## Abstract

When coherent light is used for imaging transparent objects, the images may be inferior because of Fresnel diffraction patterns from scattered light or may be degraded by granularity from diffuse illumination. This paper proposes a technique for improving image quality by using a spatially phase-modulated wavefront to illuminate the object. Analysis shows that the resulting image should be free from Fresnel diffraction patterns and should have a negligible amount of residual granularity. Experimental results verify these conclusions. Requirements of the imaging system and the wavefront are discussed. The technique is applicable to any nondiffuse, two-dimensional object and can be used in holography or with any other coherent imaging system.

© 1967 Optical Society of America

Full Article |

PDF Article
### Equations (7)

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

(1)
$$\begin{array}{l}{s}_{1}({x}_{1},{y}_{1})=n({x}_{1},{y}_{1})\{{s}_{0}({x}_{1},{y}_{1})*\text{exp}[-ik({{x}_{1}}^{2}+{{y}_{1}}^{2})]\}\\ =n({x}_{1},{y}_{1})d({x}_{1},{y}_{1})\hspace{0.17em}\text{exp}[i\alpha ({x}_{1},{y}_{1})].\end{array}$$
(2)
$${{s}_{0}}^{\prime}({x}_{0},{y}_{0})={c}_{0}s({x}_{0},{y}_{0})+\{\text{exp}[ik({{x}_{0}}^{2}+{{y}_{0}}^{2})\}*\{c({x}_{0},{y}_{0})d({x}_{0},{y}_{0})\hspace{0.17em}\text{exp}[i\alpha ({x}_{0},{y}_{0})]\}.$$
(3)
$${{s}_{0}}^{\prime}({x}_{0},{y}_{0})={c}_{0}{b}_{0}v({x}_{0},{y}_{0})\hspace{0.17em}\text{exp}[i\varphi ({x}_{0},{y}_{0})]+{d}_{0}\hspace{0.17em}\text{exp}[ik({{x}_{0}}^{2}+{{y}_{0}}^{2})+({\alpha}_{0}/k)].$$
(4)
$$\mid {{s}_{0}}^{\prime}({x}_{0},{y}_{0}){\mid}^{2}={{c}_{0}}^{2}{{b}_{0}}^{2}{v}^{2}({x}_{0},{y}_{0})+{{d}_{0}}^{2}+2{c}_{0}{b}_{0}{d}_{0}v({x}_{0},{y}_{0})\hspace{0.17em}\text{cos}[k({{x}_{0}}^{2}+{{y}_{0}}^{2})+{\alpha}_{0}-\varphi ({x}_{0},{y}_{0})].$$
(5)
$${S}_{i}={S}_{0}+U*V*\{N\hspace{0.17em}\text{exp}[-i{k}_{1}({p}^{2}+{q}^{2})]\}.$$
(6)
$${s}_{i}(x,y)={b}_{0}\int \int h(x-{x}_{0},y-{y}_{0})\hspace{0.17em}\text{exp}[i\varphi ({x}_{0},{y}_{0})]d{x}_{0}d{y}_{0}.$$
(7)
$$0\le {b}_{0}\left|\int \int h(x-{x}_{0},y-{y}_{0})\hspace{0.17em}\text{exp}[j\varphi ({x}_{0},{y}_{0})]d{x}_{0}d{y}_{0}\right|\le {b}_{0}$$