕL(ξj),
KL1,2,3,4=HL2(ξd)exp-12 ,
=δϕL(ξ1)δϕL(ξ3)-δϕL(ξ1)δϕL(ξ4)+δϕL(ξ2)δϕL(ξ4)-δϕL(ξ2)δϕL(ξ3),
HL(ξd)=exp[-Γϕ(L)(0)+Γϕ(L)(ξd)].
S0 P(ξc+ξd/2)P(ξc-ξd/2)P(ξc+ξd/2)×P(ξc-ξd/2)HL2(ξd)dξcdξcdξd,
S0 H02(ξd)HL2(ξd)dξd,
U(v) P(ξ1)P(ξ2)exp(-iv·ξ2)×exp{i[δϕA(ξ1)+δϕB(ξ2)]}dξ1dξ2.
S1= P(ξ1)P(ξ2)P(ξ3)P(ξ4)P(ξ6)exp[-iv·(ξ1-ξ2+ξ3-ξ6)]KA1,2,3,4KB1,2,3,6dξ1dξ2dξ3dξ4dξ6dv,
KB1,2,3,6HB2(ξd),
KA1,2,3,4HA(ξd)HA(ξd),
S1 H0(ξd)HA(ξd)dξd× H0(ξd)HB2(ξd)HA(ξd)dξd.
δn(ρ1)δn(ρ2)=δn2exp(-ρd2/ln2),
Γϕ(δz)(ρd)δzlnk2δn(ρ1)δn(ρ2),
Hδz(ξd)exp{-δzσϕ2[1-γϕ(δz)(ξdz sin α)]},
HL(ξd)L Hδz(ξd).
HL(ξd)exp(-Lσϕ2)+[1-exp(-Lσϕ2)]exp(-ξd2σϕ2V/ln2),
S0SHG0{exp(-2L/ls)+[1-exp(-2L/ls)]R(ls*, V)},
R(ls*, V)=ls*ls*+k2V.
V=VA+VBsin2 α3(LA3+LB3).
S1{exp(-LA/ls)+[1-exp(-LA/ls)]R(ls*, VA)}
×{exp[-(L+LB)/ls]+{1-exp[-(L+LB)/ls]}×R(ls*, V+VB)}.

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