## Abstract

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Full Article | PDF Article**Applied Optics**- Vol. 27,
- Issue 8,
- pp. 1380-1381
- (1988)
- •doi: 10.1364/AO.27.001380

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- Y. Li, E. Wolf, “Focal Shift in Focused Truncated Gaussian Beams,” Opt. Commun. 42, 151 (1982).

[CrossRef] -
Y. Li, “Optimizing Photodetection in a Focused Field,” Appl. Opt. 24, 796 (1985).

[CrossRef] [PubMed] -
K. Tanaka, O. Kanzaki, “Focus of a Diffracted Gaussian Beam Through a Finite Aperture Lens: Experimental and Numerical Investigations,” Appl. Opt. 26, 390 (1987).

[CrossRef] [PubMed] -
K. Tanaka, N. Saga, K. Hauchi, “Focusing of a Gaussian Beam Through a Finite Aperture Lens,” Appl. Opt. 24, 1098 (1985).

[CrossRef] [PubMed]

K. Tanaka, O. Kanzaki, “Focus of a Diffracted Gaussian Beam Through a Finite Aperture Lens: Experimental and Numerical Investigations,” Appl. Opt. 26, 390 (1987).

[CrossRef]
[PubMed]

Y. Li, “Optimizing Photodetection in a Focused Field,” Appl. Opt. 24, 796 (1985).

[CrossRef]
[PubMed]

K. Tanaka, N. Saga, K. Hauchi, “Focusing of a Gaussian Beam Through a Finite Aperture Lens,” Appl. Opt. 24, 1098 (1985).

[CrossRef]
[PubMed]

Y. Li, E. Wolf, “Focal Shift in Focused Truncated Gaussian Beams,” Opt. Commun. 42, 151 (1982).

[CrossRef]

K. Tanaka, N. Saga, K. Hauchi, “Focusing of a Gaussian Beam Through a Finite Aperture Lens,” Appl. Opt. 24, 1098 (1985).

[CrossRef]
[PubMed]

[CrossRef]
[PubMed]

Y. Li, “Optimizing Photodetection in a Focused Field,” Appl. Opt. 24, 796 (1985).

[CrossRef]
[PubMed]

Y. Li, E. Wolf, “Focal Shift in Focused Truncated Gaussian Beams,” Opt. Commun. 42, 151 (1982).

[CrossRef]

[CrossRef]
[PubMed]

[CrossRef]
[PubMed]

[CrossRef]
[PubMed]

[CrossRef]

Y. Li, “Optimizing Photodetection in a Focused Field,” Appl. Opt. 24, 796 (1985).

[CrossRef]
[PubMed]

[CrossRef]
[PubMed]

[CrossRef]
[PubMed]

[CrossRef]

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Position _{sd}_{0} = 1.0). The parameters _{0} and _{0}, where _{0} is the spot size of the incident beam at the position of the lens. _{st}

Position _{sd}_{0} = 0.0). Parameters are the same as in Fig. 1.

Position _{sd}_{0} = −1.0). Parameters are the same as in Fig. 1.

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$$\begin{array}{ll}P\left(z\right)/P\left(0\right)=\hfill & \frac{4{a}^{4}{b}^{2}{k}^{2}}{{w}_{0}^{2}{z}^{2}\left[1-\text{exp}\left({a}^{2}/{w}_{0}^{2}\right)\right]}{\displaystyle {\int}_{0}^{1}{\displaystyle {\int}_{0}^{1}}}\hfill \\ \hfill & \times V\left(x,{x}^{\prime}\right)\phantom{\rule{0.2em}{0ex}}\text{exp}\left[-{S}_{1}\left({x}^{2}+{{x}^{\prime}}^{2}\right)\right]\hfill \\ \hfill & \times \text{cos}\left[{S}_{2}\left({x}^{2}-{{x}^{\prime}}^{2}\right)\right]x{x}^{\prime}dxd{x}^{\prime},\hfill \end{array}$$

$$\begin{array}{l}\begin{array}{lll}k=2\pi /\lambda ,\hfill & {S}_{1}={a}^{2}/{w}_{0}^{2},\hfill & {S}_{2}={a}^{2}\left[{\xi}_{0}/{w}_{0}^{2}+k/\left(2z\right)-k/\left(2f\right)\right],\hfill \end{array}\\ V\left(x,{x}^{\prime}\right)={\displaystyle {\int}_{0}^{1}{J}_{0}\left(kabxy/z\right){J}_{0}\left(kab{x}^{\prime}y/z\right)ydy,}\\ {\xi}_{0}=-2{z}_{s}/\left({kw}_{\mathrm{s}}^{2}\right).\end{array}$$

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