## Abstract

New compound eye systems for nonunity magnification projection are shown. As all the beams of light on the optical axes of erect or inverted real image systems intersect perpendicular to the object and image planes in these systems, it becomes possible to get rid of any local variation in magnification, which deteriorates the image quality of earlier compound eye systems.

© 1990 Optical Society of America

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### Equations (13)

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(1)
$${m}_{1}=m\hspace{0.17em}\text{cos}(\alpha +\u220a)/\text{cos}(\alpha -\u220a).$$
(2)
$$m=\frac{\overline{A4,B4}}{\overline{A1,B1}}=\frac{DL2}{DL1}.$$
(3)
$$\begin{array}{l}B1=(X,l/2,h/2),\\ B2=(X,l/2,-{h}_{1}),\\ B3=(mX,-l/2,{h}_{2}),\\ B4=(mX,-l/2,-h/2).\end{array}$$
(4)
$${h}_{1}+{h}_{2}=\frac{-{(1-m)}^{2}{X}^{2}-{l}^{2}+{(L-h)}^{2}}{2(L-h)},$$
(5)
$$\begin{array}{l}L={L}_{1}+{L}_{2}+{z}_{0}\\ {L}_{1}=\frac{[1/m-\text{cos}(g{z}_{0})]}{{n}_{0}\hspace{0.17em}\text{sin}(g{z}_{0})},\\ {L}_{2}=-\frac{[m-\text{cos}(g{z}_{0})]}{{n}_{0}\hspace{0.17em}\text{sin}(g{z}_{0})},\end{array}$$
(6)
$$n={n}_{0}{(1-{g}^{2}{r}^{2}+{h}_{3}{g}^{4}{r}^{4}+\dots )}^{1/2},$$
(7)
$$m=\frac{\overline{A4,B4}}{\overline{A1,B1}}=\frac{DL{2}^{\prime}}{DL{1}^{\prime}},$$
(8)
$$\begin{array}{l}B1=(X,l/2+Y,h/2),\\ B2=(X,l/2+Y,-{h}_{1}),\\ B3=(mX,-l/2+mY,{h}_{2}),\\ B4=(mX,-l/2+mY,-h/2),\end{array}$$
(9)
$${h}_{1}+{h}_{2}=\frac{-{(1-m)}^{2}{X}^{2}-\{l+(1-m){Y}^{2}\}+{(L-h)}^{2}}{2(L-h)}.$$
(10)
$${h}_{1}=\frac{-2(1-m){X}^{2}-2(1-m)Y-4lY-{l}^{2}+{(L-h)}^{2}}{4(L-h)}+C,$$
(11)
$${h}_{2}=\frac{2m(1-m){X}^{2}+2m(1-m)Y+4mlY-{l}^{2}+{(L-h)}^{2}}{4(L-h)}-C,$$
(12)
$$Z=\frac{2(1-m){X}^{2}+2(1-m){Y}^{2}+4lY+{l}^{2}-{(L-h)}^{2}}{4(L-h)}+C,$$
(13)
$$Z=\frac{2(1-m){X}^{2}+2(1-m){Y}^{2}+4mlY-m{l}^{2}+m{(L-h)}^{2}}{4m(L-h)}-C,$$