## Abstract

We investigated the design of two broadband hybrid diffractive–refractive optical systems, a landscape lens, and a Schmidt telescope. The systems were achromatized by using the characteristically large negative dispersion of kinoforms. In the scalar wave regime kinoforms can approach 100% efficiency but only for one object point and wavelength. We evaluated polychromatic image quality, accounting for diffraction efficiency, by constructing weighted geometric point-spread functions from several diffracted orders and then calculating modulation transfer functions (MTF’s). The MTF’s of the hybrid achromats were improved at high spatial frequencies but were reduced at low frequencies because of diffraction into nondesign orders.

© 1992 Optical Society of America

Full Article |

PDF Article
### Equations (7)

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

(1)
$$n\hspace{0.17em}\text{sin}(\mathrm{\alpha}-\mathrm{\theta})={n}^{\prime}\hspace{0.17em}\text{sin}(\mathrm{\alpha}-{\mathrm{\theta}}_{0}),$$
(2)
$$d[n\hspace{0.17em}\text{sin}(\mathrm{\alpha}-\mathrm{\theta})-{n}^{\prime}\hspace{0.17em}\text{sin}(\mathrm{\alpha}-{\mathrm{\theta}}_{m})]=m\mathrm{\lambda},$$
(3)
$$n\hspace{0.17em}\text{sin}(\mathrm{\alpha}-\mathrm{\beta}-\mathrm{\theta})={n}^{\prime}\hspace{0.17em}\text{sin}(\mathrm{\alpha}-\mathrm{\beta}-{\mathrm{\theta}}_{\mathrm{\beta}}).$$
(4)
$$\mathrm{\u220a}(m,\mathrm{\lambda})={\text{sinc}}^{2}\left\{\mathrm{\pi}\left[m-{m}_{0}\frac{{\mathrm{\lambda}}_{0}}{\mathrm{\Delta}n({\mathrm{\lambda}}_{0})}\frac{\mathrm{\Delta}n(\mathrm{\lambda})}{\mathrm{\lambda}}\right]\right\},$$
(5)
$${\mathrm{\u220a}}_{m}={\text{sinc}}^{2}\left[2\mathrm{\pi}\frac{{\mathrm{\Delta}}_{m\text{F}}}{{\mathrm{\Delta}}_{02}}\right].$$
(6)
$$\begin{array}{l}{\text{MTF}}_{\text{corr}}\approx \hspace{0.17em}\overline{\mathrm{\u220a}}{\text{MTF}}_{012}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{for}\hspace{0.17em}\text{frequencies}>0,\\ {\text{MTF}}_{\text{corr}}=1\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{for}\hspace{0.17em}\text{frequency}=0.\end{array}$$
(7)
$${\text{MTF}}_{x}(\mathrm{\nu})\approx 1-2{\mathrm{\pi}}^{2}{{B}_{x}}^{2}{\mathrm{\nu}}^{2}.$$