## Abstract

Current implementations of structured illumination microscopy for depth-resolved (three-dimensional) imaging have limitations that restrict its use; specifically, they are not applicable to non-stationary objects imaged with relatively poor condenser optics and in non-fluorescent mode. This includes *in-vivo* retinal imaging. A novel implementation of structured illumination microscopy is presented that overcomes these issues. A three-wavelength illumination technique is used to obtain the three sub-images required for structured illumination simultaneously rather than sequentially, enabling use on non-stationary objects. An illumination method is presented that produces an incoherent pattern through interference, bypassing the limitations imposed by the aberrations of the condenser lens and thus enabling axial sectioning in non-fluorescent imaging. The application to retinal imaging can lead to a device with similar sectioning capabilities to confocal microscopy without the optical complexity (and cost) required for scanning systems.

© 2011 OSA

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### Equations (15)

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(1)
$${I}_{\mathrm{illumination}}({t}_{o},{w}_{o})=1+\mu \mathrm{cos}(\nu {t}_{o}+\varphi ),$$
(2)
$${I}_{\mathrm{object}}({t}_{o},{w}_{o})=[1+\mu \mathrm{cos}(\nu {t}_{o}+\varphi )]\rho ({t}_{o},{w}_{o}),$$
(3)
$$I({t}_{i},{w}_{i})=\iint [1+\mu \mathrm{cos}(\nu {t}_{o}+\varphi )]\rho ({t}_{o},{w}_{o}){\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o})\mid}^{2}d{t}_{o}d{w}_{o},$$
(4)
$${I}_{0}({t}_{i},{w}_{i})=\iint \rho ({t}_{o},{w}_{o}){\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o})\mid}^{2}d{t}_{o}d{w}_{o},$$
(5)
$${I}_{\nu}({t}_{i},{w}_{i})=\iint {e}^{i\nu {t}_{o}}\rho ({t}_{o},{w}_{o}){\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o})\mid}^{2}d{t}_{o}d{w}_{o},$$
(6)
$${I}_{-\nu}({t}_{i},{w}_{i})=\iint {e}^{-i\nu {t}_{o}}\rho ({t}_{o},{w}_{o}){\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o})\mid}^{2}d{t}_{o}d{w}_{o},$$
(7)
$$I({t}_{i},{w}_{i})={I}_{0}({t}_{i},{w}_{i})+\frac{\mu}{2}{e}^{i\varphi}{I}_{\nu}({t}_{i},{w}_{i})+\frac{\mu}{2}{e}^{-i\varphi}{I}_{-\nu}({t}_{i},{w}_{i}).$$
(8)
$$\mid {I}_{\pm \nu}\mid =\mid {I}_{1}+{I}_{2}{e}^{\frac{\mp i2\pi}{3}}+{I}_{3}{e}^{\frac{\pm i2\pi}{3}}\mid ,$$
(9)
$$\mid {I}_{\pm \nu}\mid ={\left(\frac{{({I}_{1}-{I}_{2})}^{2}+{({I}_{1}-{I}_{3})}^{2}+{({I}_{2}-{I}_{3})}^{2}}{2}\right)}^{\frac{1}{2}}.$$
(10)
$${I}_{0}=\frac{1}{3}({I}_{1}+{I}_{2}+{I}_{3}).$$
(11)
$${I}_{\nu}({t}_{i},{w}_{i})=\int \int \int \int {e}^{i\nu {t}_{o}}\Re (m,n){e}^{-i(m{t}_{o}+n{w}_{o})}{\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o})\mid}^{2}d{t}_{o}d{w}_{o}dmdn.$$
(12)
$${e}^{i(m{t}_{i}+n{w}_{i})}P(m,n)\otimes {P}^{*}(m,n)={\mathcal{F}}^{-1}\left\{{\mid h({t}_{0}+{t}_{i},{w}_{o}+{w}_{i})\mid}^{2}\right\}$$
(13)
$$\phantom{\rule{.9em}{0ex}}\phantom{\rule{.9em}{0ex}}\phantom{\rule{.9em}{0ex}}\phantom{\rule{.9em}{0ex}}=\iint {\mid h({t}_{o}+{t}_{i},{w}_{o}+{w}_{i})\mid}^{2}{e}^{-i(m{t}_{o}+n{w}_{o})}d{t}_{o}n{w}_{o}.$$
(14)
$${I}_{\nu}({t}_{i},{w}_{i})={e}^{iv{t}_{i}}\iint \Re (m,n)C(m+\nu ,n){e}^{i(m{t}_{i}+n{w}_{i})}dmdn.$$
(15)
$$I({t}_{i},{w}_{i};u)=\iint [1+\mu \mathrm{cos}(\nu {t}_{o}+\varphi )]\rho ({t}_{o},{w}_{o};u){\mid h({t}_{i}+{t}_{o},{w}_{i}+{w}_{o};u)\mid}^{2}d{t}_{o}d{w}_{o},$$