## Abstract

Empirically derived formulas are given that allow the thin-film designer to estimate in advance the number of layers needed to meet various thin-film optical performance requirements. The estimation of peak optical density and width of higher-order blocker bands and their suppression are also discussed.

© 1996 Optical Society of America

Full Article |

PDF Article
### Equations (6)

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

(1)
$$\mathrm{\Delta}g=\frac{2}{\mathrm{\pi}}\text{arcsin}\left(\frac{{n}_{\text{H}}-{n}_{\text{L}}}{{n}_{\text{H}}+{n}_{\text{L}}}\right)$$
(2)
$${\text{OD}}_{P}\approx 2\hspace{0.17em}{\text{log}}^{1/2}\left[{\left(\frac{{n}_{\text{H}}}{{n}_{\text{L}}}\right)}^{p}+{\left(\frac{{n}_{\text{L}}}{{n}_{\text{H}}}\right)}^{p}\right].$$
(3)
$$\mathrm{\Delta}\text{OD}\approx 2\hspace{0.17em}\text{log}\left(\frac{{n}_{\text{H}}}{{n}_{\text{L}}}\right).$$
(4)
$$\begin{array}{l}\text{ODBWP}\approx 1.57\mathrm{\Delta}g\mathrm{\Delta}\text{OD}\\ \approx 2\hspace{0.17em}\text{log}\left(\frac{{n}_{\text{H}}}{{n}_{\text{L}}}\right)\text{arcsin}\left(\frac{{n}_{\text{H}}-{n}_{\text{L}}}{{n}_{\text{H}}+{n}_{\text{L}}}\right).\end{array}$$
(5)
$${\text{OD}}_{N}\approx \mid {\text{OD}}_{E}\hspace{0.17em}{\text{sin}}^{1.2}\left(\frac{\mathrm{\pi}Ng}{A}\right)\hspace{0.17em}\mid ,\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}N=1,2,\dots .$$
(6)
$$dg\approx \frac{2}{3}\left(\frac{\mathrm{\Delta}g}{{{\text{OD}}_{P}}^{1.74}}\right).$$