Abstract

Focal modulation microscopy (FMM) has been demonstrated more effective than confocal microscopy for imaging of thick biological tissues. To improve its penetration depth further, we propose a simple analytical method to enlarge the modulation depth, the unique property of FMM directly linked to its signal-to-noise ratio. The modulation depth increases as the excitation intensity of the binary phase aperture status is pushed further away from the focal region of the detection optics, thereby creating a dark region in the focal volume, which we call maximally flat crater (MFC). By direct algebraic manipulation, MFCs are achieved for both scalar and vector diffraction optics. Numerical results show that the modulation depth from MFC is very close to the maximum values, with a small difference less than 3% for the same number of subapertures. Applications of bifocus produced by MFC apertures are also discussed.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
    [CrossRef]

2012

2011

2010

S. P. Chong, C. H. Wong, C. J. Sheppard, and N. Chen, Opt. Lett. 35, 1804 (2010).
[CrossRef]

W. Gong, K. Si, N. Chen, and C. J. R. Sheppard, J. Biophotonics 3, 476 (2010).
[CrossRef]

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

2008

C. J. R. Sheppard and M. Martinez-Corral, Opt. Lett. 33, 476 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

N. Chen, C. H. Wong, and C. J. Sheppard, Opt. Express 16, 18764 (2008).
[CrossRef]

2005

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

1988

1982

C. Sheppard and T. Wilson, Proc. R. Soc. A 379, 145 (1982).
[CrossRef]

1959

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Campos, J.

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

Chen, N.

Choi, H. W.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

Chong, S. P.

Dawson, M. D.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

Escalera, J. C.

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

Gao, G.

Girkin, J. M.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

Gong, W.

K. Si, W. Gong, N. Chen, and C. J. R. Sheppard, Appl. Phys. Lett. 99, 233702 (2011).
[CrossRef]

W. Gong, K. Si, N. Chen, and C. J. R. Sheppard, J. Biophotonics 3, 476 (2010).
[CrossRef]

Gu, E.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

Hegedus, Z.

Ledesma, S.

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

Li, H.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Liao, J.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Liu, C.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

Liu, Y.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Lu, R.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Martinez-Corral, M.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Sheppard, C.

C. Sheppard and Z. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
[CrossRef]

C. Sheppard and T. Wilson, Proc. R. Soc. A 379, 145 (1982).
[CrossRef]

Sheppard, C. J.

Sheppard, C. J. R.

G. Gao, S. P. Chong, C. J. R. Sheppard, and N. Chen, J. Opt. Soc. Am. A 28, 496 (2011).
[CrossRef]

K. Si, W. Gong, N. Chen, and C. J. R. Sheppard, Appl. Phys. Lett. 99, 233702 (2011).
[CrossRef]

C. J. R. Sheppard, Opt. Lett. 36, 1386 (2011).
[CrossRef]

W. Gong, K. Si, N. Chen, and C. J. R. Sheppard, J. Biophotonics 3, 476 (2010).
[CrossRef]

C. J. R. Sheppard and M. Martinez-Corral, Opt. Lett. 33, 476 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

Si, K.

K. Si, W. Gong, N. Chen, and C. J. R. Sheppard, Appl. Phys. Lett. 99, 233702 (2011).
[CrossRef]

W. Gong, K. Si, N. Chen, and C. J. R. Sheppard, J. Biophotonics 3, 476 (2010).
[CrossRef]

Tang, X.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Wilson, T.

C. Sheppard and T. Wilson, Proc. R. Soc. A 379, 145 (1982).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Wong, C. H.

Zhang, L.

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

Appl. Phys. Lett.

K. Si, W. Gong, N. Chen, and C. J. R. Sheppard, Appl. Phys. Lett. 99, 233702 (2011).
[CrossRef]

J. Appl. Phys.

H. W. Choi, E. Gu, C. Liu, J. M. Girkin, and M. D. Dawson, J. Appl. Phys. 97, 063101 (2005).
[CrossRef]

J. Biophotonics

W. Gong, K. Si, N. Chen, and C. J. R. Sheppard, J. Biophotonics 3, 476 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 913 (2008).
[CrossRef]

C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, Opt. Commun. 281, 3623 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. R. Soc. A

C. Sheppard and T. Wilson, Proc. R. Soc. A 379, 145 (1982).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Proc. SPIE

X. Tang, R. Lu, J. Liao, H. Li, L. Zhang, and Y. Liu, Proc. SPIE 7657, 765708 (2010).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Normalized intensity profiles of binary phase apertures with four (green line), six (red line), and eight (blue line) subapertures, and detection optics (d, dashed black line) along (a) radial and (b) axial axes. (c) Normalized intensity distribution of the binary phase aperture with six subapertures (color bar in logarithmic scale).

Fig. 2.
Fig. 2.

Modulation depth of FMM achieved with STPM apertures designed by EA (black diamond) and MFC (blue circle).

Fig. 3.
Fig. 3.

Normalized intensity profiles of binary phase apertures with four (green line), six (red line), and eight (blue line) subapertures, and detection optics (d, dashed black line) along (a) x, (b) y, and (c) z axes. (d) Modulation depth of FMM with STPM apertures designed by EA (black diamond) and MFC (blue circle). (e) Normalized intensity distribution of the binary phase aperture with six subapertures (color bar in logarithmic scale).

Fig. 4.
Fig. 4.

Modulation depth of FMM with the STPM aperture containing three subapertures in an imaging system with NA of 0.95.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

M=SACSDC=SmaxSminSmax+Smin.
S(t)=I(x,y,z,t)×[|h(x,y,z)|22D(x,y)]dxdydz,
E(v,u)=201P(ρ)J0(vρ)exp(iuρ22)ρdρ=01P(m)J0(vm)exp(ium2)dm,
qp=01P(m)mpdm=1p+1[2m1p+1+2m2p+1+2(1)n1mn1p+1+(1)nmnp+1].
I(v)=|E(v,0)|2=|p=0(1)p(p!)222pqpv2p|2,
I(u)=|E(0,u)|2=|p=0(i/2)pp!qpup|2.
qp=0,p=0,1,2,n2,
Ex=iA(I0+I2cos2ϕ),Ey=iAI2sin2ϕ,Ez=2AI1cosϕ,
In=+Q(c)(1c1+c)n/2Jn(kr1c2)exp(ikzc)dc,Q(c)=c(1+c)T(c).
qp=+Q(c)cpdc=j=1n(1)j[1p+3/2(cjp+3/2cj1p+3/2)+1p+5/2(cjp+5/2cj1p+5/2)].
I(r,ϕ,z)=|Ex|2+|Ey|2+|Ez|2.
I(z)=A2|j=0(ik)jj!qjzj|2.
I0=j=0[(1)jj!(kr2)2jm=0jαj,mq2m],I1=j=0[(1)j(j+1)!(kr2)2j+1m=0jαj,m(q2mq2m+1)],I2=j=0[(1)j(j+2)!(kr2)2j+2m=0jαj,m(q2m2q2m+1+q2m+2)],αj,m=(1)mm!(jm)!.

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