## Abstract

In this study, we found that the axial response curve of divided-aperture confocal microscopy has a shift while the point detector has a transverse offset from the optical axis. Based on this, a novel laser divided-aperture differential confocal sensing technology (LDDCST) with absolute zero and high axial resolution, as well as an LDDCST-based sensor, is proposed. LDDCST sets two micro-regions as virtual pinholes that are symmetrical to the optical axis along the *x*_{d} direction on the focal plane of the divided-aperture confocal system to achieve the spot-division detection and to simplify the detection system, uses differential subtraction of two intensity responses simultaneously detected from the two micro-regions to achieve high axial resolution absolute measurement and low noise, and considers both resolution and measurement range by adjusting virtual pinholes in software. Theoretical analyses and packaged LDDCST sensor experiments indicate that LDDCST has high axial resolution as well as strong anti-interference and sectioning detection capability.

© 2012 OSA

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### Equations (9)

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(1)
$${h}_{i}({v}_{x},{v}_{y},u)={\displaystyle \underset{{S}_{1}}{\iint}P({v}_{\xi},{v}_{\eta})\mathrm{exp}\left[\frac{iu}{2}\left({v}_{\xi}^{2}+{v}_{\eta}^{2}\right)\right]}\cdot \mathrm{exp}\left[i\left({v}_{x}{v}_{\xi}+{v}_{y}{v}_{\eta}\right)\right]d{v}_{\xi}d{v}_{\eta},$$
(2)
$${h}_{c}({v}_{x},{v}_{y},u,{v}_{M})={\displaystyle \underset{{S}_{2}}{\iint}P({v}_{\xi},{v}_{\eta})\mathrm{exp}\left[\frac{iu}{2}\left({v}_{\xi}^{2}+{v}_{\eta}^{2}\right)\right]}\cdot \mathrm{exp}\left\{i\left[\left({v}_{x}+{v}_{M}\right){v}_{\xi}+{v}_{y}{v}_{\eta}\right]\right\}d{v}_{\xi}d{v}_{\eta},$$
(3)
$${I}_{i}\left(u,{v}_{M}\right)={\left|{h}_{i}\left(0,0,u\right)\cdot {h}_{c}\left(0,0,u,{v}_{M}\right)\right|}^{2}.$$
(4)
$${I}_{LDDCST}\left(u,{v}_{M}\right)={I}_{A}(u,-{v}_{M})-{I}_{B}(u,{v}_{M}).$$
(5)
$${\Delta}_{\text{axial}}=k\left(u,{v}_{M}\right)=\frac{\partial {I}_{LDDCST}\left(u,{v}_{M}\right)}{\partial u},$$
(6)
$${\Delta}_{\text{axial}}=k\left(u,{v}_{M}\right)=k\left(\text{0},{v}_{M}\right).$$
(7)
$${I}_{L}\left(u,{v}_{M}\right)=\frac{\left[\eta \cdot {I}_{A}(u,-{v}_{M})+\epsilon \right]-\left[\eta \cdot {I}_{B}(u,{v}_{M})+\epsilon \right]}{\left[\eta \cdot {I}_{A}(u,-{v}_{M})+\epsilon \right]+\left[\eta \cdot {I}_{B}(u,{v}_{M})+\epsilon \right]}=\frac{{I}_{A}(u,-{v}_{M})-{I}_{B}(u,{v}_{M})}{{I}_{A}(u,-{v}_{M})+{I}_{B}(u,{v}_{M})+2\epsilon /\eta}.$$
(8)
$${I}_{L}\left(u,{v}_{M}\right)\approx \frac{{I}_{A}(u,-{v}_{M})-{I}_{B}(u,{v}_{M})}{{I}_{A}(u,-{v}_{M})+{I}_{B}(u,{v}_{M})}.$$
(9)
$${I}_{L}\left(z,C\right)\approx \frac{{I}_{A}(z,-C)-{I}_{B}(z,C)}{{I}_{A}(z,-C)+{I}_{B}(z,C)}=\frac{{I}_{A}(z,-{v}_{M}{\text{C}}_{\text{0}})-{I}_{B}(z,{v}_{M}{\text{C}}_{\text{0}})}{{I}_{A}(z,-{v}_{M}{\text{C}}_{\text{0}})+{I}_{B}(z,{v}_{M}{\text{C}}_{\text{0}})}.$$