## Abstract

Adaptive optics (AO) ophthalmoscopes have garnered increased clinical and scientific use for imaging the microscopic retina. Unlike conventional ophthalmoscopes, however, AO systems are commonly designed with spherical mirrors that must be used off-axis. This arrangement causes astigmatism to accumulate at the retina and pupil conjugate planes, degrading AO performance. To mitigate this effect and more fully tap the benefit of AO, we investigated a novel solution based on toroidal mirrors. Derived 2^{nd} order analytic solutions along with commercial ray tracing predict performance benefit of toroidal mirrors for ophthalmoscopic use. For the Indiana AO ophthalmoscope, a minimum of three toroids is required to achieve performance criteria for retinal image quality, beam displacement, and beam ellipticity. Measurements with fabricated toroids and retinal imaging on subjects substantiate the theoretical predictions. Comparison to off-the-plane method is also presented.

© 2013 Optical Society of America

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### Equations (20)

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(1)
$${f}_{t}=\frac{{r}_{t}\mathrm{cos}I}{2},\text{and}{f}_{s}=\frac{{r}_{s}}{2\mathrm{cos}I}.$$
(2)
$${L}^{\prime}=L+F.$$
(3)
$${L}^{\u2033}=\frac{{L}^{\prime}}{1-d\times {L}^{\prime}},$$
(4)
$${{L}^{\u2033}}_{t}=-\frac{2s\times \text{sec}{I}_{1}+{r}_{t1}}{2d\times s\times \mathrm{sec}{I}_{1}+(d-s){r}_{t1}},\text{and}$$
(5)
$${{L}^{\u2033}}_{s}=-\frac{2s\times \mathrm{cos}{I}_{1}+{r}_{s1}}{2d\times s\times \mathrm{cos}{I}_{1}+(d-s){r}_{s1}}.$$
(6)
$$L{\text{'}}_{t2}=\frac{-2\mathrm{sec}{I}_{1}\times {r}_{1}+2{r}_{t1}}{{r}_{1}(\left(1+M\right)\times \mathrm{sec}{I}_{1}\times {r}_{1}-\left(2+M\right)\times {r}_{t1})}+\frac{2\times \mathrm{sec}{I}_{2}}{{r}_{t2}},\text{and}$$
(7)
$$L{\text{'}}_{s2}=\frac{-2\mathrm{cos}{I}_{1}\times {r}_{1}+2{r}_{s1}}{{r}_{1}(\left(1+M\right)\times \mathrm{cos}{I}_{1}\times {r}_{1}-\left(2+M\right)\times {r}_{s1})}+\frac{2\times \mathrm{cos}{I}_{2}}{{r}_{s2}},$$
(8)
$$L{\text{'}}_{t2}=-\frac{2}{\left(1+M\right)\times {r}_{1}-\mathrm{cos}{I}_{1}\times {r}_{t1}}+\frac{2\mathrm{sec}{I}_{2}}{{r}_{t2}},\text{and}$$
(9)
$$L{\text{'}}_{s2}=-\frac{2\mathrm{cos}{I}_{1}}{\left(1+\text{M}\right)\times \mathrm{cos}{I}_{1}\times {r}_{1}-{r}_{s1}}+\frac{2\mathrm{cos}{I}_{2}}{{r}_{s2}}.$$
(10)
$${r}_{t1}=\frac{1}{4}\mathrm{sec}{I}_{1}\left(3+\sqrt{{\left(-1+M\right)}^{2}}+M\right)\times {r}_{1},$$
(11)
$${r}_{s1}=\mathrm{cos}{I}_{1}\times {r}_{1},$$
(12)
$${r}_{t2}=-\frac{1}{4}\mathrm{sec}{I}_{2}\left(-1+\sqrt{{\left(-1+M\right)}^{2}}-3\times M\right)\times {r}_{1},\text{and}$$
(13)
$${r}_{s2}=\mathrm{cos}{I}_{2}\times {r}_{2}.$$
(14)
$${r}_{t2}=\frac{M\times (-1-M+\left(2+M\right)\times \mathrm{cos}{I}_{1})\times \mathrm{sec}{I}_{2}\times {r}_{1}}{-1-2M+2\left(1+M\right)\mathrm{cos}{I}_{1}},\text{and}$$
(15)
$${r}_{s2}=\frac{M(-2-M+\left(1+M\right)\times \mathrm{cos}{I}_{1})\times \mathrm{cos}{I}_{2}\times {r}_{1}}{-2\left(1+M\right)+\left(1+2M\right)\times \mathrm{cos}{I}_{1}}.$$
(16)
$${r}_{t2}=(1+M-\mathrm{cos}{I}_{1})\times \mathrm{sec}{I}_{2}\times {r}_{1},\text{and}$$
(17)
$${r}_{s2}=(-1+\left(1+M\right)\times \mathrm{cos}{I}_{1})\times \mathrm{cos}{I}_{2}\times \mathrm{sec}{I}_{1}\times {r}_{1}.$$
(18)
$${M}_{t}=\frac{{f}_{t10}}{{f}_{t9}}\times \frac{{f}_{t8}}{{f}_{t7}}\times \mathrm{...}\times \frac{{f}_{t2}}{{f}_{t1}},$$
(19)
$${M}_{s}=\frac{{f}_{s10}}{{f}_{s9}}\times \frac{{f}_{s8}}{{f}_{s7}}\times \mathrm{...}\times \frac{{f}_{s2}}{{f}_{s1}},\text{and}$$
(20)
$$E=\frac{min({M}_{t},{M}_{s})}{max({M}_{t},{M}_{s})}.$$