## Abstract

Improved differential confocal microscopy is proposed to improve axial resolution and to enhance disturbance resistibility of confocal microscopy. The subtraction and sum values of the two defocusing detected signals are divided as the response function. Both ultrahigh signal-to-noise ratio (SNR) and wide range can be selectively obtained by controlling the defocusing amount of the two differential detectors more tightly with the reflectance disturbance resistibility. Since the detecting sensitivity of the proposed confocal microscopy is unrelated to the energy loss of the reflected beam, the multiplicative mode disturbance can be used to measure microstructures made of hybrid materials and overcome the power drift of a laser source during long scanning. In the case of ultrahigh SNR, the axial resolution reaches $1\text{\hspace{0.17em}}\mathrm{nm}$ when $\mathrm{NA}=0.75$ and $\lambda =632.8\text{\hspace{0.17em}}\mathrm{nm}$.

© 2009 Optical Society of America

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### Equations (6)

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(1)
$${I}_{1}(v,u,-{u}_{M})=\left|\right[2{\int}_{0}^{1}{e}^{\frac{\mathbf{i}u{\rho}^{2}}{2}}{J}_{0}(\rho v)\rho \mathrm{d}\rho ][2{\int}_{0}^{1}{e}^{\frac{\mathbf{i}(u+{u}_{M}){\rho}^{2}}{2}}{J}_{0}(\rho v)\rho \mathrm{d}\rho ]{|}^{2},$$
(2)
$${I}_{2}(v,u,{u}_{M})=\left|\right[2{\int}_{0}^{1}{e}^{\frac{\mathbf{i}u{\rho}^{2}}{2}}{J}_{0}(\rho v)\rho \mathrm{d}\rho ][2{\int}_{0}^{1}{e}^{\frac{\mathbf{i}(u-{u}_{M}){\rho}^{2}}{2}}{J}_{0}(\rho v)\rho \mathrm{d}\rho ]{|}^{2},$$
(3)
$$\left|2{\int}_{0}^{1}{e}^{\mathbf{i}u{\rho}^{2}/2}\rho \mathrm{d}\rho \right|=\left|\frac{2}{\mathbf{i}u}\right({e}^{\frac{\mathbf{i}u}{2}}-1\left)\right|=\left|\frac{2}{\mathbf{i}u}{e}^{\frac{\mathbf{i}u}{4}}\right({e}^{\frac{\mathbf{i}u}{4}}-{e}^{-\frac{\mathbf{i}u}{4}}\left)\right|=\left|\mathrm{sinc}\right(\frac{u}{4\pi}\left)\right|,$$
(4)
$${I}_{1}(u,-{u}_{M})={\mathrm{sinc}}^{2}(u/4\pi )\xb7{\mathrm{sinc}}^{2}((u+{u}_{M})/4\pi ),$$
(5)
$${I}_{2}(u,{u}_{M})={\mathrm{sinc}}^{2}(u/4\pi )\xb7{\mathrm{sinc}}^{2}((u-{u}_{M})/4\pi )\mathrm{.}$$
(6)
$$I(u,{u}_{M})=\frac{{n}_{m}\xb7({I}_{1}+{n}_{a})-{n}_{m}\xb7({I}_{2}+{n}_{a})}{{n}_{m}\xb7({I}_{1}+{n}_{a})+{n}_{m}\xb7({I}_{2}+{n}_{a})}=\frac{{I}_{1}-{I}_{2}}{{I}_{1}+{I}_{2}+2{n}_{a}}=\frac{{\mathrm{sinc}}^{2}((u+{u}_{M})/4\pi )-{\mathrm{sinc}}^{2}((u-{u}_{M})/4\pi )}{{\mathrm{sinc}}^{2}((u+{u}_{M})/4\pi )+{\mathrm{sinc}}^{2}((u-{u}_{M})/4\pi )+2{n}_{a}}\mathrm{.}$$