## Abstract

The correction of lens aberrations using a hologram made with a collimated reference is discussed. Two geometries in which the theoretical third-order hologram aberrations may be avoided are demonstrated. The results of experiments which demonstrate the aberration correction using the Ronchi and DeVany tests are presented.

© 1971 Optical Society of America

Full Article |

PDF Article
### Equations (9)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$O=O\hspace{0.17em}\text{exp}[j\mathrm{\Phi}(x,y)]\hspace{0.17em}\text{exp}[j({k}_{y}y-{k}_{z}z)],$$
(2)
$$A=A\hspace{0.17em}\text{exp}[-j({k}_{y}y+{k}_{z}z)].$$
(3)
$$\theta ={\text{tan}}^{-1}({k}_{y}/{k}_{z}),$$
(4)
$$I(x,y)={A}^{2}+{O}^{2}+2AO\hspace{0.17em}\text{cos}[2{k}_{y}y-\mathrm{\Phi}(x,y)].$$
(5)
$${t}_{1}(x,y)={J}_{1}(\alpha )\hspace{0.17em}\text{exp}\{j[2{k}_{y}y-\mathrm{\Phi}(x,y)]\},$$
(6)
$$w({x}_{1},{y}_{1},{z}_{1})=1/{z}_{1}\int \int u(x,y){t}_{1}(x,y)\times \text{exp}\{-j\pi [{({x}_{1}-x)}^{2}+{({y}_{1}-y)}^{2}/\mathrm{\lambda}{z}_{1}]\}\hspace{0.17em}dxdy.$$
(7)
$$u(x,y){t}_{1}(x,y)={u}^{\prime}(x,y)f(\alpha ,y)$$
(8)
$$\underset{{z}_{c}\to +\infty}{\text{lim}{y}_{c}}/{z}_{c}=\underset{{z}_{r}\to -\infty}{\text{lim}{y}_{r}}/{z}_{r}$$
(9)
$${y}_{0}/{z}_{0}={y}_{c}/{z}_{c}=-\underset{{z}_{r}\to -\infty}{\text{lim}{y}_{r}}/{z}_{r}.$$