## Abstract

We measured the modulation transfer function (MTF) of a lens in
the visible region using a random test target generated on a computer
screen. This is a simple method to determine the entire MTF curve
in one measurement. The lens was obscured by several masks so that
the measurements could be compared with the theoretically calculated
MTF. Excellent agreement was obtained. Measurement noise was
reduced by use of a large number of targets generated on the
screen.

© 1999 Optical Society of America

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### Equations (7)

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(1)
$${f}_{max}=1/2l=28.4\mathrm{cycles}/\mathrm{mm},$$
(2)
$$l={h}_{\mathrm{obj}}M/N=0.0176\mathrm{mm},$$
(3)
$${\mathrm{PSD}}_{f}\left(f\right)=\mathrm{MTF}_{\mathrm{tot}}{}^{2}\left(f\right){\mathrm{PSD}}_{i}\left(f\right),$$
(4)
$${\mathrm{PSD}}_{f}\left(f\right)={\left[{\mathrm{MTF}}_{\mathrm{sys}}\left(f\right){\mathrm{MTF}}_{\mathrm{test}}\left(f\right)\right]}^{2}{\mathrm{PSD}}_{i}\left(f\right)+\mathrm{NAS}\left(f\right),\mathrm{MTF}_{\mathrm{test}}{}^{2}\left(f\right)=\frac{\left[{\mathrm{PSD}}_{f}\left(f\right)-\mathrm{NAS}\left(f\right)\right]}{\mathrm{MTF}_{\mathrm{sys}}{}^{2}\left(f\right){\mathrm{PSD}}_{i}\left(f\right)}.$$
(5)
$$\mathrm{MTF}=\left\{\begin{array}{ccc}1-|f/{f}_{a}|& \mathrm{for}& |f|\le {f}_{a}\\ 0& \mathrm{for}& |f|>{f}_{a}\end{array}\right.;{f}_{a}=\frac{d}{F\mathrm{\lambda}},$$
(6)
$$\mathrm{MTF}=\left\{\begin{array}{ccc}1-|f/{f}_{a}|& \mathrm{for}& |f|\le {f}_{a}\\ |f/2{f}_{a}|-\left({f}_{b}+{f}_{a}\right)/2{f}_{a}& \mathrm{for}& {f}_{a}+{f}_{b}\le |f|\le 2{f}_{a}+{f}_{b}\\ \left(3{f}_{a}+{f}_{b}\right)/2{f}_{a}-|f/2{f}_{a}|& \mathrm{for}& 2{f}_{a}+{f}_{b}\le |f|\le 3{f}_{a}+{f}_{b}\\ 0& \mathrm{for}& \mathrm{else}\end{array}\right.;{f}_{b}=\frac{{d}_{1}-d}{F\mathrm{\lambda}},$$
(7)
$${\mathrm{ASF}}_{f}\left(f\right)=\mathrm{OTF}\left[{\mathrm{ASF}}_{i}\left(f\right)\right].$$