## Abstract

Lau fringes formed in the far field of a pair of gratings illuminated by spatially incoherent light are known to disappear when one grating is rotated slightly $\left(\pm {3}^{\xb0}\right)$ with respect to the other. We observed that a cylindrical lens that was appropriately rotated could restore the high-contrast Lau fringes by bringing together the rays that are coherent with respect to each other. We have developed a new refractometer based on this phenomenon, the details of which are presented. Measurement of the cylinder power and axis of the human eye is possible with good accuracy and repeatability with this instrument.

© 2002 Optical Society of America

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### Equations (6)

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(1)
$${p}_{1}=p\left({sin}^{2}\phi -{cos}^{2}\phi \right)=-pcos\left(2\phi \right)=\left({\nu}_{1}-{h}_{1}\right)c,$$
(2)
$${p}_{2}=-pcos\left[2\left(\phi +{45}^{\xb0}\right)\right]=-psin\left(2\phi \right)=\left({\nu}_{2}-{h}_{2}\right)c.$$
(3)
$$\phi =\left(1/2\right){tan}^{-1}\left[\left({\nu}_{2}-{h}_{2}\right)/\left({\nu}_{1}-{h}_{1}\right)\right],p={\left(p_{1}{}^{2}+p_{2}{}^{2}\right)}^{1/2}.$$
(4)
$${p}_{1}=-pcos\left(2\phi \right)=6\left[{cos}^{2}\left(90-{\theta}_{1}\right)-{cos}^{2}\left({\theta}_{1}\right)\right]=-6cos\left(2{\theta}_{1}\right),$$
(5)
$${p}_{2}=-psin\left(2\phi \right)=-6cos\left(2{\theta}_{2}\right).$$
(6)
$$\phi =\left(1/2\right){tan}^{-1}\left[cos\left(2{\theta}_{2}\right)/cos\left(2{\theta}_{1}\right)\right],p={\left(p_{1}{}^{2}+p_{2}{}^{2}\right)}^{1/2}.$$