## Abstract

A technique is described by which multiple reflection techniques can be used to increase the quantum efficiency of some end-on photomultiplier tubes in the red and near ir. The method can be used in practice for astronomical and other applications where field lens imaging on the cathode is required and where small cathodes are desirable. Tests of a group of unselected production model S–20 and S–1 photomultiplier tubes show quantum efficiency gains as high as factors of 3.8 and 1.8, respectively, at practical operating wavelengths.

© 1968 Optical Society of America

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### Equations (14)

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(1)
$$1.5\hspace{0.17em}\text{sin}{i}_{1}={n}_{2}\hspace{0.17em}\text{sin}{i}_{2}=1.0\hspace{0.17em}\text{sin}{i}_{3}.$$
(2)
$${s}_{8}={s}_{1}{[\text{sin}({i}_{1}-{i}_{2})/\text{sin}({i}_{1}+{i}_{2})]}^{2}\equiv {s}_{1}C,$$
(3)
$${p}_{8}={p}_{1}{[\text{tan}({i}_{1}-{i}_{2})/\text{tan}({i}_{1}+{i}_{2})]}^{2}\equiv {p}_{1}E.$$
(4)
$${s}_{2}={s}_{1}{\left[\frac{2\hspace{0.17em}\text{sin}{i}_{2}\hspace{0.17em}\text{cos}{i}_{1}}{\text{sin}({i}_{1}+{i}_{2})}\right]}^{2}\alpha \equiv {s}_{1}G\alpha ,$$
(5)
$${p}_{2}={p}_{1}{\left[\frac{2\hspace{0.17em}\text{sin}{i}_{2}\hspace{0.17em}\text{cos}{i}_{1}}{\text{sin}({i}_{1}+{i}_{2})\hspace{0.17em}\text{cos}({i}_{1}-{i}_{2})}\right]}^{2}\alpha \equiv {p}_{1}H\alpha .$$
(6)
$$\alpha =({n}_{2}/{n}_{1})(\text{cos}{i}_{2}/\text{cos}{i}_{1}).$$
(7)
$${s}_{3}=A{s}_{2}{[\text{sin}({i}_{2}-{i}_{3})/\text{sin}({i}_{2}+{i}_{3})]}^{2}\equiv A{s}_{2}D,$$
(8)
$${p}_{3}=A{p}_{2}[\text{tan}({i}_{2}-{i}_{3})/\text{tan}({i}_{2}+{i}_{3})]\equiv A{p}_{2}F.$$
(9)
$${s}_{4}=A{s}_{3}{[2\hspace{0.17em}\text{sin}{i}_{1}\hspace{0.17em}\text{cos}{i}_{2}/\text{sin}({i}_{2}+{i}_{1})]}^{2}(1/\alpha )\equiv A{s}_{3}U/\alpha ,$$
(10)
$${p}_{4}=A{p}_{3}{\left[\frac{2\hspace{0.17em}\text{sin}{i}_{1}\hspace{0.17em}\text{cos}{i}_{2}}{\text{sin}({i}_{2}+{i}_{1})\hspace{0.17em}\text{cos}({i}_{2}-{i}_{1})}\right]}^{2}\frac{1}{\alpha}\equiv A{p}_{3}\hspace{0.17em}V/\alpha $$
(11)
$$s/{s}_{1}=\alpha G(1+AD)(1+{A}^{2}CD+{A}^{4}{C}^{2}{D}^{2}+\dots ),$$
(12)
$$p/{p}_{1}=\alpha H(1+AF)(1+{A}^{2}EF+{A}^{4}{E}^{2}{D}^{2}+\dots ).$$
(13)
$$1+0.9[C+{A}^{2}GDU(1+{A}^{2}CD+{A}^{4}{C}^{2}{D}^{2}+\dots )]$$
(14)
$$1+0.9[E+{A}^{2}FHV(1+{A}^{2}EF+{A}^{4}{E}^{2}{F}^{2}+\dots )]$$