## Abstract

We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER), in which two spatially chirped ancilla fields are used to generate a spatially encoded SPIDER interferogram. We dub this new technique Spatially Encoded Arrangement for Chirped ARrangement for SPIDER (SEA-CAR-SPIDER). The single shot interferogram contains multiple shears, the spectral amplitude of the test pulse, and the reference phase, which is accurate for broadband pulses. The technique enables consistency checking through the simultaneous acquisition of multiple shears and offers a simple and precise calibration method. All calibration parameters — the shears, and the upconversion-frequency— can be accurately obtained from a single calibration trace.

©2009 Optical Society of America

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### Equations (9)

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(1)
$$S\left(\omega +{\omega}_{\mathrm{up}},x\right)=I\left(\omega +\mathrm{\alpha x}\right)+I\left(\omega -\mathrm{\alpha x}\right)+D(\omega ,x)+{D}^{*}(\omega ,x)$$
(2)
$$D(\omega ,x)=\sqrt{I\left(\omega +\mathrm{\alpha x}\right)I\left(\omega -\mathrm{\alpha x}\right)}\mathrm{exp}\left[i\Gamma (\omega ,x)\right]$$
(3)
$$\Gamma (\omega ,x)=\varphi \left(\omega +\mathrm{\alpha x}\right)-\varphi \left(\omega -\mathrm{\alpha x}\right)+{k}_{x}x+C\left(\omega \right)$$
(4)
$$C\left(\omega \right)=\genfrac{}{}{0.1ex}{}{1}{2}\mathrm{unwrap}\left[\mathrm{Arg}{\int}_{0}^{\infty}D(\omega ,x)D(\omega ,-x)dx\right]$$
(5)
$$\genfrac{}{}{0.1ex}{}{\text{d}\Gamma [\omega ,{x}_{\mathrm{con}}(\omega )]}{\text{d}\omega}=\genfrac{}{}{0.1ex}{}{\partial \Gamma [\omega ,{x}_{\mathrm{con}}(\omega )]}{\partial \omega}+\genfrac{}{}{0.1ex}{}{\partial \Gamma [\omega ,{x}_{\mathrm{con}}(\omega )]}{\partial x}\genfrac{}{}{0.1ex}{}{\partial {x}_{\mathrm{con}}(\omega )}{\partial \omega}=0$$
(6)
$$\Gamma (\omega ,x)\approx \genfrac{}{}{0.1ex}{}{\partial \varphi \left(\omega \right)}{\partial \omega}2\mathrm{\alpha x}+{k}_{x}x.$$
(7)
$$\genfrac{}{}{0.1ex}{}{\partial \Gamma (\omega ,x)}{\partial x}=\genfrac{}{}{0.1ex}{}{\partial \varphi \left(\omega \right)}{\partial \omega}2\alpha +{k}_{x}.$$
(8)
$$\genfrac{}{}{0.1ex}{}{{\partial x}_{\mathrm{con}}\left(\omega \right)}{\partial \omega}=\genfrac{}{}{0.1ex}{}{2{\mathrm{\alpha x}}_{\mathrm{con}}\left(\omega \right)}{{k}_{x}}\genfrac{}{}{0.1ex}{}{{\partial}^{2}\varphi}{\partial {\omega}^{2}}.$$
(9)
$${\gamma}^{2}=\u3008{\left\{\Delta \left[\varphi \left({\omega}_{m}\right)-\varphi \left({\omega}_{n}\right)\right]\right\}}^{2}\u3009=\sum _{k=n}^{m-1}{\eta}_{\Gamma \left({\omega}_{k}+\Omega \u20442,x\right)}^{2}.$$