## Abstract

The effect of finite aperture of a Fabry Perot interferometer on the fringe intensity distribution in the interferometer pattern is investigated. An equation is derived for a square etalon which illustrates clearly the decrease in fringe intensity for increasing angles of incidence. The computations show that this effect becomes significant only for high reflecting powers and comparatively large plate separations.

© 1949 Optical Society of America

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### Equations (16)

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(1)
$$I=1/(1+{a}^{2}\hspace{0.17em}{\text{sin}}^{2}\delta ),$$
(2)
$${I}_{p}={d}^{2}[{(1-{r}^{p})}^{2}+4{r}^{p}\hspace{0.17em}{\text{sin}}^{2}p\delta /{(1-r)}^{2}+4r\hspace{0.17em}{\text{sin}}^{2}\delta ],$$
(3)
$${E}_{p}=d{e}^{i\delta}(1+r{e}^{2i\delta}+\cdots +{r}^{p-1}{e}^{2(p-1)i\delta}).$$
(4)
$$[{A}^{2}-A(2t\theta )]/{A}^{2}=(1-2t\theta /A).$$
(5)
$${c}_{1}={(1-2t\theta /A)}^{{\scriptstyle \frac{1}{2}}}.$$
(6)
$${c}_{n}={(1-n/p)}^{{\scriptstyle \frac{1}{2}}},$$
(7)
$${c}_{n}=(1-n/2p),\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}n=1,\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}2,\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\cdots (p-1).$$
(8)
$${E}_{p}=d{e}^{i\delta}(1+{c}_{1}r{e}^{2i\delta}+\cdots +{c}_{p-1}{r}^{p-1}{e}^{2(p-1)i\delta}).$$
(9)
$${E}_{p}=(d{e}^{i\delta}/1-r{e}^{2i\delta})\{(1-{r}^{p}{e}^{2pi\delta})-(r{e}^{2pi\delta}/2p)\times [(1-{r}^{p-1})/(1-r{e}^{2i\delta})-{r}^{p-1}(p-1)]\}.$$
(10)
$${E}_{\text{max}}=(d/1-r)\{(1-{r}^{p})-(r/2p)\times [(1-{r}^{p-1})/(1-r)-(p-1){r}^{p-1}]\}.$$
(11)
$${E}_{\text{max}}=(d/1-r)\{(1-{r}^{p})\times [1-(r/2p(1-r))]+{r}^{p}/2\}.$$
(12)
$${I}_{\text{max}}={(d/1-r)}^{2}{\{(1-{r}^{p})\times [1-(r/2p(1-r))]+{r}^{p}/2\}}^{2}.$$
(13)
$$\underset{p\to \infty}{\text{lim}}{I}_{\text{max}}=1,$$
(14)
$$\underset{r\to 1}{\text{lim}}{I}_{\text{max}}=0.$$
(15)
$$\underset{r\to 1}{\text{lim}}\hspace{0.17em}(1-{r}^{p})/(1-r),$$
(16)
$$\underset{r\to 1}{\text{lim}}\hspace{0.17em}p{r}^{p-1}=p,$$