## Abstract

A new kind of lateral shearing interferometer, called the three-wave lateral shearing interferometer, was previously described [
Appl. Opt. **32**,
6242 (
1993)]. As this instrument was monochromatic and its usable light efficiency was poor, the proposed setup was well suited only for a class of wave-front sensing problems, such as optical testing, in which the source can be easily adapted. A new achromatic setup adapted to low light level applications is presented. Three replicas of the analyzed wave front are obtained by Fourier filtering of the orders diffracted by a microlens array. An important feature of these new devices is their great similarity to another class of wave-front sensors based on the Hartmann test.

© 1995 Optical Society of America

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### Equations (8)

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(1)
$$A(\mathbf{\text{x}})=exp[iW(\mathbf{\text{x}})].$$
(2)
$${\text{A}}_{i}(\mathbf{\text{x}})=exp\{i[W(\mathbf{\text{x}})+{\mathbf{\text{k}}}_{i}\cdot \mathbf{\text{x}}]\},$$
(3)
$${I}_{0}(\mathbf{\text{x}})={\left|\text{\u2211}_{i=1}^{3}{A}_{i}(\mathbf{\text{x}})\right|}^{2}=3+\text{\u2211}_{i,j={1}_{i\ne j}}^{3}exp[i({\mathbf{\text{k}}}_{i}-{\mathbf{\text{k}}}_{j})\cdot \mathbf{\text{x}}].$$
(4)
$${I}_{L}(\mathbf{\text{x}})={I}_{0}(\mathbf{\text{x}})-\frac{L}{k}\left[\nabla {I}_{0}(\mathbf{\text{x}})\cdot \nabla W(\mathbf{\text{x}})+{I}_{0}(\mathbf{\text{x}})\cdot {\nabla}^{2}W(\mathbf{\text{x}})\right],$$
(5)
$${I}_{L}(\mathbf{\text{x}})=3\left[1-\frac{L}{k}{\nabla}^{2}W(\mathbf{\text{x}})\right]+\text{\u2211}_{i,j={1}_{i\ne j}}^{3}\left\{\left[1-\frac{L}{k}{\nabla}^{2}W(\mathbf{\text{x}})\right]-i\frac{L}{k}({\mathbf{\text{k}}}_{i}-{\mathbf{\text{k}}}_{j})\nabla W(\mathbf{\text{x}})\right\}\cdot exp\left[i({\mathbf{\text{k}}}_{i}-{\mathbf{\text{k}}}_{j})\cdot \mathbf{\text{x}}\right].$$
(6)
$$\begin{array}{lll}\text{FT}\left({I}_{L}\right)(\mathbf{\text{u}})\hfill & =\hfill & 3\text{FT}\left[1-\frac{L}{k}{\nabla}^{2}W(\mathbf{\text{x}})\right]\hfill \\ \hfill & \hfill & +\text{\u2211}_{i,j={1}_{i\ne j}}^{3}\text{FT}\{\left[1-\frac{L}{k}{\nabla}^{2}W(\mathbf{\text{x}})\right]\hfill \\ \hfill & \hfill & -i\frac{L}{k}({\mathbf{\text{k}}}_{i}-{\mathbf{\text{k}}}_{j})\nabla W(\mathbf{\text{x}})\}*\delta \left[({\mathbf{\text{k}}}_{i}-{\mathbf{\text{k}}}_{j})-\mathbf{\text{u}}\right],\hfill \end{array}$$
(7)
$$\text{FT}(G)(\mathbf{\text{u}})=\text{\u2211}_{n=1}^{3}\delta (\mathbf{\text{u}}-{\mathbf{\text{u}}}_{n}),$$
(8)
$$G(\mathbf{\text{x}})=\text{\u2211}_{n=1}^{3}exp(2i\pi {\mathbf{\text{u}}}_{n}\cdot \mathbf{\text{x}}).$$